<?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>ns_to_aa1.out</source>

<heading><![CDATA[
Prover9 (64) version 2021-dec-16 (stable), March 2022.
Process 9785 was started by veroff on b146-11,
Wed Apr 12 09:50:07 2023
The command was "prover9 -f ns_to_aa1.in".
]]></heading>

<proof number="1" length="28617" max_count="71">

<comments><![CDATA[
% Proof 1 at 9192.85 (+ 396.77) seconds.: "aa1".
% Length of proof: 28617 (0 new hints)
% Level of proof: 1390
% Maximum clause weight: 513.000 (71 w/o degradation)
% Given clauses in run: 30361
% Given clauses in proof: 28604 (0 new hints)
]]></comments>

  <clause id="1" 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="2" type="assumption">
    <literal><![CDATA[
      1 * x = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      x * 1 = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      x \ (x * y) = y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="6" type="assumption">
    <literal><![CDATA[
      (x * y) / y = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="8" 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="9">
    <literal><![CDATA[
      a(x,y,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[copy(8),flip(a)].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10" 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="11">
    <literal><![CDATA[
      K(x,y) = (y * x) \ (x * y)
    ]]></literal>
    <justification jstring="[copy(10),flip(a)].">
      <j1 rule="copy" parents="10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

  <clause id="13">
    <literal><![CDATA[
      L(x,y,z) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[copy(12),flip(a)].">
      <j1 rule="copy" parents="12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14" type="assumption">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[copy(14),flip(a)].">
      <j1 rule="copy" parents="14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      x \ (y * x) = T(y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      T(x,y) = y \ (x * y)
    ]]></literal>
    <justification jstring="[copy(16),flip(a)].">
      <j1 rule="copy" parents="16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18" 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="19" 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="20">
    <literal><![CDATA[
      L(T(x,y),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[copy(19),flip(a)].">
      <j1 rule="copy" parents="19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21" 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="22">
    <literal><![CDATA[
      R(T(x,y),z,u) = T(R(x,z,u),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[
      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="24">
    <literal><![CDATA[
      R(L(x,y,z),u,w) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[copy(23),flip(a)].">
      <j1 rule="copy" parents="23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25" 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="26" 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="27" type="assumption">
    <literal><![CDATA[
      (x * x) * (y * z) = ((x * x) * y) * z
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_l")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      ((x * x) * y) * z = (x * x) * (y * z)
    ]]></literal>
    <justification jstring="[copy(27),flip(a)].">
      <j1 rule="copy" parents="27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29" 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="30" 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="31" 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="32" 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="33" 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="34" 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="35" type="assumption">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x \ u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="37" type="assumption">
    <literal><![CDATA[
      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="38" 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="39" 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="40" 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="41" 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="42" 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="43" 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="44" type="assumption">
    <literal><![CDATA[
      x \ y != x \ z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="46" type="assumption">
    <literal><![CDATA[
      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="47" 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="48" 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="49" type="assumption">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = z
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="50" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != x
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="51" type="assumption">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="52" type="assumption">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="53" type="assumption">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 5")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="54" 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="55" 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="56" 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="57" 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="58" 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="59" 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="60" 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="61" 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(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="62">
    <literal><![CDATA[
      1 \ x = x
    ]]></literal>
    <justification jstring="[para(2(a,1),4(a,1,2))].">
      <j1 rule="para" parents="2 4"/>
    </justification>
  </clause>

  <clause id="63">
    <literal><![CDATA[
      x \ x = 1
    ]]></literal>
    <justification jstring="[para(3(a,1),4(a,1,2))].">
      <j1 rule="para" parents="3 4"/>
    </justification>
  </clause>

  <clause id="64">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) = z
    ]]></literal>
    <justification jstring="[para(4(a,2),4(a,1,2))].">
      <j1 rule="para" parents="4 4"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      x \ (x * (y \ (y * z))) = z
    ]]></literal>
    <justification jstring="[para(4(a,2),4(a,1))].">
      <j1 rule="para" parents="4 4"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      (x * (x \ 1)) * y = y
    ]]></literal>
    <justification jstring="[para(5(a,2),2(a,1,1))].">
      <j1 rule="para" parents="5 2"/>
    </justification>
  </clause>

  <clause id="67">
    <literal><![CDATA[
      x * (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(5(a,2),3(a,1,2))].">
      <j1 rule="para" parents="5 3"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) = z
    ]]></literal>
    <justification jstring="[para(5(a,2),4(a,1,2))].">
      <j1 rule="para" parents="5 4"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(4(a,2),5(a,1,2))].">
      <j1 rule="para" parents="4 5"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(5(a,2),5(a,1,2))].">
      <j1 rule="para" parents="5 5"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      x / x = 1
    ]]></literal>
    <justification jstring="[para(2(a,1),6(a,1,1))].">
      <j1 rule="para" parents="2 6"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      x / 1 = x
    ]]></literal>
    <justification jstring="[para(3(a,1),6(a,1,1))].">
      <j1 rule="para" parents="3 6"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      x * (((x \ y) * z) / z) = y
    ]]></literal>
    <justification jstring="[para(6(a,2),5(a,1,2))].">
      <j1 rule="para" parents="6 5"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      x / (y \ x) = y
    ]]></literal>
    <justification jstring="[para(5(a,1),6(a,1,1))].">
      <j1 rule="para" parents="5 6"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      ((1 / x) * x) * y = y
    ]]></literal>
    <justification jstring="[para(7(a,2),2(a,1,1))].">
      <j1 rule="para" parents="7 2"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      x * ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(7(a,2),3(a,1,2))].">
      <j1 rule="para" parents="7 3"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      (x / y) \ x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),4(a,1,2))].">
      <j1 rule="para" parents="7 4"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      (x \ (x * (y / z))) * z = y
    ]]></literal>
    <justification jstring="[para(4(a,2),7(a,1,1))].">
      <j1 rule="para" parents="4 7"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      ((x * (x \ y)) / z) * z = y
    ]]></literal>
    <justification jstring="[para(7(a,2),5(a,1))].">
      <j1 rule="para" parents="7 5"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      (((x * y) / z) * z) / y = x
    ]]></literal>
    <justification jstring="[para(7(a,2),6(a,1,1))].">
      <j1 rule="para" parents="7 6"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      (((x / y) / z) * z) * y = x
    ]]></literal>
    <justification jstring="[para(7(a,2),7(a,1,1))].">
      <j1 rule="para" parents="7 7"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      (x * (y * z)) * a(x,y,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(9(a,2),5(a,1,2))].">
      <j1 rule="para" parents="9 5"/>
    </justification>
  </clause>

  <clause id="83">
    <literal><![CDATA[
      (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="87">
    <literal><![CDATA[
      (x * y) * K(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(11(a,2),5(a,1,2))].">
      <j1 rule="para" parents="11 5"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      x \ ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="89">
    <literal><![CDATA[
      ((x \ y) * x) \ y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),11(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="91">
    <literal><![CDATA[
      (x * y) \ (x * y) = L(1,y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      (x * y) * L(z,y,x) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(13(a,2),5(a,1,2))].">
      <j1 rule="para" parents="13 5"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="94">
    <literal><![CDATA[
      L(x \ y,x,z) = (z * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="5 13"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      L(x,y / x,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="7 13"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),13(a,2,2))].">
      <j1 rule="para" parents="7 13"/>
    </justification>
  </clause>

  <clause id="98">
    <literal><![CDATA[
      (x * y) / (x * y) = R(1,x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="99">
    <literal><![CDATA[
      (x * y) / (y * 1) = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(3(a,1),15(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      R(x,x \ y,z) = (y * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15(a,2,1,1))].">
      <j1 rule="para" parents="5 15"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15(a,2,1))].">
      <j1 rule="para" parents="5 15"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      R(x,y,z) * (y * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(15(a,2),7(a,1,1))].">
      <j1 rule="para" parents="15 7"/>
    </justification>
  </clause>

  <clause id="104">
    <literal><![CDATA[
      R(x / y,y,z) = (x * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(7(a,1),15(a,2,1,1))].">
      <j1 rule="para" parents="7 15"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="106">
    <literal><![CDATA[
      T(x,x) = x
    ]]></literal>
    <justification jstring="[para(17(a,2),4(a,1))].">
      <j1 rule="para" parents="17 4"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      x * T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(17(a,2),5(a,1,2))].">
      <j1 rule="para" parents="17 5"/>
    </justification>
  </clause>

  <clause id="108">
    <literal><![CDATA[
      T(x,x \ y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),17(a,2,2))].">
      <j1 rule="para" parents="5 17"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      T(x / y,y) = y \ x
    ]]></literal>
    <justification jstring="[para(7(a,1),17(a,2,2))].">
      <j1 rule="para" parents="7 17"/>
    </justification>
  </clause>

  <clause id="110">
    <literal><![CDATA[
      T(x,x * x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),13(a,2)),flip(a)].">
      <j1 rule="para" parents="17 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      T(T(R(x,y,z),u),w) = T(R(T(x,w),y,z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="112">
    <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(25(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      (x * x) * (((x * x) \ y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(5(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="114">
    <literal><![CDATA[
      ((x * x) * (y * z)) / z = (x * x) * y
    ]]></literal>
    <justification jstring="[para(28(a,1),6(a,1,1))].">
      <j1 rule="para" parents="28 6"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[para(28(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      (((x * x) * (y * z)) * u) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(28(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="28 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      (x * ((y * y) * z)) / z = x * (y * y)
    ]]></literal>
    <justification jstring="[para(29(a,1),6(a,1,1))].">
      <j1 rule="para" parents="29 6"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ (((x * (y * y)) * z) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(29(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      ((x * (y * (z * z))) * u) / (y * ((z * z) * u)) = R(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(29(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="29 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      x * ((x \ y) * (z * z)) = y * (z * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      (x * (y * (z * z))) * u = (x * y) * ((z * z) * u)
    ]]></literal>
    <justification jstring="[para(30(a,1),29(a,1,1))].">
      <j1 rule="para" parents="30 29"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2(a,1),31(b,1))].">
      <j1 rule="para" parents="2 31"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(3(a,1),31(a,1))].">
      <j1 rule="para" parents="3 31"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,1),31(a,1))].">
      <j1 rule="para" parents="5 31"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(2(a,1),32(a,1))].">
      <j1 rule="para" parents="2 32"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3(a,1),32(b,1))].">
      <j1 rule="para" parents="3 32"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(7(a,1),32(a,1))].">
      <j1 rule="para" parents="7 32"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(4(a,1),35(a,1))].">
      <j1 rule="para" parents="4 35"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(2(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="2 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(2(a,1),40(a,2))].">
      <j1 rule="para" parents="2 40"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(3(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="3 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      (x * y) * 1 != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(3(a,2),40(a,2)),flip(a)].">
      <j1 rule="para" parents="3 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x \ (x * (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(4(a,2),40(a,2)),flip(a)].">
      <j1 rule="para" parents="4 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="5 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      x * (x \ (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5(a,2),40(a,1))].">
      <j1 rule="para" parents="5 40"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      ((x * x) * y) * z != (x * x) * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(28(a,2),40(a,1))].">
      <j1 rule="para" parents="28 40"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(3(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="3 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(3(a,1),41(a,2))].">
      <j1 rule="para" parents="3 41"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x \ (x * (y * z)) != u * z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(4(a,2),41(a,1))].">
      <j1 rule="para" parents="4 41"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(5(a,1),41(a,2))].">
      <j1 rule="para" parents="5 41"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(7(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="7 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      x * (y * (z * z)) != u * (z * z)
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(30(a,1),41(a,1))].">
      <j1 rule="para" parents="30 41"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      (x * y) / z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(6(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="6 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(6(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="6 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(4(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      (x * (y * z)) \ u != a(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(9(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="9 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(17(a,2),44(a,1))].">
      <j1 rule="para" parents="17 44"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(4(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      x \ (y * z) != K(y,z)
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="11 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),46(a,1))].">
      <j1 rule="para" parents="18 46"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      T(x,y) != L(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(20(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="20 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      T(x,y) != R(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(22(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="22 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      T(L(x,y,z),u) != L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(20(a,1),47(a,1))].">
      <j1 rule="para" parents="20 47"/>
    </justification>
  </clause>

  <clause id="165">
    <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(24(a,2),47(a,1))].">
      <j1 rule="para" parents="24 47"/>
    </justification>
  </clause>

  <clause id="166">
    <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(25(a,1),47(a,1))].">
      <j1 rule="para" parents="25 47"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      T(R(x,y,z),u) != R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),48(a,1))].">
      <j1 rule="para" parents="22 48"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      R(x,y,z) != L(R(u,y,z),w,v5)
    ]]></literal>
    <literal><![CDATA[
      L(u,w,v5) = x
    ]]></literal>
    <justification jstring="[para(24(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="24 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="169">
    <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(26(a,1),48(a,1))].">
      <j1 rule="para" parents="26 48"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(54,a,7,a)].">
      <j1 rule="hyper" parents="54 7"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(54,a,5,a)].">
      <j1 rule="hyper" parents="54 5"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(55,a,5,a)].">
      <j1 rule="hyper" parents="55 5"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(55,a,4,a)].">
      <j1 rule="hyper" parents="55 4"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(56,a,7,a)].">
      <j1 rule="hyper" parents="56 7"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      (x * (x \ y)) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(56,a,5,a)].">
      <j1 rule="hyper" parents="56 5"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,5,a)].">
      <j1 rule="hyper" parents="58 5"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      x \ (y * 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(59,a,3,a)].">
      <j1 rule="hyper" parents="59 3"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,7,a,b,6,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="60 7 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="60 7 5"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(60,a,7,a,b,3,a(flip))].">
      <j1 rule="hyper" parents="60 7 3"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(60,a,7,a,b,2,a(flip))].">
      <j1 rule="hyper" parents="60 7 2"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6,a,b,3,a(flip))].">
      <j1 rule="hyper" parents="60 6 3"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5,a,b,4,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="60 5 4"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(60,a,5,a,b,3,a(flip))].">
      <j1 rule="hyper" parents="60 5 3"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      x * (x \ y) = 1 * y
    ]]></literal>
    <justification jstring="[hyper(60,a,5,a,b,2,a(flip))].">
      <j1 rule="hyper" parents="60 5 2"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      T(x,1) = x * 1
    ]]></literal>
    <justification jstring="[hyper(60,a,17,a,b,62,a)].">
      <j1 rule="hyper" parents="60 17 62"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,62,a,b,3,a)].">
      <j1 rule="hyper" parents="60 62 3"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(5(a,2),62(a,1,1))].">
      <j1 rule="para" parents="5 62"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(7(a,2),62(a,1,1))].">
      <j1 rule="para" parents="7 62"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(62(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="62 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(62(a,1),44(a,2))].">
      <j1 rule="para" parents="62 44"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x \ y != y
    ]]></literal>
    <literal><![CDATA[
      1 = x
    ]]></literal>
    <justification jstring="[para(62(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="62 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,11,a,b,63,a)].">
      <j1 rule="hyper" parents="60 11 63"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(63(a,2),2(a,1,1))].">
      <j1 rule="para" parents="63 2"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(63(a,2),3(a,1,2))].">
      <j1 rule="para" parents="63 3"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      (x / x) * y = y
    ]]></literal>
    <justification jstring="[para(71(a,2),2(a,1,1))].">
      <j1 rule="para" parents="71 2"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      x * (y / y) = x
    ]]></literal>
    <justification jstring="[para(71(a,2),3(a,1,2))].">
      <j1 rule="para" parents="71 3"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(5(a,2),72(a,1,2))].">
      <j1 rule="para" parents="5 72"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(7(a,2),72(a,1,2))].">
      <j1 rule="para" parents="7 72"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,22,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="39 22 106"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="38 20 106"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,18,a,b,106,a(flip))].">
      <j1 rule="hyper" parents="37 18 106"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(106(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(193(a,2),3(a,1,2))].">
      <j1 rule="para" parents="193 3"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,74,a,b,74,a(flip))].">
      <j1 rule="hyper" parents="60 74 74"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,74,a,b,6,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="60 74 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,74,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="60 74 5"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(54,a,74,a)].">
      <j1 rule="hyper" parents="54 74"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(33,a,15,a(flip),b,74,a),flip(a)].">
      <j1 rule="hyper" parents="33 15 74"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      (((x / y) * z) / z) \ x = y
    ]]></literal>
    <justification jstring="[hyper(33,a,6,a(flip),b,74,a),flip(a)].">
      <j1 rule="hyper" parents="33 6 74"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(11(a,2),74(a,1,2))].">
      <j1 rule="para" parents="11 74"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(13(a,2),74(a,1,2))].">
      <j1 rule="para" parents="13 74"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),74(a,1,2))].">
      <j1 rule="para" parents="17 74"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(74(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="74 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(74(a,2),74(a,1,2))].">
      <j1 rule="para" parents="74 74"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,77,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="60 77 5"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(54,a,77,a)].">
      <j1 rule="hyper" parents="54 77"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x * ((y / (x \ z)) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(35,a,4,a,b,77,a(flip))].">
      <j1 rule="hyper" parents="35 4 77"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(33,a,74,a,b,77,a(flip))].">
      <j1 rule="hyper" parents="33 74 77"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(77(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="77 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,186,a,b,3,a)].">
      <j1 rule="hyper" parents="60 186 3"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,222,a)].">
      <j1 rule="hyper" parents="52 222"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(51,a,222,a)].">
      <j1 rule="hyper" parents="51 222"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(222(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="222 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(222(a,1),46(a,2))].">
      <j1 rule="para" parents="222 46"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(63(a,2),222(a,1,2))].">
      <j1 rule="para" parents="63 222"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,224,a)].">
      <j1 rule="hyper" parents="52 224"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      (x \ x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(194(a,1),40(a,2))].">
      <j1 rule="para" parents="194 40"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      L(x,y,z) != (u \ u) * L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(194(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="194 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      R(x,y,z) != (u \ u) * R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(194(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="194 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(195(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="195 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(195(a,1),41(a,2))].">
      <j1 rule="para" parents="195 41"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,2),131(a,1,1))].">
      <j1 rule="para" parents="5 131"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(194(a,1),132(a,1)),flip(a)].">
      <j1 rule="para" parents="194 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(196(a,1),132(a,1)),flip(a)].">
      <j1 rule="para" parents="196 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5(a,2),143(a,1,2))].">
      <j1 rule="para" parents="5 143"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      x * ((1 / y) * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(7(a,2),143(a,1,2))].">
      <j1 rule="para" parents="7 143"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      (x * (x \ 1)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,2),191(a,1,1))].">
      <j1 rule="para" parents="5 191"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,2),191(a,1,1))].">
      <j1 rule="para" parents="7 191"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,18,a,b,200,a(flip))].">
      <j1 rule="hyper" parents="37 18 200"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      K(x,L(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,201,a)].">
      <j1 rule="hyper" parents="52 201"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,20,a,b,201,a(flip))].">
      <j1 rule="hyper" parents="38 20 201"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,30,a(flip),b,66,a(flip))].">
      <j1 rule="hyper" parents="31 30 66"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(66(a,1),15(a,2,1))].">
      <j1 rule="para" parents="66 15"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(67(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="67 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(67(a,1),13(a,2,2))].">
      <j1 rule="para" parents="67 13"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(31,a,30,a(flip),b,75,a(flip))].">
      <j1 rule="hyper" parents="31 30 75"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),15(a,2,1))].">
      <j1 rule="para" parents="75 15"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x * x) * (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,28,a,b,76,a(flip))].">
      <j1 rule="hyper" parents="32 28 76"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      x \ ((x * (1 / y)) * y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(76(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="76 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(60,a,107,a,b,7,a)].">
      <j1 rule="hyper" parents="60 107 7"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(60,a,107,a,b,5,a)].">
      <j1 rule="hyper" parents="60 107 5"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(59,a,107,a)].">
      <j1 rule="hyper" parents="59 107"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(55,a,107,a)].">
      <j1 rule="hyper" parents="55 107"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(54,a,107,a)].">
      <j1 rule="hyper" parents="54 107"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      T((x * x) * y,x * x) = y * (x * x)
    ]]></literal>
    <justification jstring="[hyper(31,a,30,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="31 30 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(31,a,7,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="31 7 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(32,a,7,a,b,107,a(flip))].">
      <j1 rule="hyper" parents="32 7 107"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(31,a,5,a,b,107,a(flip))].">
      <j1 rule="hyper" parents="31 5 107"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(107(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(107(a,1),9(a,2,2)),flip(a)].">
      <j1 rule="para" parents="107 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(107(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),107(a,1,2))].">
      <j1 rule="para" parents="18 107"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(20(a,2),107(a,1,2))].">
      <j1 rule="para" parents="20 107"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),107(a,1,2))].">
      <j1 rule="para" parents="22 107"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),31(a,1))].">
      <j1 rule="para" parents="107 31"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(107(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="107 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),41(a,1))].">
      <j1 rule="para" parents="107 41"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(202(a,1),107(a,1,2))].">
      <j1 rule="para" parents="202 107"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      R(x,y,z) * x = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(200(a,1),107(a,1,2))].">
      <j1 rule="para" parents="200 107"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      L(x,y,z) * x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(201(a,1),107(a,1,2))].">
      <j1 rule="para" parents="201 107"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(60,a,109,a,b,77,a)].">
      <j1 rule="hyper" parents="60 109 77"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(15(a,2),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),22(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(109(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="109 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      T(x / y,y \ x) = x / y
    ]]></literal>
    <justification jstring="[para(109(a,1),202(a,1,2))].">
      <j1 rule="para" parents="109 202"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(180(a,1),41(a,1))].">
      <j1 rule="para" parents="180 41"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(180(a,2),143(a,1))].">
      <j1 rule="para" parents="180 143"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(180(a,2),144(a,1))].">
      <j1 rule="para" parents="180 144"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(181(a,1),41(a,1))].">
      <j1 rule="para" parents="181 41"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(182(a,2),143(a,1))].">
      <j1 rule="para" parents="182 143"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(182(a,2),144(a,1))].">
      <j1 rule="para" parents="182 144"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(31,a,5,a,b,184,a(flip))].">
      <j1 rule="hyper" parents="31 5 184"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(184(a,1),40(a,1))].">
      <j1 rule="para" parents="184 40"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(184(a,2),143(a,1))].">
      <j1 rule="para" parents="184 143"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(184(a,2),144(a,1))].">
      <j1 rule="para" parents="184 144"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(185(a,1),40(a,1))].">
      <j1 rule="para" parents="185 40"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13,a,b,188,a),flip(a)].">
      <j1 rule="hyper" parents="60 13 188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,11,a,b,188,a)].">
      <j1 rule="hyper" parents="60 11 188"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13,a,b,189,a),flip(a)].">
      <j1 rule="hyper" parents="60 13 189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11,a,b,189,a)].">
      <j1 rule="hyper" parents="60 11 189"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,15,a,b,198,a),flip(a)].">
      <j1 rule="hyper" parents="60 15 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,15,a,b,199,a),flip(a)].">
      <j1 rule="hyper" parents="60 15 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),214(a,1,1))].">
      <j1 rule="para" parents="5 214"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(214(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="214 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,7,a,b,248,a)].">
      <j1 rule="hyper" parents="32 7 248"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(31,a,5,a,b,248,a)].">
      <j1 rule="hyper" parents="31 5 248"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      T(x \ 1,x * x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[para(248(a,1),17(a,2,2))].">
      <j1 rule="para" parents="248 17"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      (x * x) \ x = 1 / x
    ]]></literal>
    <justification jstring="[hyper(31,a,5,a,b,254,a)].">
      <j1 rule="hyper" parents="31 5 254"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      (x * x) * ((1 / x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(254(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="254 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(262(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="262 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(262(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="262 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(262(a,1),202(a,1,2))].">
      <j1 rule="para" parents="262 202"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(263(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="263 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      x \ y != y * y
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = x
    ]]></literal>
    <justification jstring="[para(311(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="311 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="77 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      T(T(x,y),x * x) = T(L(x,x,x),y)
    ]]></literal>
    <justification jstring="[para(110(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(107(a,1),135(a,1)),flip(b)].">
      <j1 rule="para" parents="107 135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      x * K(y,z) != y * z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,2),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5(a,1),159(a,1,2))].">
      <j1 rule="para" parents="5 159"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(15(a,2),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(214(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="214 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(263(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="263 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),293(a,1,1))].">
      <j1 rule="para" parents="5 293"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),293(a,1,1))].">
      <j1 rule="para" parents="107 293"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(181(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="181 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,1),294(a,1,1))].">
      <j1 rule="para" parents="5 294"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),294(a,1,1))].">
      <j1 rule="para" parents="107 294"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      (x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(11(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(13(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(4(a,2),298(a,1,2))].">
      <j1 rule="para" parents="4 298"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5(a,2),298(a,1,2))].">
      <j1 rule="para" parents="5 298"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(13(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(7(a,1),68(a,1,2,2,2))].">
      <j1 rule="para" parents="7 68"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(13(a,2),68(a,1,2,2))].">
      <j1 rule="para" parents="13 68"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * (z \ x) = y
    ]]></literal>
    <justification jstring="[para(69(a,1),297(a,1)),flip(b)].">
      <j1 rule="para" parents="69 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      x \ ((y * z) * (z \ (y \ x))) = a(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(70(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="70 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(70(a,1),13(a,2,2))].">
      <j1 rule="para" parents="70 13"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(135,a,79,a)].">
      <j1 rule="hyper" parents="135 79"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(15(a,2),80(a,1,1,1))].">
      <j1 rule="para" parents="15 80"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(81(a,1),15(a,2,1))].">
      <j1 rule="para" parents="81 15"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(74(a,1),81(a,1,1,1,1))].">
      <j1 rule="para" parents="74 81"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(60,a,87,a,b,5,a)].">
      <j1 rule="hyper" parents="60 87 5"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),87(a,1,1))].">
      <j1 rule="para" parents="5 87"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),87(a,1,1))].">
      <j1 rule="para" parents="7 87"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(87(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="87 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(87(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="87 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      (x * y) / T(y * x,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(87(a,1),214(a,1,1))].">
      <j1 rule="para" parents="87 214"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(342,a,108,a),flip(a)].">
      <j1 rule="hyper" parents="342 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(59,a,108,a)].">
      <j1 rule="hyper" parents="59 108"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      x / T(y,y \ z) = x / ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(57,a,108,a)].">
      <j1 rule="hyper" parents="57 108"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(55,a,108,a)].">
      <j1 rule="hyper" parents="55 108"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(54,a,108,a)].">
      <j1 rule="hyper" parents="54 108"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      T(x,y) = (x \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),108(a,1,2))].">
      <j1 rule="para" parents="4 108"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(108(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      T(x,x \ y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(108(a,2),45(a,1))].">
      <j1 rule="para" parents="108 45"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      x * T(y,y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ z = x
    ]]></literal>
    <justification jstring="[para(108(a,2),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="108 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      x / T(y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(108(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="108 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2(a,1),123(a,1))].">
      <j1 rule="para" parents="2 123"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(170(a,2),135(a,1))].">
      <j1 rule="para" parents="170 135"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(291,a,172,a),flip(a)].">
      <j1 rule="hyper" parents="291 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      (x * y) / (z * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(147,a,172,a)].">
      <j1 rule="hyper" parents="147 172"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(333,a,174,a),flip(a)].">
      <j1 rule="hyper" parents="333 174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(178(a,2),41(a,1))].">
      <j1 rule="para" parents="178 41"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(178(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="178 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(178(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="178 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(179(a,2),40(a,1))].">
      <j1 rule="para" parents="179 40"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(179(a,1),41(a,1))].">
      <j1 rule="para" parents="179 41"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      x \ (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      z / u = x
    ]]></literal>
    <justification jstring="[para(179(a,1),159(a,1,2))].">
      <j1 rule="para" parents="179 159"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(179(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="179 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(183(a,2),40(a,1))].">
      <j1 rule="para" parents="183 40"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(183(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="183 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(183(a,2),232(a,1))].">
      <j1 rule="para" parents="183 232"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(183(a,2),233(a,1))].">
      <j1 rule="para" parents="183 233"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(183(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="183 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(7(a,1),385(a,1,2))].">
      <j1 rule="para" parents="7 385"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="107 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(109(a,2),385(a,1))].">
      <j1 rule="para" parents="109 385"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(184(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="184 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      x \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(185(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="185 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      (x * x) \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(254(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="254 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(87(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="87 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,1),386(a,1,2))].">
      <j1 rule="para" parents="7 386"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(17(a,2),386(a,1))].">
      <j1 rule="para" parents="17 386"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),386(a,1,2))].">
      <j1 rule="para" parents="107 386"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(207(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="207 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      x / (y \ x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(208(a,2),40(a,1))].">
      <j1 rule="para" parents="208 40"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(208(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="208 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      (x / y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(217(a,2),40(a,1))].">
      <j1 rule="para" parents="217 40"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(217(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="217 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(370,a,5,a(flip),b,218,a),flip(a)].">
      <j1 rule="hyper" parents="370 5 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(298,a,218,a),flip(a)].">
      <j1 rule="hyper" parents="298 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(218(a,2),135(a,1))].">
      <j1 rule="para" parents="218 135"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),219(a,1,2,1,2))].">
      <j1 rule="para" parents="77 219"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * x = x * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(247(a,1),107(a,1,2))].">
      <j1 rule="para" parents="247 107"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(257(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="257 13"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(257(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="257 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(257(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="257 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      T(x,y / z) != z
    ]]></literal>
    <literal><![CDATA[
      y / (y / z) = x
    ]]></literal>
    <justification jstring="[para(282(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="282 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(77(a,2),282(a,1,2))].">
      <j1 rule="para" parents="77 282"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      T(x / (x / y),y) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(282(a,1),202(a,1,2))].">
      <j1 rule="para" parents="282 202"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(51,a,288,a)].">
      <j1 rule="hyper" parents="51 288"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      (x / y) * (y \ x) = (y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(288(a,1),107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="288 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,107,a,b,301,a)].">
      <j1 rule="hyper" parents="370 107 301"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(147,a,301,a(flip))].">
      <j1 rule="hyper" parents="147 301"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(135,a,301,a(flip))].">
      <j1 rule="hyper" parents="135 301"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      x \ K(x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(301(a,2),17(a,2,2)),flip(a)].">
      <j1 rule="para" parents="301 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      x / L(T(y,L(y,z,u) \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(20(a,2),308(a,1,2))].">
      <j1 rule="para" parents="20 308"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (z / x) \ z = y
    ]]></literal>
    <justification jstring="[para(340(a,1),385(a,1)),flip(b)].">
      <j1 rule="para" parents="340 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),346(a,1,1))].">
      <j1 rule="para" parents="15 346"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(351(a,1),15(a,2,1))].">
      <j1 rule="para" parents="351 15"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),372(a,1,1))].">
      <j1 rule="para" parents="15 372"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      (x / ((y / z) * z)) * y = x
    ]]></literal>
    <justification jstring="[para(77(a,1),372(a,1,1,2,2))].">
      <j1 rule="para" parents="77 372"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(13(a,2),374(a,1,2))].">
      <j1 rule="para" parents="13 374"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      ((x / y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(407(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="407 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(308(a,1),407(a,1,1,1))].">
      <j1 rule="para" parents="308 407"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(410(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="410 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(308(a,1),410(a,1,2,1))].">
      <j1 rule="para" parents="308 410"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(15(a,2),431(a,1,1))].">
      <j1 rule="para" parents="15 431"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(237,a,91,a),flip(a)].">
      <j1 rule="hyper" parents="237 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,439,a)].">
      <j1 rule="hyper" parents="50 439"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      a(x,y,K(1,z)) = 1
    ]]></literal>
    <justification jstring="[para(228(a,2),442(a,1,3))].">
      <j1 rule="para" parents="228 442"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(238,a,98,a),flip(a)].">
      <j1 rule="hyper" parents="238 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      (x * y) / y = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(3(a,1),99(a,1,2))].">
      <j1 rule="para" parents="3 99"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(294,a,447,a),flip(a)].">
      <j1 rule="hyper" parents="294 447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(447(a,1),293(a,1))].">
      <j1 rule="para" parents="447 293"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(3(a,1),133(a,1))].">
      <j1 rule="para" parents="3 133"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * x = y
    ]]></literal>
    <justification jstring="[para(11(a,2),243(a,1))].">
      <j1 rule="para" parents="11 243"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),244(a,1))].">
      <j1 rule="para" parents="11 244"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(13(a,2),244(a,1))].">
      <j1 rule="para" parents="13 244"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      L(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,313,a(flip),b,251,a),flip(a)].">
      <j1 rule="hyper" parents="370 313 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,176,a(flip),b,251,a),flip(a)].">
      <j1 rule="hyper" parents="370 176 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,251,a)].">
      <j1 rule="hyper" parents="58 251"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(54,a,251,a)].">
      <j1 rule="hyper" parents="54 251"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(221,a,251,a(flip))].">
      <j1 rule="hyper" parents="221 251"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(156,a,251,a(flip))].">
      <j1 rule="hyper" parents="156 251"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),251(a,2,1))].">
      <j1 rule="para" parents="7 251"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(251(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="251 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(251(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="251 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      R(1 / x,x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,198,a(flip),b,253,a),flip(a)].">
      <j1 rule="hyper" parents="370 198 253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(55,a,253,a)].">
      <j1 rule="hyper" parents="55 253"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      R(1 / x,x,y) * z = (y / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(54,a,253,a)].">
      <j1 rule="hyper" parents="54 253"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(215,a,253,a(flip))].">
      <j1 rule="hyper" parents="215 253"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(5(a,1),253(a,2,2))].">
      <j1 rule="para" parents="5 253"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(7(a,1),253(a,2,2))].">
      <j1 rule="para" parents="7 253"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(253(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="253 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(253(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="253 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      ((x * y) / z) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,2),276(a,2)),flip(a)].">
      <j1 rule="para" parents="7 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),276(a,2))].">
      <j1 rule="para" parents="107 276"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),277(a,1,2))].">
      <j1 rule="para" parents="18 277"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      x * ((1 / y) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),289(a,1,2))].">
      <j1 rule="para" parents="7 289"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      x * (y \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(63(a,2),289(a,1,2))].">
      <j1 rule="para" parents="63 289"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(180(a,2),289(a,1))].">
      <j1 rule="para" parents="180 289"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),292(a,1,1))].">
      <j1 rule="para" parents="7 292"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,2),296(a,1,2))].">
      <j1 rule="para" parents="5 296"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(182(a,2),296(a,1))].">
      <j1 rule="para" parents="182 296"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(184(a,2),296(a,1))].">
      <j1 rule="para" parents="184 296"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(5(a,2),299(a,1,1))].">
      <j1 rule="para" parents="5 299"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(18(a,1),328(a,1,2))].">
      <j1 rule="para" parents="18 328"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      x * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(20(a,2),328(a,1,2))].">
      <j1 rule="para" parents="20 328"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      x * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(22(a,2),328(a,1,2))].">
      <j1 rule="para" parents="22 328"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(181(a,2),332(a,1,1))].">
      <j1 rule="para" parents="181 332"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      T(x,y) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),389(a,1,2))].">
      <j1 rule="para" parents="107 389"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      T(x,x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,T(x,x \ y)) = z
    ]]></literal>
    <justification jstring="[para(257(a,1),389(a,1,2))].">
      <j1 rule="para" parents="257 389"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(5(a,1),390(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="5 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      x / y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z \ 1,z,x) = y
    ]]></literal>
    <justification jstring="[para(459(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="459 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(77(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="77 459"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(459(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="459 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(460(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="460 13"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(464(a,1),22(a,2,1))].">
      <j1 rule="para" parents="464 22"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      x \ y != z * y
    ]]></literal>
    <literal><![CDATA[
      R(1 / z,z,y) = x
    ]]></literal>
    <justification jstring="[para(467(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="467 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(74(a,1),467(a,1,1,1))].">
      <j1 rule="para" parents="74 467"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(467(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="467 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),494(a,1,1))].">
      <j1 rule="para" parents="6 494"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(74(a,1),494(a,1,1))].">
      <j1 rule="para" parents="74 494"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(212(a,1),494(a,1,1))].">
      <j1 rule="para" parents="212 494"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),88(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,2),88(a,1,2))].">
      <j1 rule="para" parents="107 88"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(301(a,2),89(a,1,1))].">
      <j1 rule="para" parents="301 89"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(125,a,13,a,b,189,a(flip))].">
      <j1 rule="hyper" parents="125 13 189"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,13,a,b,188,a(flip))].">
      <j1 rule="hyper" parents="125 13 188"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,351,a(flip),b,29,a(flip))].">
      <j1 rule="hyper" parents="125 351 29"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,171,a(flip),b,30,a(flip))].">
      <j1 rule="hyper" parents="125 171 30"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      (x * x) \ (y * z) = ((x * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,171,a(flip),b,28,a(flip))].">
      <j1 rule="hyper" parents="125 171 28"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      (T(x,x \ y) / z) \ ((x \ y) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(125,a,108,a(flip),b,7,a)].">
      <j1 rule="hyper" parents="125 108 7"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      (1 / x) \ (y * y) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,75,a(flip),b,30,a(flip))].">
      <j1 rule="hyper" parents="125 75 30"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      (x * (y * y)) \ z = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,29,a)].">
      <j1 rule="hyper" parents="125 70 29"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      ((x * x) * y) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,28,a)].">
      <j1 rule="hyper" parents="125 70 28"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,66,a(flip),b,30,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 66 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      ((x * x) \ 1) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,66,a(flip),b,28,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 66 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      (x * x) * ((y * (x * x)) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,29,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(128,a,15,a,b,198,a(flip))].">
      <j1 rule="hyper" parents="128 15 198"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,30,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 81 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,29,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 81 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      (x * x) * (1 / y) = (x * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,28,a),flip(a)].">
      <j1 rule="hyper" parents="128 76 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      x / ((y * y) \ 1) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,67,a(flip),b,29,a)].">
      <j1 rule="hyper" parents="128 67 29"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      (x * x) / (y \ 1) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,67,a(flip),b,28,a)].">
      <j1 rule="hyper" parents="128 67 28"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,25,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 25 13"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,24,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 24 13"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,13,a,b,176,a(flip))].">
      <j1 rule="hyper" parents="129 13 176"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,20,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 20 13"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),272(a,1,2,1))].">
      <j1 rule="para" parents="17 272"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),272(a,1,2,1))].">
      <j1 rule="para" parents="18 272"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      T(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(272(a,1),40(a,1))].">
      <j1 rule="para" parents="272 40"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(262(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),272(a,1,2,1))].">
      <j1 rule="para" parents="108 272"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(282(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="282 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      T(x \ y,z) * (y / x) = (y / x) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(419(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="419 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      (x * R(x,y,z)) \ (R(x,y,z) * (x * u)) = L(u,x,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(280(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="280 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      (x * (y * L(y,z,u))) \ ((x * L(y,z,u)) * y) = a(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(281(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="281 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="543">
    <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(281(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="281 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,284,a)].">
      <j1 rule="hyper" parents="316 284"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      T(T(T(x / y,z),u),y) = T(T(y \ x,z),u)
    ]]></literal>
    <justification jstring="[para(284(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="284 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      T(x / y,z) \ (y * T(y \ x,z)) = y
    ]]></literal>
    <justification jstring="[para(284(a,1),264(a,1,2,2))].">
      <j1 rule="para" parents="284 264"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(284(a,1),328(a,1,2))].">
      <j1 rule="para" parents="284 328"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(284(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="284 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      T(x \ 1,x * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,313,a(flip),b,312,a),flip(a)].">
      <j1 rule="hyper" parents="370 313 312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      T(T(x \ 1,y),x * x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(549(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="549 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      (x * x) \ (x * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(135,a,314,a)].">
      <j1 rule="hyper" parents="135 314"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      (1 / x) * (x \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,314,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      x * ((1 / x) \ y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,172,a(flip),b,314,a),flip(a)].">
      <j1 rule="hyper" parents="60 172 314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      x \ ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,314,a(flip))].">
      <j1 rule="hyper" parents="125 172 314"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      (x * x) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(314(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="314 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,315,a)].">
      <j1 rule="hyper" parents="316 315"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(315(a,1),46(a,2)),flip(b)].">
      <j1 rule="para" parents="315 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(315(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="315 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,317,a)].">
      <j1 rule="hyper" parents="51 317"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (x \ (1 / x)) \ (1 / x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(320(a,1),313(a,1,1))].">
      <j1 rule="para" parents="320 313"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      K(x \ 1,x) * K(x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(301(a,2),352(a,1,1))].">
      <j1 rule="para" parents="301 352"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(353(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="353 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(353(a,1),40(a,1))].">
      <j1 rule="para" parents="353 40"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(353(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="353 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      x * (y / x) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(354(a,1),40(a,1))].">
      <j1 rule="para" parents="354 40"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(354(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="354 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      x * T(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(424(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="424 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      L(K(x,x \ 1),K(x \ 1,x),y) = (y * K(x \ 1,x)) \ y
    ]]></literal>
    <justification jstring="[para(509(a,1),251(a,1,1))].">
      <j1 rule="para" parents="509 251"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      1 / (x * x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(319,a,516,a),flip(a)].">
      <j1 rule="hyper" parents="319 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      (x * x) \ (y \ (x * x)) = T(y \ 1,x * x)
    ]]></literal>
    <justification jstring="[hyper(323,a,519,a),flip(a)].">
      <j1 rule="hyper" parents="323 519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      (x \ 1) * ((y * y) * z) = (x \ (y * y)) * z
    ]]></literal>
    <justification jstring="[para(519(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="519 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      (x * (y \ 1)) * (z * z) = x * (y \ (z * z))
    ]]></literal>
    <justification jstring="[para(519(a,1),30(a,2,2))].">
      <j1 rule="para" parents="519 30"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      1 / (x \ (y * y)) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,74,a(flip),b,525,a),flip(a)].">
      <j1 rule="hyper" parents="125 74 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      (x * x) * ((1 / y) * z) = ((x * x) / y) * z
    ]]></literal>
    <justification jstring="[para(525(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="525 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      x * ((y * y) \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,178,a,b,526,a)].">
      <j1 rule="hyper" parents="34 178 526"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      ((x * x) \ y) \ 1 = y \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(33,a,208,a,b,527,a),flip(a)].">
      <j1 rule="hyper" parents="33 208 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13,a,b,551,a),flip(a)].">
      <j1 rule="hyper" parents="60 13 551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      L(x,y,y) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(128,a,13,a,b,551,a(flip))].">
      <j1 rule="hyper" parents="128 13 551"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(125,a,13,a,b,551,a(flip))].">
      <j1 rule="hyper" parents="125 13 551"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      T(x * x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,264,a(flip),b,551,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 264 551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      (x * y) \ L(y,x,x) = T(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(323,a,579,a),flip(a)].">
      <j1 rule="hyper" parents="323 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,25,a,b,579,a)].">
      <j1 rule="hyper" parents="125 25 579"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      L(T(x,y),y,y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,259,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="60 259 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      L(x \ y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,172,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="60 172 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      (1 / x) * ((x * x) * y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(579(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="579 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(580(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="580 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      (1 / x) \ y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x) = y
    ]]></literal>
    <justification jstring="[para(581(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="581 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      L(L(x,y,z),z * y,z * y) = (1 / (z * y)) * (z * (y * x))
    ]]></literal>
    <justification jstring="[para(13(a,2),586(a,1,1))].">
      <j1 rule="para" parents="13 586"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      L(T(x \ y,z),x,x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(586(a,1),20(a,2,1))].">
      <j1 rule="para" parents="586 20"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="586 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="586 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      ((x * x) \ x) * y = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(313(a,2),586(a,2,1)),flip(a)].">
      <j1 rule="para" parents="313 586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,209,a(flip),b,552,a),flip(a)].">
      <j1 rule="hyper" parents="60 209 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),553(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      x \ ((x * x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(553(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="553 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      1 / (x * (y * y)) = (y * y) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(516(a,1),575(a,1,2))].">
      <j1 rule="para" parents="516 575"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,310,a(flip),b,577,a),flip(a)].">
      <j1 rule="hyper" parents="125 310 577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      1 / (x * x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,571,a,b,599,a)].">
      <j1 rule="hyper" parents="60 571 599"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      (x \ (x \ 1)) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(599(a,1),520(a,1,1))].">
      <j1 rule="para" parents="599 520"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      x / (y \ (y \ 1)) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(599(a,1),526(a,1,2))].">
      <j1 rule="para" parents="599 526"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(599(a,1),577(a,1,2))].">
      <j1 rule="para" parents="599 577"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y * (x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(328,a,601,a),flip(a)].">
      <j1 rule="hyper" parents="328 601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      (x \ (x \ 1)) \ y = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,4,a(flip),b,601,a)].">
      <j1 rule="hyper" parents="125 4 601"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      ((x * (y \ (y \ 1))) * z) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(601(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="601 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      (x * (y * y)) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(602(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="602 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(323,a,92,a),flip(a)].">
      <j1 rule="hyper" parents="323 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(128,a,259,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="128 259 92"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(128,a,172,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="128 172 92"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,260,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="60 260 92"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,170,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="60 170 92"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      L(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(31,a,30,a,b,92,a),flip(a)].">
      <j1 rule="hyper" parents="31 30 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,29,a,b,92,a),flip(a)].">
      <j1 rule="hyper" parents="31 29 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      L(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,28,a,b,92,a),flip(a)].">
      <j1 rule="hyper" parents="31 28 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(31,a,70,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="31 70 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,171,a(flip),b,92,a(flip))].">
      <j1 rule="hyper" parents="125 171 92"/>
    </justification>
  </clause>

  <clause id="618">
    <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(92(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="619">
    <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(92(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="92 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(92(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="92 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(92(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="92 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(92(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="92 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      (x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(92(a,1),15(a,2,1)),flip(a)].">
      <j1 rule="para" parents="92 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      (x * x) * (L(y,x,x) * z) = (x * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(92(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="92 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(92(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="92 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(92(a,2),40(a,1))].">
      <j1 rule="para" parents="92 40"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      (x * (y * z)) / u != x * y
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(92(a,1),152(a,1,1))].">
      <j1 rule="para" parents="92 152"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(92(a,1),87(a,1,1))].">
      <j1 rule="para" parents="92 87"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(92(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="92 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(92(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="92 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(301(a,2),92(a,1,1))].">
      <j1 rule="para" parents="301 92"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(92(a,1),236(a,1))].">
      <j1 rule="para" parents="92 236"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),614(a,1,2))].">
      <j1 rule="para" parents="2 614"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(614(a,1),47(a,2))].">
      <j1 rule="para" parents="614 47"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(320(a,1),614(a,1,2))].">
      <j1 rule="para" parents="320 614"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a,b,634,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(634(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="634 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(634(a,1),47(a,2))].">
      <j1 rule="para" parents="634 47"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      a(x * x,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,615,a)].">
      <j1 rule="hyper" parents="50 615"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),615(a,1,3))].">
      <j1 rule="para" parents="2 615"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      L(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(615(a,1),47(a,2))].">
      <j1 rule="para" parents="615 47"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      L(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(320(a,1),615(a,1,3))].">
      <j1 rule="para" parents="320 615"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(642(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="642 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(642(a,1),47(a,2))].">
      <j1 rule="para" parents="642 47"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      L(x,y,a(z * z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(641(a,2),642(a,1,3))].">
      <j1 rule="para" parents="641 642"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * z = x * ((y \ (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,636,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 636 13"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (1 / (x \ (1 / x))) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,636,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="125 636 579"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(636(a,1),47(a,2))].">
      <j1 rule="para" parents="636 47"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      ((x \ (1 / x)) * y) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,644,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 644 13"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(370,a,264,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 264 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,258,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 258 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,189,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 189 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(370,a,188,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 188 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,176,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 176 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,90,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="370 90 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),94(a,2,1))].">
      <j1 rule="para" parents="7 94"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),94(a,2,2))].">
      <j1 rule="para" parents="7 94"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),94(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="94 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      R((x * y) \ (x * z),u,w) = L(R(y \ z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),24(a,1,1))].">
      <j1 rule="para" parents="94 24"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),94(a,2,1))].">
      <j1 rule="para" parents="107 94"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      L(K(x,y) \ z,K(x,y),y * x) = (x * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(87(a,1),94(a,2,1))].">
      <j1 rule="para" parents="87 94"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(303(a,2),94(a,2,2))].">
      <j1 rule="para" parents="303 94"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(94(a,2),374(a,1,2))].">
      <j1 rule="para" parents="94 374"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(94(a,2),243(a,1))].">
      <j1 rule="para" parents="94 243"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(94(a,2),391(a,1))].">
      <j1 rule="para" parents="94 391"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(92(a,1),94(a,2,1))].">
      <j1 rule="para" parents="92 94"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(92(a,1),94(a,2,2))].">
      <j1 rule="para" parents="92 94"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(94(a,2),94(a,1,1))].">
      <j1 rule="para" parents="94 94"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(652(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="652 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,351,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 351 103"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,260,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 260 103"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,171,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 171 103"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(125,a,170,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 170 103"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      R(x,y,T(z,x * y)) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,107,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 107 103"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      R(x,y,K(y,x)) \ (y * x) = y * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,87,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 87 103"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,259,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="60 259 103"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      R(((x * (y * z)) / z) / y,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,81,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="32 81 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,30,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="32 30 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,29,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="32 29 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,103,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 103 92"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(103(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="103 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(103(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="103 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(103(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="103 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(22(a,1),103(a,1,1))].">
      <j1 rule="para" parents="22 103"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(24(a,1),103(a,1,1))].">
      <j1 rule="para" parents="24 103"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(26(a,1),103(a,1,1))].">
      <j1 rule="para" parents="26 103"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(103(a,2),40(a,1))].">
      <j1 rule="para" parents="103 40"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),41(a,1))].">
      <j1 rule="para" parents="103 41"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="103 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(103(a,1),239(a,1)),flip(b)].">
      <j1 rule="para" parents="103 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / y,y) = z
    ]]></literal>
    <justification jstring="[para(103(a,1),240(a,1)),flip(b)].">
      <j1 rule="para" parents="103 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      R(x * y,z,u * u) != x * w
    ]]></literal>
    <literal><![CDATA[
      w = y
    ]]></literal>
    <justification jstring="[para(681(a,2),40(a,2)),flip(a)].">
      <j1 rule="para" parents="681 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      R(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(681(a,1),48(a,2))].">
      <j1 rule="para" parents="681 48"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(320(a,1),681(a,1,3))].">
      <j1 rule="para" parents="320 681"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(2(a,1),682(a,1,2))].">
      <j1 rule="para" parents="2 682"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(682(a,1),48(a,2))].">
      <j1 rule="para" parents="682 48"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(700(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="700 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) = x * (y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[para(699(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="699 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(370,a,199,a(flip),b,104,a),flip(a)].">
      <j1 rule="hyper" parents="370 199 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,198,a(flip),b,104,a),flip(a)].">
      <j1 rule="hyper" parents="370 198 104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(5(a,1),104(a,2,2))].">
      <j1 rule="para" parents="5 104"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),104(a,2,2))].">
      <j1 rule="para" parents="7 104"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="104 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),104(a,2,2))].">
      <j1 rule="para" parents="107 104"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(104(a,2),109(a,1,1))].">
      <j1 rule="para" parents="104 109"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(278(a,1),104(a,2,2))].">
      <j1 rule="para" parents="278 104"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(253(a,2),104(a,1,1))].">
      <j1 rule="para" parents="253 104"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(104(a,2),332(a,1))].">
      <j1 rule="para" parents="104 332"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(103(a,1),104(a,2,1))].">
      <j1 rule="para" parents="103 104"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(103(a,1),104(a,2,2))].">
      <j1 rule="para" parents="103 104"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(104(a,2),104(a,1,1))].">
      <j1 rule="para" parents="104 104"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      x \ y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(70(a,1),134(a,1,2)),flip(b)].">
      <j1 rule="para" parents="70 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(68(a,1),136(a,1,2))].">
      <j1 rule="para" parents="68 136"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(7(a,1),145(a,1,2,2))].">
      <j1 rule="para" parents="7 145"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      x \ x != y * z
    ]]></literal>
    <literal><![CDATA[
      1 / z = y
    ]]></literal>
    <justification jstring="[para(76(a,1),145(a,1,2))].">
      <j1 rule="para" parents="76 145"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(87(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="87 210"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(353(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="353 210"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(92(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="92 210"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),213(a,1,1,2))].">
      <j1 rule="para" parents="7 213"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x / K(x \ 1,x) = R(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(301(a,2),249(a,2,2)),flip(a)].">
      <j1 rule="para" parents="301 249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,25,a,b,300,a)].">
      <j1 rule="hyper" parents="125 25 300"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,20,a(flip),b,300,a)].">
      <j1 rule="hyper" parents="125 20 300"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      x * K(x \ 1,x) = L(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(301(a,2),300(a,1,2))].">
      <j1 rule="para" parents="301 300"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,25,a,b,302,a)].">
      <j1 rule="hyper" parents="125 25 302"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,259,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="60 259 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(304(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="304 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      R(R(x,y,z),y * z,(y * z) \ 1) = ((x * y) * z) * ((y * z) \ 1)
    ]]></literal>
    <justification jstring="[para(103(a,1),304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      x \ R(y,1 / x,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(323,a,306,a),flip(a)].">
      <j1 rule="hyper" parents="323 306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,26,a,b,306,a)].">
      <j1 rule="hyper" parents="128 26 306"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,24,a(flip),b,306,a)].">
      <j1 rule="hyper" parents="128 24 306"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,22,a(flip),b,306,a)].">
      <j1 rule="hyper" parents="128 22 306"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      K(x,1 / x) * x = R(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(303(a,2),306(a,1,1))].">
      <j1 rule="para" parents="303 306"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      T(T(x,y),x * x) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,321,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4(a,1),337(a,1,2,2,2))].">
      <j1 rule="para" parents="4 337"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x \ (1 / x)) * ((y * (x \ (1 / x))) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(129,a,344,a(flip),b,636,a(flip))].">
      <j1 rule="hyper" parents="129 344 636"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(344(a,1),20(a,2,1))].">
      <j1 rule="para" parents="344 20"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(344(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="344 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(344(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="344 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(77(a,1),344(a,1,1))].">
      <j1 rule="para" parents="77 344"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      (x * (y * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ (x \ z) = u
    ]]></literal>
    <justification jstring="[para(344(a,1),635(a,1))].">
      <j1 rule="para" parents="344 635"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      ((x * x) * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(344(a,1),643(a,1))].">
      <j1 rule="para" parents="344 643"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u * y
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(347(a,2),41(a,1))].">
      <j1 rule="para" parents="347 41"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      (x * (x \ y)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      (y / z) / w = u
    ]]></literal>
    <justification jstring="[para(179(a,1),376(a,1,1))].">
      <j1 rule="para" parents="179 376"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(74(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="74 378"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(214(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="214 378"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(422(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="422 378"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * y) * z) = w
    ]]></literal>
    <justification jstring="[para(15(a,2),379(a,1,1))].">
      <j1 rule="para" parents="15 379"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(178(a,1),379(a,1,1))].">
      <j1 rule="para" parents="178 379"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      (x / (y \ x)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(207(a,1),379(a,1,1))].">
      <j1 rule="para" parents="207 379"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(373(a,1),379(a,1,1))].">
      <j1 rule="para" parents="373 379"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (1 / x) * (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ L(y,x,x) = u
    ]]></literal>
    <justification jstring="[para(580(a,1),379(a,1,1))].">
      <j1 rule="para" parents="580 379"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(183(a,1),380(a,1,2))].">
      <j1 rule="para" parents="183 380"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      x \ ((x * x) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((1 / x) \ y) = u
    ]]></literal>
    <justification jstring="[para(553(a,1),383(a,1,2))].">
      <j1 rule="para" parents="553 383"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(92(a,2),383(a,1,2))].">
      <j1 rule="para" parents="92 383"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),383(a,1,2))].">
      <j1 rule="para" parents="103 383"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(344(a,2),383(a,1))].">
      <j1 rule="para" parents="344 383"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(4(a,2),384(a,2,2))].">
      <j1 rule="para" parents="4 384"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      x \ y != (z * u) * L(w,u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (z * (u * w)) = y
    ]]></literal>
    <justification jstring="[para(13(a,2),384(a,2,2))].">
      <j1 rule="para" parents="13 384"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),384(a,2,2))].">
      <j1 rule="para" parents="17 384"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(183(a,2),384(a,2)),flip(a)].">
      <j1 rule="para" parents="183 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(217(a,2),384(a,2)),flip(a)].">
      <j1 rule="para" parents="217 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      x * (y * T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),387(a,1,2,2))].">
      <j1 rule="para" parents="17 387"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(63(a,1),387(a,1,2,2))].">
      <j1 rule="para" parents="63 387"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(217(a,2),387(a,1,2))].">
      <j1 rule="para" parents="217 387"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      L(x \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(579(a,1),387(a,1))].">
      <j1 rule="para" parents="579 387"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * y) = w
    ]]></literal>
    <justification jstring="[para(13(a,2),402(a,1,2))].">
      <j1 rule="para" parents="13 402"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(251(a,2),404(a,1))].">
      <j1 rule="para" parents="251 404"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(94(a,2),404(a,1))].">
      <j1 rule="para" parents="94 404"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y \ z) = w
    ]]></literal>
    <justification jstring="[para(208(a,1),405(a,1,1))].">
      <j1 rule="para" parents="208 405"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      ((x * y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(459(a,1),433(a,1,1,1))].">
      <j1 rule="para" parents="459 433"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(456(a,1),201(a,1,2))].">
      <j1 rule="para" parents="456 201"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      K((x \ y) \ 1,y \ x) = 1
    ]]></literal>
    <justification jstring="[para(456(a,1),246(a,1,2))].">
      <j1 rule="para" parents="456 246"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),802(a,1,2))].">
      <j1 rule="para" parents="4 802"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(461(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="461 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(468(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="468 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      1 / (x / (y * y)) = (y * y) / x
    ]]></literal>
    <justification jstring="[hyper(698,a,469,a)].">
      <j1 rule="hyper" parents="698 469"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(7(a,2),480(a,1,1))].">
      <j1 rule="para" parents="7 480"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(178(a,1),480(a,1,1))].">
      <j1 rule="para" parents="178 480"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),485(a,1,2))].">
      <j1 rule="para" parents="4 485"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),485(a,1,2))].">
      <j1 rule="para" parents="5 485"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(104(a,2),491(a,1))].">
      <j1 rule="para" parents="104 491"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      x / ((y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(502(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="502 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="817">
    <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(22(a,2),505(a,1))].">
      <j1 rule="para" parents="22 505"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      T(x \ y,T(x,x \ y)) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(108(a,2),505(a,1,2))].">
      <j1 rule="para" parents="108 505"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      x \ y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(511(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="511 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(522(a,2),41(a,2)),flip(a)].">
      <j1 rule="para" parents="522 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(610(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="610 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ ((z * y) * u)) = x
    ]]></literal>
    <justification jstring="[para(616(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="616 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(654(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="654 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(676(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="676 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / x,x,y) \ y = z
    ]]></literal>
    <justification jstring="[para(676(a,1),392(a,1))].">
      <j1 rule="para" parents="676 392"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(705(a,1),22(a,2,1))].">
      <j1 rule="para" parents="705 22"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(171(a,2),721(a,1))].">
      <j1 rule="para" parents="171 721"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(173(a,2),721(a,1))].">
      <j1 rule="para" parents="173 721"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      x * (y * T(z,y)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(259(a,2),721(a,1))].">
      <j1 rule="para" parents="259 721"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      x \ ((x * x) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      ((1 / x) \ y) / u = z
    ]]></literal>
    <justification jstring="[para(553(a,1),722(a,1,2))].">
      <j1 rule="para" parents="553 722"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(103(a,1),722(a,1,2))].">
      <j1 rule="para" parents="103 722"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(408(a,1),742(a,1))].">
      <j1 rule="para" parents="408 742"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),784(a,1,2))].">
      <j1 rule="para" parents="4 784"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * L(z,y,x) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),784(a,1,2))].">
      <j1 rule="para" parents="92 784"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x * y) \ (x * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * L(y \ z,y,x) = w
    ]]></literal>
    <justification jstring="[para(610(a,1),785(a,1,1))].">
      <j1 rule="para" parents="610 785"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      ((x \ y) \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(308(a,1),841(a,1,1,1))].">
      <j1 rule="para" parents="308 841"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(276,a,113,a),flip(a)].">
      <j1 rule="hyper" parents="276 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      ((x * x) \ (y / z)) * z = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,7,a(flip),b,113,a),flip(a)].">
      <j1 rule="hyper" parents="125 7 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      ((x * x) \ y) \ z = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,113,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 172 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      (x * x) * ((((x * x) \ y) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[para(113(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      (x * x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * x) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(113(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="113 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      ((x * x) * y) / z = (x * x) * (y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),114(a,1,1,2))].">
      <j1 rule="para" parents="7 114"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      ((x * x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * x) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(114(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="114 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      (x * y) / (1 / y) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(254(a,1),117(a,1,1,2))].">
      <j1 rule="para" parents="254 117"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      (x / y) * (y * y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(491,a,855,a),flip(a)].">
      <j1 rule="hyper" parents="491 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      x * ((x \ y) * (x \ y)) = y / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(382,a,855,a),flip(a)].">
      <j1 rule="hyper" parents="382 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (x * x) \ ((y * x) / (1 / x)) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,855,a,b,107,a)].">
      <j1 rule="hyper" parents="125 855 107"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      x * ((y \ 1) * (y \ 1)) = (x * (y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(74(a,1),855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      x * (T(y,y \ 1) * T(y,y \ 1)) = (x * T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(308(a,1),855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="308 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      (x / y) * (y * y) != z
    ]]></literal>
    <literal><![CDATA[
      x / (1 / y) = z
    ]]></literal>
    <justification jstring="[para(855(a,1),491(a,1))].">
      <j1 rule="para" parents="855 491"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      (x \ (y / z)) * (z * z) = x \ (y / (1 / z))
    ]]></literal>
    <justification jstring="[hyper(125,a,856,a(flip),b,121,a),flip(a)].">
      <j1 rule="hyper" parents="125 856 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      (x \ (y \ 1)) * (z * z) = x \ (y \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(125,a,519,a(flip),b,121,a),flip(a)].">
      <j1 rule="hyper" parents="125 519 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      (x \ y) * ((1 / y) * (1 / y)) = x \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,252,a(flip),b,121,a),flip(a)].">
      <j1 rule="hyper" parents="125 252 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) = (x \ (y * z)) * (u * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,30,a(flip),b,121,a)].">
      <j1 rule="hyper" parents="125 30 121"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      x \ (y * (z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (z * z) = u
    ]]></literal>
    <justification jstring="[para(121(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="121 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      (((x * x) \ y) * z) * (x * x) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[para(113(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,92,a(flip),b,273,a)].">
      <j1 rule="hyper" parents="60 92 273"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,273,a(flip),b,92,a(flip))].">
      <j1 rule="hyper" parents="125 273 92"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="17 273"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),273(a,1,2,1))].">
      <j1 rule="para" parents="22 273"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(262(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="108 273"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x) * x
    ]]></literal>
    <justification jstring="[para(585(a,1),273(a,1,2))].">
      <j1 rule="para" parents="585 273"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,103,a(flip),b,274,a),flip(a)].">
      <j1 rule="hyper" parents="370 103 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,103,a(flip),b,274,a)].">
      <j1 rule="hyper" parents="125 103 274"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      R(T(x,x * x),x,x) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,103,a(flip),b,274,a),flip(a)].">
      <j1 rule="hyper" parents="31 103 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(262(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),274(a,1,2,1))].">
      <j1 rule="para" parents="108 274"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(282(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="282 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      R(L(x,x,x),x,x) = x
    ]]></literal>
    <justification jstring="[para(110(a,1),881(a,1,1))].">
      <j1 rule="para" parents="110 881"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(275,a,410,a,b,407,a)].">
      <j1 rule="hyper" parents="275 410 407"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      (1 / x) * (y * (x * x)) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(275,a,30,a,b,314,a),flip(a)].">
      <j1 rule="hyper" parents="275 30 314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      ((x * x) \ y) * (z * (x * x)) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[hyper(275,a,30,a,b,113,a),flip(a)].">
      <j1 rule="hyper" parents="275 30 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(275,a,259,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="275 259 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(275,a,92,a(flip),b,170,a(flip))].">
      <j1 rule="hyper" parents="275 92 170"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a(flip),b,891,a)].">
      <j1 rule="hyper" parents="60 20 891"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(891(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="891 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(891(a,1),273(a,1,2))].">
      <j1 rule="para" parents="891 273"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,315,a,b,893,a)].">
      <j1 rule="hyper" parents="37 315 893"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      T(x,x * y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(893(a,1),46(a,1))].">
      <j1 rule="para" parents="893 46"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),895(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = T(y,x) * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),895(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),896(a,1,2))].">
      <j1 rule="para" parents="5 896"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(896(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="896 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,285,a)].">
      <j1 rule="hyper" parents="316 285"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,286,a)].">
      <j1 rule="hyper" parents="316 286"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(253(a,1),286(a,1,1))].">
      <j1 rule="para" parents="253 286"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(286(a,1),328(a,1,2))].">
      <j1 rule="para" parents="286 328"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),286(a,1,1))].">
      <j1 rule="para" parents="104 286"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(349(a,1),286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="349 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(469(a,1),286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="469 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(706(a,1),286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="706 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,905,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 905 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(905(a,1),328(a,1,2))].">
      <j1 rule="para" parents="905 328"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      ((x * x) \ 1) \ T(y,y \ z) = (x * x) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,358,a,b,520,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 358 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(358(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="358 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(358(a,2),373(a,1,2))].">
      <j1 rule="para" parents="358 373"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      x / ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      u * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[para(360(a,1),155(a,1))].">
      <j1 rule="para" parents="360 155"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(125,a,361,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="125 361 87"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(721,a,362,a)].">
      <j1 rule="hyper" parents="721 362"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(125,a,362,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 362 92"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(364(a,1),328(a,1,2))].">
      <j1 rule="para" parents="364 328"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,552,a(flip),b,420,a),flip(a)].">
      <j1 rule="hyper" parents="60 552 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(434(a,1),742(a,1))].">
      <j1 rule="para" parents="434 742"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),503(a,1,2))].">
      <j1 rule="para" parents="107 503"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,88,a(flip),b,507,a)].">
      <j1 rule="hyper" parents="370 88 507"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(65(a,1),932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="65 932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),933(a,1,1,2))].">
      <j1 rule="para" parents="7 933"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,69,a(flip),b,512,a)].">
      <j1 rule="hyper" parents="129 69 512"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x * x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(310(a,1),512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y \ z) = (y / (x \ (1 / x))) \ z
    ]]></literal>
    <justification jstring="[para(320(a,1),512(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="320 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(603(a,2),512(a,1,1))].">
      <j1 rule="para" parents="603 512"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(742,a,936,a),flip(a)].">
      <j1 rule="hyper" parents="742 936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * x) \ ((x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(135,a,936,a)].">
      <j1 rule="hyper" parents="135 936"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * x) \ T(y,x \ 1) = x \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,17,a,b,936,a)].">
      <j1 rule="hyper" parents="125 17 936"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      x \ ((x \ 1) * y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,4,a(flip),b,936,a),flip(a)].">
      <j1 rule="hyper" parents="125 4 936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * ((1 / x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(433,a,936,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="433 936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      x * ((x * x) \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,69,a(flip),b,936,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 69 936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      (1 / x) \ (x \ y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,936,a(flip),b,553,a),flip(a)].">
      <j1 rule="hyper" parents="125 936 553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      (x * x) * ((x \ y) * z) = ((x \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(936(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="936 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * ((1 / x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(936(a,2),433(a,1))].">
      <j1 rule="para" parents="936 433"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x \ 1) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) * y = z
    ]]></literal>
    <justification jstring="[para(936(a,1),742(a,1))].">
      <j1 rule="para" parents="936 742"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      T((x \ 1) \ y,x * x) = (x \ y) * (x * x)
    ]]></literal>
    <justification jstring="[para(936(a,1),261(a,1,1))].">
      <j1 rule="para" parents="936 261"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (x \ 1) * (x * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,314,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="129 314 939"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      x * (((x * x) \ y) * z) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,113,a(flip),b,939,a),flip(a)].">
      <j1 rule="hyper" parents="129 113 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x \ 1) * (y * (x * x)) = x * T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(129,a,107,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="129 107 939"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      T(x \ 1,x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,264,a(flip),b,939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 264 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      T(x \ 1,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,313,a(flip),b,954,a),flip(a)].">
      <j1 rule="hyper" parents="370 313 954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      T(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(954(a,2),394(a,1))].">
      <j1 rule="para" parents="954 394"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      K(x \ 1,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,955,a(flip),b,424,a),flip(a)].">
      <j1 rule="hyper" parents="129 955 424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      T(T(x \ 1,y),x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(955(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="955 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      R(x \ 1,y,z) * x = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(955(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="955 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      (x * x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(940(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="940 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      x \ y != (z * z) * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * ((z \ 1) \ u) = y
    ]]></literal>
    <justification jstring="[para(940(a,1),384(a,2,2))].">
      <j1 rule="para" parents="940 384"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      x * ((x * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(942(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="942 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      ((x * y) * ((y * y) \ z)) / ((y \ 1) * z) = R(x,y,(y * y) \ z)
    ]]></literal>
    <justification jstring="[para(944(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="944 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      (x * x) \ (((x \ 1) \ y) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(940(a,1),514(a,2,1))].">
      <j1 rule="para" parents="940 514"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u = (z * z) \ ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(30(a,1),517(a,1,1))].">
      <j1 rule="para" parents="30 517"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (x * x) \ ((y \ 1) \ z) = (y \ (x * x)) \ z
    ]]></literal>
    <justification jstring="[para(519(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="519 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      (x * x) \ ((y / x) \ z) = (y / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(856(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="856 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      (((x * x) * y) * z) \ u = (y * z) \ ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(28(a,2),518(a,1,1))].">
      <j1 rule="para" parents="28 518"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      T(x,y * y) \ ((y * y) \ z) = (x * (y * y)) \ z
    ]]></literal>
    <justification jstring="[para(107(a,1),518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      (x \ y) \ ((x * x) \ z) = ((x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(936(a,1),518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="936 518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      ((x * x) * y) \ (z * u) = y \ (((x * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(514(a,1),518(a,2,2))].">
      <j1 rule="para" parents="514 518"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ z) = (y \ 1) \ z
    ]]></literal>
    <justification jstring="[para(519(a,1),521(a,1,2,1))].">
      <j1 rule="para" parents="519 521"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      (x * x) * ((y / (1 / x)) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(856(a,1),521(a,1,2,1))].">
      <j1 rule="para" parents="856 521"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      x / (y * (x * x)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[para(310(a,1),523(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      ((x \ 1) / y) \ x = y * (x * x)
    ]]></literal>
    <justification jstring="[hyper(215,a,977,a)].">
      <j1 rule="hyper" parents="215 977"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (x / ((y * y) * z)) / u = (x / z) / (u * (y * y))
    ]]></literal>
    <justification jstring="[para(524(a,1),523(a,1,1))].">
      <j1 rule="para" parents="524 523"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x = x * T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,362,a(flip),b,537,a)].">
      <j1 rule="hyper" parents="60 362 537"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(544(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="544 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(544(a,1),390(a,1,1)),flip(b)].">
      <j1 rule="para" parents="544 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(109(a,1),556(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(556(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="556 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(556(a,1),390(a,1,1)),flip(b)].">
      <j1 rule="para" parents="556 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(561(a,1),415(a,1))].">
      <j1 rule="para" parents="561 415"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (1 / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,x,x) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),588(a,1,2))].">
      <j1 rule="para" parents="5 588"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      L(x,x,x) = y
    ]]></literal>
    <justification jstring="[para(856(a,1),588(a,1))].">
      <j1 rule="para" parents="856 588"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      L(x,1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (1 / x)) \ y = z
    ]]></literal>
    <justification jstring="[para(77(a,1),668(a,1,1))].">
      <j1 rule="para" parents="77 668"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      L(K(x,x \ 1),K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * K(x \ 1,x)) \ y = z
    ]]></literal>
    <justification jstring="[para(509(a,1),668(a,1,1))].">
      <j1 rule="para" parents="509 668"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      R(x,x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / ((x \ 1) * y) = z
    ]]></literal>
    <justification jstring="[para(74(a,1),714(a,1,1))].">
      <j1 rule="para" parents="74 714"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      L(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(4(a,1),790(a,1,1))].">
      <j1 rule="para" parents="4 790"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      L(L(x,y,z),z * y,z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (1 / (z * y)) * (z * (y * x)) = u
    ]]></literal>
    <justification jstring="[para(13(a,2),790(a,1,1))].">
      <j1 rule="para" parents="13 790"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      L(x,y / x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / (y / x)) * y = z
    ]]></literal>
    <justification jstring="[para(77(a,1),790(a,1,1))].">
      <j1 rule="para" parents="77 790"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = T(y,x * x) * z
    ]]></literal>
    <justification jstring="[para(847(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="847 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      ((x * x) \ y) / z = (x * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(147,a,848,a)].">
      <j1 rule="hyper" parents="147 848"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (x * x) \ ((x * y) / z) = ((1 / x) * y) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,551,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="128 551 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      (((x * x) \ y) * z) / u = (x * x) \ ((y * z) / u)
    ]]></literal>
    <justification jstring="[hyper(128,a,514,a(flip),b,848,a)].">
      <j1 rule="hyper" parents="128 514 848"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      (x * x) \ (x / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,313,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="128 313 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (1 / x) \ ((1 / x) / y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,1001,a(flip),b,552,a)].">
      <j1 rule="hyper" parents="125 1001 552"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      x \ (((1 / y) * (1 / y)) * z) = ((y \ (1 / y)) \ x) \ z
    ]]></literal>
    <justification jstring="[para(320(a,1),849(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="320 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      (x * y) \ ((x * x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(551(a,1),849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="551 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ u = (y * z) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[para(514(a,1),849(a,1,1))].">
      <j1 rule="para" parents="514 849"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y / z) = ((x \ (1 / x)) * y) / z
    ]]></literal>
    <justification jstring="[para(320(a,1),853(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="320 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,y \ z)) * u = w
    ]]></literal>
    <justification jstring="[para(915(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="915 378"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / z = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(147,a,935,a)].">
      <j1 rule="hyper" parents="147 935"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (x * (y * ((z * z) \ u))) \ ((x * (y / (z * z))) * u) = a(x,y / (z * z),u)
    ]]></literal>
    <justification jstring="[para(935(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="935 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ ((x / (y * y)) * (z * u)) = L(u,z,x / (y * y))
    ]]></literal>
    <justification jstring="[para(935(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="935 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      ((x * (y / (z * z))) * u) / (y * ((z * z) \ u)) = R(x,y / (z * z),u)
    ]]></literal>
    <justification jstring="[para(935(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="935 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(603(a,2),935(a,1,1))].">
      <j1 rule="para" parents="603 935"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      (x / (y * y)) * (z * u) = x * (((y * y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(514(a,1),935(a,2,2))].">
      <j1 rule="para" parents="514 935"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      (x / ((y * y) * z)) * u = (x / z) * ((y * y) \ u)
    ]]></literal>
    <justification jstring="[para(524(a,1),935(a,1,1))].">
      <j1 rule="para" parents="524 935"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) \ 1) \ y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),945(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      (x * y) \ (x * ((1 / x) * y)) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(323,a,951,a),flip(a)].">
      <j1 rule="hyper" parents="323 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,252,a(flip),b,951,a)].">
      <j1 rule="hyper" parents="125 252 951"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      x * ((1 / x) * T(y,x)) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,259,a(flip),b,951,a),flip(a)].">
      <j1 rule="hyper" parents="60 259 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      ((x \ 1) * x) \ (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,951,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 951 92"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      (x \ 1) * (x * y) != x * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(951(a,2),40(a,1))].">
      <j1 rule="para" parents="951 40"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,303,a,b,1017,a),flip(a)].">
      <j1 rule="hyper" parents="370 303 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (y / z) = ((x \ (1 / x)) \ y) / z
    ]]></literal>
    <justification jstring="[para(320(a,1),998(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="320 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      (x / (y * y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1008(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1008 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,82,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="125 82 103"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),82(a,1,1,2))].">
      <j1 rule="para" parents="5 82"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),82(a,1,1,2))].">
      <j1 rule="para" parents="107 82"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="82 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(82(a,1),784(a,1,2))].">
      <j1 rule="para" parents="82 784"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,25,a,b,93,a)].">
      <j1 rule="hyper" parents="129 25 93"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      x * L(L(y,z,x / z),u,w) = (x / z) * (z * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,25,a,b,95,a)].">
      <j1 rule="hyper" parents="129 25 95"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(107(a,1),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(95(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="95 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(92(a,1),95(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="92 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(5(a,1),100(a,2,2))].">
      <j1 rule="para" parents="5 100"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(100(a,2),346(a,1,1))].">
      <j1 rule="para" parents="100 346"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(304(a,1),250(a,1,2))].">
      <j1 rule="para" parents="304 250"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,1040,a)].">
      <j1 rule="hyper" parents="156 1040"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1041(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1041 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a(flip),b,270,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      R((x * y) / z,z,K(y,x)) = (y * x) / (z * ((x * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(11(a,2),428(a,1,3))].">
      <j1 rule="para" parents="11 428"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,274,a,b,430,a)].">
      <j1 rule="hyper" parents="60 274 430"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(24(a,1),430(a,1,1))].">
      <j1 rule="para" parents="24 430"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      R(R(x,y,y \ z),u,w) * z = (R(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(26(a,1),430(a,1,1))].">
      <j1 rule="para" parents="26 430"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(430(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="430 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a,b,457,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,462,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 462 13"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(189(a,1),462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="189 462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      T((x * y) \ x,y) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(955(a,1),462(a,2,1))].">
      <j1 rule="para" parents="955 462"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1054(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(494,a,470,a),flip(a)].">
      <j1 rule="hyper" parents="494 470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),476(a,1,2))].">
      <j1 rule="para" parents="108 476"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(17(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="17 488"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,273,a(flip),b,530,a(flip))].">
      <j1 rule="hyper" parents="125 273 530"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(530(a,1),40(a,1))].">
      <j1 rule="para" parents="530 40"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(530(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="530 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(107(a,2),565(a,1,2))].">
      <j1 rule="para" parents="107 565"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(955(a,1),569(a,1,2))].">
      <j1 rule="para" parents="955 569"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      L(x \ ((x * x) * y),x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(988,a,587,a)].">
      <j1 rule="hyper" parents="988 587"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,585,a(flip),b,591,a)].">
      <j1 rule="hyper" parents="60 585 591"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,591,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="125 591 579"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(609(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="609 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(275,a,172,a(flip),b,612,a),flip(a)].">
      <j1 rule="hyper" parents="275 172 612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,273,a(flip),b,612,a(flip))].">
      <j1 rule="hyper" parents="125 273 612"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      (x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(617(a,1),392(a,1))].">
      <j1 rule="para" parents="617 392"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11,a,b,653,a)].">
      <j1 rule="hyper" parents="370 11 653"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(653(a,1),20(a,2,1))].">
      <j1 rule="para" parents="653 20"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(653(a,2),784(a,1))].">
      <j1 rule="para" parents="653 784"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(656(a,1),20(a,2,1))].">
      <j1 rule="para" parents="656 20"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(656(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="656 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(656(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="656 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ (y * u)
    ]]></literal>
    <literal><![CDATA[
      (y \ z) \ u = x
    ]]></literal>
    <justification jstring="[para(656(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="656 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      x \ ((y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * y) \ x) \ z = u
    ]]></literal>
    <justification jstring="[para(656(a,1),643(a,1))].">
      <j1 rule="para" parents="656 643"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      L(x \ y,x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(658(a,2),389(a,1))].">
      <j1 rule="para" parents="658 389"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[para(614(a,1),666(a,1,2))].">
      <j1 rule="para" parents="614 666"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (x / (y * z)) * (y * y) = x / ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(551(a,1),1082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="551 1082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      x / (((y * y) \ z) * u) = (x / (z * u)) * (y * y)
    ]]></literal>
    <justification jstring="[para(514(a,1),1082(a,1,2))].">
      <j1 rule="para" parents="514 1082"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(7(a,1),675(a,1,2))].">
      <j1 rule="para" parents="7 675"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(675(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="675 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      x \ (y * (z \ (1 / z))) = (x \ y) * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[para(699(a,1),675(a,1,1))].">
      <j1 rule="para" parents="699 675"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      L(R(x,y,K(y,L(x,z,u))),z,u) \ (y * L(x,z,u)) = y * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(24(a,1),678(a,1,1))].">
      <j1 rule="para" parents="24 678"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(707(a,2),332(a,1))].">
      <j1 rule="para" parents="707 332"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(698,a,708,a),flip(a)].">
      <j1 rule="hyper" parents="698 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(708(a,1),22(a,2,1))].">
      <j1 rule="para" parents="708 22"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(708(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="708 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(253(a,2),708(a,1,1,2))].">
      <j1 rule="para" parents="253 708"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(253(a,2),708(a,1,2))].">
      <j1 rule="para" parents="253 708"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(708(a,1),286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="708 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (x * (y * (z * z))) / u = (x * y) / (u / (z * z))
    ]]></literal>
    <justification jstring="[para(30(a,1),1090(a,1,1))].">
      <j1 rule="para" parents="30 1090"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[para(613(a,1),727(a,1,2))].">
      <j1 rule="para" parents="613 727"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      x / ((y * x) * (y * x)) = y \ ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,310,a(flip),b,1098,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 310 1098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x \ y) / (z * z) = x \ (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(125,a,175,a(flip),b,1098,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 175 1098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x * y) / (y * y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(310(a,1),1098(a,2,2))].">
      <j1 rule="para" parents="310 1098"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      (x * (y / (z * z))) \ u = (z * z) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(1098(a,1),512(a,1,1))].">
      <j1 rule="para" parents="1098 512"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      (x * (y / (z * z))) / u = (x * y) / (u * (z * z))
    ]]></literal>
    <justification jstring="[para(1098(a,1),523(a,1,1))].">
      <j1 rule="para" parents="1098 523"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      (x * (y / (z * z))) * u = (x * y) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(1098(a,1),935(a,1,1))].">
      <j1 rule="para" parents="1098 935"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(491,a,1101,a),flip(a)].">
      <j1 rule="hyper" parents="491 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      x / ((y \ x) * (y \ x)) = y * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(382,a,1101,a)].">
      <j1 rule="hyper" parents="382 1101"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x / (y \ 1)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(377,a,1101,a),flip(a)].">
      <j1 rule="hyper" parents="377 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      (x * y) * (y \ (y \ 1)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,603,a,b,1101,a)].">
      <j1 rule="hyper" parents="60 603 1101"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,104,a,b,1101,a)].">
      <j1 rule="hyper" parents="60 104 1101"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      R(x,x \ y,x \ y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,100,a,b,1101,a)].">
      <j1 rule="hyper" parents="60 100 1101"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,15,a,b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="60 15 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(128,a,15,a,b,1101,a(flip))].">
      <j1 rule="hyper" parents="128 15 1101"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      (x * y) \ (x * (y \ 1)) = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,1101,a(flip),b,603,a)].">
      <j1 rule="hyper" parents="125 1101 603"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (y * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1101(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1101 109"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      (x * x) * ((y * x) \ z) = (y * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(1101(a,1),512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1101 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1101(a,1),935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1101 935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      R(T(x / y,z),y,y) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1109(a,1),22(a,2,1))].">
      <j1 rule="para" parents="1109 22"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      T(x * (y \ 1),y) = R(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(1109(a,1),286(a,1,1))].">
      <j1 rule="para" parents="1109 286"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(323,a,1111,a),flip(a)].">
      <j1 rule="hyper" parents="323 1111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      R(x,y,y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,304,a(flip),b,1111,a)].">
      <j1 rule="hyper" parents="60 304 1111"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      R(x / y,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1111(a,1),378(a,1))].">
      <j1 rule="para" parents="1111 378"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      R(x,x \ y,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((x \ y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(1111(a,1),755(a,1))].">
      <j1 rule="para" parents="1111 755"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(1112(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1112 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      x / ((1 / y) * (1 / y)) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(789,a,1105,a),flip(a)].">
      <j1 rule="hyper" parents="789 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(323,a,1105,a),flip(a)].">
      <j1 rule="hyper" parents="323 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      (x * (y * (z * z))) \ ((x * (y / (z \ 1))) * z) = a(x,y / (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(1107(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1107 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1111,a,b,1119,a)].">
      <j1 rule="hyper" parents="370 1111 1119"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1119(a,2,1))].">
      <j1 rule="para" parents="4 1119"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1121,a,b,1131,a),flip(a)].">
      <j1 rule="hyper" parents="370 1121 1131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (x \ 1) / (y * y) = x \ (y \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(600(a,1),1100(a,2,2))].">
      <j1 rule="para" parents="600 1100"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      (x \ (y / (z * z))) \ u = (z * z) * ((x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(1100(a,1),512(a,1,1))].">
      <j1 rule="para" parents="1100 512"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) \ 1) = y \ (x * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,1108,a(flip),b,171,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 1108 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      R(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),1122(a,1,1))].">
      <j1 rule="para" parents="6 1122"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      (x \ (y \ (y \ 1))) \ z = (y * y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1133(a,1),512(a,1,1))].">
      <j1 rule="para" parents="1133 512"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),907(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      (x * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(4(a,1),960(a,1,2))].">
      <j1 rule="para" parents="4 960"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      x * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * y) = z
    ]]></literal>
    <justification jstring="[para(551(a,1),962(a,1,2))].">
      <j1 rule="para" parents="551 962"/>
    </justification>
  </clause>

  <clause id="1144">
    <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(907(a,1),982(a,1,1))].">
      <j1 rule="para" parents="907 982"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),986(a,1,1,1))].">
      <j1 rule="para" parents="6 986"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(263(a,1),986(a,1,1,1))].">
      <j1 rule="para" parents="263 986"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      T((((x * y) / x) \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),986(a,1,1))].">
      <j1 rule="para" parents="108 986"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(404,a,1044,a),flip(a)].">
      <j1 rule="hyper" parents="404 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),1044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(1044(a,1),404(a,1))].">
      <j1 rule="para" parents="1044 404"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,1053,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 1053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,1053,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="125 1053 302"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,733,a(flip),b,1152,a)].">
      <j1 rule="hyper" parents="60 733 1152"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(301(a,2),1154(a,1,2))].">
      <j1 rule="para" parents="301 1154"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1155,a)].">
      <j1 rule="hyper" parents="135 1155"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,1155,a(flip),b,209,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 1155 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,1118,a(flip),b,1111,a)].">
      <j1 rule="hyper" parents="128 1118 1111"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      T(x,y) != R(z,y,y \ 1)
    ]]></literal>
    <literal><![CDATA[
      (y * z) * (y \ 1) = x
    ]]></literal>
    <justification jstring="[para(1132(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="1132 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(1141(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="1141 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1141(a,2),315(a,1,1))].">
      <j1 rule="para" parents="1141 315"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      R(x,y,x) * (y * x) = (y * x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1141(a,2),537(a,1,1))].">
      <j1 rule="para" parents="1141 537"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a,b,1163,a)].">
      <j1 rule="hyper" parents="60 22 1163"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      T(R(x,y,x),z) * (y * x) = (y * x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(1163(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1163 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1163(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1163 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1163(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1163 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1165(a,1,1,2))].">
      <j1 rule="para" parents="7 1165"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(222(a,1),1169(a,1,1))].">
      <j1 rule="para" parents="222 1169"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1170,a(flip),b,740,a)].">
      <j1 rule="hyper" parents="128 1170 740"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      (x * T(y,x)) * T(x,y) = R(x,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,260,a,b,1164,a)].">
      <j1 rule="hyper" parents="370 260 1164"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,103,a(flip),b,1164,a),flip(a)].">
      <j1 rule="hyper" parents="60 103 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ y) = y * T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(755,a,1173,a),flip(a)].">
      <j1 rule="hyper" parents="755 1173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(378,a,1173,a),flip(a)].">
      <j1 rule="hyper" parents="378 1173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,66,a(flip),b,1173,a)].">
      <j1 rule="hyper" parents="125 66 1173"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(301(a,2),1176(a,1,1))].">
      <j1 rule="para" parents="301 1176"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,108,a(flip),b,1177,a)].">
      <j1 rule="hyper" parents="129 108 1177"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,22,a,b,111,a)].">
      <j1 rule="hyper" parents="370 22 111"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),327(a,1,2))].">
      <j1 rule="para" parents="107 327"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(24(a,2),336(a,1,2))].">
      <j1 rule="para" parents="24 336"/>
    </justification>
  </clause>

  <clause id="1186">
    <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(25(a,1),336(a,1,2))].">
      <j1 rule="para" parents="25 336"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      (x * y) * (z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * (z * z)) = u
    ]]></literal>
    <justification jstring="[para(613(a,1),336(a,1,2))].">
      <j1 rule="para" parents="613 336"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ 1,z)) = u
    ]]></literal>
    <justification jstring="[para(462(a,2),336(a,1,2))].">
      <j1 rule="para" parents="462 336"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * z = u
    ]]></literal>
    <justification jstring="[para(7(a,1),339(a,1,1))].">
      <j1 rule="para" parents="7 339"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      (x * (y \ 1)) * ((z * z) * u) = (x * (y \ (z * z))) * u
    ]]></literal>
    <justification jstring="[para(574(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="574 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      (x * x) \ ((y * (z \ 1)) \ u) = (y * (z \ (x * x))) \ u
    ]]></literal>
    <justification jstring="[para(574(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="574 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      (((x \ 1) * (x \ 1)) \ y) * z = x * ((x \ 1) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,514,a(flip),b,595,a)].">
      <j1 rule="hyper" parents="60 514 595"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x \ 1) \ y)) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(960,a,596,a),flip(a)].">
      <j1 rule="hyper" parents="960 596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,(y * y) * z,x) = w
    ]]></literal>
    <justification jstring="[para(28(a,1),629(a,1,2,2))].">
      <j1 rule="para" parents="28 629"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y),y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),629(a,1,1))].">
      <j1 rule="para" parents="107 629"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ (x \ z),y,x) = u
    ]]></literal>
    <justification jstring="[para(70(a,1),629(a,1,2))].">
      <j1 rule="para" parents="70 629"/>
    </justification>
  </clause>

  <clause id="1199">
    <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(92(a,1),629(a,1,2,2))].">
      <j1 rule="para" parents="92 629"/>
    </justification>
  </clause>

  <clause id="1200">
    <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(362(a,2),629(a,1,1))].">
      <j1 rule="para" parents="362 629"/>
    </justification>
  </clause>

  <clause id="1201">
    <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(82(a,1),629(a,1,2,2))].">
      <j1 rule="para" parents="82 629"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      L(x,x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(423(a,1),667(a,1,1))].">
      <j1 rule="para" parents="423 667"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u * (z * y)
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(87(a,1),691(a,2,2))].">
      <j1 rule="para" parents="87 691"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(301(a,2),693(a,1,1,1))].">
      <j1 rule="para" parents="301 693"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) * x = z
    ]]></literal>
    <justification jstring="[para(500(a,1),734(a,1,1))].">
      <j1 rule="para" parents="500 734"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      x \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ x) \ z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),822(a,1,1))].">
      <j1 rule="para" parents="5 822"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(z \ L(u,y,x),z,x * y) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),822(a,1,2))].">
      <j1 rule="para" parents="92 822"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      (x * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      R(x / (z / y),z / y,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),825(a,1,2))].">
      <j1 rule="para" parents="7 825"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,175,a(flip),b,859,a),flip(a)].">
      <j1 rule="hyper" parents="125 175 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(820,a,1211,a(flip))].">
      <j1 rule="hyper" parents="820 1211"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1211(a,1),595(a,1,1))].">
      <j1 rule="para" parents="1211 595"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      (x \ (1 / x)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1211(a,1),596(a,1,1))].">
      <j1 rule="para" parents="1211 596"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (x * (y \ 1)) / y = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1211(a,1),859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1211 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      L(T(x \ 1,y),x \ 1,x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1212(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1212 20"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      T(x * (y \ (1 / y)),y) = y \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(1215(a,1),109(a,1,1))].">
      <j1 rule="para" parents="1215 109"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x \ (y / z)) * ((z * z) * u) = (x \ (y / (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(863(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="863 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      ((x \ (y * y)) / z) \ (x \ 1) = z / (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,77,a(flip),b,864,a),flip(a)].">
      <j1 rule="hyper" parents="128 77 864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (x * x) \ ((y \ (z \ 1)) \ u) = (y \ (z \ (x * x))) \ u
    ]]></literal>
    <justification jstring="[para(864(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="864 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x \ y) * (y \ (1 / y)) = x \ (1 / y)
    ]]></literal>
    <justification jstring="[para(320(a,1),865(a,1,2))].">
      <j1 rule="para" parents="320 865"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      1 / (x \ (1 / x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,63,a(flip),b,1221,a)].">
      <j1 rule="hyper" parents="128 63 1221"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1222(a,1),649(a,1,1))].">
      <j1 rule="para" parents="1222 649"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      1 / ((1 / x) \ x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(723,a,1223,a)].">
      <j1 rule="hyper" parents="723 1223"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,1223,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 1223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      ((1 / x) \ x) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,69,a(flip),b,1225,a)].">
      <j1 rule="hyper" parents="129 69 1225"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      x * ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,1226,a),flip(a)].">
      <j1 rule="hyper" parents="144 1226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      L(1 / x,x,y) * x = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(251(a,1),874(a,2,2))].">
      <j1 rule="para" parents="251 874"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      L(1 / x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,944,a(flip),b,1228,a),flip(a)].">
      <j1 rule="hyper" parents="32 944 1228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      L(T(1 / x,y),x,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1229(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1229 20"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      L(L(1 / x,y,z),x,x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1229(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1229 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (x * x) * T(x \ 1,y) = x * (x * T(1 / x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,1230,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 1230 13"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(147,a,875,a),flip(a)].">
      <j1 rule="hyper" parents="147 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,92,a(flip),b,875,a),flip(a)].">
      <j1 rule="hyper" parents="128 92 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,884,a)].">
      <j1 rule="hyper" parents="327 884"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(147,a,884,a),flip(a)].">
      <j1 rule="hyper" parents="147 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,465,a(flip),b,884,a),flip(a)].">
      <j1 rule="hyper" parents="128 465 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      L(x \ (y * (x * x)),x,x) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(988,a,889,a)].">
      <j1 rule="hyper" parents="988 889"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T(x * ((x * x) \ y),x * x) = (1 / x) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(847(a,1),889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="847 889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      ((x * y) * L(L(z,y,x),u,w)) / (x * y) = L((x * (y * z)) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),902(a,1,1,2,1))].">
      <j1 rule="para" parents="13 902"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(902(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="902 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(902(a,1),390(a,1,1)),flip(b)].">
      <j1 rule="para" parents="902 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,x)
    ]]></literal>
    <justification jstring="[para(586(a,1),902(a,1,1,2))].">
      <j1 rule="para" parents="586 902"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(344(a,1),902(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="344 902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(654(a,1),902(a,1,1,2))].">
      <j1 rule="para" parents="654 902"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(1072(a,2),902(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1072 902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(904(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="904 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y \ z) = (y * ((1 / x) \ x)) \ z
    ]]></literal>
    <justification jstring="[para(77(a,1),938(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      T(((x \ 1) \ y) * z,x * x) = (x \ y) * (z * (x * x))
    ]]></literal>
    <justification jstring="[hyper(275,a,30,a,b,946,a)].">
      <j1 rule="hyper" parents="275 30 946"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) \ y) \ z) = (x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,946,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,946,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="129 946 939"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      (x * x) * (((x \ y) * z) * u) = (((x \ 1) \ y) * z) * u
    ]]></literal>
    <justification jstring="[para(946(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="946 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (x \ 1) * ((x * y) * z) = x * (((1 / x) * y) * z)
    ]]></literal>
    <justification jstring="[para(551(a,1),952(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="551 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y * (x * x)) = (x * x) * (x * T(y,x * x))
    ]]></literal>
    <justification jstring="[para(953(a,1),946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="953 946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      (x * x) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(967(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="967 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      (x * x) \ T(y,y \ 1) = (y \ (x * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,359,a,b,969,a)].">
      <j1 rule="hyper" parents="60 359 969"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      (x / ((y \ 1) \ z)) * (u * u) = x / ((y \ (u * u)) \ z)
    ]]></literal>
    <justification jstring="[para(969(a,1),1082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="969 1082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      (1 / x) \ ((y / (1 / x)) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,970,a(flip),b,552,a)].">
      <j1 rule="hyper" parents="125 970 552"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (z * (x * x)) = (x \ y) \ T(z,x * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      ((x \ 1) \ y) \ x = (x \ y) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(313(a,1),973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="313 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * z) = (x \ y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(551(a,1),973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="551 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      (x \ y) \ (1 / x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(1263(a,1),45(a,1))].">
      <j1 rule="para" parents="1263 45"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (x * x) \ ((y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (x * x)) \ z = u
    ]]></literal>
    <justification jstring="[para(975(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="975 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (x * x) \ ((y / x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / (1 / x)) \ z = u
    ]]></literal>
    <justification jstring="[para(976(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="976 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(316,a,984,a)].">
      <j1 rule="hyper" parents="316 984"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,984,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 984 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      (1 / x) \ (((1 / x) * y) / z) = x \ ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,999,a(flip),b,552,a)].">
      <j1 rule="hyper" parents="125 999 552"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      ((1 / x) * y) \ (1 / x) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(254(a,1),1004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      ((1 / x) * y) \ ((1 / x) * z) = (x * y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(314(a,1),1004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ z) = (x * y) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(936(a,1),1004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="936 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      L(x,y,y) \ (1 / y) = (y * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(579(a,1),1272(a,1,1))].">
      <j1 rule="para" parents="579 1272"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      ((x * x) \ y) * x = (1 / x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,952,a,b,1018,a)].">
      <j1 rule="hyper" parents="31 952 1018"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      T(x,y) * T(1 / y,T(x,y)) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,107,a,b,1276,a)].">
      <j1 rule="hyper" parents="370 107 1276"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (1 / x) * T((x \ 1) \ y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(940(a,1),1276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="940 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      (1 / x) * T(T(y,x \ 1),x) = (x \ (y * (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(941(a,1),1276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="941 1276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      L(x,x,x) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(341(a,1),1065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="341 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      L(x,x,x) * L(x,x,x) = x * x
    ]]></literal>
    <justification jstring="[hyper(370,a,613,a(flip),b,1280,a),flip(a)].">
      <j1 rule="hyper" parents="370 613 1280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      T((1 / x) * ((x * x) * y),x) = (1 / x) * (((1 / x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(554(a,1),1066(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="554 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (1 / ((1 / x) \ x)) * (((x \ 1) * (x \ y)) * ((1 / x) \ x)) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1225(a,1),1066(a,1,2,1))].">
      <j1 rule="para" parents="1225 1066"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (x * y) \ ((x * y) \ 1) = y \ (x \ ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,1099,a(flip),b,603,a),flip(a)].">
      <j1 rule="hyper" parents="125 1099 603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,514,a(flip),b,1114,a),flip(a)].">
      <j1 rule="hyper" parents="370 514 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      (x * x) * ((x * L(x,y,z)) \ u) = (L(x,y,z) * (x \ 1)) \ u
    ]]></literal>
    <justification jstring="[para(281(a,1),1116(a,1,2,1))].">
      <j1 rule="para" parents="281 1116"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      (x * (y \ 1)) * y = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(313(a,1),1117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="313 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ z) = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(940(a,1),1117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="940 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      x \ ((y * x) * (1 / x)) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(323,a,1288,a),flip(a)].">
      <j1 rule="hyper" parents="323 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      (x * y) * (1 / y) != z * y
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1288(a,1),41(a,1))].">
      <j1 rule="para" parents="1288 41"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      (x * (1 / y)) * (1 / (1 / y)) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(77(a,1),1288(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      x / (y \ (1 / y)) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(320(a,1),1126(a,1,2))].">
      <j1 rule="para" parents="320 1126"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      (x \ 1) \ ((x * y) / (x * x)) = (x * T(y,x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,556,a,b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="370 556 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (x \ 1) \ T(y * (x \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1130(a,1),389(a,1,2))].">
      <j1 rule="para" parents="1130 389"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),1179(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      (x / y) \ (x \ 1) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1219(a,1,1,1))].">
      <j1 rule="para" parents="4 1219"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(129,a,1233,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 1233 13"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1233(a,2),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1233 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[para(251(a,1),1233(a,2,1,2))].">
      <j1 rule="para" parents="251 1233"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(461(a,1),1233(a,2,1,2))].">
      <j1 rule="para" parents="461 1233"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(656(a,1),1233(a,2,1,2))].">
      <j1 rule="para" parents="656 1233"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[para(1236(a,1),103(a,1,1))].">
      <j1 rule="para" parents="1236 103"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(349(a,1),1236(a,2,1,2))].">
      <j1 rule="para" parents="349 1236"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(706(a,1),1236(a,2,1,2))].">
      <j1 rule="para" parents="706 1236"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(1236(a,1),327(a,1,1))].">
      <j1 rule="para" parents="1236 327"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[hyper(31,a,926,a,b,1250,a),flip(a)].">
      <j1 rule="hyper" parents="31 926 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      (x * x) \ y != (x \ z) * u
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ z) \ y = u
    ]]></literal>
    <justification jstring="[para(1250(a,1),40(a,1))].">
      <j1 rule="para" parents="1250 40"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      (x \ y) \ ((x * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(1250(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1250 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(415,a,1307,a)].">
      <j1 rule="hyper" parents="415 1307"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,955,a,b,1307,a)].">
      <j1 rule="hyper" parents="370 955 1307"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ 1) \ 1 = x
    ]]></literal>
    <justification jstring="[hyper(370,a,74,a(flip),b,1307,a),flip(a)].">
      <j1 rule="hyper" parents="370 74 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      1 / (1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,1307,a)].">
      <j1 rule="hyper" parents="221 1307"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ 1 = y
    ]]></literal>
    <justification jstring="[para(1307(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1307 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (x * x) * ((y \ 1) \ 1) = (x * x) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1307(a,1),527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1307 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,((x \ 1) \ 1) * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1307(a,1),950(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      L(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(989,a,1313,a)].">
      <j1 rule="hyper" parents="989 1313"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      T(x,x \ (1 / x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(987,a,1313,a)].">
      <j1 rule="hyper" parents="987 1313"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ 1 != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(1313(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1313 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      T(x,x \ 1) = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,1317,a)].">
      <j1 rule="hyper" parents="370 108 1317"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      1 / L(x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,1317,a(flip))].">
      <j1 rule="hyper" parents="221 1317"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(1317(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1317 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      T(x,x \ 1) * y = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(1317(a,2),362(a,2,1))].">
      <j1 rule="para" parents="1317 362"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      x * L(x,x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(1317(a,2),1227(a,1,2))].">
      <j1 rule="para" parents="1317 1227"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      ((x \ 1) \ 1) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(1317(a,1),1280(a,1,1))].">
      <j1 rule="para" parents="1317 1280"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      L(x,x,x) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[para(1317(a,2),1307(a,1,1))].">
      <j1 rule="para" parents="1317 1307"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      L(x,x,x) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ 1 = y
    ]]></literal>
    <justification jstring="[para(1321(a,1),505(a,1))].">
      <j1 rule="para" parents="1321 505"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      ((L(x,x,x) * L(x,x,x)) \ y) * L(x,x,x) = (x \ 1) * T(y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(1322(a,1),1276(a,2,1))].">
      <j1 rule="para" parents="1322 1276"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      L(L(x,x,x),x,x) = x
    ]]></literal>
    <justification jstring="[hyper(589,a,1325,a(flip))].">
      <j1 rule="hyper" parents="589 1325"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      L(T(x,x \ 1),x,x) = x
    ]]></literal>
    <justification jstring="[para(1321(a,2),1330(a,1,1))].">
      <j1 rule="para" parents="1321 1330"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(108(a,2),1311(a,2,1)),flip(a)].">
      <j1 rule="para" parents="108 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      (x \ 1) \ 1 != y
    ]]></literal>
    <literal><![CDATA[
      1 / (1 / x) = y
    ]]></literal>
    <justification jstring="[para(77(a,1),1319(a,1,1,1))].">
      <j1 rule="para" parents="77 1319"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,364,a,b,1323,a)].">
      <j1 rule="hyper" parents="60 364 1323"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      T(T(x,x \ 1),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,1331,a(flip),b,1335,a),flip(a)].">
      <j1 rule="hyper" parents="370 1331 1335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (1 / y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1276,a(flip),b,1286,a),flip(a)].">
      <j1 rule="hyper" parents="370 1276 1286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      T(x * (y \ 1),y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1290(a,1),44(a,1))].">
      <j1 rule="para" parents="1290 44"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(1175(a,1),85(a,1,2))].">
      <j1 rule="para" parents="1175 85"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      L(x,y,y) != y
    ]]></literal>
    <literal><![CDATA[
      R(y,y,y) = x
    ]]></literal>
    <justification jstring="[para(887(a,1),165(a,1)),flip(a)].">
      <j1 rule="para" parents="887 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      R(x,x,x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(1341,a,1330,a)].">
      <j1 rule="hyper" parents="1341 1330"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,462,a,b,269,a)].">
      <j1 rule="hyper" parents="129 462 269"/>
    </justification>
  </clause>

  <clause id="1344">
    <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(129,a,25,a,b,269,a)].">
      <j1 rule="hyper" parents="129 25 269"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,94,a(flip),b,463,a),flip(a)].">
      <j1 rule="hyper" parents="370 94 463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,463,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 463 13"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      R(x / (y * x),y,y \ 1) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(464(a,1),471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="464 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1347(a,1,1,2))].">
      <j1 rule="para" parents="7 1347"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(17(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="17 489"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      (x * y) * T(z * z,u) = x * (y * T(z * z,u))
    ]]></literal>
    <justification jstring="[para(613(a,1),531(a,1,2,1))].">
      <j1 rule="para" parents="613 531"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(94(a,1),531(a,1,2,1))].">
      <j1 rule="para" parents="94 531"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(344(a,1),531(a,1,2,1))].">
      <j1 rule="para" parents="344 531"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(891(a,1),531(a,1,2,1))].">
      <j1 rule="para" parents="891 531"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(455(a,1),584(a,1,2,1))].">
      <j1 rule="para" parents="455 584"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),584(a,1,2,1))].">
      <j1 rule="para" parents="586 584"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(993,a,592,a)].">
      <j1 rule="hyper" parents="993 592"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      L(T(x * (y \ 1),y),y,y) = R((1 / y) * x,y,y)
    ]]></literal>
    <justification jstring="[para(1119(a,2),592(a,1,1))].">
      <j1 rule="para" parents="1119 592"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (1 / x) * (x * L(x \ y,z,u)) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(993,a,593,a)].">
      <j1 rule="hyper" parents="993 593"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      L((x * y) \ (x * z),y,y) = L((1 / y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),593(a,1,1))].">
      <j1 rule="para" parents="94 593"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(489,a,611,a),flip(a)].">
      <j1 rule="hyper" parents="489 611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,82,a(flip),b,624,a),flip(a)].">
      <j1 rule="hyper" parents="31 82 624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1361,a)].">
      <j1 rule="hyper" parents="135 1361"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      L(x,y,y) * z != x
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(1361(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1361 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      L(x,y,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(1361(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1361 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      L(a(x,x,y) \ z,a(x,x,y),L(y,x,x)) = y \ (L(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(1361(a,1),94(a,2,1))].">
      <j1 rule="para" parents="1361 94"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(107(a,1),661(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <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(661(a,2),336(a,1,2))].">
      <j1 rule="para" parents="661 336"/>
    </justification>
  </clause>

  <clause id="1368">
    <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(60,a,258,a(flip),b,674,a)].">
      <j1 rule="hyper" parents="60 258 674"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(32,a,537,a,b,679,a)].">
      <j1 rule="hyper" parents="32 537 679"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,679,a(flip))].">
      <j1 rule="hyper" parents="31 274 679"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(1370(a,1),679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1370 679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),687(a,1,1,1))].">
      <j1 rule="para" parents="104 687"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(494,a,709,a),flip(a)].">
      <j1 rule="hyper" parents="494 709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(709(a,1),494(a,1))].">
      <j1 rule="para" parents="709 494"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      T(R(T(x / y,z),y,u),y * u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[para(709(a,1),284(a,1,1))].">
      <j1 rule="para" parents="709 284"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[para(710(a,2),109(a,1,1))].">
      <j1 rule="para" parents="710 109"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(1173(a,1),710(a,2,1))].">
      <j1 rule="para" parents="1173 710"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(655(a,1),730(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="655 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(705(a,1),739(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="705 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      L(L(T(x \ (y \ z),u),w,v5),x,y) = L(T((y * x) \ z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(745(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="745 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <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(745(a,1),336(a,1,2))].">
      <j1 rule="para" parents="745 336"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * z) \ ((x * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(30(a,1),749(a,1,1))].">
      <j1 rule="para" parents="30 749"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(183(a,2),769(a,1,2))].">
      <j1 rule="para" parents="183 769"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),781(a,2,2,2,2))].">
      <j1 rule="para" parents="4 781"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,804,a,b,95,a),flip(a)].">
      <j1 rule="hyper" parents="129 804 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(805(a,2),430(a,1,1))].">
      <j1 rule="para" parents="805 430"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ (y * z)) * (u * u) = w
    ]]></literal>
    <justification jstring="[para(30(a,1),867(a,1,2))].">
      <j1 rule="para" parents="30 867"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,458,a(flip),b,869,a)].">
      <j1 rule="hyper" parents="370 458 869"/>
    </justification>
  </clause>

  <clause id="1391">
    <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(125,a,82,a(flip),b,879,a),flip(a)].">
      <j1 rule="hyper" parents="125 82 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(z,x * y),x,y) = u
    ]]></literal>
    <justification jstring="[para(879(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="879 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      R(T(L((x * y) / x,z,u),x * w),x,w) = (x * w) \ ((x * L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(875(a,1),880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="875 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      L(x,y,(y * x) / y) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(892(a,1),537(a,1,1))].">
      <j1 rule="para" parents="892 537"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,894,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 894 13"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,901,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),985(a,1,1,1,1))].">
      <j1 rule="para" parents="7 985"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(900(a,1),985(a,1,1))].">
      <j1 rule="para" parents="900 985"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1027,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 1027 107"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ 1) * y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,804,a,b,1034,a),flip(a)].">
      <j1 rule="hyper" parents="60 804 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      R(x * (y * z),a(x,y,z),((x * y) * z) \ u) \ u = ((x * (y * z)) \ ((x * y) * z)) * (((x * y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,2),1038(a,1,1,2))].">
      <j1 rule="para" parents="9 1038"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      x / ((y \ z) * (z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ z,z \ x) = u
    ]]></literal>
    <justification jstring="[para(1038(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1038 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(125,a,170,a(flip),b,1047,a),flip(a)].">
      <j1 rule="hyper" parents="125 170 1047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(456(a,1),1059(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="456 1059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(656(a,1),1059(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="656 1059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(658(a,1),1150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="658 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1244(a,2,1,2,1))].">
      <j1 rule="para" parents="7 1244"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(17(a,2),1244(a,2,1,2))].">
      <j1 rule="para" parents="17 1244"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      L((x \ y) / z,z,x) != u / z
    ]]></literal>
    <literal><![CDATA[
      z * ((x * z) \ y) = u
    ]]></literal>
    <justification jstring="[para(1244(a,2),43(a,1))].">
      <j1 rule="para" parents="1244 43"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(268(a,1),1244(a,2,1,2))].">
      <j1 rule="para" parents="268 1244"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      L((x \ y) / x,x,x) = ((x \ 1) * y) / x
    ]]></literal>
    <justification jstring="[para(944(a,1),1244(a,2,1))].">
      <j1 rule="para" parents="944 1244"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      x \ y != T(z,z \ u) * w
    ]]></literal>
    <literal><![CDATA[
      x * (((z \ u) \ u) * w) = y
    ]]></literal>
    <justification jstring="[para(434(a,1),1385(a,2))].">
      <j1 rule="para" parents="434 1385"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      x * T(y,x * y) != z * x
    ]]></literal>
    <literal><![CDATA[
      L(y,x,(x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1395(a,1),41(a,1))].">
      <j1 rule="para" parents="1395 41"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(1404(a,1),430(a,1,1))].">
      <j1 rule="para" parents="1404 430"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      (x * y) * ((z * z) * L(u,y * (z * z),x)) = x * ((y * (z * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(336,a,122,a),flip(a)].">
      <j1 rule="hyper" parents="336 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x * x) * z) = (x * T(y,x * x)) * z
    ]]></literal>
    <justification jstring="[para(953(a,1),122(a,1,1)),flip(a)].">
      <j1 rule="para" parents="953 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,603,a(flip),b,604,a),flip(a)].">
      <j1 rule="hyper" parents="370 603 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      T(x * y,y \ (y \ 1)) = (y * y) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,1108,a(flip),b,604,a),flip(a)].">
      <j1 rule="hyper" parents="129 1108 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,603,a(flip),b,604,a)].">
      <j1 rule="hyper" parents="129 603 604"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      (x * x) * (y \ (z / (x * x))) = T(y \ z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,1100,a(flip),b,1419,a)].">
      <j1 rule="hyper" parents="129 1100 1419"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      (x * x) * (y * (z / (x * x))) = T(y * z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,1098,a(flip),b,1419,a)].">
      <j1 rule="hyper" parents="129 1098 1419"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x * x) * (y / ((x * x) * z)) = T(y / z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,524,a(flip),b,1419,a)].">
      <j1 rule="hyper" parents="129 524 1419"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      (1 / x) \ (y / (x * x)) = x \ T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,1419,a(flip),b,552,a)].">
      <j1 rule="hyper" parents="125 1419 552"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x \ (x \ 1)) = z
    ]]></literal>
    <justification jstring="[para(1419(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1419 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (x * x) * ((y / (x * x)) * z) = T(y,x \ (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1419(a,1),113(a,1,2,1))].">
      <j1 rule="para" parents="1419 113"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      (x / (y * y)) \ ((y * y) \ z) = T(x,y \ (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(1421(a,1),518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1421 518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[para(1214(a,1),651(a,1,1))].">
      <j1 rule="para" parents="1214 651"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      x * ((x \ y) * (z \ (1 / z))) = y * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[hyper(755,a,704,a),flip(a)].">
      <j1 rule="hyper" parents="755 704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      L(x \ (1 / x),y,z) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(625,a,704,a)].">
      <j1 rule="hyper" parents="625 704"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      ((x \ (1 / x)) * (y * z)) \ (y * (z * (x \ (1 / x)))) = K(y * z,x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(125,a,704,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="125 704 87"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      L((x \ (1 / x)) \ ((y * z) \ u),x \ (1 / x),y * z) = (y * (z * (x \ (1 / x)))) \ u
    ]]></literal>
    <justification jstring="[para(704(a,1),344(a,2,1))].">
      <j1 rule="para" parents="704 344"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) * u = (x * y) * ((z \ (1 / z)) * u)
    ]]></literal>
    <justification jstring="[para(704(a,1),648(a,1,1))].">
      <j1 rule="para" parents="704 648"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x \ (1 / x)) * ((y \ (1 / x)) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(1221(a,1),744(a,1,2,1))].">
      <j1 rule="para" parents="1221 744"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      ((x * x) \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * x) * z) = u
    ]]></literal>
    <justification jstring="[para(615(a,1),798(a,1))].">
      <j1 rule="para" parents="615 798"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ ((y * y) * (x * ((y * y) \ z))) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),1439(a,1))].">
      <j1 rule="para" parents="17 1439"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      (1 / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      x \ ((x * x) * y) = z
    ]]></literal>
    <justification jstring="[para(313(a,1),1439(a,1,1))].">
      <j1 rule="para" parents="313 1439"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ ((x * x) * u) = w
    ]]></literal>
    <justification jstring="[para(514(a,1),1439(a,1,1))].">
      <j1 rule="para" parents="514 1439"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      (x \ (y * (z / u))) * (u * u) = x \ (y * (z / (1 / u)))
    ]]></literal>
    <justification jstring="[para(856(a,1),866(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="856 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      T(x * (y / (z * z)),z * z) = ((z * z) \ x) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = T(y * (1 / x),x * x)
    ]]></literal>
    <justification jstring="[para(579(a,1),890(a,1,2))].">
      <j1 rule="para" parents="579 890"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      T(x * ((y * y) \ z),y * y) = ((y * y) \ x) * T(z,y * y)
    ]]></literal>
    <justification jstring="[para(847(a,1),890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="847 890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      (x * x) \ (((1 / x) * y) \ z) = T(x * y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(889(a,1),968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="889 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      T(x,y * y) \ ((y * y) \ z) = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,517,a(flip),b,972,a),flip(a)].">
      <j1 rule="hyper" parents="370 517 972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x * (y * y)) \ ((y \ 1) \ z) = T(x,y * y) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(940(a,1),972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="940 972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      x \ (((y * y) \ z) * ((y * y) * x)) = T(z,(y * y) * x)
    ]]></literal>
    <justification jstring="[hyper(389,a,974,a),flip(a)].">
      <j1 rule="hyper" parents="389 974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      T(x,y * y) * ((y * y) \ z) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,997,a),flip(a)].">
      <j1 rule="hyper" parents="387 997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = y * ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,997,a(flip),b,514,a)].">
      <j1 rule="hyper" parents="129 997 514"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x * (y * z)) \ ((u * u) * ((((u * u) \ x) * y) * z)) = a((u * u) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9,a,b,1005,a),flip(a)].">
      <j1 rule="hyper" parents="60 9 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (x / (((y \ 1) * y) * (1 / y))) * z = (x / y) * (((y \ 1) * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(1288(a,1),1014(a,1,1,2))].">
      <j1 rule="para" parents="1288 1014"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) \ 1) \ R(y,x,x)) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1120(a,1),1015(a,2,2))].">
      <j1 rule="para" parents="1120 1015"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      L(T(1 / x,y),y,x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,270,a(flip),b,1016,a)].">
      <j1 rule="hyper" parents="60 270 1016"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) \ ((((x * y) \ 1) * x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(301(a,2),1029(a,1,1))].">
      <j1 rule="para" parents="301 1029"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1067(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (x \ 1) * (y \ (1 / y)) != z
    ]]></literal>
    <literal><![CDATA[
      x \ (y \ (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(1087(a,1),392(a,1))].">
      <j1 rule="para" parents="1087 392"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      x \ (y * (z * (u \ (1 / u)))) = (x \ (y * z)) * (u \ (1 / u))
    ]]></literal>
    <justification jstring="[para(704(a,1),1087(a,1,2))].">
      <j1 rule="para" parents="704 1087"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      ((x * y) * z) / ((y * (z * (u * u))) / (u * u)) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(693,a,1097,a),flip(a)].">
      <j1 rule="hyper" parents="693 1097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      ((x * x) * y) / (z * (x * x)) = T(y,x \ (x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(1421(a,1),1103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1421 1103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (x * (y * ((z * z) \ u))) \ ((x * (y / (z * z))) * u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,1104,a,b,82,a)].">
      <j1 rule="hyper" parents="125 1104 82"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (x * (y * z)) * ((z * z) \ u) = (x * (y * (z \ 1))) * u
    ]]></literal>
    <justification jstring="[para(1101(a,1),1104(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1101 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      (x * x) * ((y \ x) \ z) = (y \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(310(a,1),1134(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="310 1134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      (x \ y) * ((y * y) \ z) = (x \ (y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(781,a,1469,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="781 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (x \ 1) * ((y \ (x \ 1)) \ z) = x * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1469,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="129 1469 939"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      x \ y != (z * z) * ((u \ z) \ y)
    ]]></literal>
    <literal><![CDATA[
      u \ (z \ 1) = x
    ]]></literal>
    <justification jstring="[para(1469(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1469 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      (x \ (y \ 1)) * ((y \ 1) \ z) = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(940(a,1),1470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="940 1470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      (x \ (y * ((y \ x) \ 1))) \ z = ((y \ x) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(1135(a,1),605(a,1,1))].">
      <j1 rule="para" parents="1135 605"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,536,a(flip),b,1160,a),flip(a)].">
      <j1 rule="hyper" parents="370 536 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((((1 / x) \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(841,a,1251,a),flip(a)].">
      <j1 rule="hyper" parents="841 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,y \ 1) = z \ (y * ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(125,a,1251,a(flip),b,530,a),flip(a)].">
      <j1 rule="hyper" parents="125 1251 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (x \ y) \ ((1 / x) * T(z,x)) = ((x \ 1) \ y) \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,258,a(flip),b,1264,a),flip(a)].">
      <j1 rule="hyper" parents="60 258 1264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(4(a,1),1269(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 1269"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(1269(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1269 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,522,a,b,1270,a)].">
      <j1 rule="hyper" parents="60 522 1270"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),1270(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 1270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(104(a,2),1270(a,1,1,1,2))].">
      <j1 rule="para" parents="104 1270"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,13,a,b,1273,a)].">
      <j1 rule="hyper" parents="129 13 1273"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(625,a,1487,a)].">
      <j1 rule="hyper" parents="625 1487"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      L(x \ ((1 / y) \ z),x,y) = ((1 / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,1487,a),flip(a)].">
      <j1 rule="hyper" parents="125 70 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      L(x,y,1 / (z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,615,a(flip),b,1488,a),flip(a)].">
      <j1 rule="hyper" parents="370 615 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      L(x \ y,x,y) = ((1 / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,659,a(flip),b,1488,a),flip(a)].">
      <j1 rule="hyper" parents="60 659 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      L(x,y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),1488(a,1,3)),flip(a)].">
      <j1 rule="para" parents="74 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) = x
    ]]></literal>
    <justification jstring="[para(571(a,1),1490(a,1,3))].">
      <j1 rule="para" parents="571 1490"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1493(a,1),47(a,2))].">
      <j1 rule="para" parents="1493 47"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1488,a,b,1492,a)].">
      <j1 rule="hyper" parents="370 1488 1492"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,579,a,b,1492,a)].">
      <j1 rule="hyper" parents="370 579 1492"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,586,a(flip),b,1492,a),flip(a)].">
      <j1 rule="hyper" parents="370 586 1492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,585,a(flip),b,1492,a),flip(a)].">
      <j1 rule="hyper" parents="370 585 1492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,455,a(flip),b,1492,a),flip(a)].">
      <j1 rule="hyper" parents="370 455 1492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(125,a,1492,a,b,579,a)].">
      <j1 rule="hyper" parents="125 1492 579"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ z),x,y) = ((y \ 1) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,344,a(flip),b,1492,a),flip(a)].">
      <j1 rule="hyper" parents="60 344 1492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,y,x) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1492,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 1492 13"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      L(x,y,(z * z) \ (u \ 1)) = L(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[para(517(a,1),1492(a,1,3))].">
      <j1 rule="para" parents="517 1492"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1492(a,2),877(a,2,1))].">
      <j1 rule="para" parents="1492 877"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      ((x \ 1) * x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,1499,a(flip),b,251,a(flip))].">
      <j1 rule="hyper" parents="129 1499 251"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1499(a,1),459(a,1,2))].">
      <j1 rule="para" parents="1499 459"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(758,a,1505,a)].">
      <j1 rule="hyper" parents="758 1505"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,301,a,b,1506,a),flip(a)].">
      <j1 rule="hyper" parents="370 301 1506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(798,a,1501,a),flip(a)].">
      <j1 rule="hyper" parents="798 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ 1) \ z)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,1501,a)].">
      <j1 rule="hyper" parents="60 94 1501"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * ((x \ 1) \ z)) = u
    ]]></literal>
    <justification jstring="[para(1501(a,1),798(a,1))].">
      <j1 rule="para" parents="1501 798"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1111,a(flip),b,1289,a),flip(a)].">
      <j1 rule="hyper" parents="370 1111 1289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      R(x,y \ 1,y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(1125,a,1515,a)].">
      <j1 rule="hyper" parents="1125 1515"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      R(x,y,y) * ((y \ 1) \ 1) = R(x * y,y,y)
    ]]></literal>
    <justification jstring="[para(1111(a,1),1515(a,1,1))].">
      <j1 rule="para" parents="1111 1515"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      x / (1 / (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,254,a(flip),b,1292,a)].">
      <j1 rule="hyper" parents="128 254 1292"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      (x * (1 / y)) * ((y \ 1) \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(1313(a,1),1292(a,1,2))].">
      <j1 rule="para" parents="1313 1292"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,303,a,b,1519,a),flip(a)].">
      <j1 rule="hyper" parents="370 303 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      K(x,1 / x) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(215,a,1521,a)].">
      <j1 rule="hyper" parents="215 1521"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),1296(a,1,1,1))].">
      <j1 rule="para" parents="104 1296"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(711(a,1),1296(a,1,1)),flip(a)].">
      <j1 rule="para" parents="711 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      x \ (y * T(z * z,u)) = (x \ y) * T(z * z,u)
    ]]></literal>
    <justification jstring="[hyper(831,a,1350,a)].">
      <j1 rule="hyper" parents="831 1350"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = L(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,874,a,b,1354,a),flip(a)].">
      <j1 rule="hyper" parents="370 874 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(275,a,1371,a,b,xx)].">
      <j1 rule="hyper" parents="275 1371"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1058,a,1378,a),flip(a)].">
      <j1 rule="hyper" parents="1058 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(328,a,1378,a),flip(a)].">
      <j1 rule="hyper" parents="328 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,1378,a)].">
      <j1 rule="hyper" parents="135 1378"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(783,a,1378,a(flip))].">
      <j1 rule="hyper" parents="783 1378"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,533,a(flip),b,1378,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 533 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),1378(a,2,2,1))].">
      <j1 rule="para" parents="3 1378"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1378(a,2,2,1))].">
      <j1 rule="para" parents="5 1378"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1378(a,1),328(a,1))].">
      <j1 rule="para" parents="1378 328"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x \ T(x * y,z)) = w
    ]]></literal>
    <justification jstring="[para(1378(a,2),719(a,1))].">
      <j1 rule="para" parents="1378 719"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(1 / (x \ 1),y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(547,a,1534,a)].">
      <j1 rule="hyper" parents="547 1534"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,538,a(flip),b,1534,a)].">
      <j1 rule="hyper" parents="60 538 1534"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,1534,a(flip),b,538,a(flip))].">
      <j1 rule="hyper" parents="125 1534 538"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,T(x,y),x \ 1) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1539(a,1),911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1539 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1539(a,1),269(a,1,2,2))].">
      <j1 rule="para" parents="1539 269"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1540(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1540 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(538(a,2),1544(a,1))].">
      <j1 rule="para" parents="538 1544"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(985,a,1379,a),flip(a)].">
      <j1 rule="hyper" parents="985 1379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(981,a,1379,a)].">
      <j1 rule="hyper" parents="981 1379"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1379(a,2,1,1))].">
      <j1 rule="para" parents="2 1379"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1379(a,1),981(a,1))].">
      <j1 rule="para" parents="1379 981"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(981,a,1549,a)].">
      <j1 rule="hyper" parents="981 1549"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,539,a(flip),b,1549,a)].">
      <j1 rule="hyper" parents="60 539 1549"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,1549,a(flip),b,539,a(flip))].">
      <j1 rule="hyper" parents="128 1549 539"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(401,a,1553,a),flip(a)].">
      <j1 rule="hyper" parents="401 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(323,a,1553,a),flip(a)].">
      <j1 rule="hyper" parents="323 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1553(a,1),401(a,1))].">
      <j1 rule="para" parents="1553 401"/>
    </justification>
  </clause>

  <clause id="1558">
    <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(1553(a,1),896(a,1,2))].">
      <j1 rule="para" parents="1553 896"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      x \ ((x / y) * K(y \ 1,y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(301(a,2),1401(a,1,2,2))].">
      <j1 rule="para" parents="301 1401"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,507,a,b,1405,a)].">
      <j1 rule="hyper" parents="370 507 1405"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,507,a,b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="125 507 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      x \ T(y * x,x \ (x \ 1)) = (1 / x) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,1420,a,b,553,a)].">
      <j1 rule="hyper" parents="125 1420 553"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      T(x * y,y \ (y \ 1)) * z = (y * y) * ((x * (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(1420(a,2),28(a,1,1))].">
      <j1 rule="para" parents="1420 28"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      T(x * y,y \ (y \ 1)) \ z = (x * (y \ 1)) \ ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(1420(a,2),518(a,1,1))].">
      <j1 rule="para" parents="1420 518"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ 1) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,1430,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 1430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x \ 1) = x \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(275,a,1430,a,b,1214,a(flip))].">
      <j1 rule="hyper" parents="275 1430 1214"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      (x \ 1) \ ((y \ x) \ z) = x \ ((y \ (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1438,a(flip),b,1214,a(flip))].">
      <j1 rule="hyper" parents="125 1438 1214"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x * x) \ (y \ ((x * x) * z)) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(4(a,1),1449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[para(1461(a,1),508(a,1,2))].">
      <j1 rule="para" parents="1461 508"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(155,a,1475,a)].">
      <j1 rule="hyper" parents="155 1475"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(195(a,1),1512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="195 1512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      x \ y != (x \ z) * T(u * u,w)
    ]]></literal>
    <literal><![CDATA[
      z * T(u * u,w) = y
    ]]></literal>
    <justification jstring="[para(1525(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1525 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),1530(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      (x * x) \ T(x * y,x \ 1) = (1 / x) * (((x \ 1) \ y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(1530(a,1),552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1530 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      x \ T(x * (((x \ 1) \ 1) \ y),x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(945(a,2),1530(a,2,1))].">
      <j1 rule="para" parents="945 1530"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1531(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1531 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1535,a(flip),b,536,a)].">
      <j1 rule="hyper" parents="128 1535 536"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1548(a,2,1,1))].">
      <j1 rule="para" parents="7 1548"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1548(a,1),328(a,1))].">
      <j1 rule="para" parents="1548 328"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1550(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(156,a,1559,a),flip(a)].">
      <j1 rule="hyper" parents="156 1559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(251(a,2),1561(a,1,1,1))].">
      <j1 rule="para" parents="251 1561"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1573(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1584(a,1),89(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1584 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1587(a,2,1,2))].">
      <j1 rule="para" parents="106 1587"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,1589,a)].">
      <j1 rule="hyper" parents="52 1589"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(77(a,1),1590(a,1,1,2))].">
      <j1 rule="para" parents="77 1590"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),1591(a,1,1,1))].">
      <j1 rule="para" parents="5 1591"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(53,a,1592,a)].">
      <j1 rule="hyper" parents="53 1592"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = y \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(936(a,1),343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="936 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(1496(a,1),355(a,1,1))].">
      <j1 rule="para" parents="1496 355"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      T(x \ 1,T(x,x \ 1)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,1332,a)].">
      <j1 rule="hyper" parents="493 1332"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) / T(x * y,L(L(z,y,x),u,w)) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,528,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 528 107"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(344(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="344 528"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(891(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="891 528"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(251(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="251 529"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(94(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="94 529"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(344(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="344 529"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(662(a,2),336(a,1,2))].">
      <j1 rule="para" parents="662 336"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),688(a,1,1,1))].">
      <j1 rule="para" parents="104 688"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(104(a,1),689(a,1,1,1))].">
      <j1 rule="para" parents="104 689"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(655(a,1),729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="655 729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      (x \ 1) * L(x \ 1,y,z) = x \ L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1212(a,1),729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1212 729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ ((x \ 1) \ u),L(x \ 1,y,z),x) = (x \ L(1 / x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(1607(a,1),1501(a,2,1))].">
      <j1 rule="para" parents="1607 1501"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1152(a,1),732(a,1,2,1))].">
      <j1 rule="para" parents="1152 732"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x
    ]]></literal>
    <justification jstring="[para(469(a,1),737(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="469 737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[para(705(a,1),737(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="705 737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      L(T(x / ((1 / x) * x),y),z,u) / x = L(T(1 / (1 / x),y),z,u) * (1 / x)
    ]]></literal>
    <justification jstring="[para(470(a,2),738(a,1,1,1))].">
      <j1 rule="para" parents="470 738"/>
    </justification>
  </clause>

  <clause id="1613">
    <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(746(a,1),336(a,1,2))].">
      <j1 rule="para" parents="746 336"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1072(a,2),824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1072 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(1553(a,1),1614(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1553 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,1495,a,b,1615,a)].">
      <j1 rule="hyper" parents="38 1495 1615"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(155,a,1616,a)].">
      <j1 rule="hyper" parents="155 1616"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(108(a,1),1616(a,1,1))].">
      <j1 rule="para" parents="108 1616"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,1617,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 1617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (K(x,x \ 1) * (x * y)) = L(y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1620(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1620 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1620(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1620 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(129,a,1076,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 1076 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(1076(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="1076 617"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(1091(a,1),438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1091 438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      (x * y) * T(T(y,x),z) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,687,a(flip),b,1166,a),flip(a)].">
      <j1 rule="hyper" parents="60 687 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      (x * y) * T(T(y,z),x) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(18(a,1),1626(a,1,2))].">
      <j1 rule="para" parents="18 1626"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      R(T(T(x,y),z * x),z,x) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(31,a,879,a,b,1627,a)].">
      <j1 rule="hyper" parents="31 879 1627"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      ((x * (y / ((1 / y) * y))) / x) / y = ((x * (1 / (1 / y))) / x) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,1237,a(flip),b,306,a)].">
      <j1 rule="hyper" parents="128 1237 306"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(1237(a,1),103(a,1,1))].">
      <j1 rule="para" parents="1237 103"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1526(a,2),1241(a,1))].">
      <j1 rule="para" parents="1526 1241"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      (x * x) \ T(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ (x * x)) \ 1 = z
    ]]></literal>
    <justification jstring="[para(108(a,2),1266(a,1,2))].">
      <j1 rule="para" parents="108 1266"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      L(T(x / y,z),u,w) * y != v5
    ]]></literal>
    <literal><![CDATA[
      y * L(T(y \ x,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(544(a,1),1299(a,1,1,1))].">
      <j1 rule="para" parents="544 1299"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(129,a,1300,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 1300 13"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ 1)) / z)) = u
    ]]></literal>
    <justification jstring="[para(1300(a,1),336(a,1,2))].">
      <j1 rule="para" parents="1300 336"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      (x \ y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(940(a,1),1309(a,1,2))].">
      <j1 rule="para" parents="940 1309"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,y \ 1) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,93,a(flip),b,1477,a),flip(a)].">
      <j1 rule="hyper" parents="370 93 1477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      L(((x \ 1) \ y) \ z,x \ y,x) = y \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(798,a,1638,a),flip(a)].">
      <j1 rule="hyper" parents="798 1638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1524(a,2,1,2))].">
      <j1 rule="para" parents="2 1524"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,1586,a,b,457,a),flip(a)].">
      <j1 rule="hyper" parents="129 1586 457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      L(((x \ 1) * (x \ 1)) * y,x \ 1,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(939(a,1),1639(a,1,1))].">
      <j1 rule="para" parents="939 1639"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,885,a)].">
      <j1 rule="hyper" parents="31 274 885"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,1650,a,b,5,a)].">
      <j1 rule="hyper" parents="125 1650 5"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      ((x * x) \ 1) \ T(y,y \ 1) = (x * x) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1315,a(flip),b,913,a),flip(a)].">
      <j1 rule="hyper" parents="370 1315 913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      x \ (((1 / y) * (1 / y)) * z) = (y * ((y \ 1) \ x)) \ z
    ]]></literal>
    <justification jstring="[para(1213(a,1),1003(a,2,1))].">
      <j1 rule="para" parents="1213 1003"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (y / z) = ((x \ 1) * (x \ y)) / z
    ]]></literal>
    <justification jstring="[para(1214(a,1),1006(a,2,1))].">
      <j1 rule="para" parents="1214 1006"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ (y / z) = (x * ((x \ 1) \ y)) / z
    ]]></literal>
    <justification jstring="[para(1213(a,1),1024(a,2,1))].">
      <j1 rule="para" parents="1213 1024"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * z = x * ((x \ 1) \ (y * z))
    ]]></literal>
    <justification jstring="[para(595(a,1),1194(a,1,1))].">
      <j1 rule="para" parents="595 1194"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),x) = (x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(275,a,1657,a,b,xx)].">
      <j1 rule="hyper" parents="275 1657"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      T((x \ 1) * y,x * x) = (1 / x) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(944(a,1),1239(a,1,1))].">
      <j1 rule="para" parents="944 1239"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      x / (y \ (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,937,a(flip),b,1248,a(flip))].">
      <j1 rule="hyper" parents="36 937 1248"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      x / ((1 / y) \ y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(377,a,1661,a),flip(a)].">
      <j1 rule="hyper" parents="377 1661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      (x / (1 / y)) * y = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1293,a(flip),b,1661,a)].">
      <j1 rule="hyper" parents="60 1293 1661"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      (((x \ 1) \ y) \ z) * (x * x) = (x \ y) \ T(z,x * x)
    ]]></literal>
    <justification jstring="[hyper(867,a,1262,a)].">
      <j1 rule="hyper" parents="867 1262"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (1 / x) * T(T(y,x),x \ 1) = (x \ (y * (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),1279(a,1,2))].">
      <j1 rule="para" parents="18 1279"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      (x \ 1) \ (x * (y / (x * x))) = (x * T(y,x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(1098(a,1),1294(a,1,2))].">
      <j1 rule="para" parents="1098 1294"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(488,a,1353,a),flip(a)].">
      <j1 rule="hyper" parents="488 1353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(272(a,1),1667(a,1,2)),flip(a)].">
      <j1 rule="para" parents="272 1667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(811,a,1668,a),flip(a)].">
      <j1 rule="hyper" parents="811 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(787,a,1668,a),flip(a)].">
      <j1 rule="hyper" parents="787 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(764,a,1668,a)].">
      <j1 rule="hyper" parents="764 1668"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,1668,a),flip(a)].">
      <j1 rule="hyper" parents="387 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(370,a,172,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="370 172 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (x * y) / (x * (T(x,z) \ y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,172,a(flip),b,1668,a)].">
      <j1 rule="hyper" parents="128 172 1668"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,1668,a)].">
      <j1 rule="hyper" parents="125 172 1668"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1668(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1668(a,2),40(a,1))].">
      <j1 rule="para" parents="1668 40"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(147,a,1676,a)].">
      <j1 rule="hyper" parents="147 1676"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,1676,a)].">
      <j1 rule="hyper" parents="135 1676"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (x / y) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),1676(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1680(a,1),1581(a,2,1))].">
      <j1 rule="para" parents="1680 1581"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(135,a,1669,a)].">
      <j1 rule="hyper" parents="135 1669"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1669(a,1),337(a,1,2,2))].">
      <j1 rule="para" parents="1669 337"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1672(a,1),40(a,1))].">
      <j1 rule="para" parents="1672 40"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1672(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1672 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(474,a,1673,a),flip(a)].">
      <j1 rule="hyper" parents="474 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ u) = z
    ]]></literal>
    <justification jstring="[para(1673(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1673 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1673(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1673 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (T(x,y) \ z)) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(1674(a,1),494(a,1,1))].">
      <j1 rule="para" parents="1674 494"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      T(x,y) \ (x \ z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1684(a,2),44(a,1))].">
      <j1 rule="para" parents="1684 44"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(31,a,530,a,b,1670,a),flip(a)].">
      <j1 rule="hyper" parents="31 530 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(155,a,1683,a)].">
      <j1 rule="hyper" parents="155 1683"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),1695(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(536(a,1),1677(a,1,2))].">
      <j1 rule="para" parents="536 1677"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,1017,a(flip),b,1700,a)].">
      <j1 rule="hyper" parents="275 1017 1700"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) * K((x \ y) \ 1,y / x) = ((x \ y) \ 1) * (y / x)
    ]]></literal>
    <justification jstring="[para(1700(a,1),87(a,1,1))].">
      <j1 rule="para" parents="1700 87"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,1701,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 1701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1701(a,1),1171(a,1,1))].">
      <j1 rule="para" parents="1701 1171"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1703(a,1),556(a,1,1,2))].">
      <j1 rule="para" parents="1703 556"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1622,a,1704,a),flip(a)].">
      <j1 rule="hyper" parents="1622 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),1704(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1704(a,1),1622(a,1))].">
      <j1 rule="para" parents="1704 1622"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(453,a,1706,a),flip(a)].">
      <j1 rule="hyper" parents="453 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1022,a,b,1706,a)].">
      <j1 rule="hyper" parents="60 1022 1706"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(129,a,1706,a(flip),b,1022,a)].">
      <j1 rule="hyper" parents="129 1706 1022"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(125,a,1706,a(flip),b,303,a(flip))].">
      <j1 rule="hyper" parents="125 1706 303"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(74(a,1),1706(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1706(a,1),453(a,1))].">
      <j1 rule="para" parents="1706 453"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(1706(a,1),1522(a,1,1))].">
      <j1 rule="para" parents="1706 1522"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      K(x \ 1,x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,957,a,b,1709,a)].">
      <j1 rule="hyper" parents="370 957 1709"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,509,a,b,1709,a)].">
      <j1 rule="hyper" parents="60 509 1709"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1709(a,2),1064(a,1))].">
      <j1 rule="para" parents="1709 1064"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z != a(x,y,1 / y)
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1709(a,2),157(a,1,1,2))].">
      <j1 rule="para" parents="1709 157"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1709(a,2),1690(a,1,2))].">
      <j1 rule="para" parents="1709 1690"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      K(x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(452,a,1716,a),flip(a)].">
      <j1 rule="hyper" parents="452 1716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      K(x,x \ 1) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,1716,a(flip),b,301,a(flip))].">
      <j1 rule="hyper" parents="128 1716 301"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      K(x,x \ 1) \ (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1724(a,2),1019(a,1,1))].">
      <j1 rule="para" parents="1724 1019"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1509,a(flip),b,1707,a),flip(a)].">
      <j1 rule="hyper" parents="370 1509 1707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1708,a,1730,a)].">
      <j1 rule="hyper" parents="1708 1730"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(77(a,1),1731(a,1,2))].">
      <j1 rule="para" parents="77 1731"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),1732(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1157,a(flip),b,1733,a)].">
      <j1 rule="hyper" parents="60 1157 1733"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,1733,a(flip),b,1157,a(flip))].">
      <j1 rule="hyper" parents="129 1733 1157"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * (K(x,x \ 1) * y)) = L(y,K(x,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(1735(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1735 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      T(x / y,z) * u != (x / y) * (y * T(y \ x,z))
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(1699(a,2),40(a,2))].">
      <j1 rule="para" parents="1699 40"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(559,a,1705,a),flip(a)].">
      <j1 rule="hyper" parents="559 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(263(a,1),1739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,1492,a(flip),b,1727,a)].">
      <j1 rule="hyper" parents="129 1492 1727"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1355(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1356(a,2,1))].">
      <j1 rule="para" parents="3 1356"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,1743,a)].">
      <j1 rule="hyper" parents="135 1743"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(911(a,2),1743(a,1,2))].">
      <j1 rule="para" parents="911 1743"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(135,a,1746,a)].">
      <j1 rule="hyper" parents="135 1746"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      (x / (y * x)) / ((x / (y * x)) * y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(128,a,253,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="128 253 1746"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(1748(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1748 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1744(a,1),1043(a,1))].">
      <j1 rule="para" parents="1744 1043"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      (x * (x * L(x \ y,z,u))) \ ((x * x) * w) = L((1 / x) * y,z,u) \ w
    ]]></literal>
    <justification jstring="[para(1358(a,1),1004(a,2,1))].">
      <j1 rule="para" parents="1358 1004"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,1386,a)].">
      <j1 rule="hyper" parents="135 1386"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(981,a,1387,a),flip(a)].">
      <j1 rule="hyper" parents="981 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(564,a,1390,a)].">
      <j1 rule="hyper" parents="564 1390"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,1754,a,b,536,a)].">
      <j1 rule="hyper" parents="128 1754 536"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = z
    ]]></literal>
    <justification jstring="[para(1724(a,2),1393(a,1,2,1))].">
      <j1 rule="para" parents="1724 1393"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x \ ((y \ (x * z)) * y)) = w
    ]]></literal>
    <justification jstring="[para(1406(a,2),719(a,1))].">
      <j1 rule="para" parents="1406 719"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(536(a,1),1416(a,2,1))].">
      <j1 rule="para" parents="536 1416"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      T(x \ y,y \ (y \ 1)) = (y * y) * (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(310(a,1),1422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="310 1422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      T(x \ y,y \ (y \ 1)) \ z = (x \ (y \ 1)) \ ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(1759(a,2),518(a,1,1))].">
      <j1 rule="para" parents="1759 518"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      T((x \ y) * z,x \ (x \ 1)) = ((x \ 1) \ y) * (z / (x * x))
    ]]></literal>
    <justification jstring="[hyper(1256,a,1423,a),flip(a)].">
      <j1 rule="hyper" parents="1256 1423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      (x * x) * (y * ((x * x) \ z)) = T(y,x \ (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(935(a,1),1427(a,1,2))].">
      <j1 rule="para" parents="935 1427"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      (x * x) * (y \ ((x * x) \ z)) = T(y,x \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,512,a(flip),b,1429,a)].">
      <j1 rule="hyper" parents="60 512 1429"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      x \ (T(y,z * z) * x) = T(y,(z * z) * x)
    ]]></literal>
    <justification jstring="[para(997(a,1),1451(a,1,2))].">
      <j1 rule="para" parents="997 1451"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(389,a,1764,a)].">
      <j1 rule="hyper" parents="389 1764"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y * y),z) = u
    ]]></literal>
    <justification jstring="[para(1764(a,1),389(a,1))].">
      <j1 rule="para" parents="1764 389"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (x * x) * (y / (z * (x * x))) = T(y,x \ (x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,853,a(flip),b,1465,a)].">
      <j1 rule="hyper" parents="60 853 1465"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      (x * (y * (z \ 1))) * z = (x * (y * z)) * (1 / z)
    ]]></literal>
    <justification jstring="[para(313(a,1),1468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="313 1468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1606(a,2,2,1))].">
      <j1 rule="para" parents="3 1606"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,876,a(flip),b,1769,a)].">
      <j1 rule="hyper" parents="60 876 1769"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,1769,a(flip),b,876,a(flip))].">
      <j1 rule="hyper" parents="125 1769 876"/>
    </justification>
  </clause>

  <clause id="1774">
    <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(1771(a,1),911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1771 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1771(a,1),1529(a,1,2,1,2))].">
      <j1 rule="para" parents="1771 1529"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1772(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1772 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(876(a,2),1776(a,1))].">
      <j1 rule="para" parents="876 1776"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,273,a(flip),b,1609,a),flip(a)].">
      <j1 rule="hyper" parents="370 273 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(456(a,1),1778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="456 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(72(a,1),1610(a,2,1,1))].">
      <j1 rule="para" parents="72 1610"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,886,a(flip),b,1780,a)].">
      <j1 rule="hyper" parents="60 886 1780"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,1780,a(flip),b,886,a(flip))].">
      <j1 rule="hyper" parents="128 1780 886"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      ((1 / x) * R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(155,a,1781,a(flip))].">
      <j1 rule="hyper" parents="155 1781"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1782(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1782 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1247,a,1611,a)].">
      <j1 rule="hyper" parents="1247 1611"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) \ z = y \ ((x \ (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(320(a,1),1654(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="320 1654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[para(320(a,1),1655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="320 1655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ 1) * (x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,1788,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 1788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = (x \ (1 / x)) \ (y / z)
    ]]></literal>
    <justification jstring="[para(320(a,1),1656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="320 1656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = x * ((x \ 1) \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1213,a(flip),b,1790,a),flip(a)].">
      <j1 rule="hyper" parents="370 1213 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      (x * T(y,x \ 1)) / x = (x * x) * (y / (x * x))
    ]]></literal>
    <justification jstring="[hyper(949,a,1666,a),flip(a)].">
      <j1 rule="hyper" parents="949 1666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      (x * T(y,x \ 1)) / x = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,1421,a(flip),b,1792,a),flip(a)].">
      <j1 rule="hyper" parents="370 1421 1792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      T((x * y) / x,x \ 1) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(559,a,1793,a)].">
      <j1 rule="hyper" parents="559 1793"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) * y = y * T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(155,a,1793,a)].">
      <j1 rule="hyper" parents="155 1793"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1679(a,1,2,1))].">
      <j1 rule="para" parents="109 1679"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(262(a,1),1679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(282(a,1),1679(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="282 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,1796,a),flip(a)].">
      <j1 rule="hyper" parents="387 1796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ 1) = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,1796,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 1796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      (x \ y) * z != (y / x) * ((x \ y) * u)
    ]]></literal>
    <literal><![CDATA[
      (y / x) * u = z
    ]]></literal>
    <justification jstring="[para(1796(a,2),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1796 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (x / y) \ (y \ x) != (y \ x) * z
    ]]></literal>
    <literal><![CDATA[
      (x / y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1800(a,1),40(a,1))].">
      <j1 rule="para" parents="1800 40"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x \ y) * z != (y / x) * u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * ((x \ y) \ u) = z
    ]]></literal>
    <justification jstring="[para(1799(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1799 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(263(a,1),1740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,1742,a),flip(a)].">
      <j1 rule="hyper" parents="135 1742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1063,a,1752,a)].">
      <j1 rule="hyper" parents="1063 1752"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y / x),y) = z
    ]]></literal>
    <justification jstring="[para(1752(a,1),1063(a,1))].">
      <j1 rule="para" parents="1752 1063"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,1552,a(flip),b,1806,a),flip(a)].">
      <j1 rule="hyper" parents="370 1552 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1534,a(flip),b,1806,a),flip(a)].">
      <j1 rule="hyper" parents="370 1534 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1556(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="1556 1806"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(155,a,1808,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="155 1808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(905(a,1),1808(a,2,1))].">
      <j1 rule="para" parents="905 1808"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(262(a,1),1809(a,2,2))].">
      <j1 rule="para" parents="262 1809"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(109(a,1),1753(a,1,1,1))].">
      <j1 rule="para" parents="109 1753"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(536(a,1),1753(a,1,1))].">
      <j1 rule="para" parents="536 1753"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1538(a,1),1753(a,1,1))].">
      <j1 rule="para" parents="1538 1753"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(758,a,1814,a)].">
      <j1 rule="hyper" parents="758 1814"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1758(a,1,1,2))].">
      <j1 rule="para" parents="2 1758"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,1818,a(flip),b,353,a)].">
      <j1 rule="hyper" parents="275 1818 353"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) \ ((y * y) * z) = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),1805(a,2,2,1))].">
      <j1 rule="para" parents="74 1805"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) != z
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(1813(a,2),505(a,1,2))].">
      <j1 rule="para" parents="1813 505"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1815(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1815 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      ((x * x) * ((y * z) * u)) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(28(a,1),116(a,1,1))].">
      <j1 rule="para" parents="28 116"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      L(K(x,y) \ T(T(x,y),z),K(x,y),y * x) = (x * y) \ ((T(x,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(1626(a,1),664(a,2,2))].">
      <j1 rule="para" parents="1626 664"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (x / y) * (y * L(y \ 1,z,u)) = x * L(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(461(a,1),1033(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="461 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(658(a,1),1033(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="658 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(468(a,1),1048(a,1,1,1))].">
      <j1 rule="para" parents="468 1048"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      R((x * (y \ z)) / z,u,w) * z = (R(x / y,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(707(a,1),1049(a,1,1,1))].">
      <j1 rule="para" parents="707 1049"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,1077,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 1077 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1077(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="1077 617"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1078(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="1078 617"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(1092(a,1),438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1092 438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,688,a(flip),b,1167,a),flip(a)].">
      <j1 rule="hyper" parents="60 688 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,689,a(flip),b,1168,a),flip(a)].">
      <j1 rule="hyper" parents="60 689 1168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(1234(a,2),43(a,1))].">
      <j1 rule="para" parents="1234 43"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      L(((x * y) * T(z,y)) / (x * y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1234(a,2,1,2))].">
      <j1 rule="para" parents="107 1234"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = (x * y) * R(L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),1235(a,1,1,1,1))].">
      <j1 rule="para" parents="92 1235"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(94(a,1),1298(a,1,2,1,2))].">
      <j1 rule="para" parents="94 1298"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(344(a,1),1298(a,1,2,1,2))].">
      <j1 rule="para" parents="344 1298"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1301,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="129 1301 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,1366,a(flip),b,269,a)].">
      <j1 rule="hyper" parents="129 1366 269"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,1375,a(flip),b,283,a)].">
      <j1 rule="hyper" parents="129 1375 283"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a,b,1376,a)].">
      <j1 rule="hyper" parents="60 22 1376"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1549(a,1),1398(a,1))].">
      <j1 rule="para" parents="1549 1398"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,556,a(flip),b,1410,a),flip(a)].">
      <j1 rule="hyper" parents="370 556 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1671(a,1),1412(a,1,1,1))].">
      <j1 rule="para" parents="1671 1412"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),1536(a,1,2,1))].">
      <j1 rule="para" parents="7 1536"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      (x * x) * (((y * z) * u) / (z * u)) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,853,a(flip),b,1825,a)].">
      <j1 rule="hyper" parents="60 853 1825"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y)
    ]]></literal>
    <justification jstring="[para(1173(a,1),1846(a,2,2))].">
      <j1 rule="para" parents="1173 1846"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      R((x * x) * y,z,u) = (x * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(15(a,2),1851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 1851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      T(R((x * x) * y,z,u),x * x) = R(y,z,u) * (x * x)
    ]]></literal>
    <justification jstring="[para(1853(a,2),261(a,1,1))].">
      <j1 rule="para" parents="1853 261"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      R(T((x * x) * y,x * x),z,u) = R(y,z,u) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a,b,1854,a)].">
      <j1 rule="hyper" parents="60 22 1854"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      R(x * (y * y),z,u) = R(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[para(261(a,1),1855(a,1,1))].">
      <j1 rule="para" parents="261 1855"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      R(x * (y * y),y,y) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,103,a(flip),b,1856,a),flip(a)].">
      <j1 rule="hyper" parents="370 103 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      R(x / (y * y),z,u) * (y * y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),1856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      R(x * (y * y),z,u) \ w = (y * y) \ (R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(1856(a,2),517(a,1,1))].">
      <j1 rule="para" parents="1856 517"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      ((((x * x) \ y) * z) * x) * x = R(T(y * z,x * x),x,x)
    ]]></literal>
    <justification jstring="[para(868(a,1),1857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="868 1857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      R((x * x) \ y,z,u) = (x * x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,1858,a(flip),b,883,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 1858 883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      x * R((x * x) \ y,z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,1861,a,b,942,a)].">
      <j1 rule="hyper" parents="129 1861 942"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      (x \ 1) * R(x,y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(313(a,1),1862(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="313 1862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(940(a,1),1862(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="940 1862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      (x * x) \ (R(y \ 1,z,u) \ w) = R(y \ (x * x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(519(a,1),1859(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="519 1859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      R(T(x * y,x * x),x,x) = (((1 / x) * y) * x) * x
    ]]></literal>
    <justification jstring="[para(313(a,1),1860(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="313 1860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * y)) * (z * z) = L(L(z,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[hyper(1389,a,621,a)].">
      <j1 rule="hyper" parents="1389 621"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      ((x * x) \ (y * z)) \ (((x * x) \ 1) * (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(520(a,1),621(a,1,1))].">
      <j1 rule="para" parents="520 621"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(344(a,1),1185(a,1,2,1))].">
      <j1 rule="para" parents="344 1185"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = (1 / x) * (((1 / x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(587(a,1),1282(a,1,1))].">
      <j1 rule="para" parents="587 1282"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      (x * x) * ((x * L(x,y,z)) \ u) = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(1771(a,1),1287(a,2,1))].">
      <j1 rule="para" parents="1771 1287"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x * x) * u) = (x * L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(1385,a,1873,a(flip))].">
      <j1 rule="hyper" parents="1385 1873"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,909,a(flip),b,1348,a),flip(a)].">
      <j1 rule="hyper" parents="370 909 1348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((x / y) \ 1) = y / x
    ]]></literal>
    <justification jstring="[hyper(1161,a,1875,a(flip))].">
      <j1 rule="hyper" parents="1161 1875"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(147,a,1876,a)].">
      <j1 rule="hyper" parents="147 1876"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = ((y \ x) / x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),1877(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 1877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      ((x \ y) / y) / (x \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(401,a,1878,a),flip(a)].">
      <j1 rule="hyper" parents="401 1878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(155,a,1880,a)].">
      <j1 rule="hyper" parents="155 1880"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,468,a,b,1882,a),flip(a)].">
      <j1 rule="hyper" parents="370 468 1882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <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(1709(a,2),1352(a,1,1))].">
      <j1 rule="para" parents="1709 1352"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(985,a,1372,a),flip(a)].">
      <j1 rule="hyper" parents="985 1372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(537(a,1),1885(a,1,1))].">
      <j1 rule="para" parents="537 1885"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(809,a,1886,a)].">
      <j1 rule="hyper" parents="809 1886"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,1886,a),flip(a)].">
      <j1 rule="hyper" parents="482 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(378,a,1886,a),flip(a)].">
      <j1 rule="hyper" parents="378 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,260,a(flip),b,1886,a),flip(a)].">
      <j1 rule="hyper" parents="370 260 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,170,a(flip),b,1886,a),flip(a)].">
      <j1 rule="hyper" parents="370 170 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      (x * T(y,x * y)) * y = y * (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,107,a(flip),b,1886,a),flip(a)].">
      <j1 rule="hyper" parents="370 107 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,1886,a)].">
      <j1 rule="hyper" parents="135 1886"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,107,a(flip),b,1886,a)].">
      <j1 rule="hyper" parents="128 107 1886"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,1886,a),flip(a)].">
      <j1 rule="hyper" parents="128 81 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1886(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      x \ ((y * z) * T(z,u)) != z
    ]]></literal>
    <literal><![CDATA[
      y * T(z,u) = x
    ]]></literal>
    <justification jstring="[para(1886(a,1),159(a,1,2))].">
      <j1 rule="para" parents="1886 159"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(147,a,1888,a)].">
      <j1 rule="hyper" parents="147 1888"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(135,a,1888,a)].">
      <j1 rule="hyper" parents="135 1888"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1900(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1900 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      (1 / T(x,y)) * T(x,z) = T(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1901(a,1),1582(a,1,2,1))].">
      <j1 rule="para" parents="1901 1582"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1901(a,1),1584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1901 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1887(a,2),276(a,2)),flip(a)].">
      <j1 rule="para" parents="1887 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1889(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="1889 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,107,a(flip),b,1891,a),flip(a)].">
      <j1 rule="hyper" parents="128 107 1891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      x \ (y * T(z,u)) != z
    ]]></literal>
    <literal><![CDATA[
      (y / z) * T(z,u) = x
    ]]></literal>
    <justification jstring="[para(1891(a,1),159(a,1,2))].">
      <j1 rule="para" parents="1891 159"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(401,a,1908,a),flip(a)].">
      <j1 rule="hyper" parents="401 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1908,a),flip(a)].">
      <j1 rule="hyper" parents="135 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      (x / y) / T(y,y \ x) = (y \ x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,175,a(flip),b,1908,a)].">
      <j1 rule="hyper" parents="128 175 1908"/>
    </justification>
  </clause>

  <clause id="1915">
    <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(459(a,1),1908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="459 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      x \ ((y * (x * y)) / y) = T(y,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1912(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6 1912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      (x / y) * T(y,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((y * x) / y) = u
    ]]></literal>
    <justification jstring="[para(1912(a,2),485(a,1,2))].">
      <j1 rule="para" parents="1912 485"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1893(a,1),1641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1893 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      x \ ((y * (x * y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x * y) = z
    ]]></literal>
    <justification jstring="[para(1894(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1894 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = (y \ 1) \ ((y \ x) / (y * y))
    ]]></literal>
    <justification jstring="[para(1913(a,2),1127(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1913 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      x * T(y,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (x * y)) / y = z
    ]]></literal>
    <justification jstring="[para(1916(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1916 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      x * T(y,x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      ((y * (x * y)) / y) / u = z
    ]]></literal>
    <justification jstring="[para(1916(a,1),380(a,1,2))].">
      <j1 rule="para" parents="1916 380"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      x * T(y,x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((y * (x * y)) / y) = u
    ]]></literal>
    <justification jstring="[para(1916(a,1),485(a,1,2))].">
      <j1 rule="para" parents="1916 485"/>
    </justification>
  </clause>

  <clause id="1925">
    <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(1918(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="1918 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(895(a,1),1918(a,1,1,2))].">
      <j1 rule="para" parents="895 1918"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(147,a,1904,a)].">
      <j1 rule="hyper" parents="147 1904"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1804(a,1),1905(a,1,1))].">
      <j1 rule="para" parents="1804 1905"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1928(a,1),1895(a,1,1,1))].">
      <j1 rule="para" parents="1928 1895"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(272(a,1),1890(a,1,1))].">
      <j1 rule="para" parents="272 1890"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,66,a(flip),b,1930,a)].">
      <j1 rule="hyper" parents="128 66 1930"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1898(a,1,2))].">
      <j1 rule="para" parents="109 1898"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(262(a,1),1898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(809,a,1935,a)].">
      <j1 rule="hyper" parents="809 1935"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(482,a,1935,a),flip(a)].">
      <j1 rule="hyper" parents="482 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(275,a,1938,a,b,1506,a(flip))].">
      <j1 rule="hyper" parents="275 1938 1506"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1939(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1939 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1939(a,1),161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1939 161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      (x / (x / y)) / (y \ x) = y / (x / y)
    ]]></literal>
    <justification jstring="[hyper(752,a,1937,a)].">
      <j1 rule="hyper" parents="752 1937"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1937(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1539,a(flip),b,1931,a),flip(a)].">
      <j1 rule="hyper" parents="370 1539 1931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(490,a,1396,a),flip(a)].">
      <j1 rule="hyper" parents="490 1396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(274(a,1),1946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="274 1946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(811,a,1947,a),flip(a)].">
      <j1 rule="hyper" parents="811 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(787,a,1947,a),flip(a)].">
      <j1 rule="hyper" parents="787 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(769,a,1947,a)].">
      <j1 rule="hyper" parents="769 1947"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(764,a,1947,a)].">
      <j1 rule="hyper" parents="764 1947"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      x \ ((x * x) * y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(759,a,1947,a)].">
      <j1 rule="hyper" parents="759 1947"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(483,a,1947,a),flip(a)].">
      <j1 rule="hyper" parents="483 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(387,a,1947,a),flip(a)].">
      <j1 rule="hyper" parents="387 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(135,a,1947,a)].">
      <j1 rule="hyper" parents="135 1947"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,1947,a)].">
      <j1 rule="hyper" parents="125 172 1947"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,1947,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(1947(a,1),387(a,1))].">
      <j1 rule="para" parents="1947 387"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      (x * R(x,y,z)) \ (x * (R(x,y,z) * u)) = L(u,x,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1947(a,1),541(a,1,2))].">
      <j1 rule="para" parents="1947 541"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      R(x,x,y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(837,a,1952,a),flip(a)].">
      <j1 rule="hyper" parents="837 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      R(x,x,y) * y = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(597,a,1952,a),flip(a)].">
      <j1 rule="hyper" parents="597 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      R(x,x,y) * y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(1952(a,1),597(a,1))].">
      <j1 rule="para" parents="1952 597"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ (((1 / x) \ y) * z) = a(R(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[para(1961(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1961 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      ((x * R(y,y,z)) * z) / ((1 / y) \ z) = R(x,R(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(1961(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1961 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,885,a,b,1953,a)].">
      <j1 rule="hyper" parents="60 885 1953"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,1953,a(flip),b,274,a)].">
      <j1 rule="hyper" parents="128 1953 274"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u != (x \ 1) * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1953(a,1),356(a,1,1))].">
      <j1 rule="para" parents="1953 356"/>
    </justification>
  </clause>

  <clause id="1968">
    <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(1953(a,1),911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1953 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      x \ (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,1957,a)].">
      <j1 rule="hyper" parents="135 1957"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,1957,a(flip),b,510,a),flip(a)].">
      <j1 rule="hyper" parents="129 1957 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      R(x,y,z) \ T(R(x,y,z) * (R(x,y,z) \ x),u) = T(x,u) * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1957(a,1),1529(a,1,2,1,2))].">
      <j1 rule="para" parents="1957 1529"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      R(x,y,z) \ (x \ u) = x \ (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(135,a,1948,a)].">
      <j1 rule="hyper" parents="135 1948"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(210(a,1),1948(a,1,2,2))].">
      <j1 rule="para" parents="210 1948"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(1950(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1950 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1950(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1950 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1951(a,1),391(a,1))].">
      <j1 rule="para" parents="1951 391"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      L(R(x,y,z) * (x \ u),x,x) != w
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(1951(a,1),790(a,1,1))].">
      <j1 rule="para" parents="1951 790"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(430(a,1),1951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="430 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      R(x,x,y) * (x \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(1961(a,1),1951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      R(x,y,x) * (x \ (y * x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(275,a,103,a(flip),b,1954,a),flip(a)].">
      <j1 rule="hyper" parents="275 103 1954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1981(a,1,2))].">
      <j1 rule="para" parents="17 1981"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,1982,a)].">
      <j1 rule="hyper" parents="135 1982"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(1973(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1973 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(147,a,1974,a),flip(a)].">
      <j1 rule="hyper" parents="147 1974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      x * R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1864,a(flip),b,1965,a)].">
      <j1 rule="hyper" parents="60 1864 1965"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      x \ (x \ R(x,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,1965,a(flip),b,1864,a(flip))].">
      <j1 rule="hyper" parents="125 1965 1864"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      x \ R(x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(912,a,1987,a),flip(a)].">
      <j1 rule="hyper" parents="912 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      R(1 / x,y,z) * x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(906,a,1987,a)].">
      <j1 rule="hyper" parents="906 1987"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1965,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="60 1965 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1864,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="60 1864 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      x \ R(x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(1987(a,1),912(a,1))].">
      <j1 rule="para" parents="1987 912"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      x * R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1988(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1988 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1991(a,1),1247(a,1))].">
      <j1 rule="para" parents="1991 1247"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      T(x,R(x \ 1,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,1993,a(flip),b,1953,a)].">
      <j1 rule="hyper" parents="275 1993 1953"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(433,a,1997,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="433 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(77(a,1),1999(a,1,2,1))].">
      <j1 rule="para" parents="77 1999"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1999(a,1),1153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1999 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,77,a(flip),b,2000,a),flip(a)].">
      <j1 rule="hyper" parents="370 77 2000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,2000,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 2000 17"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(253(a,1),2002(a,1,2))].">
      <j1 rule="para" parents="253 2002"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2004(a,1),1941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2004 1941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,2005,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),2006(a,1,2,2))].">
      <j1 rule="para" parents="7 2006"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      (x / (y * x)) * ((y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x / (y * x)) = z
    ]]></literal>
    <justification jstring="[para(2006(a,1),328(a,1,2))].">
      <j1 rule="para" parents="2006 328"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,909,a,b,2007,a)].">
      <j1 rule="hyper" parents="60 909 2007"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2007(a,1),537(a,1,1))].">
      <j1 rule="para" parents="2007 537"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,y / x) = z
    ]]></literal>
    <justification jstring="[para(2007(a,1),982(a,1,1))].">
      <j1 rule="para" parents="2007 982"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1977,a,2003,a),flip(a)].">
      <j1 rule="hyper" parents="1977 2003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1784,a,2012,a)].">
      <j1 rule="hyper" parents="1784 2012"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (1 / x) = (x * R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(2012(a,1),1272(a,1,1))].">
      <j1 rule="para" parents="2012 1272"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R(x,y,z),x) = (1 / x) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2012(a,1),1487(a,1,1))].">
      <j1 rule="para" parents="2012 1487"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2012(a,1),1783(a,1,1))].">
      <j1 rule="para" parents="2012 1783"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(215,a,2014,a)].">
      <j1 rule="hyper" parents="215 2014"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(33,a,308,a,b,2014,a)].">
      <j1 rule="hyper" parents="33 308 2014"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(2014(a,1),715(a,1,1))].">
      <j1 rule="para" parents="2014 715"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      R(x,y,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2020(a,1),369(a,1,2))].">
      <j1 rule="para" parents="2020 369"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1747(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="1747 2020"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[para(1987(a,2),2020(a,1,2))].">
      <j1 rule="para" parents="1987 2020"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      T(x,(y / (x * y)) * x) = x
    ]]></literal>
    <justification jstring="[para(1990(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="1990 2020"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1992(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="1992 2020"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(198(a,1),2026(a,1,2,1))].">
      <j1 rule="para" parents="198 2026"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2028(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="2028 1165"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(885(a,1),2025(a,1,2))].">
      <j1 rule="para" parents="885 2025"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,2029,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      x / K(x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,728,a,b,2031,a)].">
      <j1 rule="hyper" parents="60 728 2031"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (x \ 1)) * u = R(x,y,z) * ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(2017(a,1),1117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2017 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1744(a,1),2017(a,1,1))].">
      <j1 rule="para" parents="1744 2017"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ 1) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1992(a,1),2017(a,1,1))].">
      <j1 rule="para" parents="1992 2017"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,2032,a)].">
      <j1 rule="hyper" parents="215 2032"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2032(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2032 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2027(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2027 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2030(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="2030 1165"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      (x \ 1) \ R(x,y,z) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1265,a,2015,a)].">
      <j1 rule="hyper" parents="1265 2015"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      T((x * R(x,y,z)) * u,x * x) = (x \ R(x,y,z)) * (u * (x * x))
    ]]></literal>
    <justification jstring="[para(2041(a,1),1249(a,1,1,1))].">
      <j1 rule="para" parents="2041 1249"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1987(a,1),2034(a,1,1))].">
      <j1 rule="para" parents="1987 2034"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      x \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = u
    ]]></literal>
    <justification jstring="[para(103(a,1),1976(a,1,2))].">
      <j1 rule="para" parents="103 1976"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1037(a,1),1979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1037 1979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(4(a,1),1984(a,1,2,2))].">
      <j1 rule="para" parents="4 1984"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(31,a,980,a(flip),b,2010,a(flip))].">
      <j1 rule="hyper" parents="31 980 2010"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1156,a(flip),b,2001,a),flip(a)].">
      <j1 rule="hyper" parents="370 1156 2001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      x * T(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(77(a,1),2048(a,1,2,2,1))].">
      <j1 rule="para" parents="77 2048"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      (x * y) * ((y \ (1 / y)) * z) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),1437(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * (y \ z)) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[para(1214(a,1),2050(a,1,2))].">
      <j1 rule="para" parents="1214 2050"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(127,a,2051,a(flip),b,859,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 2051 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      (x * (y * z)) * (((z \ 1) * (z \ 1)) * u) = (x * ((y * (1 / z)) * 1)) * u
    ]]></literal>
    <justification jstring="[para(2051(a,1),122(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2051 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      (x * (1 / y)) * ((y \ 1) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1195(a,1),2051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1195 2051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (y / ((z * (1 / x)) * 1)) = T(y,(x \ 1) \ ((x \ 1) \ 1)) / (z * x)
    ]]></literal>
    <justification jstring="[para(2051(a,1),1767(a,1,2,2))].">
      <j1 rule="para" parents="2051 1767"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      R(x,y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(1111(a,1),2052(a,1,1))].">
      <j1 rule="para" parents="1111 2052"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      R(x / (1 / y),y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(377,a,2057,a),flip(a)].">
      <j1 rule="hyper" parents="377 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      x * T(y * (1 / x),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(318,a,2057,a)].">
      <j1 rule="hyper" parents="318 2057"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(155,a,2057,a)].">
      <j1 rule="hyper" parents="155 2057"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      T(x * (1 / y),y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(2057(a,1),109(a,1,1))].">
      <j1 rule="para" parents="2057 109"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      (x / (1 / y)) * R(x / (1 / y),y,y) = (x * y) * (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(2058(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2058 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      R(x,y \ 1,y \ 1) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,1516,a,b,2060,a)].">
      <j1 rule="hyper" parents="370 1516 2060"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      (x \ (y * z)) * (z \ (1 / z)) = x \ (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1463(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      (x \ (y * z)) * ((z \ 1) * (z \ 1)) = x \ (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(1211(a,2),2064(a,1,2))].">
      <j1 rule="para" parents="1211 2064"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(77(a,1),1476(a,2,2,1,1))].">
      <j1 rule="para" parents="77 1476"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1872,a,b,2066,a)].">
      <j1 rule="hyper" parents="60 1872 2066"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      (1 / x) * (x * y) = x * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),2066(a,1,2,1))].">
      <j1 rule="para" parents="77 2066"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      x * ((x \ 1) * (x \ y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(407(a,1),2066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="407 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      (x \ 1) * (x \ ((1 / x) \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(811,a,2069,a),flip(a)].">
      <j1 rule="hyper" parents="811 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      x \ L(y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(765,a,2069,a)].">
      <j1 rule="hyper" parents="765 2069"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      x \ ((1 / x) * y) = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(764,a,2069,a)].">
      <j1 rule="hyper" parents="764 2069"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(588,a,2069,a),flip(a)].">
      <j1 rule="hyper" parents="588 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,300,a(flip),b,2069,a),flip(a)].">
      <j1 rule="hyper" parents="370 300 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      (1 / x) * (x * ((x \ 1) \ y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(370,a,172,a(flip),b,2069,a),flip(a)].">
      <j1 rule="hyper" parents="370 172 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      (1 / x) \ (x * y) = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,2069,a)].">
      <j1 rule="hyper" parents="125 172 2069"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      x * ((x \ 1) \ (x \ y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,2069,a),flip(a)].">
      <j1 rule="hyper" parents="125 70 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(2069(a,1),588(a,1))].">
      <j1 rule="para" parents="2069 588"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(783,a,2072,a),flip(a)].">
      <j1 rule="hyper" parents="783 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(384,a,2072,a),flip(a)].">
      <j1 rule="hyper" parents="384 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      x * (x * ((1 / x) * y)) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,951,a(flip),b,2072,a)].">
      <j1 rule="hyper" parents="129 951 2072"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,1606,a(flip),b,2072,a),flip(a)].">
      <j1 rule="hyper" parents="35 1606 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      x \ L(L(y,x,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(25(a,1),2072(a,1,2))].">
      <j1 rule="para" parents="25 2072"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      L((x \ 1) * y,x,x) = (1 / x) * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(2072(a,1),586(a,1,1))].">
      <j1 rule="para" parents="2072 586"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      x \ T((1 / x) * y,z) = (x \ 1) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(591(a,1),2072(a,1,2))].">
      <j1 rule="para" parents="591 2072"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      (x \ 1) * T(1 / x,y) = x \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1230(a,1),2072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1230 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * ((y \ 1) * z)) = (x * (1 / y)) * L(z,y,y)
    ]]></literal>
    <justification jstring="[para(2072(a,1),2051(a,1,2,2))].">
      <j1 rule="para" parents="2072 2051"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,2074,a(flip),b,1251,a)].">
      <j1 rule="hyper" parents="125 2074 1251"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      x \ L(y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2074(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2074 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * (y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(2074(a,1),787(a,1))].">
      <j1 rule="para" parents="2074 787"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1492,a,b,2082,a)].">
      <j1 rule="hyper" parents="60 1492 2082"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      L(R((x \ 1) \ y,z,u),x,x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(2082(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2082 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      L(x,y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ z = x
    ]]></literal>
    <justification jstring="[para(2082(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2082 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(939(a,1),2082(a,1,1))].">
      <j1 rule="para" parents="939 2082"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(862,a,2075,a),flip(a)].">
      <j1 rule="hyper" parents="862 2075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1202,a,2097,a)].">
      <j1 rule="hyper" parents="1202 2097"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2097,a(flip),b,731,a)].">
      <j1 rule="hyper" parents="125 2097 731"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2097(a,1),1202(a,1))].">
      <j1 rule="para" parents="2097 1202"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      (x \ 1) * (x \ (((1 / x) \ y) * z)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,2066,a(flip),b,2070,a),flip(a)].">
      <j1 rule="hyper" parents="31 2066 2070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      (1 / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2070(a,1),632(a,1))].">
      <j1 rule="para" parents="2070 632"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(135,a,2071,a)].">
      <j1 rule="hyper" parents="135 2071"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ ((1 / x) \ y) = z
    ]]></literal>
    <justification jstring="[para(2071(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2071 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (x \ 1) * L(x \ ((1 / x) \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1805(a,2),2071(a,1,2))].">
      <j1 rule="para" parents="1805 2071"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * ((1 / x) * y) = z
    ]]></literal>
    <justification jstring="[para(2073(a,1),790(a,1,1))].">
      <j1 rule="para" parents="2073 790"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (x \ ((1 / x) * y)) * z = (x \ 1) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[para(2073(a,2),1565(a,1,1))].">
      <j1 rule="para" parents="2073 1565"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = z
    ]]></literal>
    <justification jstring="[para(2076(a,1),588(a,1))].">
      <j1 rule="para" parents="2076 588"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      L(x \ (y * ((y \ 1) \ z)),x,y) = ((1 / y) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(2077(a,1),1489(a,1,1,2))].">
      <j1 rule="para" parents="2077 1489"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ z) = (x * y) \ ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[para(2078(a,1),1512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2078 1512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(1637,a,2104,a)].">
      <j1 rule="hyper" parents="1637 2104"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      (x \ 1) * T(x \ ((1 / x) \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(2104(a,1),1535(a,1,2,1))].">
      <j1 rule="para" parents="2104 1535"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(2104(a,1),1576(a,1,1))].">
      <j1 rule="para" parents="2104 1576"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(2104(a,1),1594(a,2,2))].">
      <j1 rule="para" parents="2104 1594"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      T(T(x,x \ 1) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(1321(a,2),2067(a,1,1,1))].">
      <j1 rule="para" parents="1321 2067"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      T(L(x,y,y),y \ 1) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a(flip),b,2081,a)].">
      <j1 rule="hyper" parents="60 20 2081"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(384,a,2090,a),flip(a)].">
      <j1 rule="hyper" parents="384 2090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(1317(a,2),2090(a,2,1))].">
      <j1 rule="para" parents="1317 2090"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1492(a,1),2090(a,1,2))].">
      <j1 rule="para" parents="1492 2090"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x) = 1 \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,62,a,b,2120,a),flip(a)].">
      <j1 rule="hyper" parents="370 62 2120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      L(x,y,y) != (y \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      ((y \ 1) \ 1) \ z = x
    ]]></literal>
    <justification jstring="[para(2120(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2120 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) \ 1,y) = x * T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(841,a,2088,a),flip(a)].">
      <j1 rule="hyper" parents="841 2088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      L(T(1 / x,y),x \ 1,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(820,a,2088,a(flip))].">
      <j1 rule="hyper" parents="820 2088"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      x \ L(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2084(a,1),2091(a,1,2))].">
      <j1 rule="para" parents="2084 2091"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,2094,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 2094 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / T(y,a(x,x,x \ (x \ y))) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(2117(a,2),308(a,1,2,2))].">
      <j1 rule="para" parents="2117 308"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      T(L(x,y,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * (y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(20(a,1),2092(a,1))].">
      <j1 rule="para" parents="20 2092"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) * z) = x \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(135,a,2102,a)].">
      <j1 rule="hyper" parents="135 2102"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      (x \ y) * (((1 / x) \ y) \ z) = (x \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),2102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      (x \ 1) * T((1 / x) \ y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(17(a,2),2102(a,1,2))].">
      <j1 rule="para" parents="17 2102"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      (x * y) \ (((1 / x) \ z) * 1) = ((x \ 1) * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,177,a,b,2113,a)].">
      <j1 rule="hyper" parents="370 177 2113"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y != x \ ((1 / x) \ z)
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ z = y
    ]]></literal>
    <justification jstring="[para(2114(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2114 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      L(x \ (y \ (((1 / y) \ z) * u)),x,y) = ((y \ 1) * x) \ ((y \ z) * u)
    ]]></literal>
    <justification jstring="[para(2132(a,1),1501(a,1,1,2))].">
      <j1 rule="para" parents="2132 1501"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      (x \ 1) \ ((x \ (R(1 / x,y,z) \ (1 / x))) * u) = x \ ((R(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1969(a,1),2132(a,2,2,1))].">
      <j1 rule="para" parents="1969 2132"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      T(x \ 1,x \ y) = ((1 / x) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(276,a,2133,a)].">
      <j1 rule="hyper" parents="276 2133"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ z) = (x \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2071,a(flip),b,2133,a),flip(a)].">
      <j1 rule="hyper" parents="125 2071 2133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * z) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,173,a(flip),b,2133,a),flip(a)].">
      <j1 rule="hyper" parents="125 173 2133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) \ 1,y) = x * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1313(a,1),2125(a,2,2,1))].">
      <j1 rule="para" parents="1313 2125"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      x \ R(x * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,1864,a(flip),b,2129,a),flip(a)].">
      <j1 rule="hyper" parents="60 1864 2129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ (x \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),2129(a,2,2,1))].">
      <j1 rule="para" parents="5 2129"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = (x \ 1) * R(T(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),2129(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 2129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      x * R(x \ (x \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),2144(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(2135(a,1),391(a,1))].">
      <j1 rule="para" parents="2135 391"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      x * T((x \ 1) \ 1,y) = (1 / x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),2143(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 2143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      (x / y) * T(((x / y) \ 1) \ 1,y) = (1 / (x / y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),2149(a,2,2))].">
      <j1 rule="para" parents="109 2149"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      (x \ 1) * R(x \ ((1 / x) \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2104(a,1),2145(a,1,2,1))].">
      <j1 rule="para" parents="2104 2145"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(489,a,1599,a),flip(a)].">
      <j1 rule="hyper" parents="489 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(273(a,1),2152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="273 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(833,a,2153,a)].">
      <j1 rule="hyper" parents="833 2153"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(811,a,2153,a),flip(a)].">
      <j1 rule="hyper" parents="811 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(764,a,2153,a)].">
      <j1 rule="hyper" parents="764 2153"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(387,a,2153,a),flip(a)].">
      <j1 rule="hyper" parents="387 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(135,a,2153,a)].">
      <j1 rule="hyper" parents="135 2153"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,172,a(flip),b,2153,a)].">
      <j1 rule="hyper" parents="128 172 2153"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,2153,a)].">
      <j1 rule="hyper" parents="125 172 2153"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,2153,a),flip(a)].">
      <j1 rule="hyper" parents="125 70 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,2153,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (L(x,y,z) * x) \ (x * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,2153,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 2153 92"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      ((x * y) * L(x,z,u)) \ (x * (L(x,z,u) * y)) = K(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2153,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="125 2153 87"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(2153(a,1),387(a,1))].">
      <j1 rule="para" parents="2153 387"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z) \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(826,a,2162,a)].">
      <j1 rule="hyper" parents="826 2162"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,2162,a)].">
      <j1 rule="hyper" parents="135 2162"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      (x \ 1) * (L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1)) = L(L((x \ 1) \ 1,y,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,2162,a(flip),b,2090,a)].">
      <j1 rule="hyper" parents="129 2162 2090"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,2162,a(flip),b,510,a),flip(a)].">
      <j1 rule="hyper" parents="129 2162 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      x * (L(x,y,z) \ (1 / L(x,y,z))) = (L(x,y,z) \ x) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2162(a,1),1215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2162 1215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <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(2162(a,2),1819(a,1,2))].">
      <j1 rule="para" parents="2162 1819"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      x * (L(x,y,z) * (L(x,u,w) \ 1)) = L(x,y,z) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(2162(a,1),2153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2162 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(2169(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2169 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2169(a,1),1818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2169 1818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(135,a,2155,a)].">
      <j1 rule="hyper" parents="135 2155"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      x \ (L(x,y,z) \ (u * x)) = L(x,y,z) \ T(u,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,17,a,b,2155,a),flip(a)].">
      <j1 rule="hyper" parents="125 17 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      x \ (L(x,y,z) \ ((x * x) * u)) = L(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,554,a(flip),b,2155,a),flip(a)].">
      <j1 rule="hyper" parents="125 554 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      (x / y) \ (L(x / y,z,u) \ x) = L(x / y,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,77,a(flip),b,2155,a),flip(a)].">
      <j1 rule="hyper" parents="125 77 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(2155(a,1),337(a,1,2,2))].">
      <j1 rule="para" parents="2155 337"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      1 / (L(x,y,z) * (x \ L(x,y,z))) = (L(x,y,z) * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(2156(a,1),575(a,1,2))].">
      <j1 rule="para" parents="2156 575"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      x \ (L(x,y,z) * ((x \ 1) * u)) = L(x,y,z) * ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(942(a,1),2156(a,2,2))].">
      <j1 rule="para" parents="942 2156"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      L(L(x,y,z) * (x \ u),x,x) != w
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(2156(a,1),790(a,1,1))].">
      <j1 rule="para" parents="2156 790"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      L(x,y,y) \ (L(L(x,y,y),z,u) * x) = L(L(x,y,y),z,u) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(1362(a,1),2156(a,2,2))].">
      <j1 rule="para" parents="1362 2156"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      L(L(x \ 1,y,z) * ((x \ 1) \ u),x,x) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2156(a,1),2082(a,1,1))].">
      <j1 rule="para" parents="2156 2082"/>
    </justification>
  </clause>

  <clause id="2189">
    <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(323,a,2157,a),flip(a)].">
      <j1 rule="hyper" parents="323 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(2157(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2157 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2158(a,1),1848(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2158 1848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2159(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2159 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * (x * (L(x,y,z) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(2159(a,1),785(a,1,1))].">
      <j1 rule="para" parents="2159 785"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ T(x,L(x,y,z) \ 1) = x * (L(x,y,z) \ (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,941,a,b,2160,a)].">
      <j1 rule="hyper" parents="60 941 2160"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      x * (L(x,y,z) \ T(u,x)) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,258,a(flip),b,2160,a),flip(a)].">
      <j1 rule="hyper" parents="60 258 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (L(x,u,w) * v5) = L(x,u,w) * (L(L(x,u,w),y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(25(a,1),2160(a,1,1))].">
      <j1 rule="para" parents="25 2160"/>
    </justification>
  </clause>

  <clause id="2199">
    <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(2160(a,1),108(a,1,2))].">
      <j1 rule="para" parents="2160 108"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(301(a,2),2160(a,1,2))].">
      <j1 rule="para" parents="301 2160"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ T(x,L(x,y,z) \ 1) = L(x,y,z) \ (L(x,y,z) \ (x * 1))
    ]]></literal>
    <justification jstring="[para(2160(a,2),941(a,2,2))].">
      <j1 rule="para" parents="2160 941"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1709(a,2),2160(a,1,2))].">
      <j1 rule="para" parents="1709 2160"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ 1) * u)) = L(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[para(2074(a,1),2160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2074 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (x \ ((1 / x) \ u))) = L(x \ 1,y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(2071(a,1),2160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2071 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      x \ y != L(z,u,w) * (z \ (L(z,u,w) \ v5))
    ]]></literal>
    <literal><![CDATA[
      x * (z \ v5) = y
    ]]></literal>
    <justification jstring="[para(2161(a,1),781(a,2,2,2))].">
      <j1 rule="para" parents="2161 781"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      (x \ (L(x,y,z) \ u)) * L((L(x,y,z) \ (x \ u)) \ (x \ u),w,v5) = L(L(x,y,z),w,v5) * (L(x,y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[para(2178(a,1),876(a,1,1))].">
      <j1 rule="para" parents="2178 876"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(423(a,1),2183(a,1,2,2))].">
      <j1 rule="para" parents="423 2183"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (x \ ((1 / x) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = w
    ]]></literal>
    <justification jstring="[para(2104(a,1),2183(a,1,2,2))].">
      <j1 rule="para" parents="2104 2183"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      (x * (y * z)) * R(((x * y) * L(z,y,x)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(92(a,1),1600(a,1,1))].">
      <j1 rule="para" parents="92 1600"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1623(a,2,2,1,2))].">
      <j1 rule="para" parents="3 1623"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(135,a,2212,a),flip(a)].">
      <j1 rule="hyper" parents="135 2212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1806(a,2),2212(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1806 2212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(721,a,2214,a),flip(a)].">
      <j1 rule="hyper" parents="721 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      x \ (y * K(z \ (z / (y \ x)),z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,2214,a)].">
      <j1 rule="hyper" parents="135 2214"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(60,a,1582,a(flip),b,2214,a),flip(a)].">
      <j1 rule="hyper" parents="60 1582 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1535,a(flip),b,2214,a),flip(a)].">
      <j1 rule="hyper" parents="60 1535 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),2214(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <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(13(a,2),2214(a,2,2,1,2,2))].">
      <j1 rule="para" parents="13 2214"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z)
    ]]></literal>
    <justification jstring="[para(77(a,1),2214(a,1,2,1))].">
      <j1 rule="para" parents="77 2214"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),2215(a,1,1,2))].">
      <j1 rule="para" parents="6 2215"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      x \ (y * K((y \ x) \ 1,y \ x)) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(71(a,1),2216(a,1,2,2,1,2))].">
      <j1 rule="para" parents="71 2216"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(1917,a,2221,a),flip(a)].">
      <j1 rule="hyper" parents="1917 2221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),1624(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,536,a(flip),b,1625,a),flip(a)].">
      <j1 rule="hyper" parents="370 536 1625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = T(y / (x / z),u) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,536,a(flip),b,1625,a)].">
      <j1 rule="hyper" parents="128 536 1625"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = T(y / x,z) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1625(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1625"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      (T(1 / (x / y),z) * (x / y)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,536,a(flip),b,2228,a),flip(a)].">
      <j1 rule="hyper" parents="370 536 2228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(536(a,1),2229(a,1,1))].">
      <j1 rule="para" parents="536 2229"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,2230,a),flip(a)].">
      <j1 rule="hyper" parents="147 2230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(421(a,1),2230(a,1,1))].">
      <j1 rule="para" parents="421 2230"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1806(a,2),2230(a,1,1))].">
      <j1 rule="para" parents="1806 2230"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(147,a,2233,a),flip(a)].">
      <j1 rule="hyper" parents="147 2233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <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(15(a,2),2234(a,1,1,2,2))].">
      <j1 rule="para" parents="15 2234"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,533,a(flip),b,2232,a),flip(a)].">
      <j1 rule="hyper" parents="370 533 2232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),1696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 1696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),2237(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 2237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(77(a,1),1761(a,2,1,1))].">
      <j1 rule="para" parents="77 1761"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      T((x \ y) * (z * x),x \ (x \ 1)) = ((x \ 1) \ y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(1101(a,1),1761(a,2,2))].">
      <j1 rule="para" parents="1101 1761"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      T((x \ y) * z,x \ (x \ 1)) \ u = (x * x) * ((((x \ 1) \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(1761(a,2),1102(a,1,1))].">
      <j1 rule="para" parents="1761 1102"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      T((x \ (1 / x)) * y,x \ (x \ 1)) = K(x,x \ 1) * (y / (x * x))
    ]]></literal>
    <justification jstring="[para(1710(a,1),1761(a,2,1))].">
      <j1 rule="para" parents="1710 1761"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1775(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),2243(a,2,2))].">
      <j1 rule="para" parents="20 2243"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),2245(a,1,1))].">
      <j1 rule="para" parents="20 2245"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(483,a,2247,a),flip(a)].">
      <j1 rule="hyper" parents="483 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(472,a,2247,a),flip(a)].">
      <j1 rule="hyper" parents="472 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,2247,a),flip(a)].">
      <j1 rule="hyper" parents="387 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,2249,a),flip(a)].">
      <j1 rule="hyper" parents="147 2249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = T(y * x,y) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,1377,a,b,2252,a)].">
      <j1 rule="hyper" parents="60 1377 2252"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(2252(a,1),262(a,1,1))].">
      <j1 rule="para" parents="2252 262"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(2252(a,1),1369(a,1,1))].">
      <j1 rule="para" parents="2252 1369"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      T(T(x,x / y) / y,(x / y) * y) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2254(a,1,1,1,1))].">
      <j1 rule="para" parents="7 2254"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(304(a,1),2254(a,1,1,1,1))].">
      <j1 rule="para" parents="304 2254"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      x * R(y,x,T(y,x)) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2255,a(flip),b,109,a(flip))].">
      <j1 rule="hyper" parents="129 2255 109"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2256(a,1,2))].">
      <j1 rule="para" parents="7 2256"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(316,a,2259,a),flip(a)].">
      <j1 rule="hyper" parents="316 2259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(155,a,2260,a)].">
      <j1 rule="hyper" parents="155 2260"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1269,a,b,2260,a)].">
      <j1 rule="hyper" parents="34 1269 2260"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      x \ L((y * ((x \ 1) \ y)) / y,x \ 1,x) = T(y,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1071,a,2262,a)].">
      <j1 rule="hyper" parents="1071 2262"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(77(a,1),2262(a,1,2,1,2))].">
      <j1 rule="para" parents="77 2262"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(263(a,1),2264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="263 2264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(275,a,7,a(flip),b,2250,a)].">
      <j1 rule="hyper" parents="275 7 2250"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,2266,a,b,xx)].">
      <j1 rule="hyper" parents="128 2266"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2266,a,b,107,a),flip(a)].">
      <j1 rule="hyper" parents="125 2266 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,2266,a,b,xx)].">
      <j1 rule="hyper" parents="125 2266"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),2266(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(467(a,1),2266(a,2,2)),flip(a)].">
      <j1 rule="para" parents="467 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(502(a,1),2266(a,2,2)),flip(a)].">
      <j1 rule="para" parents="502 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2268(a,1),315(a,1,1))].">
      <j1 rule="para" parents="2268 315"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(2268(a,1),1397(a,1,1))].">
      <j1 rule="para" parents="2268 1397"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,2276,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 2276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(128,a,262,a(flip),b,2270,a),flip(a)].">
      <j1 rule="hyper" parents="128 262 2270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(841,a,1798,a),flip(a)].">
      <j1 rule="hyper" parents="841 1798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,76,a(flip),b,2280,a),flip(a)].">
      <j1 rule="hyper" parents="370 76 2280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1709(a,2),2282(a,1,2))].">
      <j1 rule="para" parents="1709 2282"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(1241,a,1830,a),flip(a)].">
      <j1 rule="hyper" parents="1241 1830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),1845(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(536(a,1),1845(a,2,1))].">
      <j1 rule="para" parents="536 1845"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      (x \ 1) * (R(y \ 1,z,u) \ w) = x * (R(y \ (x * x),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,1865,a(flip),b,942,a),flip(a)].">
      <j1 rule="hyper" parents="129 1865 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(1482,a,1929,a)].">
      <j1 rule="hyper" parents="1482 1929"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1936(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(809,a,2289,a)].">
      <j1 rule="hyper" parents="809 2289"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,75,a(flip),b,2289,a),flip(a)].">
      <j1 rule="hyper" parents="128 75 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(2264(a,1),2289(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2264 2289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      ((x * (y \ 1)) / x) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((x * (y \ 1)) / x) = z
    ]]></literal>
    <justification jstring="[para(2291(a,1),401(a,1))].">
      <j1 rule="para" parents="2291 401"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(378,a,2293,a),flip(a)].">
      <j1 rule="hyper" parents="378 2293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / ((z * y) / z)) * y = u
    ]]></literal>
    <justification jstring="[para(1944(a,1),742(a,1))].">
      <j1 rule="para" parents="1944 742"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      L(x,R(y,z,u),y) = L(x,y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(629,a,1959,a)].">
      <j1 rule="hyper" parents="629 1959"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      R(x,y,z) * ((x * x) \ u) = R(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[para(2035(a,1),2033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2035 2033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      R(x \ 1,y,z) * ((x \ 1) \ u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(940(a,1),2301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="940 2301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      (x \ 1) \ (R(x \ 1,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(2046,a,2302,a)].">
      <j1 rule="hyper" parents="2046 2302"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      R((1 / x) \ 1,x,y) * (((1 / x) \ 1) \ z) = (y / (x * y)) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,466,a(flip),b,2302,a),flip(a)].">
      <j1 rule="hyper" parents="370 466 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      L(R(x,y,z) * (x \ u),x,x) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2303(a,1),2082(a,1,1))].">
      <j1 rule="para" parents="2303 2082"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (x * (y \ 1)) * ((T(y,y \ 1) \ 1) \ z) = (x * (1 / (y \ 1))) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(108(a,2),2055(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="108 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(281(a,1),2163(a,1,1))].">
      <j1 rule="para" parents="281 2163"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      T(x,y) * T((y \ (x * y)) \ (y \ z),u) = y \ ((x * y) * T((x * y) \ z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),2225(a,1,1))].">
      <j1 rule="para" parents="17 2225"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(536(a,1),2226(a,1,1))].">
      <j1 rule="para" parents="536 2226"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,536,a(flip),b,2227,a),flip(a)].">
      <j1 rule="hyper" parents="370 536 2227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,1303,a(flip),b,2272,a)].">
      <j1 rule="hyper" parents="60 1303 2272"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(1270(a,1),2311(a,1,1))].">
      <j1 rule="para" parents="1270 2311"/>
    </justification>
  </clause>

  <clause id="2313">
    <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(1676(a,1),2312(a,1,1,2,1))].">
      <j1 rule="para" parents="1676 2312"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(874(a,1),2284(a,1,1))].">
      <j1 rule="para" parents="874 2284"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,1352,a(flip),b,2285,a),flip(a)].">
      <j1 rule="hyper" parents="370 1352 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(109(a,1),2285(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1352,a(flip),b,2316,a)].">
      <j1 rule="hyper" parents="60 1352 2316"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,1351,a(flip),b,2316,a),flip(a)].">
      <j1 rule="hyper" parents="60 1351 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,1052,a(flip),b,2316,a),flip(a)].">
      <j1 rule="hyper" parents="60 1052 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),2319(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(1378(a,1),2317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1378 2317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1548(a,1),2317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1548 2317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(263(a,1),2318(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="263 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(275,a,2323,a(flip),b,259,a(flip))].">
      <j1 rule="hyper" parents="275 2323 259"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,2324,a,b,xx)].">
      <j1 rule="hyper" parents="128 2324"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(2324(a,2),73(a,1,2,1))].">
      <j1 rule="para" parents="2324 73"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2326(a,1,1,1,1))].">
      <j1 rule="para" parents="4 2326"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(2326(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2326 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(78(a,1),2326(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 2326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,1547,a(flip),b,2328,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 1547 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(537(a,1),2328(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="537 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(875(a,1),2328(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="875 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1352,a(flip),b,2286,a)].">
      <j1 rule="hyper" parents="60 1352 2286"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,1052,a(flip),b,2286,a),flip(a)].">
      <j1 rule="hyper" parents="60 1052 2286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(275,a,2286,a(flip),b,1352,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 2286 1352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),2286(a,1,2,1,2))].">
      <j1 rule="para" parents="2 2286"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),2339(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2342,a,b,xx)].">
      <j1 rule="hyper" parents="125 2342"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2343(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(2331(a,1),2344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2331 2344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(156,a,2346,a),flip(a)].">
      <j1 rule="hyper" parents="156 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(y,x) / x,z) = u
    ]]></literal>
    <justification jstring="[para(2347(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2347 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1352,a(flip),b,2340,a)].">
      <j1 rule="hyper" parents="60 1352 2340"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(275,a,1052,a(flip),b,2340,a(flip))].">
      <j1 rule="hyper" parents="275 1052 2340"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(2350(a,1),1169(a,1,1))].">
      <j1 rule="para" parents="2350 1169"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(538(a,1),2350(a,1,2))].">
      <j1 rule="para" parents="538 2350"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1534(a,1),2350(a,1,2))].">
      <j1 rule="para" parents="1534 2350"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1552(a,1),2350(a,1,2))].">
      <j1 rule="para" parents="1552 2350"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2354,a)].">
      <j1 rule="hyper" parents="51 2354"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(2355(a,1),556(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2355 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2353(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="2353 1165"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(2356(a,1),1073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2356 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1072,a,b,2359,a)].">
      <j1 rule="hyper" parents="370 1072 2359"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),2360(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 2360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(51,a,2361,a)].">
      <j1 rule="hyper" parents="51 2361"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2361(a,1),328(a,1,2))].">
      <j1 rule="para" parents="2361 328"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) * (x \ 1) = (x \ 1) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2362(a,1),538(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2362 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(2363,a,1711,a)].">
      <j1 rule="hyper" parents="2363 1711"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(787,a,2349,a),flip(a)].">
      <j1 rule="hyper" parents="787 2349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1378(a,1),2349(a,1,2))].">
      <j1 rule="para" parents="1378 2349"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y
    ]]></literal>
    <justification jstring="[para(1817(a,2),2349(a,1,2))].">
      <j1 rule="para" parents="1817 2349"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y
    ]]></literal>
    <justification jstring="[para(108(a,2),2366(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="108 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) * (x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,5,a(flip),b,2364,a),flip(a)].">
      <j1 rule="hyper" parents="370 5 2364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(146,a,2370,a)].">
      <j1 rule="hyper" parents="146 2370"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2372,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 2372 17"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(77(a,1),2372(a,1,2,1))].">
      <j1 rule="para" parents="77 2372"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      K(x,y) * (1 / x) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2374,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 2374 17"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(2374(a,1),1091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2374 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2098,a(flip),b,2373,a),flip(a)].">
      <j1 rule="hyper" parents="370 2098 2373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * a(1 / x,K(x,y),z) = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(2375(a,2),82(a,2,1))].">
      <j1 rule="para" parents="2375 82"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(421(a,1),2368(a,2,1))].">
      <j1 rule="para" parents="421 2368"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = K(x \ 1,x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(135,a,2379,a)].">
      <j1 rule="hyper" parents="135 2379"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2379(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      K(x \ 1,x) * y != x * (K(x \ 1,x) * z)
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(2381(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="2381 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (x * (K(x \ 1,x) * y)) = L(T(x,y),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2381(a,1),270(a,1,2))].">
      <j1 rule="para" parents="2381 270"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(370,a,469,a(flip),b,2376,a),flip(a)].">
      <j1 rule="hyper" parents="370 469 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(2(a,1),2385(a,1,1,1))].">
      <j1 rule="para" parents="2 2385"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2386(a,1),284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2386 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,2387,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 2387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1676(a,1),2288(a,1,2,1))].">
      <j1 rule="para" parents="1676 2288"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(629,a,2307,a)].">
      <j1 rule="hyper" parents="629 2307"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,L(x,y,z)) = (x * L(x,y,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),2307(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      L(x,y \ z,L(y \ z,y,y)) = L(x,(1 / y) * z,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),2390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="586 2390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,1352,a(flip),b,2309,a)].">
      <j1 rule="hyper" parents="128 1352 2309"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,1351,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="128 1351 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,107,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="128 107 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(536(a,1),2315(a,1,1))].">
      <j1 rule="para" parents="536 2315"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(1405(a,1),2320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1405 2320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(88(a,1),2397(a,2,2))].">
      <j1 rule="para" parents="88 2397"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2398(a,1,1,1))].">
      <j1 rule="para" parents="4 2398"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2399(a,2,2,1))].">
      <j1 rule="para" parents="4 2399"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(371,a,2400,a)].">
      <j1 rule="hyper" parents="371 2400"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(251(a,2),2400(a,1,2))].">
      <j1 rule="para" parents="251 2400"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(2348,a,2335,a),flip(a)].">
      <j1 rule="hyper" parents="2348 2335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(787,a,2337,a)].">
      <j1 rule="hyper" parents="787 2337"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2334,a,b,2337,a)].">
      <j1 rule="hyper" parents="60 2334 2337"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),2337(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="5 2337"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * u = (x * y) * (u * T(u \ L(y \ u,y,x),z))
    ]]></literal>
    <justification jstring="[para(94(a,2),2337(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="94 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z)
    ]]></literal>
    <justification jstring="[para(412(a,2),2405(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="412 2405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y * T(y \ (z / x),u),x)
    ]]></literal>
    <justification jstring="[hyper(323,a,2396,a),flip(a)].">
      <j1 rule="hyper" parents="323 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ (z / x),u),x) = w
    ]]></literal>
    <justification jstring="[para(2396(a,1),389(a,1,2))].">
      <j1 rule="para" parents="2396 389"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(1378(a,1),2396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1378 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1585(a,2),2396(a,1,1))].">
      <j1 rule="para" parents="1585 2396"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(63(a,1),2413(a,2,2,2,1,2))].">
      <j1 rule="para" parents="63 2413"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,259,a(flip),b,2414,a),flip(a)].">
      <j1 rule="hyper" parents="370 259 2414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(421(a,1),2414(a,2,2))].">
      <j1 rule="para" parents="421 2414"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,103,a(flip),b,2415,a),flip(a)].">
      <j1 rule="hyper" parents="32 103 2415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(869(a,1),267(a,1,1))].">
      <j1 rule="para" parents="869 267"/>
    </justification>
  </clause>

  <clause id="2420">
    <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(5(a,1),2419(a,1,1,2))].">
      <j1 rule="para" parents="5 2419"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / ((y * y) \ z) = R(x,y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1012(a,1),606(a,1,1))].">
      <j1 rule="para" parents="1012 606"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(294,a,2421,a),flip(a)].">
      <j1 rule="hyper" parents="294 2421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),2422(a,1,2,2))].">
      <j1 rule="para" parents="77 2422"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (((1 / y) \ y) * z)
    ]]></literal>
    <justification jstring="[para(2424(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2424 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (y * ((y \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(1226(a,1),2425(a,2,2))].">
      <j1 rule="para" parents="1226 2425"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      x * (y * ((y \ 1) \ z)) != u * z
    ]]></literal>
    <literal><![CDATA[
      x * ((1 / y) \ y) = u
    ]]></literal>
    <justification jstring="[para(2426(a,1),41(a,1))].">
      <j1 rule="para" parents="2426 41"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      R(x,y,(y * y) \ z) = ((x * (y \ 1)) * z) / ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1117(a,1),963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1117 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      R(x,y,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2428(a,2),693(a,1))].">
      <j1 rule="para" parents="2428 693"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      R(x,y * z,a(x,z,T(y,z))) \ ((x * z) * T(y,z)) = (z * T(y,z)) * a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),1026(a,1,1,2))].">
      <j1 rule="para" parents="107 1026"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      R(x,x * (x \ y),a(x,x,x \ y)) \ ((x \ 1) \ y) = (x * (x \ y)) * a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(936(a,1),1026(a,1,2))].">
      <j1 rule="para" parents="936 1026"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ 1,x)) = z
    ]]></literal>
    <justification jstring="[para(2316(a,1),1189(a,1))].">
      <j1 rule="para" parents="2316 1189"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,1302,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 1302 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(1302(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="1302 617"/>
    </justification>
  </clause>

  <clause id="2435">
    <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(663(a,1),1344(a,1,2,1))].">
      <j1 rule="para" parents="663 1344"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      L(a(x,x,y) \ z,a(x,x,y),L(y,x,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(1365(a,2),2191(a,1))].">
      <j1 rule="para" parents="1365 2191"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(456(a,1),1779(a,1,1)),flip(a)].">
      <j1 rule="para" parents="456 1779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(156,a,2437,a)].">
      <j1 rule="hyper" parents="156 2437"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),2437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(323,a,2438,a)].">
      <j1 rule="hyper" parents="323 2438"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2439(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(156,a,2441,a)].">
      <j1 rule="hyper" parents="156 2441"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      L(T(((x * y) * z) / (x * y),y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(556(a,1),1839(a,1,1))].">
      <j1 rule="para" parents="556 1839"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(896(a,1),1852(a,1,1))].">
      <j1 rule="para" parents="896 1852"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a(flip),b,2444,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 2444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,2445,a)].">
      <j1 rule="hyper" parents="60 24 2445"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      R(z,y,T(z,y)) = x
    ]]></literal>
    <justification jstring="[para(2445(a,1),165(a,1)),flip(a)].">
      <j1 rule="para" parents="2445 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(2447(a,1),1233(a,2,1,2))].">
      <j1 rule="para" parents="2447 1233"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(1236(a,2),2449(a,1,1))].">
      <j1 rule="para" parents="1236 2449"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),2193(a,2,1))].">
      <j1 rule="para" parents="6 2193"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2451(a,1),537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2451 537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(31,a,273,a,b,2452,a)].">
      <j1 rule="hyper" parents="31 273 2452"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      x \ ((y * (1 \ (x * y))) / y) = T(y,y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1302(a,1),2263(a,1,2))].">
      <j1 rule="para" parents="1302 2263"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      x \ ((y * (x * y)) / y) = T(y,y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(62(a,1),2454(a,1,2,1,2))].">
      <j1 rule="para" parents="62 2454"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      T(x,x / (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * x) = z
    ]]></literal>
    <justification jstring="[para(2455(a,1),1919(a,1))].">
      <j1 rule="para" parents="2455 1919"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(544(a,1),2352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="544 2352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(544(a,1),2457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="544 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <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(2153(a,1),543(a,1,1))].">
      <j1 rule="para" parents="2153 543"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      x * (y * L(y \ (x \ L(y,x,x)),z,u)) = (x * y) * L(T(1 / x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(583(a,1),1598(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="583 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      x * (y * R(y \ (x \ 1),z,u)) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1995,a,1602,a),flip(a)].">
      <j1 rule="hyper" parents="1995 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((x * T(T(y,x),z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(272(a,1),1602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="272 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      x * (y * R(y \ (x \ 1),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ R(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1602(a,1),1995(a,1))].">
      <j1 rule="para" parents="1602 1995"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1299,a,1604,a),flip(a)].">
      <j1 rule="hyper" parents="1299 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1241,a,1604,a)].">
      <j1 rule="hyper" parents="1241 1604"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(875(a,1),2464(a,1,1))].">
      <j1 rule="para" parents="875 2464"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(809,a,2466,a)].">
      <j1 rule="hyper" parents="809 2466"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(761,a,2466,a)].">
      <j1 rule="hyper" parents="761 2466"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(482,a,2466,a),flip(a)].">
      <j1 rule="hyper" parents="482 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) * L(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(378,a,2466,a),flip(a)].">
      <j1 rule="hyper" parents="378 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,170,a(flip),b,2466,a),flip(a)].">
      <j1 rule="hyper" parents="370 170 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      (x * L(y,y,x)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,92,a(flip),b,2466,a),flip(a)].">
      <j1 rule="hyper" parents="370 92 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,66,a(flip),b,2466,a),flip(a)].">
      <j1 rule="hyper" parents="370 66 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,2466,a)].">
      <j1 rule="hyper" parents="135 2466"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      ((x / L(y,z,u)) / y) * L(y,z,u) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,2466,a),flip(a)].">
      <j1 rule="hyper" parents="128 81 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,75,a(flip),b,2466,a),flip(a)].">
      <j1 rule="hyper" parents="128 75 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,170,a(flip),b,2466,a)].">
      <j1 rule="hyper" parents="125 170 2466"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) \ (y * (x * L(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(2466(a,1),396(a,1,1))].">
      <j1 rule="para" parents="2466 396"/>
    </justification>
  </clause>

  <clause id="2479">
    <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(2466(a,1),542(a,1,2))].">
      <j1 rule="para" parents="2466 542"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      x * L(y,y,x) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,1107,a,b,2472,a),flip(a)].">
      <j1 rule="hyper" parents="32 1107 2472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(135,a,2480,a),flip(a)].">
      <j1 rule="hyper" parents="135 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1112,a(flip),b,2480,a),flip(a)].">
      <j1 rule="hyper" parents="125 1112 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      x * L(1 / y,1 / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(77(a,1),2480(a,2,2))].">
      <j1 rule="para" parents="77 2480"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) * L(z,z,(1 / x) \ y)) = x \ (((1 / x) \ y) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2480(a,1),2132(a,2,2))].">
      <j1 rule="para" parents="2480 2132"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) / x) = T(1 / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(323,a,2476,a),flip(a)].">
      <j1 rule="hyper" parents="323 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(2468(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2468 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x)
    ]]></literal>
    <justification jstring="[para(213(a,1),2468(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="213 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,92,a(flip),b,2471,a),flip(a)].">
      <j1 rule="hyper" parents="128 92 2471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      (x * L(y,z,u)) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x / y) * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2471(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2471 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      ((x * L(y,z,u)) / L(y,z,u)) * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2474(a,1),2310(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2474 2310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,2488,a),flip(a)].">
      <j1 rule="hyper" parents="135 2488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      (x * (y * z)) / z != L(z,y,x) * u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / z,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(2488(a,1),276(a,2)),flip(a)].">
      <j1 rule="para" parents="2488 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (y * z)) / z = u
    ]]></literal>
    <justification jstring="[para(2491(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2491 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(251(a,1),2473(a,1,1,2))].">
      <j1 rule="para" parents="251 2473"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(2495(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2495 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      R(L(x,y,z),T(1 / x,L(x,y,z)),x) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(2485(a,1),1085(a,1,1,2))].">
      <j1 rule="para" parents="2485 1085"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = u
    ]]></literal>
    <justification jstring="[para(2(a,1),2486(a,1,1))].">
      <j1 rule="para" parents="2 2486"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      L(x,y,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2(a,1),2489(a,1,1))].">
      <j1 rule="para" parents="2 2489"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1247,a,1605,a)].">
      <j1 rule="hyper" parents="1247 1605"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1482,a,1630,a)].">
      <j1 rule="hyper" parents="1482 1630"/>
    </justification>
  </clause>

  <clause id="2502">
    <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(103(a,1),1630(a,1,2))].">
      <j1 rule="para" parents="103 1630"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,2262,a(flip),b,1635,a),flip(a)].">
      <j1 rule="hyper" parents="60 2262 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2262,a(flip),b,1635,a(flip))].">
      <j1 rule="hyper" parents="125 2262 1635"/>
    </justification>
  </clause>

  <clause id="2505">
    <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(92(a,1),1635(a,1,1))].">
      <j1 rule="para" parents="92 1635"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(2288(a,1),2503(a,1,2))].">
      <j1 rule="para" parents="2288 2503"/>
    </justification>
  </clause>

  <clause id="2507">
    <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(1749(a,1),498(a,1))].">
      <j1 rule="para" parents="1749 498"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),1822(a,1,1,2,1))].">
      <j1 rule="para" parents="74 1822"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      (x / y) * (y * L(y \ ((x / y) \ z),u,w)) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),1829(a,2,2,1,2))].">
      <j1 rule="para" parents="5 1829"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ w) = w * R(w \ (x * (y \ w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(1247,a,1831,a),flip(a)].">
      <j1 rule="hyper" parents="1247 1831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      x * ((x \ y) \ R(x \ y,z,u)) = y * R(y \ (x * 1),z,u)
    ]]></literal>
    <justification jstring="[para(1987(a,1),1832(a,1,2))].">
      <j1 rule="para" parents="1987 1832"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      x * ((x \ y) \ R(x \ y,z,u)) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3(a,1),2512(a,2,2,1,2))].">
      <j1 rule="para" parents="3 2512"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,2513,a),flip(a)].">
      <j1 rule="hyper" parents="135 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      x * (T(y,x) \ R(x \ (y * x),z,u)) = (y * x) * R((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),2513(a,1,2,1))].">
      <j1 rule="para" parents="17 2513"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1996,a,2514,a)].">
      <j1 rule="hyper" parents="1996 2514"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      (x \ 1) \ ((y / (x * x)) * R((y / (x * x)) \ (x \ 1),z,u)) = T(y / x,x \ 1) \ R((x \ 1) \ (y / (x * x)),z,u)
    ]]></literal>
    <justification jstring="[para(1127(a,1),2514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1127 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * R(((z * x) * y) \ (x * y),u,w)) = R(T(z,x * y),x,y) \ R((x * y) \ ((z * x) * y),u,w)
    ]]></literal>
    <justification jstring="[para(880(a,1),2514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="880 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (x \ z),u,w) = x \ (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),1833(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1834(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ z),u,w) = x \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),1834(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2522">
    <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(9(a,2),1834(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1835(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1835"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,883,a(flip),b,2523,a),flip(a)].">
      <j1 rule="hyper" parents="370 883 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(883(a,1),2524(a,1,1))].">
      <j1 rule="para" parents="883 2524"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,2525,a),flip(a)].">
      <j1 rule="hyper" parents="147 2525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <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(15(a,2),2526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,529,a(flip),b,1840,a),flip(a)].">
      <j1 rule="hyper" parents="370 529 1840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),2528(a,1,1,1,1,2))].">
      <j1 rule="para" parents="107 2528"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(274(a,1),2529(a,2,2))].">
      <j1 rule="para" parents="274 2529"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * (y * (x * x))) / (((x \ 1) \ 1) * (x * x))) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,1255,a(flip),b,2530,a),flip(a)].">
      <j1 rule="hyper" parents="370 1255 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(135,a,1843,a)].">
      <j1 rule="hyper" parents="135 1843"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = (y \ 1) \ (y \ (x / (y * y)))
    ]]></literal>
    <justification jstring="[para(1100(a,1),1921(a,2,2))].">
      <j1 rule="para" parents="1100 1921"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) * u) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1978,a,2305,a)].">
      <j1 rule="hyper" parents="1978 2305"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R(x,y,z),x) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2534,a(flip),b,2016,a),flip(a)].">
      <j1 rule="hyper" parents="370 2534 2016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,274,a(flip),b,2146,a),flip(a)].">
      <j1 rule="hyper" parents="370 274 2146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <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(1676(a,1),2536(a,1,2,1,2))].">
      <j1 rule="para" parents="1676 2536"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),2238(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x \ (x \ 1)) = K(x,x \ 1) * (y / (x * x))
    ]]></literal>
    <justification jstring="[para(1214(a,1),2242(a,1,1))].">
      <j1 rule="para" parents="1214 2242"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(1306,a,2273,a)].">
      <j1 rule="hyper" parents="1306 2273"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2248(a,1),2541(a,1,1))].">
      <j1 rule="para" parents="2248 2541"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(2542(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2542 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      (x \ 1) * (R(x \ 1,y,z) \ u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2287(a,2,2,1,1))].">
      <j1 rule="para" parents="4 2287"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (x \ 1) \ L(R((x \ 1) \ 1,y,z) \ u,x,x) = (x \ 1) * (R(x \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2090,a,b,2544,a)].">
      <j1 rule="hyper" parents="60 2090 2544"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,2327,a(flip),b,2322,a),flip(a)].">
      <j1 rule="hyper" parents="128 2327 2322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(1052(a,1),2338(a,1,1))].">
      <j1 rule="para" parents="1052 2338"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(1029,a,2459,a),flip(a)].">
      <j1 rule="hyper" parents="1029 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <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(2459(a,1),1029(a,1))].">
      <j1 rule="para" parents="2459 1029"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1598,a(flip),b,2465,a)].">
      <j1 rule="hyper" parents="60 1598 2465"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),2465(a,1,2,1,2))].">
      <j1 rule="para" parents="2 2465"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(874(a,1),2465(a,2,1))].">
      <j1 rule="para" parents="874 2465"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(874(a,1),2551(a,2,1))].">
      <j1 rule="para" parents="874 2551"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1598,a(flip),b,2553,a)].">
      <j1 rule="hyper" parents="60 1598 2553"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(275,a,1346,a(flip),b,2553,a(flip))].">
      <j1 rule="hyper" parents="275 1346 2553"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2553,a(flip),b,611,a(flip))].">
      <j1 rule="hyper" parents="275 2553 611"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,2555,a)].">
      <j1 rule="hyper" parents="52 2555"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(456(a,1),2555(a,1,2,2))].">
      <j1 rule="para" parents="456 2555"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(876(a,1),2555(a,1,2))].">
      <j1 rule="para" parents="876 2555"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      T(x \ 1,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1769(a,1),2555(a,1,2))].">
      <j1 rule="para" parents="1769 2555"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2560(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="2560 1165"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2554(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 2554"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      a(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1029,a,2479,a),flip(a)].">
      <j1 rule="hyper" parents="1029 2479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),2500(a,1,2,1,2))].">
      <j1 rule="para" parents="2 2500"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(883(a,1),2500(a,2,1))].">
      <j1 rule="para" parents="883 2500"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(883(a,1),2566(a,2,1))].">
      <j1 rule="para" parents="883 2566"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x \ R(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(1991(a,1),2566(a,2,1))].">
      <j1 rule="para" parents="1991 2566"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x \ R(x,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1602,a(flip),b,2569,a)].">
      <j1 rule="hyper" parents="60 1602 2569"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(1987(a,2),2570(a,2,1))].">
      <j1 rule="para" parents="1987 2570"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1601,a(flip),b,2568,a)].">
      <j1 rule="hyper" parents="60 1601 2568"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(1270(a,1),2501(a,2,1))].">
      <j1 rule="para" parents="1270 2501"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(2507,a,2024,a)].">
      <j1 rule="hyper" parents="2507 2024"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[para(5(a,1),2575(a,1,3,2))].">
      <j1 rule="para" parents="5 2575"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      L((x / y) \ 1,x / y,y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),2575(a,1,3,2))].">
      <j1 rule="para" parents="7 2575"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (1 / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(129,a,2576,a(flip),b,251,a(flip))].">
      <j1 rule="hyper" parents="129 2576 251"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(668,a,2577,a)].">
      <j1 rule="hyper" parents="668 2577"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(129,a,2577,a(flip),b,251,a(flip))].">
      <j1 rule="hyper" parents="129 2577 251"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(128,a,6,a(flip),b,2580,a),flip(a)].">
      <j1 rule="hyper" parents="128 6 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),2581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,2510,a(flip),b,2554,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 2510 2554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      (x / y) * (y * L(y \ ((x / y) \ z),u,w)) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ (x * L(x \ z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(2510(a,2),721(a,1))].">
      <j1 rule="para" parents="2510 721"/>
    </justification>
  </clause>

  <clause id="2585">
    <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(15(a,2),2583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 2583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ w) = w * R(w \ (y * (x \ w)),z,u)
    ]]></literal>
    <justification jstring="[para(883(a,1),2511(a,1,1))].">
      <j1 rule="para" parents="883 2511"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      ((1 / x) \ y) * L((x \ y) \ (x \ z),u,w) = (1 / x) \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(2141(a,1),2521(a,1,2,1))].">
      <j1 rule="para" parents="2141 2521"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2532(a,1,2,2,1))].">
      <j1 rule="para" parents="5 2532"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(568,a,2588,a)].">
      <j1 rule="hyper" parents="568 2588"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(2588(a,1),568(a,1))].">
      <j1 rule="para" parents="2588 568"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(74(a,1),2589(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1554(a,1),2589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1554 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <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(1927(a,1),2589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1927 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,2591,a(flip),b,2504,a),flip(a)].">
      <j1 rule="hyper" parents="129 2591 2504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(101(a,2),2594(a,1,2))].">
      <j1 rule="para" parents="101 2594"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2595(a,2,2,2))].">
      <j1 rule="para" parents="6 2595"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(2596(a,1),1671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2596 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(538(a,2),2592(a,1,2,1))].">
      <j1 rule="para" parents="538 2592"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2596(a,1),2597(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2596 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(391,a,2599,a),flip(a)].">
      <j1 rule="hyper" parents="391 2599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      T(x * K(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2600,a,b,183,a(flip))].">
      <j1 rule="hyper" parents="275 2600 183"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = y \ ((1 / y) \ (x / (y * y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,2104,a(flip),b,2533,a),flip(a)].">
      <j1 rule="hyper" parents="370 2104 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,R(x,y,z)) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2300(a,1),2535(a,1,2))].">
      <j1 rule="para" parents="2300 2535"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(874(a,1),2550(a,2,1))].">
      <j1 rule="para" parents="874 2550"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(275,a,2552,a(flip),b,1598,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 2552 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),2552(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),2606(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,2609,a,b,xx)].">
      <j1 rule="hyper" parents="125 2609"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2610(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(2331(a,1),2611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2331 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,2336,a(flip),b,2613,a),flip(a)].">
      <j1 rule="hyper" parents="60 2336 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1602,a(flip),b,2567,a)].">
      <j1 rule="hyper" parents="60 1602 2567"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      ((x * y) * R((x * y) \ x,z,u)) * y = (x * y) * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,1600,a(flip),b,2567,a),flip(a)].">
      <j1 rule="hyper" parents="60 1600 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(275,a,2567,a(flip),b,1832,a),flip(a)].">
      <j1 rule="hyper" parents="275 2567 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(275,a,2567,a(flip),b,1602,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 2567 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,2567,a(flip),b,1832,a),flip(a)].">
      <j1 rule="hyper" parents="125 2567 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2567(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2620(a,1,1,2,1))].">
      <j1 rule="para" parents="4 2620"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(482,a,2623,a),flip(a)].">
      <j1 rule="hyper" parents="482 2623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(378,a,2623,a),flip(a)].">
      <j1 rule="hyper" parents="378 2623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,2623,a)].">
      <j1 rule="hyper" parents="135 2623"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(2625(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2625 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2626(a,1),1641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2626 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(1374,a,2628,a)].">
      <j1 rule="hyper" parents="1374 2628"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,2628,a(flip),b,880,a)].">
      <j1 rule="hyper" parents="129 2628 880"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * (y * R(x,z,u)) = (y * R(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2628(a,1),274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2628 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      x / R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = u
    ]]></literal>
    <justification jstring="[para(2(a,1),2627(a,1,1))].">
      <j1 rule="para" parents="2 2627"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) = x * R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),2618(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,2634,a,b,xx)].">
      <j1 rule="hyper" parents="125 2634"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,2629,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,1635,a(flip),b,2574,a),flip(a)].">
      <j1 rule="hyper" parents="60 1635 2574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      T((x / y) / T(y,y \ x),y \ 1) = y \ (y \ T(x,y \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1425(a,1),2603(a,2,2))].">
      <j1 rule="para" parents="1425 2603"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,2510,a(flip),b,2605,a),flip(a)].">
      <j1 rule="hyper" parents="60 2510 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),2605(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      (x * (y * L(y \ (x \ z),u,w))) / y = x * L(x \ (z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,1598,a(flip),b,2607,a)].">
      <j1 rule="hyper" parents="128 1598 2607"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (T(x,x \ y) * R(T(x,x \ y) \ u,w,v5)) * z
    ]]></literal>
    <justification jstring="[hyper(928,a,2615,a)].">
      <j1 rule="hyper" parents="928 2615"/>
    </justification>
  </clause>

  <clause id="2647">
    <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(210(a,1),2615(a,1,2,2,1,2))].">
      <j1 rule="para" parents="210 2615"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      x \ (x \ T(y,x \ (x \ 1))) = T((x \ y) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1913(a,1),2641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1913 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      x \ (x \ T(y * x,x \ (x \ 1))) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(17(a,2),2648(a,2,1,1))].">
      <j1 rule="para" parents="17 2648"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y
    ]]></literal>
    <justification jstring="[para(2577(a,1),2642(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2577 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,2510,a(flip),b,2643,a),flip(a)].">
      <j1 rule="hyper" parents="128 2510 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      (x * (y * L(y \ (x \ x),z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,1828,a,b,2644,a),flip(a)].">
      <j1 rule="hyper" parents="370 1828 2644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1912(a,2),2651(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1912 2651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(871(a,1),2653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="871 2653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),2654(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(2655(a,1),109(a,1,1))].">
      <j1 rule="para" parents="2655 109"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2154,a(flip),b,2656,a),flip(a)].">
      <j1 rule="hyper" parents="370 2154 2656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(29(a,1),119(a,1,2))].">
      <j1 rule="para" parents="29 119"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      ((x * y) * ((z * z) * u)) / (y * ((z * z) * u)) = R(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(122(a,1),120(a,1,1))].">
      <j1 rule="para" parents="122 120"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9,a,b,669,a)].">
      <j1 rule="hyper" parents="370 9 669"/>
    </justification>
  </clause>

  <clause id="2661">
    <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(669(a,2),1029(a,1))].">
      <j1 rule="para" parents="669 1029"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ (x * (((y * y) \ z) * u)) = L(u,z,x / (y * y))
    ]]></literal>
    <justification jstring="[para(1013(a,1),1010(a,1,2))].">
      <j1 rule="para" parents="1013 1010"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      ((x * y) * ((z * z) \ u)) / (y * ((z * z) \ u)) = R(x,y / (z * z),u)
    ]]></literal>
    <justification jstring="[para(1104(a,1),1011(a,1,1))].">
      <j1 rule="para" parents="1104 1011"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      a(x,y / (z \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * z) \ ((x * y) \ ((x * (y / (z \ 1))) * z)) = u
    ]]></literal>
    <justification jstring="[para(1128(a,1),1382(a,1))].">
      <j1 rule="para" parents="1128 1382"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      (x * y) * ((z * z) * L(u,y * (z * z),x)) = x * (y * ((z * z) * u))
    ]]></literal>
    <justification jstring="[para(29(a,1),1417(a,2,2))].">
      <j1 rule="para" parents="29 1417"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      ((x * y) * z) / (y * ((z * (u * u)) / (u * u))) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(1098(a,1),1464(a,1,2))].">
      <j1 rule="para" parents="1098 1464"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(1305(a,1),1484(a,1,1))].">
      <j1 rule="para" parents="1305 1484"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      ((x * (y * ((1 / z) \ 1))) / x) / z = (1 / z) * ((x * ((1 / z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),2668(a,1,2))].">
      <j1 rule="para" parents="77 2668"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x \ 1,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(596(a,1),1643(a,1,1))].">
      <j1 rule="para" parents="596 1643"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2582(a,1),1812(a,1,1,2))].">
      <j1 rule="para" parents="2582 1812"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,933,a(flip),b,2671,a),flip(a)].">
      <j1 rule="hyper" parents="60 933 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(155,a,2672,a)].">
      <j1 rule="hyper" parents="155 2672"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ z) * u) = (x * y) \ (((1 / x) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,344,a(flip),b,2138,a),flip(a)].">
      <j1 rule="hyper" parents="60 344 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      L(T(x,x * (L(x,y,z) \ u)),y,z) = (L(x,y,z) \ (x * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a,b,2199,a)].">
      <j1 rule="hyper" parents="60 20 2199"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(304(a,1),2257(a,1,2))].">
      <j1 rule="para" parents="304 2257"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      T(R(T(x,x * y),y,y \ 1) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),2678(a,1,1,1))].">
      <j1 rule="para" parents="22 2678"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(522(a,1),2679(a,1,1))].">
      <j1 rule="para" parents="522 2679"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(2680(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2680 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      T(x * y,R(x,y,y \ 1)) = T(x * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1527(a,1),2681(a,1,1))].">
      <j1 rule="para" parents="1527 2681"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),2682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 2682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(706(a,1),2683(a,2,2))].">
      <j1 rule="para" parents="706 2683"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),2684(a,1,1))].">
      <j1 rule="para" parents="7 2684"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),2685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 2685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),2686(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 2686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      T(x,x * T(y,y \ 1)) = T(x,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(108(a,2),2686(a,1,2,2))].">
      <j1 rule="para" parents="108 2686"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(712(a,1),2313(a,2,2))].">
      <j1 rule="para" parents="712 2313"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(2(a,1),2689(a,2,2,1))].">
      <j1 rule="para" parents="2 2689"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(2389(a,1),2690(a,1,1))].">
      <j1 rule="para" parents="2389 2690"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(291,a,2691,a),flip(a)].">
      <j1 rule="hyper" parents="291 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,2506,a,b,2692,a)].">
      <j1 rule="hyper" parents="60 2506 2692"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2389(a,2),2694(a,1,2))].">
      <j1 rule="para" parents="2389 2694"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1709(a,2),2650(a,2,1))].">
      <j1 rule="para" parents="1709 2650"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      R(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * z) * u) = w
    ]]></literal>
    <justification jstring="[para(2659(a,1),693(a,1))].">
      <j1 rule="para" parents="2659 693"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u / (y * y))
    ]]></literal>
    <justification jstring="[hyper(629,a,2663,a)].">
      <j1 rule="hyper" parents="629 2663"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      L(x,(y * y) \ 1,z) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,634,a(flip),b,2698,a),flip(a)].">
      <j1 rule="hyper" parents="370 634 2698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      L(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(599(a,1),2699(a,1,2))].">
      <j1 rule="para" parents="599 2699"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      L(x,(y / (z * z)) \ ((z * z) * (y \ 1)),u) = x
    ]]></literal>
    <justification jstring="[para(512(a,1),2700(a,1,2,2))].">
      <j1 rule="para" parents="512 2700"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      L(x,(y * y) * (z \ ((y * y) * (z \ 1))),u) = x
    ]]></literal>
    <justification jstring="[para(512(a,1),2701(a,1,2))].">
      <j1 rule="para" parents="512 2701"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      L(x,(y * y) * (z \ ((y * y) * (z \ 1))),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(2702(a,1),47(a,2))].">
      <j1 rule="para" parents="2702 47"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      R(x,y / (z * z),u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(693,a,2664,a),flip(a)].">
      <j1 rule="hyper" parents="693 2664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      R(x,y * z,(z * z) \ u) = R(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(1101(a,1),2704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1101 2704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * (z * ((x * x) * u)))) = L(u,z * (x * x),y)
    ]]></literal>
    <justification jstring="[para(2666(a,1),64(a,1,2,2))].">
      <j1 rule="para" parents="2666 64"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(6(a,1),2667(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 2667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15,a,b,2707,a),flip(a)].">
      <j1 rule="hyper" parents="370 15 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      R(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2707(a,2),693(a,1))].">
      <j1 rule="para" parents="2707 693"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      R(x,y,z * (u * (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(30(a,1),2708(a,1,3))].">
      <j1 rule="para" parents="30 2708"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(248(a,1),2708(a,1,3)),flip(a)].">
      <j1 rule="para" parents="248 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(252(a,1),2708(a,1,3))].">
      <j1 rule="para" parents="252 2708"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      R(x,y,z \ (u * u)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(519(a,1),2708(a,1,3))].">
      <j1 rule="para" parents="519 2708"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1138,a,2711,a)].">
      <j1 rule="hyper" parents="1138 2711"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a(flip),b,2711,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 2711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2063,a(flip),b,2711,a)].">
      <j1 rule="hyper" parents="60 2063 2711"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,2711,a(flip),b,2063,a(flip))].">
      <j1 rule="hyper" parents="128 2711 2063"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * w) * 1)) = R(x,y,((w * w) \ z) * u)
    ]]></literal>
    <justification jstring="[para(1005(a,1),2711(a,1,3))].">
      <j1 rule="para" parents="1005 2711"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(2711(a,1),2168(a,1,1))].">
      <j1 rule="para" parents="2711 2168"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a,b,2712,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1119,a,b,2712,a),flip(a)].">
      <j1 rule="hyper" parents="370 1119 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1111,a,b,2712,a)].">
      <j1 rule="hyper" parents="370 1111 2712"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      R(x,y,1 / (1 / z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2712,a(flip),b,2712,a),flip(a)].">
      <j1 rule="hyper" parents="370 2712 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2716(a,1),103(a,1,1))].">
      <j1 rule="para" parents="2716 103"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(695,a,2717,a)].">
      <j1 rule="hyper" parents="695 2717"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(378,a,2717,a),flip(a)].">
      <j1 rule="hyper" parents="378 2717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(2717(a,1),255(a,1,2))].">
      <j1 rule="para" parents="2717 255"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,827,a(flip),b,2726,a),flip(a)].">
      <j1 rule="hyper" parents="60 827 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),2726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      R(x,(1 / y) \ 1,1 / y) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2098(a,2),2718(a,2,2))].">
      <j1 rule="para" parents="2098 2718"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2718(a,1),2418(a,1,1))].">
      <j1 rule="para" parents="2718 2418"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2469(a,1),2723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2469 2723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2727(a,1),2638(a,1,1,2))].">
      <j1 rule="para" parents="2727 2638"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      R(x,y,z \ (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a(flip),b,2713,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 2713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(248(a,1),2709(a,1,3))].">
      <j1 rule="para" parents="248 2709"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      R(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(252(a,1),2709(a,1,3))].">
      <j1 rule="para" parents="252 2709"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      R(x,y,z \ (u / (1 / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = v5
    ]]></literal>
    <justification jstring="[para(863(a,1),2709(a,1,3))].">
      <j1 rule="para" parents="863 2709"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      R(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(2712(a,2),2736(a,1))].">
      <j1 rule="para" parents="2712 2736"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      R(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2721(a,1),2737(a,1))].">
      <j1 rule="para" parents="2721 2737"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      R(x,y,z \ (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2713(a,2),2741(a,1))].">
      <j1 rule="para" parents="2713 2741"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      R(x,y,z * (u * (w * (v5 * v5)))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(30(a,1),2710(a,1,3,2))].">
      <j1 rule="para" parents="30 2710"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(378,a,2732,a),flip(a)].">
      <j1 rule="hyper" parents="378 2732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,z / y) = R(x,(y / z) \ 1,y / z)
    ]]></literal>
    <justification jstring="[para(2007(a,2),2715(a,1,2))].">
      <j1 rule="para" parents="2007 2715"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2725(a,1),41(a,1))].">
      <j1 rule="para" parents="2725 41"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      (L(x,y,z) * R(L(x,y,z) \ 1,x,1 / x)) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,904,a,b,2733,a)].">
      <j1 rule="hyper" parents="60 904 2733"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      R(x,y,(z * u) \ (w * w)) = R(x,y,((w * w) \ z) * u)
    ]]></literal>
    <justification jstring="[para(3(a,1),2719(a,1,3,2))].">
      <j1 rule="para" parents="3 2719"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      R(x,y,((z * z) \ u) * w) = R(x,y,u * w)
    ]]></literal>
    <justification jstring="[hyper(2742,a,2748,a),flip(a)].">
      <j1 rule="hyper" parents="2742 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      R(x,y,((z * z) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u * w) = v5
    ]]></literal>
    <justification jstring="[para(2748(a,1),2742(a,1))].">
      <j1 rule="para" parents="2748 2742"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      R(x,y,(z * z) * u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(194(a,1),2749(a,1,3)),flip(a)].">
      <j1 rule="para" parents="194 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      R(x,y,(1 / z) * u) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(313(a,1),2749(a,1,3,1))].">
      <j1 rule="para" parents="313 2749"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),2752(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 2752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      R(x,y,z * (z * u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(92(a,1),2752(a,1,3))].">
      <j1 rule="para" parents="92 2752"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(936(a,1),2752(a,1,3))].">
      <j1 rule="para" parents="936 2752"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      R(x,y,(z * (u \ 1)) \ w) = R(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(1116(a,1),2752(a,1,3))].">
      <j1 rule="para" parents="1116 2752"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2429,a,2755,a)].">
      <j1 rule="hyper" parents="2429 2755"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      R(x,y * (z \ 1),u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2705,a(flip),b,2755,a)].">
      <j1 rule="hyper" parents="60 2705 2755"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2755(a,1),2429(a,1))].">
      <j1 rule="para" parents="2755 2429"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      R(x,x,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(992,a,2759,a),flip(a)].">
      <j1 rule="hyper" parents="992 2759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2759,a(flip),b,2759,a),flip(a)].">
      <j1 rule="hyper" parents="370 2759 2759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),2759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 2759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      R(x \ 1,x,y) * y = (1 / (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2759(a,1),1961(a,1,1))].">
      <j1 rule="para" parents="2759 1961"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2741,a,2765,a)].">
      <j1 rule="hyper" parents="2741 2765"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2759,a,b,2765,a),flip(a)].">
      <j1 rule="hyper" parents="370 2759 2765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2759,a(flip),b,2763,a)].">
      <j1 rule="hyper" parents="60 2759 2763"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      ((1 / x) \ y) / y = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1960,a(flip),b,2763,a)].">
      <j1 rule="hyper" parents="60 1960 2763"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2764(a,1),103(a,1,1))].">
      <j1 rule="para" parents="2764 103"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2764(a,1),502(a,1,1))].">
      <j1 rule="para" parents="2764 502"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      R(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2768(a,2),2741(a,1))].">
      <j1 rule="para" parents="2768 2741"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(1089,a,2769,a),flip(a)].">
      <j1 rule="hyper" parents="1089 2769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      R(x,1 / y,1 / (1 / z)) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2724,a(flip),b,2769,a),flip(a)].">
      <j1 rule="hyper" parents="370 2724 2769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      R(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2769(a,1),2774(a,1))].">
      <j1 rule="para" parents="2769 2774"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(2763(a,1),2778(a,1))].">
      <j1 rule="para" parents="2763 2778"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      R(x,y,z \ R(z,u,w)) = R(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2012(a,1),2753(a,1,3))].">
      <j1 rule="para" parents="2012 2753"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      R(x,R(y,y,z \ 1) * z,u) = R(x,(1 / y) \ (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(1961(a,1),2760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 2760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2162(a,1),2760(a,1,2))].">
      <j1 rule="para" parents="2162 2760"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      R(x \ 1,x,y) * y = x \ y
    ]]></literal>
    <justification jstring="[para(74(a,1),2766(a,2,1))].">
      <j1 rule="para" parents="74 2766"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      R(x \ 1,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,2784,a),flip(a)].">
      <j1 rule="hyper" parents="147 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      R(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,63,a(flip),b,2784,a),flip(a)].">
      <j1 rule="hyper" parents="128 63 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      R(T(x \ 1,y),x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2784,a(flip),b,274,a),flip(a)].">
      <j1 rule="hyper" parents="125 2784 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      T(x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(2786(a,1),2025(a,1,2,2))].">
      <j1 rule="para" parents="2786 2025"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),2790(a,1,2,2,1))].">
      <j1 rule="para" parents="4 2790"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      T(x,y / (z * y)) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y / (z * y),z) = x
    ]]></literal>
    <justification jstring="[para(2791(a,1),897(a,1)),flip(a)].">
      <j1 rule="para" parents="2791 897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      R(L(T(x,y),x,x),x \ 1,y) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1323(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="1323 2788"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,2009,a(flip),b,2770,a),flip(a)].">
      <j1 rule="hyper" parents="60 2009 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(108(a,2),2770(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="108 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,362,a,b,2773,a),flip(a)].">
      <j1 rule="hyper" parents="370 362 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = (((y / x) \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2009(a,1),2773(a,1,1))].">
      <j1 rule="para" parents="2009 2773"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      R(x,1 / y,(1 / z) \ 1) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2739,a,2776,a)].">
      <j1 rule="hyper" parents="2739 2776"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      R(x,y \ 1,(x * y) \ z) \ z = (y \ 1) * ((x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(2758(a,1),427(a,1,1))].">
      <j1 rule="para" parents="2758 427"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      L(x,y / (x * y),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2792,a,2004,a)].">
      <j1 rule="hyper" parents="2792 2004"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      L(T(x,y),z / (x * z),x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2800(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2800 20"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      R(L(T(x,y),x,x),x,y) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(2778,a,2793,a)].">
      <j1 rule="hyper" parents="2778 2793"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      L(R(T(x,y),x,y),x,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,2802,a)].">
      <j1 rule="hyper" parents="60 24 2802"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2794(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6 2794"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2779,a,2804,a)].">
      <j1 rule="hyper" parents="2779 2804"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ 1 = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,2786,a(flip),b,2805,a),flip(a)].">
      <j1 rule="hyper" parents="60 2786 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(2771(a,2),2806(a,1,1,1))].">
      <j1 rule="para" parents="2771 2806"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      R(x,y,(1 / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(313(a,1),2750(a,1,3,1))].">
      <j1 rule="para" parents="313 2750"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2772(a,1),41(a,1))].">
      <j1 rule="para" parents="2772 41"/>
    </justification>
  </clause>

  <clause id="2811">
    <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(2775(a,2),90(a,1,2,2))].">
      <j1 rule="para" parents="2775 90"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      R(x,y,1 / y) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),2731(a,1,1,2))].">
      <j1 rule="para" parents="77 2731"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (y * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2721(a,1),2812(a,1,1))].">
      <j1 rule="para" parents="2721 2812"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(2098(a,1),2813(a,2,2))].">
      <j1 rule="para" parents="2098 2813"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = (y \ 1) * ((x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(2759(a,1),2799(a,1,1))].">
      <j1 rule="para" parents="2759 2799"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      L(T(x,x * (L(x,y,z) \ u)),y,z) = (x * (L(x,y,z) \ u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(2160(a,1),2677(a,2,1))].">
      <j1 rule="para" parents="2160 2677"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),2696(a,1,2,1,2))].">
      <j1 rule="para" parents="2 2696"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(x \ (y * x),x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2817(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="6 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      (x * x) \ L((x * x) * y,z,u) = L(y,z * (x * x),u)
    ]]></literal>
    <justification jstring="[para(13(a,2),2706(a,1,2))].">
      <j1 rule="para" parents="13 2706"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      L(((x * x) \ y) * z,u * (x * x),w) = (x * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(113(a,1),2819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 2819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2727(a,1),2734(a,1,2,2))].">
      <j1 rule="para" parents="2727 2734"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      L(x,y,z) != (u * (L(u,y,z) \ w)) \ (u * w)
    ]]></literal>
    <literal><![CDATA[
      T(u,u * (L(u,y,z) \ w)) = x
    ]]></literal>
    <justification jstring="[para(2816(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2816 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2823">
    <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(660(a,1),1382(a,1))].">
      <j1 rule="para" parents="660 1382"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = (x \ 1) * T(y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(1281(a,1),1329(a,1,1,1))].">
      <j1 rule="para" parents="1281 1329"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      (x \ 1) * T(y,L(x,x,x)) = T(y * (1 / x),x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1446,a(flip),b,2824,a),flip(a)].">
      <j1 rule="hyper" parents="60 1446 2824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1343(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2340,a(flip),b,2826,a),flip(a)].">
      <j1 rule="hyper" parents="275 2340 2826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(1807,a,2827,a),flip(a)].">
      <j1 rule="hyper" parents="1807 2827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(328,a,2827,a),flip(a)].">
      <j1 rule="hyper" parents="328 2827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,2827,a)].">
      <j1 rule="hyper" parents="135 2827"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      T(x \ T(x,y),z) = K(y \ (y / T(x \ 1,z)),y)
    ]]></literal>
    <justification jstring="[para(1534(a,1),2828(a,1,1))].">
      <j1 rule="para" parents="1534 2828"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1642(a,2),2828(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1642 2828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      T(x \ T(x,y),T(x,x \ 1)) = K(y \ (y / T(x \ 1,x)),y)
    ]]></literal>
    <justification jstring="[para(1596(a,1),2832(a,2,1,2,2))].">
      <j1 rule="para" parents="1596 2832"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * T(x \ 1,z),y) = u
    ]]></literal>
    <justification jstring="[para(2830(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2830 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(2354(a,1),2830(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2354 2830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      T(x \ T(x,y),T(x,x \ 1)) = T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2832,a,b,2834,a),flip(a)].">
      <j1 rule="hyper" parents="370 2832 2834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = L(T(y \ T(y,x),y),y,x)
    ]]></literal>
    <justification jstring="[para(2837(a,1),1073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2837 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2836(a,2,2,1))].">
      <j1 rule="para" parents="5 2836"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(224(a,1),2839(a,2,2))].">
      <j1 rule="para" parents="224 2839"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * T(y \ 1,x),z) = u
    ]]></literal>
    <justification jstring="[para(1806(a,2),2835(a,1))].">
      <j1 rule="para" parents="1806 2835"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = T((x * y) \ (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1073,a(flip),b,2838,a),flip(a)].">
      <j1 rule="hyper" parents="370 1073 2838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      T((x * y) \ (y * x),T(y,y \ 1)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[para(11(a,2),2844(a,2,1))].">
      <j1 rule="para" parents="11 2844"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      T(K(x,y),T(x,x \ 1)) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(11(a,2),2845(a,1,1))].">
      <j1 rule="para" parents="11 2845"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      (x / y) * (((y \ 1) * (y \ 1)) \ z) = (x / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1505(a,1),1455(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1505 1455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      (x / y) * (y * ((y \ 1) \ z)) = (x / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(595(a,1),2847(a,1,2))].">
      <j1 rule="para" parents="595 2847"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      (x / y) * ((1 / y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2427,a,2848,a)].">
      <j1 rule="hyper" parents="2427 2848"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (x / y) * (y * (y \ (((1 / y) \ z) * u))) = (x / (y \ 1)) * ((y \ z) * u)
    ]]></literal>
    <justification jstring="[para(2132(a,1),2848(a,1,2,2))].">
      <j1 rule="para" parents="2132 2848"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (x * y) / (y \ 1) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[para(199(a,1),1629(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="199 1629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(1482,a,2852,a)].">
      <j1 rule="hyper" parents="1482 2852"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2853(a,1),2639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2853 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2574,a(flip),b,1841,a),flip(a)].">
      <j1 rule="hyper" parents="60 2574 1841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2286,a(flip),b,1844,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 2286 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[para(1693(a,1),1844(a,2,2))].">
      <j1 rule="para" parents="1693 1844"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(11(a,2),2857(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 2857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),2045(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (x * (y * z)) * (((z \ 1) * (z \ 1)) * u) = (x * (y * (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(3(a,1),2054(a,2,1,2))].">
      <j1 rule="para" parents="3 2054"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      (x * (y * z)) * ((z \ 1) * (z \ u)) = (x * (y * (1 / z))) * u
    ]]></literal>
    <justification jstring="[para(596(a,1),2861(a,1,2))].">
      <j1 rule="para" parents="596 2861"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      (x * (y * (1 / z))) * (z * u) = (x * (y * z)) * ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      L(x,y,y) \ (x * L(L(x,y,y),z,u)) = L(L(x,y,y),z,u) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(411(a,1),2187(a,1,2))].">
      <j1 rule="para" parents="411 2187"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y))
    ]]></literal>
    <justification jstring="[para(2559(a,1),2222(a,2,2,2))].">
      <j1 rule="para" parents="2559 2222"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2005(a,1),2236(a,2,1))].">
      <j1 rule="para" parents="2005 2236"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y
    ]]></literal>
    <justification jstring="[para(1405(a,1),2369(a,2,1))].">
      <j1 rule="para" parents="1405 2369"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[para(88(a,1),2869(a,2,1))].">
      <j1 rule="para" parents="88 2869"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(787,a,2412,a),flip(a)].">
      <j1 rule="hyper" parents="787 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(2329,a,2871,a)].">
      <j1 rule="hyper" parents="2329 2871"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(78(a,1),2872(a,1,1))].">
      <j1 rule="para" parents="78 2872"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,2873,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="125 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2873(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      R(T((x \ 1) \ 1,T(y,x)),x \ 1,T(y,x)) = T(y,x) \ ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[para(2874(a,2),2788(a,2,2))].">
      <j1 rule="para" parents="2874 2788"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(88(a,1),2875(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="88 2875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(3(a,1),2433(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 2433"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(2589(a,2),2433(a,1,2))].">
      <j1 rule="para" parents="2589 2433"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(3(a,1),2880(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 2880"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(17(a,2),2881(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[hyper(135,a,2879,a),flip(a)].">
      <j1 rule="hyper" parents="135 2879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2574,a(flip),b,2882,a(flip))].">
      <j1 rule="hyper" parents="275 2574 2882"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2589,a(flip),b,2884,a)].">
      <j1 rule="hyper" parents="370 2589 2884"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(2591(a,1),2884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2591 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(2388(a,1),2886(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2388 2886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(74(a,1),2887(a,2,2,1))].">
      <j1 rule="para" parents="74 2887"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2888(a,1,1,2))].">
      <j1 rule="para" parents="6 2888"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2890(a,1,2,1))].">
      <j1 rule="para" parents="6 2890"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2891(a,2,2))].">
      <j1 rule="para" parents="6 2891"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2892,a)].">
      <j1 rule="hyper" parents="51 2892"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2892,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 2892 17"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(2892(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2892 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2892(a,1),328(a,1,2))].">
      <j1 rule="para" parents="2892 328"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2892(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2892 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2892(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2892 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <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(2892(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="2892 489"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(2893(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2893 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2893(a,1),328(a,1,2))].">
      <j1 rule="para" parents="2893 328"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2893(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2893 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      K(x,y) * R(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(y,z),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2893(a,1),490(a,1,2,1))].">
      <j1 rule="para" parents="2893 490"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2885(a,2,1,2,1))].">
      <j1 rule="para" parents="5 2885"/>
    </justification>
  </clause>

  <clause id="2908">
    <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(538(a,2),2885(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="538 2885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1676(a,1),2907(a,1,2,1))].">
      <j1 rule="para" parents="1676 2907"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1709(a,2),2909(a,2,1))].">
      <j1 rule="para" parents="1709 2909"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2910(a,1),2695(a,1,2))].">
      <j1 rule="para" parents="2910 2695"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2911(a,1),40(a,1))].">
      <j1 rule="para" parents="2911 40"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),2434(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = y * (T(x,y) \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),2515(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(1987(a,2),2914(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1987 2914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),2537(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2553(a,1),2563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2553 2563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <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(1769(a,1),2917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1769 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2568(a,1),2572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2568 2572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2920">
    <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(1965(a,1),2919(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1965 2919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <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(1695(a,1),2593(a,1,2,1))].">
      <j1 rule="para" parents="1695 2593"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      ((x * y) * R((x * y) \ x,z,u)) * y = (x * y) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1987(a,1),2616(a,2,2))].">
      <j1 rule="para" parents="1987 2616"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      (x * (y * R(y \ 1,z,u))) * y = (x * y) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1600(a,1),2922(a,1,1))].">
      <j1 rule="para" parents="1600 2922"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * y = (x * y) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1987(a,1),2923(a,1,1,2))].">
      <j1 rule="para" parents="1987 2923"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(17(a,2),2617(a,1,1))].">
      <j1 rule="para" parents="17 2617"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(17(a,2),2925(a,1,2,1,1))].">
      <j1 rule="para" parents="17 2925"/>
    </justification>
  </clause>

  <clause id="2927">
    <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(4(a,1),2926(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2926"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(63(a,1),2652(a,1,1,2,2,1,2))].">
      <j1 rule="para" parents="63 2652"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),2669(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 2669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (x / (y \ 1)) * ((y \ z) * u) = (x / y) * (((1 / y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(387,a,2850,a),flip(a)].">
      <j1 rule="hyper" parents="387 2850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      x * (L(x,y,y) \ L(L(x,y,y),z,u)) = L(L(x,y,y),z,u) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(2194,a,2864,a)].">
      <j1 rule="hyper" parents="2194 2864"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,295,a(flip),b,2865,a),flip(a)].">
      <j1 rule="hyper" parents="370 295 2865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(2934(a,1),1755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2934 1755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2440,a(flip),b,2936,a)].">
      <j1 rule="hyper" parents="60 2440 2936"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(498,a,2937,a)].">
      <j1 rule="hyper" parents="498 2937"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),2937(a,1,1,2))].">
      <j1 rule="para" parents="4 2937"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2938(a,1,3))].">
      <j1 rule="para" parents="4 2938"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4(a,1),2939(a,2,2))].">
      <j1 rule="para" parents="4 2939"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(221,a,2941,a)].">
      <j1 rule="hyper" parents="221 2941"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2942(a,1),1811(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2942 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(668,a,2940,a)].">
      <j1 rule="hyper" parents="668 2940"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2568,a(flip),b,2915,a),flip(a)].">
      <j1 rule="hyper" parents="275 2568 2915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <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(2561(a,1),2945(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2561 2945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),118(a,1,2,1))].">
      <j1 rule="para" parents="29 118"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      L((x * (y * z)) / (x * y),u,w) = (x * (y * L(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(528(a,1),1240(a,1,1)),flip(a)].">
      <j1 rule="para" parents="528 1240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      L((x * (y * z)) / (x * y),u,w) != v5 / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2948(a,2),43(a,1))].">
      <j1 rule="para" parents="2948 43"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      R(L(T((x * y) / x,x * z),u,w),x,z) = (x * z) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(20(a,2),1394(a,1,1))].">
      <j1 rule="para" parents="20 1394"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = (y * (z * u)) \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(850(a,1),1454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="850 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,9,a,b,2951,a),flip(a)].">
      <j1 rule="hyper" parents="370 9 2951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      a((x * x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2951(a,2),1029(a,1))].">
      <j1 rule="para" parents="2951 1029"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(13(a,2),2952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(313(a,1),2952(a,1,1))].">
      <j1 rule="para" parents="313 2952"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      a((1 / x) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(551(a,1),2952(a,1,1))].">
      <j1 rule="para" parents="551 2952"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(940(a,1),2952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="940 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(967(a,1),2952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="967 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      a((x * (y \ (z * z))) \ u,w,v5) = a((x * (y \ 1)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1193(a,1),2952(a,1,1))].">
      <j1 rule="para" parents="1193 2952"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),2957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 2957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2957,a,b,2962,a)].">
      <j1 rule="hyper" parents="370 2957 2962"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      a((x * x) \ (y \ 1),z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(517(a,1),2962(a,1,1))].">
      <j1 rule="para" parents="517 2962"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      L(a(x,y,z),u,w * w) = a((v5 * v5) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,615,a,b,2955,a)].">
      <j1 rule="hyper" parents="370 615 2955"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(943(a,1),2955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="943 2955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      a((x * (y \ 1)) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1116(a,1),2955(a,1,1))].">
      <j1 rule="para" parents="1116 2955"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      a((x \ 1) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),2958(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 2958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      a(1 / x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(313(a,1),2954(a,1,1))].">
      <j1 rule="para" parents="313 2954"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      a((1 / x) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(551(a,1),2954(a,1,1))].">
      <j1 rule="para" parents="551 2954"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(94(a,2),2954(a,1,1))].">
      <j1 rule="para" parents="94 2954"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),2969(a,1,1))].">
      <j1 rule="para" parents="74 2969"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      a(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2963(a,1),2969(a,1))].">
      <j1 rule="para" parents="2963 2969"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      a((x * x) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2965(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="2965 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      a(x * (x * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(y,x,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),2975(a,1,1))].">
      <j1 rule="para" parents="92 2975"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(936(a,1),2975(a,1,1))].">
      <j1 rule="para" parents="936 2975"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),2975(a,1,1))].">
      <j1 rule="para" parents="946 2975"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      a((x * (y \ 1)) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(1116(a,1),2975(a,1,1))].">
      <j1 rule="para" parents="1116 2975"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * R(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(2012(a,1),2970(a,1,1))].">
      <j1 rule="para" parents="2012 2970"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(2954,a,2964,a),flip(a)].">
      <j1 rule="hyper" parents="2954 2964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2962,a(flip),b,2981,a),flip(a)].">
      <j1 rule="hyper" parents="370 2962 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      a(x * (y * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2981(a,2),2973(a,1))].">
      <j1 rule="para" parents="2981 2973"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      a(x * (y * (z * z)),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),2983(a,1,1))].">
      <j1 rule="para" parents="30 2983"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      a(x \ (y * y),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(519(a,1),2983(a,1,1))].">
      <j1 rule="para" parents="519 2983"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      a(x \ (y * (z / (1 / u))),w,v5) = a(x \ (y * (z / u)),w,v5)
    ]]></literal>
    <justification jstring="[para(1444(a,1),2983(a,1,1))].">
      <j1 rule="para" parents="1444 2983"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      a(x \ (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2962,a(flip),b,2986,a),flip(a)].">
      <j1 rule="hyper" parents="370 2962 2986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      a(L(x,y,z) * (x \ L(x,y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(2156(a,1),2988(a,1,1))].">
      <j1 rule="para" parents="2156 2988"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2160(a,1),2988(a,1,1))].">
      <j1 rule="para" parents="2160 2988"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      a(x * (y * (z * z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),2984(a,1,1))].">
      <j1 rule="para" parents="30 2984"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      a((x * y) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(R(x,y,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),2984(a,1,1))].">
      <j1 rule="para" parents="103 2984"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      a(x / (1 / y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x / y,z,u) = w
    ]]></literal>
    <justification jstring="[para(856(a,1),2984(a,1,1))].">
      <j1 rule="para" parents="856 2984"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      a(x \ (y * (1 / z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y * z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(2065(a,1),2984(a,1,1))].">
      <j1 rule="para" parents="2065 2984"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(248(a,1),2985(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="248 2985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      a(x * (1 / y),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(252(a,1),2985(a,1,1,2))].">
      <j1 rule="para" parents="252 2985"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      a(x * (y \ (1 / z)),u,w) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(865(a,1),2985(a,1,1,2))].">
      <j1 rule="para" parents="865 2985"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2162(a,1),2995(a,1,1))].">
      <j1 rule="para" parents="2162 2995"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      a((x * (1 / y)) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),2967(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      a((x * ((y * z) \ ((u * u) * 1))) \ w,v5,v6) = a((x * (((u * u) \ y) * z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(1005(a,1),2967(a,1,1,1,2))].">
      <j1 rule="para" parents="1005 2967"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      a((x * y) * R(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(y \ 1,x * y,x * y),z,u) = w
    ]]></literal>
    <justification jstring="[para(1111(a,1),2976(a,1,1,2))].">
      <j1 rule="para" parents="1111 2976"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      a((x * y) * ((y * y) \ (L(x * (y \ 1),z,u) \ (x * (y \ 1)))),w,v5) = a(L(x * (y \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1117(a,2),2990(a,1,1))].">
      <j1 rule="para" parents="1117 2990"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,w) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),2997(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      a(x * (R(y / z,z,y \ (u \ 1)) \ u),w,v5) = a(x * (z * (y \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(673(a,1),3003(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="673 3003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      a(R(x,x,y \ (z \ 1)) * (y \ z),u,w) = a((1 / x) \ (y \ (z \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(1961(a,1),3003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1961 3003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      a(x * (1 / y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(252(a,1),2991(a,1,1,2))].">
      <j1 rule="para" parents="252 2991"/>
    </justification>
  </clause>

  <clause id="3007">
    <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(2961(a,2),2979(a,1))].">
      <j1 rule="para" parents="2961 2979"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      a(x,y / (z * z),u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,1009,a(flip),b,1466,a)].">
      <j1 rule="hyper" parents="60 1009 1466"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      a(x,y * (z * z),(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),3009(a,1,3))].">
      <j1 rule="para" parents="4 3009"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2357,a(flip),b,1558,a)].">
      <j1 rule="hyper" parents="60 2357 1558"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(3011(a,1),984(a,1,1))].">
      <j1 rule="para" parents="3011 984"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(1242,a,3013,a),flip(a)].">
      <j1 rule="hyper" parents="1242 3013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(3014(a,1),2592(a,1,2))].">
      <j1 rule="para" parents="3014 2592"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (u * R(u \ (x \ u),y,z)) = w
    ]]></literal>
    <justification jstring="[para(2569(a,1),1871(a,1))].">
      <j1 rule="para" parents="2569 1871"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,531,a(flip),b,1915,a),flip(a)].">
      <j1 rule="hyper" parents="370 531 1915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(3017(a,1),560(a,1,2))].">
      <j1 rule="para" parents="3017 560"/>
    </justification>
  </clause>

  <clause id="3019">
    <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(3017(a,1),2248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3017 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3020">
    <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(3017(a,1),2291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3017 2291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1560(a,2),3018(a,1,2,2))].">
      <j1 rule="para" parents="1560 3018"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(2213(a,1),3018(a,1,2,2))].">
      <j1 rule="para" parents="2213 3018"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(51,a,3021,a)].">
      <j1 rule="hyper" parents="51 3021"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(2278(a,1),3022(a,1,2,2,2,2))].">
      <j1 rule="para" parents="2278 3022"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),3024(a,1,2,2,2))].">
      <j1 rule="para" parents="5 3024"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3025(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3025 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1691,a,3026,a)].">
      <j1 rule="hyper" parents="1691 3026"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(221,a,3027,a)].">
      <j1 rule="hyper" parents="221 3027"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1906,a,3028,a)].">
      <j1 rule="hyper" parents="1906 3028"/>
    </justification>
  </clause>

  <clause id="3030">
    <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(3028(a,2),896(a,1,2))].">
      <j1 rule="para" parents="3028 896"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3029(a,1),536(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3029 536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      R(x,x,y) * (((1 / x) \ 1) \ z) = (y / (x * y)) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[para(77(a,1),2304(a,1,1,1))].">
      <j1 rule="para" parents="77 2304"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = (y / (x * y)) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[para(77(a,1),3032(a,1,2,1))].">
      <j1 rule="para" parents="77 3032"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * a(x,K(x,y),z) = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(2957(a,1),2378(a,1,2))].">
      <j1 rule="para" parents="2957 2378"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      L(T(x,y),y,K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = z
    ]]></literal>
    <justification jstring="[para(2384(a,1),389(a,1))].">
      <j1 rule="para" parents="2384 389"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,115,a(flip),b,2947,a),flip(a)].">
      <j1 rule="hyper" parents="60 115 2947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      a(x,(y * y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2984,a,3036,a),flip(a)].">
      <j1 rule="hyper" parents="2984 3036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      a(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3036(a,1),2984(a,1))].">
      <j1 rule="para" parents="3036 2984"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 3037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),3037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 3037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      a(x,(1 / y) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(314(a,1),3037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 3037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(113(a,1),3037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 3037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(936(a,1),3037(a,1,2))].">
      <j1 rule="para" parents="936 3037"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      a(x,((y \ 1) \ z) * u,w) = a(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(946(a,1),3037(a,1,2))].">
      <j1 rule="para" parents="946 3037"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      a(x,(y * (y * z)) * u,w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(624(a,1),3037(a,1,2))].">
      <j1 rule="para" parents="624 3037"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      a(x,y * (y * L(z,u,w)),v5) = a(x,L(L(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(528(a,1),3037(a,1,2))].">
      <j1 rule="para" parents="528 3037"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(2973,a,3041,a),flip(a)].">
      <j1 rule="hyper" parents="2973 3041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      a(x,1 / (y * (z * z)),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3010,a(flip),b,3041,a),flip(a)].">
      <j1 rule="hyper" parents="370 3010 3041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),3041(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 3041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) = a(x,z \ (y * y),u)
    ]]></literal>
    <justification jstring="[para(575(a,1),3041(a,1,2))].">
      <j1 rule="para" parents="575 3041"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3041,a,b,3050,a)].">
      <j1 rule="hyper" parents="370 3041 3050"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3050,a(flip),b,3050,a),flip(a)].">
      <j1 rule="hyper" parents="370 3050 3050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(94(a,2),3040(a,1,2))].">
      <j1 rule="para" parents="94 3040"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      a(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3048(a,1),2973(a,1))].">
      <j1 rule="para" parents="3048 2973"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2728,a,b,3052,a)].">
      <j1 rule="hyper" parents="60 2728 3052"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),3055(a,1,2))].">
      <j1 rule="para" parents="74 3055"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      a(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3052(a,1),3055(a,1))].">
      <j1 rule="para" parents="3052 3055"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      a(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(3041(a,2),3057(a,1))].">
      <j1 rule="para" parents="3041 3057"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3042(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 3042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      a(x,y * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),3038(a,1,2))].">
      <j1 rule="para" parents="92 3038"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(936(a,1),3038(a,1,2))].">
      <j1 rule="para" parents="936 3038"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      a(x,((y \ 1) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),3038(a,1,2))].">
      <j1 rule="para" parents="946 3038"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2728(a,2),3059(a,1))].">
      <j1 rule="para" parents="2728 3059"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      a(x,y \ (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3040,a(flip),b,3051,a),flip(a)].">
      <j1 rule="hyper" parents="60 3040 3051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      a(x,L(y,z,u) * (y \ L(y,z,u)),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(2156(a,1),3066(a,1,2))].">
      <j1 rule="para" parents="2156 3066"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      a(x,((1 / y) \ z) * u,w) = a(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),3045(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 3045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      a(x,(y * y) \ (1 / z),u) = a(x,z,(y * y) * u)
    ]]></literal>
    <justification jstring="[para(598(a,1),3049(a,1,2))].">
      <j1 rule="para" parents="598 3049"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,1 / y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3040,a(flip),b,3070,a),flip(a)].">
      <j1 rule="hyper" parents="60 3040 3070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3041,a(flip),b,3072,a),flip(a)].">
      <j1 rule="hyper" parents="370 3041 3072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      a(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3072(a,2),3055(a,1))].">
      <j1 rule="para" parents="3072 3055"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3010,a,b,3074,a)].">
      <j1 rule="hyper" parents="60 3010 3074"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="254 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(314(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="314 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(92(a,1),3074(a,1,3))].">
      <j1 rule="para" parents="92 3074"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(113(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(936(a,1),3074(a,1,3))].">
      <j1 rule="para" parents="936 3074"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      a(x,y,(1 / z) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(943(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="943 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(946(a,1),3074(a,1,3))].">
      <j1 rule="para" parents="946 3074"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) \ w) = a(x,y,(z \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(975(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="975 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(1116(a,1),3074(a,1,3))].">
      <j1 rule="para" parents="1116 3074"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      a(x,y,(z * u) * (u \ z)) = a(x,y,a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[para(1027(a,1),3074(a,1,3))].">
      <j1 rule="para" parents="1027 3074"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) * w) * v5) = a(x,y,(u * w) * v5)
    ]]></literal>
    <justification jstring="[para(850(a,1),3074(a,1,3)),flip(a)].">
      <j1 rule="para" parents="850 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(3058,a,3078,a),flip(a)].">
      <j1 rule="hyper" parents="3058 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      a(x,x,1 / y) = L(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,1362,a,b,3078,a),flip(a)].">
      <j1 rule="hyper" parents="370 1362 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),3078(a,1,3)),flip(a)].">
      <j1 rule="para" parents="74 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(575(a,1),3078(a,1,3))].">
      <j1 rule="para" parents="575 3078"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3078,a,b,3091,a)].">
      <j1 rule="hyper" parents="370 3078 3091"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3091,a(flip),b,3091,a),flip(a)].">
      <j1 rule="hyper" parents="370 3091 3091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      a(x,y / (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),3076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      a(x,y * (z * (u * u)),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),3076(a,1,2))].">
      <j1 rule="para" parents="30 3076"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      a(x,y \ (1 / z),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(865(a,1),3076(a,1,2))].">
      <j1 rule="para" parents="865 3076"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(94(a,2),3077(a,1,3))].">
      <j1 rule="para" parents="94 3077"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      a(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3089(a,1),3058(a,1))].">
      <j1 rule="para" parents="3089 3058"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(1101(a,1),3097(a,1,2))].">
      <j1 rule="para" parents="1101 3097"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),3102(a,1,3))].">
      <j1 rule="para" parents="74 3102"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      a(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3093(a,1),3102(a,1))].">
      <j1 rule="para" parents="3093 3102"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(u / z,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(673(a,1),3106(a,1,3))].">
      <j1 rule="para" parents="673 3106"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3079(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="74 3079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2012(a,1),3079(a,1,3))].">
      <j1 rule="para" parents="2012 3079"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ w) = a(x,y,(u \ (z * z)) \ w)
    ]]></literal>
    <justification jstring="[para(578(a,1),3082(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="578 3082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      a(x,y \ (z \ 1),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3099(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 3099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2162(a,1),3104(a,1,2))].">
      <j1 rule="para" parents="2162 3104"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u) * w) = a(x,y,((1 / u) * z) * w)
    ]]></literal>
    <justification jstring="[para(1491(a,2),3109(a,1,3,1))].">
      <j1 rule="para" parents="1491 3109"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      a(x,y,z * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="92 3075"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(936(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="936 3075"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="946 3075"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      a(x,y,T(z,u \ (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z / (u * u)) = w
    ]]></literal>
    <justification jstring="[para(1421(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="1421 3075"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(((v6 * v6) \ z) * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(850(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="850 3075"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(1469(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="1469 3075"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      a(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3010(a,2),3075(a,1))].">
      <j1 rule="para" parents="3010 3075"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      a(x,y * (z * (u * u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),3123(a,1,2))].">
      <j1 rule="para" parents="30 3123"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(551(a,1),3081(a,1,3,1))].">
      <j1 rule="para" parents="551 3081"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      a(x,y,((z \ (u \ (w * w))) \ v5) * v6) = a(x,y,((z \ (u \ 1)) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(1220(a,1),3081(a,1,3,1))].">
      <j1 rule="para" parents="1220 3081"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      a(x,y,(T(z * u,z * z) \ w) * v5) = a(x,y,(((1 / z) * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(1448(a,1),3081(a,1,3,1))].">
      <j1 rule="para" parents="1448 3081"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3077,a(flip),b,3092,a),flip(a)].">
      <j1 rule="hyper" parents="60 3077 3092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (z \ L(z,u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2156(a,1),3130(a,1,3))].">
      <j1 rule="para" parents="2156 3130"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      a(x,y * (z * (u \ (1 / u))),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(320(a,1),3098(a,1,2,2,2))].">
      <j1 rule="para" parents="320 3098"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      a(x,y,((1 / z) \ u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(77(a,1),3084(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="77 3084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(3085(a,2),3116(a,1))].">
      <j1 rule="para" parents="3085 3116"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      a(x,y,(z / u) * R(z / u,u,u)) = a(x,y,(z / u) \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1109(a,1),3110(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1109 3110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(74(a,1),3127(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      a(x,y * (z \ (u * (w * (v5 \ (1 / v5))))),v6) = a(x,y * (z \ (u * w)),v6)
    ]]></literal>
    <justification jstring="[para(1463(a,2),3133(a,1,2,2))].">
      <j1 rule="para" parents="1463 3133"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = w
    ]]></literal>
    <justification jstring="[para(248(a,1),3125(a,1,2,2))].">
      <j1 rule="para" parents="248 3125"/>
    </justification>
  </clause>

  <clause id="3141">
    <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(863(a,1),3125(a,1,2,2))].">
      <j1 rule="para" parents="863 3125"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      a(x,y,(((1 / z) * u) * w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(551(a,1),3088(a,1,3,1,1))].">
      <j1 rule="para" parents="551 3088"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) \ w) = a(x,y,z \ ((u * u) * w))
    ]]></literal>
    <justification jstring="[para(849(a,1),3111(a,1,3)),flip(a)].">
      <j1 rule="para" parents="849 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(3136,a,3143,a),flip(a)].">
      <j1 rule="hyper" parents="3136 3143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(5(a,1),3144(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 3144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      a(x,y,z \ (1 / u)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(254(a,1),3144(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="254 3144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      a(x,y,z \ ((1 / u) * w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(314(a,1),3144(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="314 3144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      a(x,y,z \ (u * (u * w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(92(a,1),3144(a,1,3,2))].">
      <j1 rule="para" parents="92 3144"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ w) * v5)) = a(x,y,z \ (w * v5))
    ]]></literal>
    <justification jstring="[para(113(a,1),3144(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="113 3144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(936(a,1),3144(a,1,3,2))].">
      <j1 rule="para" parents="936 3144"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) * v5)) = a(x,y,z \ ((u \ w) * v5))
    ]]></literal>
    <justification jstring="[para(946(a,1),3144(a,1,3,2))].">
      <j1 rule="para" parents="946 3144"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(1004(a,1),3144(a,1,3))].">
      <j1 rule="para" parents="1004 3144"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ 1)) \ v5)) = a(x,y,z \ ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(1469(a,1),3144(a,1,3,2))].">
      <j1 rule="para" parents="1469 3144"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      a(x,y,z \ (u \ 1)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3147(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="74 3147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w * w))) \ 1) = a(x,y,(w * w) \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1193(a,1),3155(a,1,3))].">
      <j1 rule="para" parents="1193 3155"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      a(x,y,z \ L(T(u,w),w,w)) = a(x,y,z \ (w * (u * w)))
    ]]></literal>
    <justification jstring="[para(270(a,1),3146(a,1,3,2))].">
      <j1 rule="para" parents="270 3146"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(74(a,1),3148(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="74 3148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(74(a,1),3153(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(579(a,1),3153(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="579 3153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) * w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),3142(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u * (w \ 1))) = a(x,y,u * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(3106,a,3156,a),flip(a)].">
      <j1 rule="hyper" parents="3106 3156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * (w \ 1)) = a(x,y,u * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[para(514(a,1),3162(a,1,3))].">
      <j1 rule="para" parents="514 3162"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      a(x,y,(z / u) \ (z * (u \ 1))) = a(x,y,(z / u) * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1109(a,1),3137(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1109 3137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      a(x,y,((z \ (u \ 1)) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),3128(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      a(x,y,((z \ (u \ (w * w))) \ v5) * v6) = a(x,y,((z \ u) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,3128,a,b,3165,a)].">
      <j1 rule="hyper" parents="60 3128 3165"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      L(R(T((x * y) / x,x * z),x,z),u,w) = (x * z) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,2950,a)].">
      <j1 rule="hyper" parents="60 24 2950"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      a(R(x,x,y \ (z \ 1)) * (y \ z),u,w) = a(x \ (y \ (z \ 1)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2966,a(flip),b,3005,a),flip(a)].">
      <j1 rule="hyper" parents="370 2966 3005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      L((x * y) \ ((x * z) * y),u,w) = (x * y) \ ((x * L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(1373(a,1),3167(a,1,1))].">
      <j1 rule="para" parents="1373 3167"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      L((x * y) \ ((x * z) * y),u,w) != (x * y) \ v5
    ]]></literal>
    <literal><![CDATA[
      (x * L(z,u,w)) * y = v5
    ]]></literal>
    <justification jstring="[para(3169(a,2),44(a,1))].">
      <j1 rule="para" parents="3169 44"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u * (y * y))
    ]]></literal>
    <justification jstring="[hyper(1196,a,2658,a)].">
      <j1 rule="hyper" parents="1196 2658"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      L(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(u * u) * y,z) = w
    ]]></literal>
    <justification jstring="[para(2658(a,1),1196(a,1))].">
      <j1 rule="para" parents="2658 1196"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(922(a,1),1200(a,1))].">
      <j1 rule="para" parents="922 1200"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      ((x \ 1) * (x \ (y * z))) \ (y * (z * (x \ (1 / x)))) = K(y * z,x \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1214(a,1),1433(a,1,1))].">
      <j1 rule="para" parents="1214 1433"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(199(a,1),1612(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="199 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1634,a,3175,a)].">
      <j1 rule="hyper" parents="1634 3175"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),3176(a,1,2,1,1))].">
      <j1 rule="para" parents="77 3176"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),3178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),3179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 3179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ (x \ (x * y)) = y * (R((x * y) / x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),3180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),3181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 3181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(1 / x,(1 / x) \ 1)) = (x \ 1) * (L(x \ 1,y,z) \ (x \ (1 / (1 / x))))
    ]]></literal>
    <justification jstring="[para(1712(a,1),2204(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1712 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      x \ ((y * x) * T((y * x) \ z,u)) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(17(a,2),2308(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17 2308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y,x) * T(T(y,x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(1352(a,1),3184(a,1,2))].">
      <j1 rule="para" parents="1352 3184"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ (y \ z),u) = T(x * T(x \ (z / y),u),y)
    ]]></literal>
    <justification jstring="[hyper(2411,a,3185,a),flip(a)].">
      <j1 rule="hyper" parents="2411 3185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),3186(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 3186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(263(a,1),3187(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 3187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      a(x,x \ y,T(z,x * (x \ y))) = (L(z,x \ y,x) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2420(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 2420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),3189(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 3189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3192">
    <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(275,a,2607,a,b,2435,a(flip))].">
      <j1 rule="hyper" parents="275 2607 2435"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,2552,a(flip),b,2435,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 2552 2435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <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(263(a,1),3192(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 3192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(224(a,1),3194(a,1,2,1,2))].">
      <j1 rule="para" parents="224 3194"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      T(x \ y,z) * L(T(x \ y,z) \ T(u,z),x \ y,x) = T((x \ y) * (y \ (x * u)),z)
    ]]></literal>
    <justification jstring="[para(656(a,1),3194(a,2,1,2))].">
      <j1 rule="para" parents="656 3194"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,3195,a)].">
      <j1 rule="hyper" parents="135 3195"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != T(x,u) * w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u) \ 1,y,z) = w
    ]]></literal>
    <justification jstring="[para(3195(a,1),40(a,1))].">
      <j1 rule="para" parents="3195 40"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(251(a,1),3195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="251 3195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <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(456(a,1),3197(a,1,2,1,2))].">
      <j1 rule="para" parents="456 3197"/>
    </justification>
  </clause>

  <clause id="3201">
    <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(1553(a,1),3199(a,2,2,1))].">
      <j1 rule="para" parents="1553 3199"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(3015(a,1),3201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3015 3201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <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(885(a,1),2619(a,2,2,1))].">
      <j1 rule="para" parents="885 2619"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(2853(a,1),2854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2853 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(147,a,3204,a)].">
      <j1 rule="hyper" parents="147 3204"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3205(a,1),1304(a,1,1))].">
      <j1 rule="para" parents="3205 1304"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(815,a,3206,a),flip(a)].">
      <j1 rule="hyper" parents="815 3206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3207(a,1),984(a,1,1))].">
      <j1 rule="para" parents="3207 984"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(494,a,3208,a),flip(a)].">
      <j1 rule="hyper" parents="494 3208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11,a,b,3209,a)].">
      <j1 rule="hyper" parents="370 11 3209"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),3210(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(309,a,3211,a)].">
      <j1 rule="hyper" parents="309 3211"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(3212(a,1),284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3212 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,3213,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      T(K(x,y),y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,3214,a)].">
      <j1 rule="hyper" parents="51 3214"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3214(a,1),462(a,2,1))].">
      <j1 rule="para" parents="3214 462"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),3216(a,1,1,1))].">
      <j1 rule="para" parents="5 3216"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,456,a(flip),b,3217,a),flip(a)].">
      <j1 rule="hyper" parents="370 456 3217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3218,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 3218 17"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(2574(a,1),2855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2574 2855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z)
    ]]></literal>
    <justification jstring="[para(2589(a,2),3220(a,1,1))].">
      <j1 rule="para" parents="2589 3220"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2943(a,1,1,1))].">
      <j1 rule="para" parents="4 2943"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      (x * y) \ (z * ((z \ 1) \ (x * (y * (z \ (1 / z)))))) = K(x * y,z \ (1 / z))
    ]]></literal>
    <justification jstring="[hyper(1513,a,3174,a)].">
      <j1 rule="hyper" parents="1513 3174"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      K(x * y,z \ (1 / z)) != (x * y) \ u
    ]]></literal>
    <literal><![CDATA[
      z * ((z \ 1) \ (x * (y * (z \ (1 / z))))) = u
    ]]></literal>
    <justification jstring="[para(3224(a,1),44(a,1))].">
      <j1 rule="para" parents="3224 44"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1306,a,1486,a),flip(a)].">
      <j1 rule="hyper" parents="1306 1486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),3226(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(1270(a,1),3226(a,2,1))].">
      <j1 rule="para" parents="1270 3226"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(378,a,3227,a),flip(a)].">
      <j1 rule="hyper" parents="378 3227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = (x * ((x / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(1636,a,3229,a)].">
      <j1 rule="hyper" parents="1636 3229"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,1842,a(flip),b,3229,a)].">
      <j1 rule="hyper" parents="60 1842 3229"/>
    </justification>
  </clause>

  <clause id="3233">
    <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(428(a,2),3232(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="428 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2574(a,1),3232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2574 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(378,a,3228,a),flip(a)].">
      <j1 rule="hyper" parents="378 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(275,a,3228,a(flip),b,2433,a),flip(a)].">
      <j1 rule="hyper" parents="275 3228 2433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(17(a,2),3237(a,1,1))].">
      <j1 rule="para" parents="17 3237"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(17(a,2),3239(a,1,2,1,2,1))].">
      <j1 rule="para" parents="17 3239"/>
    </justification>
  </clause>

  <clause id="3241">
    <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="[hyper(60,a,2945,a(flip),b,1542,a)].">
      <j1 rule="hyper" parents="60 2945 1542"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(2358(a,1),3241(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2358 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,2829,a(flip),b,3242,a),flip(a)].">
      <j1 rule="hyper" parents="32 2829 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3243(a,1),109(a,1,1))].">
      <j1 rule="para" parents="3243 109"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,2841,a(flip),b,3244,a),flip(a)].">
      <j1 rule="hyper" parents="60 2841 3244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(1052(a,1),2408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1052 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      x * (y * L(y \ (x \ L(y,x,x)),z,u)) = L(1 / x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,273,a(flip),b,2460,a),flip(a)].">
      <j1 rule="hyper" parents="370 273 2460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      x * (y * L(y \ ((x \ 1) * y),z,u)) = L(1 / x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(2072(a,1),3248(a,1,2,2,1,2))].">
      <j1 rule="para" parents="2072 3248"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      L(1 / x,y,z) * (x * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(871(a,1),3249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="871 3249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      L(1 / x,y,z) \ (x * u) = x * (L(x \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,3250,a)].">
      <j1 rule="hyper" parents="125 172 3250"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      (1 / x) * (L((1 / x) \ 1,y,z) * (x * u)) = L(1 / (1 / x),y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(579(a,1),3250(a,1,2)),flip(a)].">
      <j1 rule="para" parents="579 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(2194,a,2496,a)].">
      <j1 rule="hyper" parents="2194 2496"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(129,a,2496,a(flip),b,457,a(flip))].">
      <j1 rule="hyper" parents="129 2496 457"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      (x \ 1) \ L(R((x \ 1) \ 1,y,z) \ u,x,x) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2544,a(flip),b,2545,a),flip(a)].">
      <j1 rule="hyper" parents="370 2544 2545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <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(1911(a,1),3030(a,1,1))].">
      <j1 rule="para" parents="1911 3030"/>
    </justification>
  </clause>

  <clause id="3257">
    <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(1693(a,1),3256(a,1,1))].">
      <j1 rule="para" parents="1693 3256"/>
    </justification>
  </clause>

  <clause id="3258">
    <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(3028(a,1),3257(a,1,2))].">
      <j1 rule="para" parents="3028 3257"/>
    </justification>
  </clause>

  <clause id="3259">
    <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(60,a,20,a,b,3258,a)].">
      <j1 rule="hyper" parents="60 20 3258"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(3025(a,1),3259(a,1,1))].">
      <j1 rule="para" parents="3025 3259"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1693,a,b,3260,a)].">
      <j1 rule="hyper" parents="60 1693 3260"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(3260(a,1),2858(a,1,2))].">
      <j1 rule="para" parents="3260 2858"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3031,a(flip),b,3261,a),flip(a)].">
      <j1 rule="hyper" parents="60 3031 3261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) * L(u,x,x) = (1 / x) * (L(x,y,z) * (x * u))
    ]]></literal>
    <justification jstring="[para(77(a,1),3252(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) * L(u,x,x) = (1 / x) * (x * (L(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(2153(a,1),3264(a,2,2))].">
      <j1 rule="para" parents="2153 3264"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) * L(u,x,x) = L(L(x,y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,579,a(flip),b,3265,a),flip(a)].">
      <j1 rule="hyper" parents="370 579 3265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * L(u,x,x) = L(L(x,y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[para(1313(a,1),3266(a,1,1,1))].">
      <j1 rule="para" parents="1313 3266"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(1051(a,1),3253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1051 3253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <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(1709(a,2),1884(a,1,2,1,1))].">
      <j1 rule="para" parents="1709 1884"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ (x * y)) * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(2077(a,1),2239(a,1,1,1))].">
      <j1 rule="para" parents="2077 2239"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      (x * (y \ 1)) * ((T(y,y \ 1) \ 1) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(74(a,1),2306(a,2,1,2))].">
      <j1 rule="para" parents="74 2306"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      (x * (y \ 1)) * (T(y \ 1,y) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1332(a,1),3272(a,1,2,1))].">
      <j1 rule="para" parents="1332 3272"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      (x * (y \ 1)) * ((1 / y) \ z) = (x * y) * (((y \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(955(a,1),3274(a,1,2,1))].">
      <j1 rule="para" parents="955 3274"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (y / (((x \ 1) * x) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(3275(a,1),1424(a,1,2,2))].">
      <j1 rule="para" parents="3275 1424"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x
    ]]></literal>
    <justification jstring="[para(17(a,2),2393(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(70(a,1),2406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 2406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(756,a,3278,a)].">
      <j1 rule="hyper" parents="756 3278"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3279(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(3279(a,1),41(a,1))].">
      <j1 rule="para" parents="3279 41"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      x * ((y * x) * (1 / x)) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,3281,a(flip),b,2061,a(flip))].">
      <j1 rule="hyper" parents="129 3281 2061"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(3281(a,2),41(a,1))].">
      <j1 rule="para" parents="3281 41"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1769(a,1),2918(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1769 2918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,3285,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3287">
    <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(3286(a,1),40(a,1))].">
      <j1 rule="para" parents="3286 40"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1965(a,1),2920(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1965 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,3288,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 3288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      a((x * ((y * z) \ (u * u))) \ w,v5,v6) = a((x * (((u * u) \ y) * z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3(a,1),3000(a,1,1,1,2,2))].">
      <j1 rule="para" parents="3 3000"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      a((x * (((y * y) \ z) * u)) \ w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x * (z * u)) \ w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(3290(a,1),3007(a,1))].">
      <j1 rule="para" parents="3290 3007"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(3017(a,1),3019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3017 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a(flip),b,3292,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,4,a(flip),b,3292,a)].">
      <j1 rule="hyper" parents="125 4 3292"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1534(a,1),3293(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1534 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1642(a,2),3294(a,1,1,2))].">
      <j1 rule="para" parents="1642 3294"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1545,a,3296,a),flip(a)].">
      <j1 rule="hyper" parents="1545 3296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      (x * K(y,x)) \ K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(1642(a,2),3297(a,1,2))].">
      <j1 rule="para" parents="1642 3297"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      K(x,y) / (y \ 1) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(221,a,3299,a)].">
      <j1 rule="hyper" parents="221 3299"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) / u = z
    ]]></literal>
    <justification jstring="[para(3299(a,1),380(a,1,2))].">
      <j1 rule="para" parents="3299 380"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),3300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      T(x * K(y,x),x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3300(a,1),494(a,1,1))].">
      <j1 rule="para" parents="3300 494"/>
    </justification>
  </clause>

  <clause id="3304">
    <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(370,a,302,a(flip),b,3020,a),flip(a)].">
      <j1 rule="hyper" parents="370 302 3020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(3017(a,1),3304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3017 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1560(a,2),3305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1560 3305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1560(a,2),3306(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1560 3306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3236(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7 3236"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(147,a,3308,a)].">
      <j1 rule="hyper" parents="147 3308"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),3309(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2 3309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1548(a,1),3270(a,2,2))].">
      <j1 rule="para" parents="1548 3270"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2327,a(flip),b,3311,a),flip(a)].">
      <j1 rule="hyper" parents="370 2327 3311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1058,a,3312,a),flip(a)].">
      <j1 rule="hyper" parents="1058 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3312(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),3313(a,2,1))].">
      <j1 rule="para" parents="109 3313"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      L(x * ((x \ 1) \ ((y * z) \ u)),x \ (1 / x),y * z) = (y * (z * (x \ (1 / x)))) \ u
    ]]></literal>
    <justification jstring="[para(1213(a,1),1434(a,1,1))].">
      <j1 rule="para" parents="1213 1434"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(1367,a,2220,a),flip(a)].">
      <j1 rule="hyper" parents="1367 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(1052(a,1),3317(a,2,2))].">
      <j1 rule="para" parents="1052 3317"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(625,a,3318,a)].">
      <j1 rule="hyper" parents="625 3318"/>
    </justification>
  </clause>

  <clause id="3320">
    <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(370,a,1806,a(flip),b,3319,a)].">
      <j1 rule="hyper" parents="370 1806 3319"/>
    </justification>
  </clause>

  <clause id="3321">
    <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="[para(71(a,1),3319(a,2,1,2))].">
      <j1 rule="para" parents="71 3319"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(328,a,3320,a),flip(a)].">
      <j1 rule="hyper" parents="328 3320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3320(a,1),2177(a,1,1))].">
      <j1 rule="para" parents="3320 2177"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(421(a,1),3324(a,1,1,1))].">
      <j1 rule="para" parents="421 3324"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(2286(a,1),2235(a,2,1))].">
      <j1 rule="para" parents="2286 2235"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(2340(a,1),3327(a,2,1,1))].">
      <j1 rule="para" parents="2340 3327"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,15,a,b,3328,a)].">
      <j1 rule="hyper" parents="370 15 3328"/>
    </justification>
  </clause>

  <clause id="3330">
    <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(3328(a,2),693(a,1))].">
      <j1 rule="para" parents="3328 693"/>
    </justification>
  </clause>

  <clause id="3331">
    <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(370,a,1806,a(flip),b,3329,a)].">
      <j1 rule="hyper" parents="370 1806 3329"/>
    </justification>
  </clause>

  <clause id="3332">
    <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(1966(a,1),3329(a,2,1,2))].">
      <j1 rule="para" parents="1966 3329"/>
    </justification>
  </clause>

  <clause id="3333">
    <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(3331(a,1),277(a,1))].">
      <j1 rule="para" parents="3331 277"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      R(x,y,a(x,x,x \ y)) \ ((x \ 1) \ y) = (x * (x \ y)) * a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2431(a,1,1,2))].">
      <j1 rule="para" parents="5 2431"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      R(x,y,a(x,x,x \ y)) \ ((x \ 1) \ y) = y * a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,171,a(flip),b,3334,a),flip(a)].">
      <j1 rule="hyper" parents="370 171 3334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(T(y,x),x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(17(a,2),2818(a,2,2,1))].">
      <j1 rule="para" parents="17 2818"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * T(1 / (1 / y),x)
    ]]></literal>
    <justification jstring="[para(2801(a,1),3337(a,2,2))].">
      <j1 rule="para" parents="2801 3337"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = (1 / (1 / y)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,107,a(flip),b,3338,a),flip(a)].">
      <j1 rule="hyper" parents="370 107 3338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      (x * (y * (z \ (1 / z)))) \ u = z * ((z \ 1) \ ((x * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(650,a,3316,a),flip(a)].">
      <j1 rule="hyper" parents="650 3316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ (((x * x) \ 1) * (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(514(a,1),1868(a,1,1))].">
      <j1 rule="para" parents="514 1868"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ (1 / y)) * (x / ((z * (1 / y)) * 1))
    ]]></literal>
    <justification jstring="[para(1211(a,1),2056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1211 2056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ (1 / y)) * (x / (z * (1 / y)))
    ]]></literal>
    <justification jstring="[para(3(a,1),3345(a,2,2,2))].">
      <j1 rule="para" parents="3 3345"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,3346,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 3346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      T(x,1 \ (y * ((y \ 1) \ 1))) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[para(1135(a,1),3347(a,1,1,2))].">
      <j1 rule="para" parents="1135 3347"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      T(x,1 \ ((1 / y) \ y)) / (z * y) = (y \ 1) * (y \ (x / (z * (1 / y))))
    ]]></literal>
    <justification jstring="[para(1227(a,1),3348(a,1,1,2,2))].">
      <j1 rule="para" parents="1227 3348"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      (x \ 1) * (x \ (y / (z * (1 / x)))) = T(y,(1 / x) \ x) / (z * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),3349(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="62 3349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3351">
    <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(3320(a,1),2173(a,1,1))].">
      <j1 rule="para" parents="3320 2173"/>
    </justification>
  </clause>

  <clause id="3352">
    <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(421(a,1),3351(a,1,1,1))].">
      <j1 rule="para" parents="421 3351"/>
    </justification>
  </clause>

  <clause id="3353">
    <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(2162(a,1),3352(a,1,2))].">
      <j1 rule="para" parents="2162 3352"/>
    </justification>
  </clause>

  <clause id="3354">
    <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(60,a,20,a,b,3353,a)].">
      <j1 rule="hyper" parents="60 20 3353"/>
    </justification>
  </clause>

  <clause id="3355">
    <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(2169(a,1),3354(a,2,1))].">
      <j1 rule="para" parents="2169 3354"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      L(R(x,T(1 / x,L(x,y,z)),x),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(24(a,1),2497(a,1,1))].">
      <j1 rule="para" parents="24 2497"/>
    </justification>
  </clause>

  <clause id="3357">
    <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(88(a,1),3203(a,1,1))].">
      <j1 rule="para" parents="88 3203"/>
    </justification>
  </clause>

  <clause id="3358">
    <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(88(a,1),3357(a,1,2,1,1))].">
      <j1 rule="para" parents="88 3357"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ ((x * x) \ (y * (z * u))) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(520(a,1),3344(a,1,2))].">
      <j1 rule="para" parents="520 3344"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ (((x * x) \ y) * (z * u)) = L(L(u,z,y),y * z,(x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(514(a,1),3359(a,1,2))].">
      <j1 rule="para" parents="514 3359"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      L(L(x,y,z),z * y,(u * u) \ 1) = L(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(629,a,3360,a),flip(a)].">
      <j1 rule="hyper" parents="629 3360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(1494,a,3361,a),flip(a)].">
      <j1 rule="hyper" parents="1494 3361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3361(a,1),1494(a,1))].">
      <j1 rule="para" parents="3361 1494"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1503,a(flip),b,3362,a)].">
      <j1 rule="hyper" parents="60 1503 3362"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      L(x,y,(z * z) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      L(x,y,z * (z * u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(13(a,2),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(17(a,2),3362(a,1,3))].">
      <j1 rule="para" parents="17 3362"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(551(a,1),3362(a,1,3))].">
      <j1 rule="para" parents="551 3362"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(94(a,2),3362(a,1,3))].">
      <j1 rule="para" parents="94 3362"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(940(a,1),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="940 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      L(x,y,z * ((z \ 1) \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(595(a,1),3362(a,1,3))].">
      <j1 rule="para" parents="595 3362"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(967(a,1),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="967 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      L(x,y,(z * (u \ (w * w))) \ v5) = L(x,y,(z * (u \ 1)) \ v5)
    ]]></literal>
    <justification jstring="[para(1193(a,1),3362(a,1,3))].">
      <j1 rule="para" parents="1193 3362"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      L(L(x,y,z),u,w * w) = L(x,y,(v5 * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,615,a,b,3366,a)].">
      <j1 rule="hyper" parents="370 615 3366"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(943(a,1),3366(a,1,3)),flip(a)].">
      <j1 rule="para" parents="943 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      L(x,y,(z * (u \ 1)) \ w) = L(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(1116(a,1),3366(a,1,3))].">
      <j1 rule="para" parents="1116 3366"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * w) = L(x,y,z * ((u * u) * w))
    ]]></literal>
    <justification jstring="[para(1453(a,1),3366(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1453 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,3365,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 3365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3172,a,3380,a)].">
      <j1 rule="hyper" parents="3172 3380"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      L(x,y,z / (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3380(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      L(x,y,z * (u * (w * w))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(30(a,1),3380(a,1,3))].">
      <j1 rule="para" parents="30 3380"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(519(a,1),3380(a,1,3))].">
      <j1 rule="para" parents="519 3380"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      L(x,y,z \ (1 / u)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(865(a,1),3380(a,1,3))].">
      <j1 rule="para" parents="865 3380"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(314(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      L(x,y * (y * z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(92(a,1),3381(a,1,2))].">
      <j1 rule="para" parents="92 3381"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) = L(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(113(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(936(a,1),3381(a,1,2))].">
      <j1 rule="para" parents="936 3381"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(946(a,1),3381(a,1,2))].">
      <j1 rule="para" parents="946 3381"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) = L(x,(y \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(975(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="975 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      L(x,(y / (1 / z)) \ u,w) = L(x,(y / z) \ u,w)
    ]]></literal>
    <justification jstring="[para(976(a,1),3381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="976 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      L(x,(y * z) * (z \ y),u) = L(x,a(y,z,z \ y),u)
    ]]></literal>
    <justification jstring="[para(1027(a,1),3381(a,1,2))].">
      <j1 rule="para" parents="1027 3381"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      L(x,y \ ((z * z) * (y \ 1)),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(3381(a,1),2703(a,1))].">
      <j1 rule="para" parents="3381 2703"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(990,a,3388,a),flip(a)].">
      <j1 rule="hyper" parents="990 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2074,a,b,3388,a)].">
      <j1 rule="hyper" parents="370 2074 3388"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      L(x,1 / y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1488,a(flip),b,3388,a),flip(a)].">
      <j1 rule="hyper" parents="370 1488 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),3388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      x / L(y,y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(3388(a,1),497(a,1,2))].">
      <j1 rule="para" parents="3388 497"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      x * L(1 / y,y,x) = x / y
    ]]></literal>
    <justification jstring="[para(3388(a,1),2483(a,1,2))].">
      <j1 rule="para" parents="3388 2483"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3388,a,b,3401,a)].">
      <j1 rule="hyper" parents="370 3388 3401"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a,b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3401,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="370 3401 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      L(x,y \ 1,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),x,x) = 1 \ ((x \ 1) * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,2670,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="60 2670 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      L((x \ 1) \ (y \ z),x,y) = (y * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,344,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="60 344 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      L((x \ 1) \ y,x,z) = (z * (x \ 1)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="60 94 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      (x * (y \ 1)) * L(z,y,x) = x * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3401,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 3401 13"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      L(x,x \ 1,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,3401,a,b,3398,a)].">
      <j1 rule="hyper" parents="60 3401 3398"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      (x * (1 / y)) \ x = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,2481,a(flip),b,3398,a),flip(a)].">
      <j1 rule="hyper" parents="60 2481 3398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      x / L(1 / y,y,x) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(3388(a,1),3402(a,1,2))].">
      <j1 rule="para" parents="3388 3402"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(3401(a,2),3402(a,1,2))].">
      <j1 rule="para" parents="3401 3402"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      L(1 / x,x,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(135,a,3403,a),flip(a)].">
      <j1 rule="hyper" parents="135 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,74,a(flip),b,3403,a),flip(a)].">
      <j1 rule="hyper" parents="125 74 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      R(x,y,L(1 / z,z,y)) * (y / z) = (x * y) * L(1 / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,3403,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="129 3403 210"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      x \ (x / y) != z
    ]]></literal>
    <literal><![CDATA[
      L(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(3403(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3403 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(1 / x,x,y),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(3403(a,1),94(a,2,1))].">
      <j1 rule="para" parents="3403 94"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      x * T(y \ x,x \ y) = x / (x \ y)
    ]]></literal>
    <justification jstring="[para(1055(a,1),3403(a,1,2))].">
      <j1 rule="para" parents="1055 3403"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      (x / y) * K(x \ (x / y),x) = L(1 / y,y,x) * x
    ]]></literal>
    <justification jstring="[para(3417(a,2),353(a,2,1))].">
      <j1 rule="para" parents="3417 353"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(3417(a,1),1242(a,1,1))].">
      <j1 rule="para" parents="3417 1242"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(1101(a,1),3382(a,1,3))].">
      <j1 rule="para" parents="1101 3382"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      L(x,y \ (z * (y \ 1)),u) = L(x,T(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(941(a,1),3387(a,1,2))].">
      <j1 rule="para" parents="941 3387"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      L(x,y \ 1,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(3404(a,1),3173(a,1))].">
      <j1 rule="para" parents="3404 3173"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      L(x,T(y,y \ 1),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(108(a,2),3406(a,1,2))].">
      <j1 rule="para" parents="108 3406"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3431,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 3431 13"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3416(a,2),933(a,1,1,2))].">
      <j1 rule="para" parents="3416 933"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      (1 / (x \ y)) \ L(1 / (x \ y),x \ y,y) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3418,a,b,2438,a)].">
      <j1 rule="hyper" parents="125 3418 2438"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      (x * ((y \ x) * (1 / (y \ x)))) / ((y \ x) * (x \ y)) = R(x,y \ x,L(1 / (y \ x),y \ x,x))
    ]]></literal>
    <justification jstring="[para(3418(a,1),623(a,1,2,2))].">
      <j1 rule="para" parents="3418 623"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      (x \ y) * (L((x \ y) \ 1,x \ y,y) \ z) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(3418(a,1),3251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3418 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(643,a,3369,a),flip(a)].">
      <j1 rule="hyper" parents="643 3369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3369(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="74 3369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(303(a,2),3437(a,1,3))].">
      <j1 rule="para" parents="303 3437"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(957(a,2),3437(a,1,3))].">
      <j1 rule="para" parents="957 3437"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1709(a,2),3437(a,1,3))].">
      <j1 rule="para" parents="1709 3437"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,3439,a),flip(a)].">
      <j1 rule="hyper" parents="1838 3439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(129,a,3439,a(flip),b,3417,a(flip))].">
      <j1 rule="hyper" parents="129 3439 3417"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3035,a,3440,a)].">
      <j1 rule="hyper" parents="3035 3440"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,3440,a),flip(a)].">
      <j1 rule="hyper" parents="1838 3440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,K(x \ 1,x)) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1075,a,3440,a),flip(a)].">
      <j1 rule="hyper" parents="1075 3440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,3440,a)].">
      <j1 rule="hyper" parents="60 94 3440"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[hyper(129,a,3440,a(flip),b,3417,a(flip))].">
      <j1 rule="hyper" parents="129 3440 3417"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3440(a,1),47(a,2))].">
      <j1 rule="para" parents="3440 47"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3440(a,1),727(a,1,2))].">
      <j1 rule="para" parents="3440 727"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      K(x \ 1,x) * y != (K(x \ 1,x) * z) * u
    ]]></literal>
    <literal><![CDATA[
      z * u = y
    ]]></literal>
    <justification jstring="[para(3440(a,1),626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3440 626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,3441,a),flip(a)].">
      <j1 rule="hyper" parents="1838 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,3441,a)].">
      <j1 rule="hyper" parents="60 94 3441"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,3441,a(flip),b,1621,a),flip(a)].">
      <j1 rule="hyper" parents="129 3441 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(129,a,3441,a(flip),b,3417,a(flip))].">
      <j1 rule="hyper" parents="129 3441 3417"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(3441(a,1),727(a,1,2))].">
      <j1 rule="para" parents="3441 727"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) * L(z,z,x \ y)) = x \ (((1 / x) \ y) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3376(a,1),2484(a,1,2,2))].">
      <j1 rule="para" parents="3376 2484"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,3384,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 3384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      L(x,y,z * (u * (z * u))) = L(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(9(a,2),3458(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      L(x,y,z \ (u \ 1)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3385(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="74 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(635,a,3389,a),flip(a)].">
      <j1 rule="hyper" parents="635 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      L(x,y \ z,L(y \ z,y,y)) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2392,a,b,3389,a)].">
      <j1 rule="hyper" parents="60 2392 3389"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      L(x,(1 / (y * (z * z))) * u,w) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(29(a,1),3389(a,2,2))].">
      <j1 rule="para" parents="29 3389"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3389(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      L(x,y * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3389(a,1),635(a,1))].">
      <j1 rule="para" parents="3389 635"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = L(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2012(a,1),3389(a,1,2))].">
      <j1 rule="para" parents="2012 3389"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      L(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(957(a,2),3461(a,1,2))].">
      <j1 rule="para" parents="957 3461"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(1709(a,2),3461(a,1,2))].">
      <j1 rule="para" parents="1709 3461"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,3467,a),flip(a)].">
      <j1 rule="hyper" parents="1838 3467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * K(x \ 1,x)) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1411,a,3467,a)].">
      <j1 rule="hyper" parents="1411 3467"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ x = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(991,a,3467,a)].">
      <j1 rule="hyper" parents="991 3467"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,3467,a(flip),b,570,a(flip))].">
      <j1 rule="hyper" parents="129 3467 570"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = u
    ]]></literal>
    <justification jstring="[para(3467(a,1),336(a,1,2))].">
      <j1 rule="para" parents="3467 336"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,3468,a),flip(a)].">
      <j1 rule="hyper" parents="1838 3468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,3468,a(flip),b,1736,a),flip(a)].">
      <j1 rule="hyper" parents="129 3468 1736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,y \ 1) * z) = u
    ]]></literal>
    <justification jstring="[para(3468(a,1),336(a,1,2))].">
      <j1 rule="para" parents="3468 336"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      L(x,((y * y) \ z) \ u,w) = L(x,(z \ (y * y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(578(a,1),3392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="578 3392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(74(a,1),3413(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 3413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,(z * (u * u)) * w)
    ]]></literal>
    <justification jstring="[para(29(a,1),3426(a,1,3))].">
      <j1 rule="para" parents="29 3426"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      L(x,y,z * ((u / (w * w)) \ 1)) = L(x,y,(z * u) / (w * w))
    ]]></literal>
    <justification jstring="[para(1098(a,2),3426(a,2,3))].">
      <j1 rule="para" parents="1098 3426"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(2162(a,1),3426(a,1,3))].">
      <j1 rule="para" parents="2162 3426"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3438,a(flip),b,3438,a),flip(a)].">
      <j1 rule="hyper" parents="370 3438 3438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      L(x,y \ L(z,y,y),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(2072(a,2),3464(a,1,2))].">
      <j1 rule="para" parents="2072 3464"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(159,a,3471,a),flip(a)].">
      <j1 rule="hyper" parents="159 3471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(3471(a,1),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3471 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3471(a,1),298(a,1,2))].">
      <j1 rule="para" parents="3471 298"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2732(a,1),3472(a,1,1))].">
      <j1 rule="para" parents="2732 3472"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      x / ((y \ 1) \ 1) = x * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(156,a,3479,a),flip(a)].">
      <j1 rule="hyper" parents="156 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      x / (((x \ y) \ 1) \ 1) = x * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,176,a(flip),b,3479,a),flip(a)].">
      <j1 rule="hyper" parents="129 176 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      L(x \ ((1 / y) \ (((1 / y) * x) / ((z \ 1) \ 1))),x,y) = (((1 / y) * x) * z) \ ((1 / y) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1489,a,b,3479,a)].">
      <j1 rule="hyper" parents="60 1489 3479"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      (x * (y \ 1)) \ x = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(1307(a,1),3479(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1307 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3487(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="3487 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      R((x * K(y,y \ 1)) / z,z,K(y \ 1,y)) = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3487(a,1),104(a,2,1))].">
      <j1 rule="para" parents="3487 104"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ x = z
    ]]></literal>
    <justification jstring="[para(3491(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3491 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(496,a,3492,a)].">
      <j1 rule="hyper" parents="496 3492"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = (x * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,3492,a),flip(a)].">
      <j1 rule="hyper" parents="215 3492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) \ (x * y) = (x * y) \ (x * (y * y))
    ]]></literal>
    <justification jstring="[para(855(a,1),3494(a,2,2))].">
      <j1 rule="para" parents="855 3494"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(77(a,1),3499(a,2,1,2))].">
      <j1 rule="para" parents="77 3499"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      1 / ((x * y) \ x) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,3501,a)].">
      <j1 rule="hyper" parents="221 3501"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ 1 = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(3501(a,1),1312(a,1,1,1))].">
      <j1 rule="para" parents="3501 1312"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (1 * R(1 \ ((x \ (x / y)) \ 1),z,u)) = ((x * y) \ x) \ R(((x \ (x / y)) \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3501(a,1),2514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3501 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) = a(x,y,z \ (z / u))
    ]]></literal>
    <justification jstring="[para(3501(a,1),3094(a,1,3))].">
      <j1 rule="para" parents="3501 3094"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(3479(a,2),3502(a,1,2))].">
      <j1 rule="para" parents="3479 3502"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = y \ (y / (y \ x))
    ]]></literal>
    <justification jstring="[para(5(a,1),3503(a,1,1,1,1))].">
      <j1 rule="para" parents="5 3503"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,3417,a,b,3508,a)].">
      <j1 rule="hyper" parents="370 3417 3508"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      x * (((y \ x) \ 1) \ 1) = x / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,3508,a,b,xx)].">
      <j1 rule="hyper" parents="129 3508"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(31,a,3422,a,b,3510,a)].">
      <j1 rule="hyper" parents="31 3422 3510"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,3511,a(flip))].">
      <j1 rule="hyper" parents="221 3511"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,3511,a(flip),b,2223,a),flip(a)].">
      <j1 rule="hyper" parents="129 3511 2223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,3511,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 3511 17"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      T(x \ y,y \ x) \ 1 = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(3511(a,2),1307(a,1,1))].">
      <j1 rule="para" parents="3511 1307"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      1 / T((x * y) \ x,y) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),3513(a,1,2,2))].">
      <j1 rule="para" parents="4 3513"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(313(a,1),3363(a,1,3))].">
      <j1 rule="para" parents="313 3363"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(94(a,2),3363(a,1,3))].">
      <j1 rule="para" parents="94 3363"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),3518(a,1,3))].">
      <j1 rule="para" parents="74 3518"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      L(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1495(a,1),3518(a,1))].">
      <j1 rule="para" parents="1495 3518"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      L(x,1 / y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3388(a,2),3518(a,1))].">
      <j1 rule="para" parents="3388 3518"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1488(a,2),3520(a,1))].">
      <j1 rule="para" parents="1488 3520"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(77(a,1),3522(a,1,3))].">
      <j1 rule="para" parents="77 3522"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      L(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(3365(a,2),3522(a,1))].">
      <j1 rule="para" parents="3365 3522"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      L(x,y \ 1,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3401(a,2),3522(a,1))].">
      <j1 rule="para" parents="3401 3522"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      L(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3405(a,2),3522(a,1))].">
      <j1 rule="para" parents="3405 3522"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(3407(a,1),3522(a,1))].">
      <j1 rule="para" parents="3407 3522"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(3384(a,2),3522(a,1))].">
      <j1 rule="para" parents="3384 3522"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ 1) \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),3530(a,1))].">
      <j1 rule="para" parents="94 3530"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3401(a,2),3530(a,1))].">
      <j1 rule="para" parents="3401 3530"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      L(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3404(a,2),3530(a,1))].">
      <j1 rule="para" parents="3404 3530"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      L(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(3388(a,2),3531(a,1))].">
      <j1 rule="para" parents="3388 3531"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      x / L(1 / y,y,x) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1313(a,1),3415(a,2,2))].">
      <j1 rule="para" parents="1313 3415"/>
    </justification>
  </clause>

  <clause id="3538">
    <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(1595(a,2),3525(a,1))].">
      <j1 rule="para" parents="1595 3525"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      L(x,y,(z * u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,R(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),3528(a,1,3))].">
      <j1 rule="para" parents="103 3528"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      L(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3171(a,2),3528(a,1))].">
      <j1 rule="para" parents="3171 3528"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,u) = w
    ]]></literal>
    <justification jstring="[para(360(a,2),3536(a,1,2))].">
      <j1 rule="para" parents="360 3536"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      L(1 / x,x,y) = (y * ((x \ 1) \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,3537,a),flip(a)].">
      <j1 rule="hyper" parents="215 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      L(x,y * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),3540(a,1,2))].">
      <j1 rule="para" parents="92 3540"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(936(a,1),3540(a,1,2))].">
      <j1 rule="para" parents="936 3540"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),3540(a,1,2))].">
      <j1 rule="para" parents="946 3540"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3380,a(flip),b,3368,a),flip(a)].">
      <j1 rule="hyper" parents="370 3380 3368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w * (v5 * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,z * u,w) = v6
    ]]></literal>
    <justification jstring="[para(3391(a,2),3528(a,1))].">
      <j1 rule="para" parents="3391 3528"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (K(x,x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(764,a,3454,a)].">
      <j1 rule="hyper" parents="764 3454"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(387,a,3454,a),flip(a)].">
      <j1 rule="hyper" parents="387 3454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,362,a,b,3454,a),flip(a)].">
      <j1 rule="hyper" parents="370 362 3454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(3454(a,2),846(a,1))].">
      <j1 rule="para" parents="3454 846"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,434,a(flip),b,3475,a),flip(a)].">
      <j1 rule="hyper" parents="125 434 3475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,3475,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 3475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2136,a,3553,a),flip(a)].">
      <j1 rule="hyper" parents="2136 3553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(3554(a,1),742(a,1))].">
      <j1 rule="para" parents="3554 742"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(787,a,3555,a)].">
      <j1 rule="hyper" parents="787 3555"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,2866,a,b,3555,a)].">
      <j1 rule="hyper" parents="32 2866 3555"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1385,a,3559,a(flip))].">
      <j1 rule="hyper" parents="1385 3559"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1803,a,3565,a)].">
      <j1 rule="hyper" parents="1803 3565"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1801,a,3565,a),flip(a)].">
      <j1 rule="hyper" parents="1801 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,1786,a(flip),b,3565,a),flip(a)].">
      <j1 rule="hyper" parents="370 1786 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,3565,a(flip),b,2072,a),flip(a)].">
      <j1 rule="hyper" parents="129 3565 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(3566(a,1),742(a,1))].">
      <j1 rule="para" parents="3566 742"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      (x \ 1) * T(x \ ((x \ 1) \ y),z) = x \ T(K(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3566(a,1),2087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3566 2087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      ((x \ 1) \ 1) * ((x \ 1) * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(3567(a,1),3475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3567 3475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      L(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3375(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="3375 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      L(x,y,z * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),3573(a,1,3))].">
      <j1 rule="para" parents="92 3573"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      L(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,((v5 * v5) \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),3573(a,1,3))].">
      <j1 rule="para" parents="113 3573"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(936(a,1),3573(a,1,3))].">
      <j1 rule="para" parents="936 3573"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),3573(a,1,3))].">
      <j1 rule="para" parents="946 3573"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      L(x,y,(z * (u \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(1116(a,1),3573(a,1,3))].">
      <j1 rule="para" parents="1116 3573"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      R(x,y,y) * L(z,y,x * y) = (x * y) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1111(a,1),3411(a,1,1))].">
      <j1 rule="para" parents="1111 3411"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3319,a,b,3433,a)].">
      <j1 rule="hyper" parents="60 3319 3433"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      (x * (y \ x)) \ x = z
    ]]></literal>
    <justification jstring="[para(3498(a,1),668(a,1))].">
      <j1 rule="para" parents="3498 668"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      L((x \ ((1 / x) \ y)) \ 1,(x \ 1) \ (x \ y),x \ y) = (((x \ y) \ (x \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2104(a,1),3498(a,1,1,1))].">
      <j1 rule="para" parents="2104 3498"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,1313,a,b,3509,a),flip(a)].">
      <j1 rule="hyper" parents="370 1313 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      L(x,y * R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(2041(a,1),3545(a,1,2))].">
      <j1 rule="para" parents="2041 3545"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(77(a,1),3581(a,1,2))].">
      <j1 rule="para" parents="77 3581"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      x * ((x \ y) * (1 / (x \ y))) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(129,a,3585,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 3585 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((y \ x) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3585(a,2),1314(a,1))].">
      <j1 rule="para" parents="3585 1314"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(3585(a,1),3415(a,1,2))].">
      <j1 rule="para" parents="3585 3415"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      L(x,y,(z * (((z * z) \ u) \ 1)) \ w) = L(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[para(944(a,1),3377(a,2,3,1))].">
      <j1 rule="para" parents="944 3377"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3392,a(flip),b,3394,a),flip(a)].">
      <j1 rule="hyper" parents="370 3392 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(3394(a,2),3545(a,1))].">
      <j1 rule="para" parents="3394 3545"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      L(x,(L(y,z,u) * (y \ L(y,z,u))) \ w,v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(2156(a,1),3592(a,1,2,1))].">
      <j1 rule="para" parents="2156 3592"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      L(x,T(y * y,z \ 1),u) = x
    ]]></literal>
    <justification jstring="[hyper(3397,a,3428,a),flip(a)].">
      <j1 rule="hyper" parents="3397 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      L(x,T(y * y,z),u) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),3595(a,1,2,2))].">
      <j1 rule="para" parents="77 3595"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      (x * T(y * y,z)) \ u = T(y * y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(747,a,3596,a),flip(a)].">
      <j1 rule="hyper" parents="747 3596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3445(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3445 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(1178(a,1),3445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1178 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1508(a,1),3445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1508 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2377(a,1),3445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2377 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(2383,a,3601,a),flip(a)].">
      <j1 rule="hyper" parents="2383 3601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(387,a,3601,a),flip(a)].">
      <j1 rule="hyper" parents="387 3601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(387,a,3602,a),flip(a)].">
      <j1 rule="hyper" parents="387 3602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3602(a,1),3444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3602 3444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,2381,a(flip),b,3603,a)].">
      <j1 rule="hyper" parents="60 2381 3603"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,3339,a,b,3603,a)].">
      <j1 rule="hyper" parents="32 3339 3603"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((1 / (1 / x)) * y) = u
    ]]></literal>
    <justification jstring="[para(3603(a,2),721(a,1))].">
      <j1 rule="para" parents="3603 721"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,3604,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(31,a,3475,a(flip),b,3604,a),flip(a)].">
      <j1 rule="hyper" parents="31 3475 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(31,a,3475,a,b,3604,a(flip))].">
      <j1 rule="hyper" parents="31 3475 3604"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      (x * y) \ ((K(x \ 1,x) * y) * ((x \ 1) \ 1)) = K(K(x \ 1,x) * y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3604(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3604 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      K(x,x \ 1) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(387,a,3614,a),flip(a)].">
      <j1 rule="hyper" parents="387 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(135,a,3614,a)].">
      <j1 rule="hyper" parents="135 3614"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(31,a,3603,a,b,3614,a),flip(a)].">
      <j1 rule="hyper" parents="31 3603 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(31,a,3445,a(flip),b,3614,a),flip(a)].">
      <j1 rule="hyper" parents="31 3445 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(3614(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="3614 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(3559(a,1),3614(a,1,2))].">
      <j1 rule="para" parents="3559 3614"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(3615(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="3615 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      K(x \ 1,x) * (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1727,a(flip),b,3617,a),flip(a)].">
      <j1 rule="hyper" parents="60 1727 3617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x \ 1,x) * y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(3617(a,1),3311(a,1,2,1))].">
      <j1 rule="para" parents="3617 3311"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      K(x * y,(x * y) \ 1) * ((((x * y) \ 1) * x) * y) = a((x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(1459,a,3618,a),flip(a)].">
      <j1 rule="hyper" parents="1459 3618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(3606(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3606 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      x \ T(K(x \ 1,x) * y,x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3606(a,1),1578(a,1,2,1))].">
      <j1 rule="para" parents="3606 1578"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,3609,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 3609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,1817,a(flip),b,3613,a)].">
      <j1 rule="hyper" parents="60 1817 3613"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1716(a,1),3613(a,1,1))].">
      <j1 rule="para" parents="1716 3613"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(353(a,1),3619(a,1,2))].">
      <j1 rule="para" parents="353 3619"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(31,a,3614,a,b,3629,a)].">
      <j1 rule="hyper" parents="31 3614 3629"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (((x \ 1) \ 1) \ y) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3631,a(flip),b,3554,a)].">
      <j1 rule="hyper" parents="125 3631 3554"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(562(a,1),3447(a,1,2))].">
      <j1 rule="para" parents="562 3447"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(3614(a,1),3447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3614 3447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3614(a,1),3447(a,1,2))].">
      <j1 rule="para" parents="3614 3447"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(1204,a,3450,a),flip(a)].">
      <j1 rule="hyper" parents="1204 3450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,2674,a,b,3640,a)].">
      <j1 rule="hyper" parents="32 2674 3640"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),3641(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),3642(a,2,1))].">
      <j1 rule="para" parents="6 3642"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(3642(a,1),2232(a,1,1))].">
      <j1 rule="para" parents="3642 2232"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2810,a,3452,a)].">
      <j1 rule="hyper" parents="2810 3452"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      x * T(K(y,y \ 1) * z,x) = K(y,y \ 1) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(329,a,3452,a)].">
      <j1 rule="hyper" parents="329 3452"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(3567(a,1),3452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 3452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * z) = ((1 / (1 / x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(3619(a,1),3453(a,1,1))].">
      <j1 rule="para" parents="3619 3453"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(2365(a,1),3456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2365 3456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      L(x,(y / (1 / z)) * R(y / (1 / z),z,z),u) = L(x,(y / (1 / z)) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(2058(a,1),3466(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2058 3466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(1178(a,1),3469(a,2,2))].">
      <j1 rule="para" parents="1178 3469"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1508(a,1),3469(a,2,2))].">
      <j1 rule="para" parents="1508 3469"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,7,a(flip),b,3652,a),flip(a)].">
      <j1 rule="hyper" parents="128 7 3652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3487(a,1),3652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3487 3652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,7,a(flip),b,3653,a),flip(a)].">
      <j1 rule="hyper" parents="128 7 3653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3653(a,1),2717(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3653 2717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * (y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(3487(a,1),3653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3487 3653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,360,a,b,3654,a),flip(a)].">
      <j1 rule="hyper" parents="370 360 3654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,3654,a(flip),b,1585,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 3654 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,361,a,b,3655,a),flip(a)].">
      <j1 rule="hyper" parents="370 361 3655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,436,a(flip),b,3655,a),flip(a)].">
      <j1 rule="hyper" parents="128 436 3655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3495,a,3656,a)].">
      <j1 rule="hyper" parents="3495 3656"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3659(a,1),2417(a,1,1))].">
      <j1 rule="para" parents="3659 2417"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(77(a,1),3660(a,2,2,2,1))].">
      <j1 rule="para" parents="77 3660"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,1891,a,b,3661,a)].">
      <j1 rule="hyper" parents="32 1891 3661"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,1886,a,b,3661,a),flip(a)].">
      <j1 rule="hyper" parents="32 1886 3661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(370,a,522,a(flip),b,3663,a),flip(a)].">
      <j1 rule="hyper" parents="370 522 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),3665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,361,a(flip),b,3667,a)].">
      <j1 rule="hyper" parents="60 361 3667"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,3667,a(flip),b,3661,a)].">
      <j1 rule="hyper" parents="128 3667 3661"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,361,a(flip),b,3668,a),flip(a)].">
      <j1 rule="hyper" parents="370 361 3668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(108(a,1),3670(a,1,1,2))].">
      <j1 rule="para" parents="108 3670"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3487(a,1),3470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3487 3470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3675(a,1),3470(a,1,2,1))].">
      <j1 rule="para" parents="3675 3470"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      L(x,y,z * L(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(1362(a,1),3483(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1362 3483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * L((z \ 1) \ u,z,z)) = L(x,y,(z * u) \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2082(a,1),3483(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2082 3483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(220(a,1),3507(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="220 3507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      ((x * y) \ x) * (x \ (x * y)) = y * ((((x * y) \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),3515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(215,a,3590,a)].">
      <j1 rule="hyper" parents="215 3590"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(77(a,1),3590(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="77 3590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (K(x \ 1,x) * z) * u = y
    ]]></literal>
    <justification jstring="[para(3620(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="3620 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ 1) * T((1 / ((x \ 1) \ 1)) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3635(a,1),2134(a,2,1))].">
      <j1 rule="para" parents="3635 2134"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ 1 = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,177,a(flip),b,3638,a),flip(a)].">
      <j1 rule="hyper" parents="370 177 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(3672(a,1),494(a,1,1))].">
      <j1 rule="para" parents="3672 494"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1716(a,1),3678(a,2,1))].">
      <j1 rule="para" parents="1716 3678"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(221,a,3682,a)].">
      <j1 rule="hyper" parents="221 3682"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),3685(a,1,1,2,2,2))].">
      <j1 rule="para" parents="17 3685"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (x \ 1)) \ z) = (y * (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(3490(a,1),3692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3490 3692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(74(a,1),3693(a,2,2,2,2))].">
      <j1 rule="para" parents="74 3693"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      L(x,y \ z,y * z) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(3519,a,3462,a)].">
      <j1 rule="hyper" parents="3519 3462"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(107(a,1),3556(a,1,2))].">
      <j1 rule="para" parents="107 3556"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      K(x,x \ 1) * (x * ((1 / x) * y)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1716(a,1),3624(a,1,1))].">
      <j1 rule="para" parents="1716 3624"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(2380(a,1),3627(a,1))].">
      <j1 rule="para" parents="2380 3627"/>
    </justification>
  </clause>

  <clause id="3702">
    <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(2319(a,1),3657(a,2,1))].">
      <j1 rule="para" parents="2319 3657"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2814(a,1),3669(a,1,1))].">
      <j1 rule="para" parents="2814 3669"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(3488,a,3703,a)].">
      <j1 rule="hyper" parents="3488 3703"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(809,a,3703,a)].">
      <j1 rule="hyper" parents="809 3703"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3672,a(flip),b,3706,a)].">
      <j1 rule="hyper" parents="60 3672 3706"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      T(x,x \ 1) * ((1 / x) * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3556,a,3700,a)].">
      <j1 rule="hyper" parents="3556 3700"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      T(x,x \ 1) * ((1 / x) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,3708,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 3708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      L((1 / x) \ y,x,x) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(387,a,3709,a),flip(a)].">
      <j1 rule="hyper" parents="387 3709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,3709,a(flip),b,362,a(flip))].">
      <j1 rule="hyper" parents="125 3709 362"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      L((1 / x) * y,x,x) = (x \ 1) * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(3711(a,1),2120(a,1,1))].">
      <j1 rule="para" parents="3711 2120"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      T((x \ 1) * y,K(x \ 1,x)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3602(a,1),3446(a,1,1))].">
      <j1 rule="para" parents="3602 3446"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      L(x,((y * y) \ z) \ u,w) = L(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3592,a(flip),b,3478,a),flip(a)].">
      <j1 rule="hyper" parents="370 3592 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      L(x,((y * y) * z) \ u,w) = L(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),3715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      L(x,((1 / y) * z) \ u,w) = L(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(551(a,1),3715(a,1,2,1))].">
      <j1 rule="para" parents="551 3715"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) \ u,w) = L(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(940(a,1),3715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="940 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(849(a,1),3715(a,1,2))].">
      <j1 rule="para" parents="849 3715"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(518(a,1),3717(a,1,2))].">
      <j1 rule="para" parents="518 3717"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      L(x,y \ (1 / z),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(254(a,1),3720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="254 3720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      L(x,y \ ((1 / z) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(943(a,1),3720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="943 3720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),3722(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 3722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ z,x \ y,x) = (y \ 1) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(798,a,3724,a),flip(a)].">
      <j1 rule="hyper" parents="798 3724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      L(x,((y \ 1) * z) \ y,u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(1574(a,1),3724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1574 3724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,((x \ 1) * y) \ x,(x \ 1) * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[para(1574(a,1),3725(a,1,1,1))].">
      <j1 rule="para" parents="1574 3725"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      (x * y) \ (x * (y * y)) = R(x,y,y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1111(a,1),3500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1111 3500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(629,a,3729,a),flip(a)].">
      <j1 rule="hyper" parents="629 3729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3733">
    <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(1771(a,1),3533(a,1,1))].">
      <j1 rule="para" parents="1771 3533"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * x) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,3580,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 3580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      R(x,y,y) \ ((x * y) * ((y \ 1) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x * y) = u
    ]]></literal>
    <justification jstring="[para(3580(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3580 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1055(a,1),3589(a,1))].">
      <j1 rule="para" parents="1055 3589"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,3564,a(flip),b,3644,a),flip(a)].">
      <j1 rule="hyper" parents="60 3564 3644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),3737(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(1313(a,1),3649(a,2,1,1))].">
      <j1 rule="para" parents="1313 3649"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(1756,a,3740,a)].">
      <j1 rule="hyper" parents="1756 3740"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,1640,a(flip),b,3741,a)].">
      <j1 rule="hyper" parents="60 1640 3741"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(108(a,2),3742(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="108 3742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      1 \ ((x \ 1) * ((x \ 1) * y)) = (1 / x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(2108,a,3408,a),flip(a)].">
      <j1 rule="hyper" parents="2108 3408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * y) = (x \ 1) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(191,a,3744,a),flip(a)].">
      <j1 rule="hyper" parents="191 3744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      x * ((1 / x) * ((1 / x) * y)) = L((x \ 1) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,3745,a,b,2072,a)].">
      <j1 rule="hyper" parents="129 3745 2072"/>
    </justification>
  </clause>

  <clause id="3747">
    <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(3432(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="3432 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      K(x \ 1,x) * y != (K(x \ 1,x) / z) * u
    ]]></literal>
    <literal><![CDATA[
      (1 / z) * u = y
    ]]></literal>
    <justification jstring="[para(3448(a,1),3451(a,2,1))].">
      <j1 rule="para" parents="3448 3451"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * u = y
    ]]></literal>
    <justification jstring="[para(3613(a,1),3451(a,2,1))].">
      <j1 rule="para" parents="3613 3451"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1552(a,1),3587(a,1,1))].">
      <j1 rule="para" parents="1552 3587"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,1246,a(flip),b,3750,a),flip(a)].">
      <j1 rule="hyper" parents="60 1246 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3751(a,2),262(a,1,1))].">
      <j1 rule="para" parents="3751 262"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      T(K(1 / (x \ 1),y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(308(a,1),3752(a,1,1,1,2))].">
      <j1 rule="para" parents="308 3752"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      T(K(x,y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(74(a,1),3753(a,1,1,1))].">
      <j1 rule="para" parents="74 3753"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2846,a(flip),b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="60 2846 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),3756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <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(3374(a,2),3578(a,1))].">
      <j1 rule="para" parents="3374 3578"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      L(x,((y * y) \ (1 / z)) * u,w) = L(x,z * ((y * y) * u),w)
    ]]></literal>
    <justification jstring="[para(598(a,1),3463(a,1,2,1))].">
      <j1 rule="para" parents="598 3463"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,z * ((u * u) * w))
    ]]></literal>
    <justification jstring="[para(29(a,1),3481(a,2,3))].">
      <j1 rule="para" parents="29 3481"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * (w \ 1))) = L(x,y,(z * w) / (u * u))
    ]]></literal>
    <justification jstring="[para(512(a,1),3482(a,1,3,2))].">
      <j1 rule="para" parents="512 3482"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      ((x * y) \ x) * (x \ (x * y)) = y * (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(3503(a,1),3683(a,2,2))].">
      <j1 rule="para" parents="3503 3683"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      ((x * y) \ x) * y = y * (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(742,a,3762,a)].">
      <j1 rule="hyper" parents="742 3762"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,(1 / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3391,a(flip),b,3759,a),flip(a)].">
      <j1 rule="hyper" parents="60 3391 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3389,a(flip),b,3765,a),flip(a)].">
      <j1 rule="hyper" parents="370 3389 3765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      L(x,y * ((z * z) \ u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),3767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 3767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      L(x,y * ((z * z) \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(67(a,1),3767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="67 3767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(254(a,1),3767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="254 3767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      L(x,y * (z * (z * u)),w) = L(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(92(a,1),3767(a,1,2,2))].">
      <j1 rule="para" parents="92 3767"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      L(x,y * (((z * z) \ u) * w),v5) = L(x,y * (u * w),v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),3767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 3767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      L(x,y * ((1 / z) \ u),w) = L(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(943(a,1),3767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="943 3767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      L(x,y * (((((z * z) * u) / (z * z)) * z) * z),w) = L(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(1235(a,2),3767(a,1,2,2))].">
      <j1 rule="para" parents="1235 3767"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      L(x,y / (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(577(a,1),3769(a,1,2))].">
      <j1 rule="para" parents="577 3769"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      L(x,y * (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      L(x,y * (z / (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(1098(a,1),3775(a,1,2))].">
      <j1 rule="para" parents="1098 3775"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(1101(a,1),3775(a,1,2))].">
      <j1 rule="para" parents="1101 3775"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * ((z * x) * x))) = L(a(z,x,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(2823,a,3776,a)].">
      <j1 rule="hyper" parents="2823 3776"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      (x * x) \ L((x * x) * y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2819,a,b,3776,a)].">
      <j1 rule="hyper" parents="60 2819 3776"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      L(((x * x) \ y) * z,u,w) = (x * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,2820,a(flip),b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="60 2820 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      L((x * x) * y,z,u) = (x * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,3776,a(flip),b,2819,a),flip(a)].">
      <j1 rule="hyper" parents="129 3776 2819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      L(x,y * (z * (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),3776(a,1,2))].">
      <j1 rule="para" parents="30 3776"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3770,a,b,3778,a)].">
      <j1 rule="hyper" parents="370 3770 3778"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2162(a,1),3778(a,1,2))].">
      <j1 rule="para" parents="2162 3778"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      L(x,(y * (z \ 1)) * u,w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(1117(a,1),3768(a,1,2))].">
      <j1 rule="para" parents="1117 3768"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),w) = L(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(1101(a,1),3777(a,1,2,2))].">
      <j1 rule="para" parents="1101 3777"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3780(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      (x * x) \ L(x,y,z) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),3780(a,1,2,1))].">
      <j1 rule="para" parents="254 3780"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      L((x * x) * y,z,u) * w = (x * x) * (L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),113(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3780 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      (x * x) \ L((x \ 1) \ y,z,u) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(936(a,1),3780(a,1,2,1))].">
      <j1 rule="para" parents="936 3780"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      a(L((x * x) * y,z,u),w,v5) = a(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3780(a,1),2952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3780 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3780(a,1),3077(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3780 3077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      L(x,y,L((z * z) * u,w,v5)) = L(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3780(a,1),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3780 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      L(x,L((y * y) * z,u,w),v5) = L(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3780(a,1),3387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3780 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      (x \ 1) * L(x,y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3790,a(flip),b,942,a),flip(a)].">
      <j1 rule="hyper" parents="129 3790 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3790,a(flip),b,552,a)].">
      <j1 rule="hyper" parents="125 3790 552"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = L(x,y,z) \ (x * x)
    ]]></literal>
    <justification jstring="[para(3790(a,1),578(a,1,1))].">
      <j1 rule="para" parents="3790 578"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      L(x,y,z) \ ((x * x) * u) = L(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3790(a,1),849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3790 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      R(x,y,L(1 / z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3790(a,1),2755(a,1,3))].">
      <j1 rule="para" parents="3790 2755"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      a(L(1 / x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3790(a,1),2952(a,1,1))].">
      <j1 rule="para" parents="3790 2952"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      L(x,y,L(1 / z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3790(a,1),3362(a,1,3))].">
      <j1 rule="para" parents="3790 3362"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      L(x,L(1 / y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3790(a,1),3387(a,1,2))].">
      <j1 rule="para" parents="3790 3387"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      L(((1 / x) * (1 / x)) * y,z,u) = (x \ (1 / x)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(320(a,1),3782(a,2,1))].">
      <j1 rule="para" parents="320 3782"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      (x \ 1) * L((y * y) * z,u,w) = (x \ (y * y)) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(3782(a,2),573(a,1,2))].">
      <j1 rule="para" parents="3782 573"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      L((x * x) * y,z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ ((x * x) \ w) = v5
    ]]></literal>
    <justification jstring="[para(3782(a,2),750(a,1,1))].">
      <j1 rule="para" parents="3782 750"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      L(x,y,L((z * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(3782(a,2),3573(a,1,3))].">
      <j1 rule="para" parents="3782 3573"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      L(x,y * ((z * (u * w)) * ((w \ 1) * w)),v5) = L(x,y * (z * (u * (1 / w))),v5)
    ]]></literal>
    <justification jstring="[para(2863(a,1),3783(a,1,2,2))].">
      <j1 rule="para" parents="2863 3783"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      L((x * y) * x,z,u) = (x * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(3170,a,3789,a),flip(a)].">
      <j1 rule="hyper" parents="3170 3789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      L((x * x) \ y,z,u) \ w = L(y,z,u) \ ((x * x) * w)
    ]]></literal>
    <justification jstring="[para(3789(a,2),849(a,1,1))].">
      <j1 rule="para" parents="3789 849"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1631,a,3798,a)].">
      <j1 rule="hyper" parents="1631 3798"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3798,a(flip),b,1354,a(flip))].">
      <j1 rule="hyper" parents="125 3798 1354"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1777,a,3816,a),flip(a)].">
      <j1 rule="hyper" parents="1777 3816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      x * (y * L(y \ (x \ 1),z,u)) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1613,a,3816,a)].">
      <j1 rule="hyper" parents="1613 3816"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = x * (y * ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(336,a,3816,a),flip(a)].">
      <j1 rule="hyper" parents="336 3816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,2520,a(flip),b,3816,a),flip(a)].">
      <j1 rule="hyper" parents="60 2520 3816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      (x \ y) * (x \ (y * L(y \ x,z,u))) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,2520,a(flip),b,3816,a(flip))].">
      <j1 rule="hyper" parents="129 2520 3816"/>
    </justification>
  </clause>

  <clause id="3825">
    <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(129,a,3816,a(flip),b,2158,a),flip(a)].">
      <j1 rule="hyper" parents="129 3816 2158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x \ 1,y,z),x) = (x \ L(x,y,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(3816(a,1),94(a,2,1))].">
      <j1 rule="para" parents="3816 94"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) = z
    ]]></literal>
    <justification jstring="[para(3816(a,1),336(a,1))].">
      <j1 rule="para" parents="3816 336"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      R(T(x / y,y \ L(y,z,u)),y,L(y \ 1,z,u)) = (y * L(y \ 1,z,u)) \ (x * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3816(a,1),1373(a,1,1,2))].">
      <j1 rule="para" parents="3816 1373"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3816(a,1),1777(a,1))].">
      <j1 rule="para" parents="3816 1777"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(3816(a,1),2314(a,1,1))].">
      <j1 rule="para" parents="3816 2314"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3816(a,1),2473(a,1,1))].">
      <j1 rule="para" parents="3816 2473"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[para(3816(a,1),2555(a,1,2))].">
      <j1 rule="para" parents="3816 2555"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(3816(a,1),2554(a,2,1))].">
      <j1 rule="para" parents="3816 2554"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      x * ((x * L(x \ 1,y,z)) * u) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(3816(a,1),2917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3816 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      ((1 / x) \ y) * L((x \ y) \ (x \ 1),z,u) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3816(a,1),2587(a,2,2))].">
      <j1 rule="para" parents="3816 2587"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      T(x \ L(x,y,z),x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,3833,a)].">
      <j1 rule="hyper" parents="51 3833"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3833,a(flip),b,108,a(flip))].">
      <j1 rule="hyper" parents="129 3833 108"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3833(a,1),308(a,1,2))].">
      <j1 rule="para" parents="3833 308"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3833(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3833 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,2473,a,b,3838,a),flip(a)].">
      <j1 rule="hyper" parents="32 2473 3838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) / L(y,z,u) = R(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3838(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3838 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x \ L(x,y,z)) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(3838(a,1),92(a,1,1))].">
      <j1 rule="para" parents="3838 92"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(3838(a,1),693(a,1,2))].">
      <j1 rule="para" parents="3838 693"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2499,a,3839,a)].">
      <j1 rule="hyper" parents="2499 3839"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3839(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3839 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      x \ ((y * y) * (((y * y) \ x) \ L((y * y) \ x,z,u))) = L(((y * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(1439,a,3817,a)].">
      <j1 rule="hyper" parents="1439 3817"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      x * L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3817(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3817 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3852">
    <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(3817(a,1),1834(a,2,2,1))].">
      <j1 rule="para" parents="3817 1834"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3816,a,b,3846,a),flip(a)].">
      <j1 rule="hyper" parents="370 3816 3846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,209,a(flip),b,3846,a(flip))].">
      <j1 rule="hyper" parents="129 209 3846"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      (x * x) * (x \ L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,3846,a(flip),b,551,a)].">
      <j1 rule="hyper" parents="129 3846 551"/>
    </justification>
  </clause>

  <clause id="3857">
    <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(3846(a,1),2808(a,1,3))].">
      <j1 rule="para" parents="3846 2808"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3846(a,1),2958(a,1,1))].">
      <j1 rule="para" parents="3846 2958"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(3846(a,1),2970(a,1,1))].">
      <j1 rule="para" parents="3846 2970"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3846(a,1),3042(a,1,2))].">
      <j1 rule="para" parents="3846 3042"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3846(a,1),3079(a,1,3))].">
      <j1 rule="para" parents="3846 3079"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3846(a,1),3369(a,1,3))].">
      <j1 rule="para" parents="3846 3369"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3846(a,1),3389(a,1,2))].">
      <j1 rule="para" parents="3846 3389"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,3799,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 3799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,3799,a,b,2160,a(flip))].">
      <j1 rule="hyper" parents="125 3799 2160"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 != u \ (x * x)
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3799(a,2),45(a,1))].">
      <j1 rule="para" parents="3799 45"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      R(x,y,L(1 / z,u,w)) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a,b,3802,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),3803(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      a(L(x \ y,x \ y,y),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3418(a,1),3803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3418 3803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(74(a,1),3804(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="74 3804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(74(a,1),3805(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 3805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      L(x,L(L(y,y,y),z,u),w) = L(x,L(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(1322(a,1),3805(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1322 3805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(1349,a,3806,a),flip(a)].">
      <j1 rule="hyper" parents="1349 3806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2552,a(flip),b,3806,a)].">
      <j1 rule="hyper" parents="60 2552 3806"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      L(x / (y * y),z,u) = L(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,3806,a(flip),b,874,a),flip(a)].">
      <j1 rule="hyper" parents="128 3806 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,3806,a(flip),b,1598,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 3806 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      L((x * y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3812(a,2),41(a,1))].">
      <j1 rule="para" parents="3812 41"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      (x * ((y \ L(y,z,u)) * y)) * (1 / y) = (x * L(y \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(3832(a,1),1768(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3832 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(960,a,3855,a)].">
      <j1 rule="hyper" parents="960 3855"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      (1 / x) * L(1 / x,y,z) = x \ L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(947,a,3855,a),flip(a)].">
      <j1 rule="hyper" parents="947 3855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <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(3855(a,1),3038(a,1,2))].">
      <j1 rule="para" parents="3855 3038"/>
    </justification>
  </clause>

  <clause id="3884">
    <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(3855(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="3855 3075"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(501,a,3881,a)].">
      <j1 rule="hyper" parents="501 3881"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      a((x \ L(x,y,z)) * u,w,v5) = a((x * L(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3881(a,1),2960(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3881 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3885(a,1),2720(a,1,1))].">
      <j1 rule="para" parents="3885 2720"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      x * ((y * y) \ (L(x / (y * y),z,u) \ (x / (y * y)))) = L(1 / (x / (y * y)),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,935,a(flip),b,3864,a)].">
      <j1 rule="hyper" parents="370 935 3864"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3864(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3864 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) = y \ (x * (L(1 / (x \ y),z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(3864(a,2),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3864 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      R(L(x,y,z) / x,x,L(x,y,z) \ x) = x / (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3864(a,2),428(a,2,2))].">
      <j1 rule="para" parents="3864 428"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * (L(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(3417(a,1),3864(a,1,1))].">
      <j1 rule="para" parents="3417 3864"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      L(x,y,z) \ x != x \ u
    ]]></literal>
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(3865(a,1),44(a,1))].">
      <j1 rule="para" parents="3865 44"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * (L(1 / (x \ y),z,u) \ 1)) = w
    ]]></literal>
    <justification jstring="[para(3865(a,1),798(a,1,1))].">
      <j1 rule="para" parents="3865 798"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      x \ (((1 / x) \ (L(1 / x,y,z) \ 1)) * u) = (x \ 1) \ ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(3865(a,1),2132(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3865 2132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u * z)) = L(x,y,R(u,z,z) \ (u * z))
    ]]></literal>
    <justification jstring="[para(3734(a,1),3871(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3734 3871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x \ 1,y,z)) = (1 / L(x \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(790,a,3872,a),flip(a)].">
      <j1 rule="hyper" parents="790 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ (u \ w),L(x,y,z),u) = (u * L(x \ 1,y,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(60,a,344,a(flip),b,3872,a),flip(a)].">
      <j1 rule="hyper" parents="60 344 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      L(x * (y * y),z,u) * w = L(x,z,u) * ((y * y) * w)
    ]]></literal>
    <justification jstring="[para(3874(a,2),29(a,1,1))].">
      <j1 rule="para" parents="3874 29"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      L(x * (y * y),z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ (L(x,z,u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(3874(a,2),749(a,1,1))].">
      <j1 rule="para" parents="3874 749"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      x \ L(y * (z * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (x \ L(y,u,w)) * (z * z) = v5
    ]]></literal>
    <justification jstring="[para(3874(a,2),867(a,1,2))].">
      <j1 rule="para" parents="3874 867"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      (x * L(y * (z * z),u,w)) * v5 = (x * L(y,u,w)) * ((z * z) * v5)
    ]]></literal>
    <justification jstring="[para(3874(a,2),122(a,1,1,2))].">
      <j1 rule="para" parents="3874 122"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      L(x * y,z,u) != w * y
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3875(a,1),41(a,1))].">
      <j1 rule="para" parents="3875 41"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      L(x * (x * y),z,u) = x * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2949,a,3876,a),flip(a)].">
      <j1 rule="hyper" parents="2949 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      L(x,y,z) / (x * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(310(a,1),3876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L(x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(215,a,3906,a)].">
      <j1 rule="hyper" parents="215 3906"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      L(x,y,z) \ L(x \ 1,y,z) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,3906,a(flip),b,603,a)].">
      <j1 rule="hyper" parents="125 3906 603"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      (x * x) * (L(x,y,z) \ u) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3906(a,1),512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3906 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      L(x,y,z) * ((x * x) \ u) = L(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[para(3906(a,1),935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3906 935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3906(a,1),3097(a,1,2))].">
      <j1 rule="para" parents="3906 3097"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      L((x \ 1) \ L(x \ (x \ y),z,u),x,x) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2111,a,3877,a)].">
      <j1 rule="hyper" parents="2111 3877"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      L(x \ (x \ y),z,u) = x \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,3877,a),flip(a)].">
      <j1 rule="hyper" parents="135 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,63,a(flip),b,3877,a),flip(a)].">
      <j1 rule="hyper" parents="125 63 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),3877(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x \ L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(3877(a,2),719(a,1))].">
      <j1 rule="para" parents="3877 719"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ (x \ 1),u,w) = L(x,y,z) \ L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1772(a,1),3877(a,1,2,1,2))].">
      <j1 rule="para" parents="1772 3877"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ (x * L(x,y,z)),u,w) = (x \ 1) \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3881(a,1),3877(a,1,2,1,2))].">
      <j1 rule="para" parents="3881 3877"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(3877(a,1),3875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3877 3875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(156,a,3887,a)].">
      <j1 rule="hyper" parents="156 3887"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(3887(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3887 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      x * (x * L(x \ y,z,u)) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),3905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 3905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      (x * y) * ((x * y) * L(L(z,y,x),u,w)) = L((x * y) * (x * (y * z)),u,w)
    ]]></literal>
    <justification jstring="[para(92(a,1),3905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="92 3905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      a(x,L((1 / (y \ z)) \ 1,y \ z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(3418(a,1),3911(a,2,2))].">
      <j1 rule="para" parents="3418 3911"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3914(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3914 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      x * L(L(x \ (x \ y),z,u),w,v5) = x \ L(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3914(a,2),3877(a,1,2,1))].">
      <j1 rule="para" parents="3914 3877"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2128,a,3916,a)].">
      <j1 rule="hyper" parents="2128 3916"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      L(x * (y * x),z,u) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(129,a,871,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="129 871 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(3916(a,2),3875(a,1,1))].">
      <j1 rule="para" parents="3916 3875"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(230,a,3920,a),flip(a)].">
      <j1 rule="hyper" parents="230 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3920(a,2),41(a,1))].">
      <j1 rule="para" parents="3920 41"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(78(a,1),3920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="78 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(344(a,1),3920(a,2,1,2))].">
      <j1 rule="para" parents="344 3920"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(655(a,1),3920(a,2,1,2))].">
      <j1 rule="para" parents="655 3920"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      L((x \ y) * x,x,x) = ((x \ 1) * y) * x
    ]]></literal>
    <justification jstring="[para(2072(a,1),3920(a,2,1))].">
      <j1 rule="para" parents="2072 3920"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(147,a,3932,a)].">
      <j1 rule="hyper" parents="147 3932"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,3932,a)].">
      <j1 rule="hyper" parents="135 3932"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3932(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3932 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      a(x,x,y) * L(y,x,x) = y
    ]]></literal>
    <justification jstring="[para(1362(a,1),3932(a,1,1))].">
      <j1 rule="para" parents="1362 3932"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,3942,a)].">
      <j1 rule="hyper" parents="135 3942"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      x \ (a(y,y,x) * (L(x,y,y) * z)) = L(z,L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[para(3942(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3942 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      a(x,x,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3398,a(flip),b,3943,a),flip(a)].">
      <j1 rule="hyper" parents="36 3398 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      K(x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1709,a,b,3946,a)].">
      <j1 rule="hyper" parents="370 1709 3946"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      a((x \ 1) \ y,(x \ 1) \ y,x \ y) = K((x \ 1) \ y,((x \ 1) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3082,a(flip),b,3947,a)].">
      <j1 rule="hyper" parents="370 3082 3947"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      (x \ 1) \ a(x,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,3947,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="125 3947 1724"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      x * a(x,x,x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(3950(a,1),2082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3950 2082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * a(x,x,x),y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3950(a,1),3916(a,2,2,1))].">
      <j1 rule="para" parents="3950 3916"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      x \ L(x,x,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,3951,a)].">
      <j1 rule="hyper" parents="135 3951"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2498,a,3938,a)].">
      <j1 rule="hyper" parents="2498 3938"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      L(x,y,z) \ x != u * x
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3954(a,1),41(a,1))].">
      <j1 rule="para" parents="3954 41"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,L(z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(3954(a,1),3079(a,1,3))].">
      <j1 rule="para" parents="3954 3079"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3954(a,1),3602(a,1,2))].">
      <j1 rule="para" parents="3954 3602"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3921(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3921 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      x \ L(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3924(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3924 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      L(x * y,z,u) \ ((x * x) * w) = L((1 / x) * y,z,u) \ w
    ]]></literal>
    <justification jstring="[para(3924(a,1),1751(a,1,1))].">
      <j1 rule="para" parents="3924 1751"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      L(x,y,L(L(z \ u,w,v5),z,z)) = L(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(3924(a,1),3367(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3924 3367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      L(x * (y * x),z,u) != x * w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(3930(a,2),40(a,1))].">
      <j1 rule="para" parents="3930 40"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      L(x * y,z,u) / y = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(147,a,3931,a)].">
      <j1 rule="hyper" parents="147 3931"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3934(a,1),73(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3934 73"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x != w
    ]]></literal>
    <literal><![CDATA[
      L(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3964(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3964 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2520(a,1),3850(a,1))].">
      <j1 rule="para" parents="2520 3850"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      L(x,y * L(y,z,z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),3785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1362 3785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      L(x,a(y,y,y \ z),u) = L(x,(y \ z) * ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[para(586(a,1),3968(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="586 3968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      ((x \ 1) \ y) \ L((x \ 1) \ z,u,w) = (x \ y) \ L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,3792,a(flip),b,1250,a),flip(a)].">
      <j1 rule="hyper" parents="125 3792 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),v5) = a(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3792(a,1),3040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3792 3040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      a(x,y,L((z \ 1) \ u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(3792(a,1),3077(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3792 3077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      L(x,y,L((z \ 1) \ u,w,v5)) = L(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(3792(a,1),3362(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3792 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      L(x,L((y \ 1) \ z,u,w),v5) = L(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3792(a,1),3387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3792 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      a(L((1 / x) * y,z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(314(a,1),3793(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="314 3793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      a(L(x \ L(x,y,z),u,w),v5,v6) = a(L(x * L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(3855(a,1),3793(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3855 3793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3977">
    <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(92(a,1),3794(a,1,3,1))].">
      <j1 rule="para" parents="92 3794"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(3855(a,1),3794(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3855 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      L(x,y,L((1 / z) * u,w,v5)) = L(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(314(a,1),3795(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="314 3795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      L(x,y,L(z * (z * u),w,v5)) = L(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(92(a,1),3795(a,1,3,1))].">
      <j1 rule="para" parents="92 3795"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6)) = L(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(3855(a,1),3795(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3855 3795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      L(x,L((1 / y) * z,u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(314(a,1),3796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="314 3796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      L(x,L(y * (y * z),u,w),v5) = L(x,L(L(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(92(a,1),3796(a,1,2,1))].">
      <j1 rule="para" parents="92 3796"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(3855(a,1),3796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3855 3796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(254(a,1),3800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,x,x) = L(x,y,z) \ (x * (x * u))
    ]]></literal>
    <justification jstring="[para(92(a,1),3800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="92 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      L(x,y,z) \ ((1 / x) \ u) = x \ (L(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3800(a,1),2180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3800 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (1 / x) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(3985(a,1),3939(a,1,1))].">
      <j1 rule="para" parents="3985 3939"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,x \ y,x) = ((x \ y) \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(456(a,1),3842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="456 3842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,251,a(flip),b,3854,a)].">
      <j1 rule="hyper" parents="370 251 3854"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(251(a,1),3990(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="251 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(135,a,3991,a)].">
      <j1 rule="hyper" parents="135 3991"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,3991,a(flip),b,3254,a),flip(a)].">
      <j1 rule="hyper" parents="124 3991 3254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,3993,a(flip),b,3268,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 3993 3268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,3994,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 3994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,3994,a(flip),b,3222,a),flip(a)].">
      <j1 rule="hyper" parents="128 3994 3222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(87(a,1),3995(a,1,2,1))].">
      <j1 rule="para" parents="87 3995"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1618,a(flip),b,3996,a),flip(a)].">
      <j1 rule="hyper" parents="370 1618 3996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3996(a,2),1622(a,1))].">
      <j1 rule="para" parents="3996 1622"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),3998(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),3998(a,1,2,1))].">
      <j1 rule="para" parents="7 3998"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,934,a,b,4001,a)].">
      <j1 rule="hyper" parents="60 934 4001"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(3992(a,1),344(a,1,1))].">
      <j1 rule="para" parents="3992 344"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1714,a,4000,a)].">
      <j1 rule="hyper" parents="1714 4000"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(4000(a,1),3441(a,1,3))].">
      <j1 rule="para" parents="4000 3441"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1838,a,4006,a),flip(a)].">
      <j1 rule="hyper" parents="1838 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(4005(a,1),3588(a,1,2))].">
      <j1 rule="para" parents="4005 3588"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z)) = a(x,y,(z \ u) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(586(a,1),3861(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="586 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ L((z \ 1) * u,u,z)) = a(x,y,(z \ 1) * (u * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(1502(a,1),3861(a,2,3))].">
      <j1 rule="para" parents="1502 3861"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x * L(x,y,z),x) = L(x,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(798,a,3863,a),flip(a)].">
      <j1 rule="hyper" parents="798 3863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      L(x,y,z) * L(u,x * L(x,y,z),x) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,3863,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="129 3863 93"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      R(x,y,L(1 / z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3868(a,2),2741(a,1))].">
      <j1 rule="para" parents="3868 2741"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      (1 / (x \ y)) * L(1 / (x \ y),x \ y,y) = (x \ y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3418(a,1),3882(a,2,2))].">
      <j1 rule="para" parents="3418 3882"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      (x \ 1) \ (x * (L(x,y,z) \ u)) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(1142,a,3909,a)].">
      <j1 rule="hyper" parents="1142 3909"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x * x) * u) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(1385,a,3909,a(flip))].">
      <j1 rule="hyper" parents="1385 3909"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,3909,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="129 3909 939"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ u) * w) = (L(x \ 1,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(3909(a,1),28(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3909 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(3909(a,1),854(a,1,1))].">
      <j1 rule="para" parents="3909 854"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,x,x) = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(3909(a,1),2096(a,1,1))].">
      <j1 rule="para" parents="3909 2096"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,v5) = a(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3909(a,1),2955(a,1,1))].">
      <j1 rule="para" parents="3909 2955"/>
    </justification>
  </clause>

  <clause id="4023">
    <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(3909(a,1),3144(a,1,3,2))].">
      <j1 rule="para" parents="3909 3144"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3909(a,1),3381(a,1,2))].">
      <j1 rule="para" parents="3909 3381"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(3909(a,1),3540(a,1,2))].">
      <j1 rule="para" parents="3909 3540"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      L(1 / x,y,z) \ (L(x,u,w) \ v5) = L(x,y,z) \ (L(x \ 1,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(3909(a,1),3800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3909 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,3910,a(flip),b,2185,a),flip(a)].">
      <j1 rule="hyper" parents="129 3910 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      L(x,y,z) * ((x * x) \ u) != w * u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,y,z) = w
    ]]></literal>
    <justification jstring="[para(3910(a,2),41(a,1))].">
      <j1 rule="para" parents="3910 41"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(940(a,1),3910(a,1,2)),flip(a)].">
      <j1 rule="para" parents="940 3910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(281(a,1),3957(a,2,3))].">
      <j1 rule="para" parents="281 3957"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      x \ (y * K(y \ x,x \ y)) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(721,a,4008,a)].">
      <j1 rule="hyper" parents="721 4008"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      L(x,y,z) * ((x * x) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(4016(a,1),387(a,1))].">
      <j1 rule="para" parents="4016 387"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(1362(a,1),4030(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1362 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,u,z) \ ((z \ 1) * u)) = a(x,y,(z \ 1) * (u * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(1502(a,1),4030(a,2,3))].">
      <j1 rule="para" parents="1502 4030"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      L(x \ (1 / (1 / (y \ (y * x)))),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4031(a,1),616(a,1,1,2))].">
      <j1 rule="para" parents="4031 616"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      L(x,L(L(y,y,y),z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3872,a(flip),b,3873,a),flip(a)].">
      <j1 rule="hyper" parents="370 3872 3873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      L(x,L(L(y,z,u),y,y),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(25(a,1),4036(a,1,2))].">
      <j1 rule="para" parents="25 4036"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x / y) * L((x / y) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / y) \ L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(77(a,1),3927(a,1,2,1,2))].">
      <j1 rule="para" parents="77 3927"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      x * L(L(x \ 1,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ L(L(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(3817(a,1),3927(a,1,2,1))].">
      <j1 rule="para" parents="3817 3927"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      L(x,y,z) * (u * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * (u * u),y,z) = w
    ]]></literal>
    <justification jstring="[para(3780(a,1),3966(a,1,1))].">
      <j1 rule="para" parents="3780 3966"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      L(x,y * ((1 / z) * T(u,z)),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(1276(a,1),3772(a,1,2,2))].">
      <j1 rule="para" parents="1276 3772"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L((x * y) \ (x * (y * z)),u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),3823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),3823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = (x \ (x / y)) \ L((((x * y) \ x) \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3503(a,1),3823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3503 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (x \ y) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3823(a,1),3838(a,1,1))].">
      <j1 rule="para" parents="3823 3838"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (x \ y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3823(a,1),3847(a,1,1))].">
      <j1 rule="para" parents="3823 3847"/>
    </justification>
  </clause>

  <clause id="4048">
    <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(3824(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3824 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ u) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (u * L(u \ (x \ u),y,z)) = v5
    ]]></literal>
    <justification jstring="[para(3831(a,2),721(a,1))].">
      <j1 rule="para" parents="3831 721"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(125,a,3840,a(flip),b,1672,a)].">
      <j1 rule="hyper" parents="125 3840 1672"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (L(1 / x,y,z) \ (1 / x)),y,z) = L(x,y,z) \ ((x * x) * 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3800,a,b,3915,a),flip(a)].">
      <j1 rule="hyper" parents="370 3800 3915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      x * L(x \ (y * (x \ 1)),z,u) = L(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1349,a,3929,a),flip(a)].">
      <j1 rule="hyper" parents="1349 3929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),v5,v6)) = L(x,y,L(z * R(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(2041(a,1),3973(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2041 3973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      L(x,L(y \ R(y,z,u),w,v5),v6) = L(x,L(y * R(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(2041(a,1),3974(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2041 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),3982(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 3982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(11(a,2),3997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(505,a,4057,a),flip(a)].">
      <j1 rule="hyper" parents="505 4057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2893,a(flip),b,4058,a),flip(a)].">
      <j1 rule="hyper" parents="60 2893 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1334,a,4059,a)].">
      <j1 rule="hyper" parents="1334 4059"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,z) \ 1 = x
    ]]></literal>
    <justification jstring="[para(4059(a,1),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4059 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * (L(x \ 1,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,2160,a(flip),b,4015,a)].">
      <j1 rule="hyper" parents="129 2160 4015"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ z) = x * (L(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,457,a(flip),b,4015,a)].">
      <j1 rule="hyper" parents="129 457 4015"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2161(a,1),4015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2161 4015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x \ y,x) \ z) = ((x \ y) \ 1) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4065(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      x * (L(x,x,y) \ (((y * x) \ y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * z = u
    ]]></literal>
    <justification jstring="[para(4065(a,1),742(a,1))].">
      <j1 rule="para" parents="4065 742"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ ((1 / x) \ u))) = L(x \ 1,y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(2208,a,4017,a),flip(a)].">
      <j1 rule="hyper" parents="2208 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,3864,a,b,4017,a),flip(a)].">
      <j1 rule="hyper" parents="370 3864 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      x * (L(x \ 1,y,z) * (u * u)) = L(x,y,z) * (x \ (u * u))
    ]]></literal>
    <justification jstring="[para(519(a,1),4027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="519 4027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      L(L(x,y,z) * (x \ u),x,x) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(4029(a,1),2188(a,1,1))].">
      <j1 rule="para" parents="4029 2188"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      L((1 / x) \ x,y,z) = ((1 / x) \ (x * (x \ (1 / x)))) * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1432(a,1),4046(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1432 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      (x \ (y * L(y \ (1 / x),z,u))) * ((1 / x) \ y) = (x \ 1) * (x \ L((1 / x) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(4046(a,1),2102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4046 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      x * ((1 / x) * (y * (x \ 1))) = L(y,x,x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(586(a,1),4053(a,1,2))].">
      <j1 rule="para" parents="586 4053"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      (x \ 1) * (x * (y * ((x \ 1) \ 1))) = L(y,x,x) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2082(a,1),4053(a,1,2))].">
      <j1 rule="para" parents="2082 4053"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ (L(x,y,z) \ x),u,w) = L(x,u,w) * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2162(a,1),4053(a,1,2,1,2))].">
      <j1 rule="para" parents="2162 4053"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,3887,a(flip),b,4066,a),flip(a)].">
      <j1 rule="hyper" parents="370 3887 4066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) != (x \ 1) \ w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(4066(a,2),44(a,1))].">
      <j1 rule="para" parents="4066 44"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(4066(a,2),3959(a,1))].">
      <j1 rule="para" parents="4066 3959"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3985,a,b,4079,a)].">
      <j1 rule="hyper" parents="370 3985 4079"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,4079,a(flip),b,4079,a),flip(a)].">
      <j1 rule="hyper" parents="370 4079 4079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      L(x,x,y) \ x = ((y * x) \ y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,457,a(flip),b,4079,a),flip(a)].">
      <j1 rule="hyper" parents="60 457 4079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x \ 1,x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2207,a,4070,a)].">
      <j1 rule="hyper" parents="2207 4070"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,L(1 / x,y,z),L(1 / x,y,z)) = ((x \ 1) * (L(x \ 1,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(4070(a,2),2072(a,2,1))].">
      <j1 rule="para" parents="4070 2072"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      L(x \ 1,y,z) \ K(x,x \ 1) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1716(a,1),4086(a,1,2))].">
      <j1 rule="para" parents="1716 4086"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      L(x,y,L((z \ 1) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(936(a,1),3810(a,1,3,1))].">
      <j1 rule="para" parents="936 3810"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(77(a,1),3926(a,1,2,1))].">
      <j1 rule="para" parents="77 3926"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,3935,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 3935 13"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ (y \ z))) * x,y \ 1,y) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(188(a,1),3935(a,2,1,2))].">
      <j1 rule="para" parents="188 3935"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,3936,a(flip),b,300,a),flip(a)].">
      <j1 rule="hyper" parents="125 3936 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,x,x) = x * (L(x,y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,3986,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 3986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      L(x,y,y) != y * (y * (L(y,z,u) \ w))
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(4020(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="4020 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(2186,a,4072,a)].">
      <j1 rule="hyper" parents="2186 4072"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,x,x) = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(2160(a,1),4100(a,2,2))].">
      <j1 rule="para" parents="2160 4100"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      L(x,y,(z * u) / (w * w)) = L(x,y,z * ((w * w) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3760,a(flip),b,3761,a),flip(a)].">
      <j1 rule="hyper" parents="60 3760 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3382,a(flip),b,4105,a),flip(a)].">
      <j1 rule="hyper" parents="60 3382 4105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3378,a,b,4106,a)].">
      <j1 rule="hyper" parents="60 3378 4106"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),4106(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) \ w)) = L(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(936(a,1),4106(a,1,3,2))].">
      <j1 rule="para" parents="936 4106"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      L(x,y,z * (u \ L(u,w,v5))) = L(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(3855(a,1),4106(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3855 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      L(x,y,z * (u \ R(u,w,v5))) = L(x,y,z * (u * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2041(a,1),4110(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2041 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      L((x \ (1 / x)) * y,z,u) = (x \ (1 / x)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(320(a,1),3807(a,1,1,1))].">
      <j1 rule="para" parents="320 3807"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      L((x \ (1 / x)) * y,z,u) = (x \ 1) * (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,4114,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 4114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      L((x \ 1) * (x \ y),z,u) = (x \ 1) * (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1214(a,1),4115(a,1,1))].">
      <j1 rule="para" parents="1214 4115"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      (x \ 1) * L((y * y) * L(z,u,w),v5,v6) = (x \ (y * y)) * L(L(z,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,1),3808(a,2,2))].">
      <j1 rule="para" parents="25 3808"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(3816(a,1),3835(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3816 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * u) = x * ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,4118,a)].">
      <j1 rule="hyper" parents="125 172 4118"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      L(x,y,R(z,u,u) \ (z * u)) = L(x,y,L(u,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3871,a(flip),b,3897,a),flip(a)].">
      <j1 rule="hyper" parents="60 3871 3897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      x \ L(L(x * y,z,u),w,v5) = x * L(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),3928(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      a(x,L(y * z,u,w) \ ((y * y) * 1),v5) = a(x,L((1 / y) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3961(a,2),3050(a,1,2))].">
      <j1 rule="para" parents="3961 3050"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      x * L((x \ 1) * (y * y),z,u) = L(x,z,u) * (x \ (y * y))
    ]]></literal>
    <justification jstring="[para(3874(a,2),4071(a,1,2))].">
      <j1 rule="para" parents="3874 4071"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      L(x * L(L(x \ y,z,u),w,v5),x,x) = (1 / x) * L(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4121(a,1),586(a,1,1))].">
      <j1 rule="para" parents="4121 586"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * u)) = x * L(x \ (u * u),y,z)
    ]]></literal>
    <justification jstring="[para(519(a,1),4123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="519 4123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      R(x,y,L(z,z,y)) * (y / z) = (x * y) * L(1 / z,z,y)
    ]]></literal>
    <justification jstring="[para(3802(a,1),3419(a,1,1))].">
      <j1 rule="para" parents="3802 3419"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(x,x,y),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3805,a(flip),b,3421,a)].">
      <j1 rule="hyper" parents="60 3805 3421"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z * u,w) = v5
    ]]></literal>
    <justification jstring="[para(3380(a,1),3550(a,1))].">
      <j1 rule="para" parents="3380 3550"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(313(a,1),4128(a,1,2,1))].">
      <j1 rule="para" parents="313 4128"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(594(a,1),4128(a,1,2))].">
      <j1 rule="para" parents="594 4128"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * ((y \ z) * y),u) = w
    ]]></literal>
    <justification jstring="[para(1066(a,1),4129(a,1,2))].">
      <j1 rule="para" parents="1066 4129"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * u,w) = v5
    ]]></literal>
    <justification jstring="[para(3765(a,2),4129(a,1))].">
      <j1 rule="para" parents="3765 4129"/>
    </justification>
  </clause>

  <clause id="4133">
    <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(3846(a,1),4129(a,1,2))].">
      <j1 rule="para" parents="3846 4129"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3691,a,3315,a)].">
      <j1 rule="hyper" parents="3691 3315"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,4136,a)].">
      <j1 rule="hyper" parents="156 4136"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),4137(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,4138,a)].">
      <j1 rule="hyper" parents="2810 4138"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1716(a,2),4139(a,1,3))].">
      <j1 rule="para" parents="1716 4139"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4140(a,1),327(a,1,1))].">
      <j1 rule="para" parents="4140 327"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (y \ x) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(456(a,1),3989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="456 3989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) * z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4142(a,1),2960(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4142 2960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(304(a,1),4004(a,2,1))].">
      <j1 rule="para" parents="304 4004"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = (x \ y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3418(a,1),4014(a,1,2))].">
      <j1 rule="para" parents="3418 4014"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      L((x \ y) \ (y \ x),x \ y,y \ x) = ((y \ x) \ (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(4145(a,1),1491(a,2,1))].">
      <j1 rule="para" parents="4145 1491"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      x * ((1 / x) * (y * ((x \ 1) \ 1))) = L(y,x,x) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,951,a(flip),b,4077,a)].">
      <j1 rule="hyper" parents="60 951 4077"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      L(x,y,L(z * R(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(2041(a,1),4092(a,1,3,1))].">
      <j1 rule="para" parents="2041 4092"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      L(x,y,(z * (u \ (z * z))) \ w) = L(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[para(578(a,1),3591(a,1,3,1,2))].">
      <j1 rule="para" parents="578 3591"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(4150(a,1),3758(a,1))].">
      <j1 rule="para" parents="4150 3758"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x * L(x,y,z)) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(3862(a,1),3844(a,1,2))].">
      <j1 rule="para" parents="3862 3844"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      (x * L(y \ 1,z,u)) * y = (x * L(y,z,u)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(3838(a,1),3880(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3838 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      R(x \ L(x,y,z),x,L(x,y,z) \ x) = x / (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3839(a,1),3891(a,1,1))].">
      <j1 rule="para" parents="3839 3891"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      L(x,y,L(z * L(z,u,w),z,w * u)) = L(x,y,((w * u) * z) \ (w * (u * z)))
    ]]></literal>
    <justification jstring="[para(670(a,1),3981(a,1,3)),flip(a)].">
      <j1 rule="para" parents="670 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x * L(x,y,z),x) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,4011,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x * L(x,y,z),x) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * (x * (L(x,y,z) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(4011(a,2),2195(a,1))].">
      <j1 rule="para" parents="4011 2195"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = L(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(2183,a,4069,a),flip(a)].">
      <j1 rule="hyper" parents="2183 4069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = x \ (L(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3987,a(flip),b,4159,a),flip(a)].">
      <j1 rule="hyper" parents="370 3987 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ u) = x \ (L(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4066,a(flip),b,4160,a)].">
      <j1 rule="hyper" parents="60 4066 4160"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      (x \ 1) * (x \ (L(1 / x,y,z) \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(129,a,4160,a(flip),b,4066,a(flip))].">
      <j1 rule="hyper" parents="129 4160 4066"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) \ ((x \ y) \ z) = (x \ y) \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(3418(a,1),4160(a,2,2,1))].">
      <j1 rule="para" parents="3418 4160"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ L(u,L(x,y,z),L(x,y,z))) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2072(a,1),4161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2072 4161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      (1 / x) * (L(1 / x,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,4162,a(flip),b,2073,a),flip(a)].">
      <j1 rule="hyper" parents="129 4162 2073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      ((1 / x) * y) / (x * (L(x,z,u) \ y)) = L(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(4166(a,1),2159(a,1,2))].">
      <j1 rule="para" parents="4166 2159"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x * L(x,y,z)) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,4118,a(flip),b,4152,a),flip(a)].">
      <j1 rule="hyper" parents="370 4118 4152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)) = L(u,x * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(31,a,4012,a,b,4168,a)].">
      <j1 rule="hyper" parents="31 4012 4168"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      L(x,y \ 1,y * L(y,z,u)) = L(x,y * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3401,a,b,4170,a)].">
      <j1 rule="hyper" parents="370 3401 4170"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      (x * (x * L(x,y,z))) \ (x * (x * (L(x,y,z) * u))) = L(L(u,L(x,y,z),x),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,621,a,b,4170,a)].">
      <j1 rule="hyper" parents="60 621 4170"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4171(a,1),3530(a,1))].">
      <j1 rule="para" parents="4171 3530"/>
    </justification>
  </clause>

  <clause id="4174">
    <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(370,a,4170,a(flip),b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="370 4170 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,x,x * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(4169(a,2),4173(a,1))].">
      <j1 rule="para" parents="4169 4173"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) \ R(x \ L(x,y,z),u,w))) = L(R((x \ L(x,y,z)) \ 1,u,w),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1987(a,1),4174(a,1,2,2))].">
      <j1 rule="para" parents="1987 4174"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      (x \ y) * ((((y \ x) \ 1) \ 1) \ z) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(3498(a,1),3436(a,1,2,1))].">
      <j1 rule="para" parents="3498 3436"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / (z \ 1)) = x \ (((1 / x) \ y) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2480(a,1),3457(a,1,2))].">
      <j1 rule="para" parents="2480 3457"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3445(a,1),3598(a,1,1))].">
      <j1 rule="para" parents="3445 3598"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,(z \ u) * ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(586(a,1),4009(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="586 4009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      L(x \ (1 / (1 / x)),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4(a,1),4035(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 4035"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      L(K(x \ 1,x),x,y) = K((y * x) \ y,y \ (y * x))
    ]]></literal>
    <justification jstring="[para(2099(a,1),4181(a,1,1))].">
      <j1 rule="para" parents="2099 4181"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      L((1 / x) \ x,y,z) = 1 * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(295(a,1),4074(a,2,1))].">
      <j1 rule="para" parents="295 4074"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      L((1 / x) \ x,y,z) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,4183,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 4183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      (x * y) * ((1 / z) \ z) = x * (y * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,4184,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 4184 13"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      x \ (y * ((1 / z) \ z)) = (x \ y) * ((1 / z) \ z)
    ]]></literal>
    <justification jstring="[para(4184(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="4184 617"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      x \ (y * (z * ((1 / u) \ u))) = (x \ (y * z)) * ((1 / u) \ u)
    ]]></literal>
    <justification jstring="[para(4186(a,1),4187(a,1,2))].">
      <j1 rule="para" parents="4186 4187"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) \ ((x \ y) \ z) != (x \ y) \ u
    ]]></literal>
    <literal><![CDATA[
      (y \ x) \ z = u
    ]]></literal>
    <justification jstring="[para(4163(a,2),44(a,1))].">
      <j1 rule="para" parents="4163 44"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) \ ((y \ x) \ z) = (y \ x) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(3498(a,1),4163(a,1,1))].">
      <j1 rule="para" parents="3498 4163"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3450,a(flip),b,4179,a)].">
      <j1 rule="hyper" parents="60 3450 4179"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(15(a,2),4191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 4191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,4192,a,b,3617,a)].">
      <j1 rule="hyper" parents="129 4192 3617"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1508(a,1),4192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1508 4192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3621,a,4194,a)].">
      <j1 rule="hyper" parents="3621 4194"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(3614(a,1),4193(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3614 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(4196(a,2),3568(a,1,2))].">
      <j1 rule="para" parents="4196 3568"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * ((x \ 1) \ u)) = (x \ L(1 / x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,1608,a(flip),b,3826,a),flip(a)].">
      <j1 rule="hyper" parents="60 1608 3826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) \ ((x \ 1) \ u)) = (x \ L(1 / x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,4119,a(flip),b,4198,a)].">
      <j1 rule="hyper" parents="60 4119 4198"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,3325,a,b,3958,a),flip(a)].">
      <j1 rule="hyper" parents="32 3325 3958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      L(x,y,z) != K(L(u,y,z) \ 1,L(u,y,z))
    ]]></literal>
    <literal><![CDATA[
      K(u \ 1,u) = x
    ]]></literal>
    <justification jstring="[para(4200(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="4200 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      x \ ((y * x) * L((y * x) \ x,z,u)) = T(y,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),4044(a,2,2,1))].">
      <j1 rule="para" parents="17 4044"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ x),z,u))) = T(y,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1598(a,1),4202(a,1,2))].">
      <j1 rule="para" parents="1598 4202"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = y \ ((x \ L(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3834(a,1),4203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3834 4203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = T(x \ L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a,b,4204,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 4204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) * (T(x,u) \ 1) = L(T(x,u) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4205(a,1),3832(a,1,1))].">
      <j1 rule="para" parents="4205 3832"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      a(x,L(y * z,u,w) \ (y * y),v5) = a(x,L((1 / y) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3(a,1),4122(a,1,2,2))].">
      <j1 rule="para" parents="3 4122"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(3559(a,1),4197(a,1,2,1))].">
      <j1 rule="para" parents="3559 4197"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      R((x \ y) * x,z,u) / x = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2145,a(flip),b,4209,a),flip(a)].">
      <j1 rule="hyper" parents="60 2145 4209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(155,a,4210,a),flip(a)].">
      <j1 rule="hyper" parents="155 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(78(a,1),4210(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(231,a,4211,a),flip(a)].">
      <j1 rule="hyper" parents="231 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(706(a,1),4211(a,2,1,2))].">
      <j1 rule="para" parents="706 4211"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2727(a,1),4211(a,2,1,2))].">
      <j1 rule="para" parents="2727 4211"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(147,a,4213,a)].">
      <j1 rule="hyper" parents="147 4213"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      x / R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(4213(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4213 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2633,a,4216,a)].">
      <j1 rule="hyper" parents="2633 4216"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,4218,a,b,1957,a)].">
      <j1 rule="hyper" parents="275 4218 1957"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      L(T(1 / R(x,y,z),x),R(x,y,z),u) = (u * R(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(4219(a,2),251(a,1,1))].">
      <j1 rule="para" parents="4219 251"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(156,a,4212,a),flip(a)].">
      <j1 rule="hyper" parents="156 4212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,4214,a(flip),b,304,a)].">
      <j1 rule="hyper" parents="128 4214 304"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(128,a,4215,a(flip),b,2717,a),flip(a)].">
      <j1 rule="hyper" parents="128 4215 2717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      L(T(1 / R(x,y,z),x),x,R(x,y,z)) = (x * R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,2300,a(flip),b,4221,a)].">
      <j1 rule="hyper" parents="60 2300 4221"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,2322,a(flip),b,4224,a)].">
      <j1 rule="hyper" parents="60 2322 4224"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      T(R(x,y,z) \ 1,R(x,y,z) * x) = (x * R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,1457,a(flip),b,4225,a)].">
      <j1 rule="hyper" parents="60 1457 4225"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      T(R(x,y,z) \ 1,R(x,y,z) * x) != u \ x
    ]]></literal>
    <literal><![CDATA[
      x * R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4227(a,2),45(a,1))].">
      <j1 rule="para" parents="4227 45"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      a((x * y) \ 1,x,y) / y = (1 / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,3626,a(flip),b,3648,a(flip))].">
      <j1 rule="hyper" parents="128 3626 3648"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      L(x,y * ((((z * z) * (u / (z * z))) * z) * z),w) = L(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(853(a,1),3774(a,1,2,2,1,1))].">
      <j1 rule="para" parents="853 3774"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      L((x * y) * (x * (y * z)),u,w) = (x * y) * (x * (y * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(528(a,1),3925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="528 3925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ 1) = a((x \ 1) \ y,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3063,a,3949,a),flip(a)].">
      <j1 rule="hyper" parents="3063 3949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ 1) = a(x \ y,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2959,a(flip),b,4232,a),flip(a)].">
      <j1 rule="hyper" parents="370 2959 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      L(x,y * ((T(z,u \ (u \ 1)) * u) * u),w) = L(x,y * R(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(1421(a,1),4230(a,1,2,2,1,1))].">
      <j1 rule="para" parents="1421 4230"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      L(x,y * ((z * T(u,z \ 1)) * z),w) = L(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(1795(a,1),4234(a,1,2,2,1))].">
      <j1 rule="para" parents="1795 4234"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      x \ T(K(x,x \ 1) * y,x \ 1) = ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1716(a,1),3628(a,1,2,1,1))].">
      <j1 rule="para" parents="1716 3628"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      L(x,y * ((z * (u * w)) * K(w,w \ 1)),v5) = L(x,y * (z * (u * (1 / w))),v5)
    ]]></literal>
    <justification jstring="[para(1724(a,2),3811(a,1,2,2,2))].">
      <j1 rule="para" parents="1724 3811"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ x) * u) = x \ ((L(1 / x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(2181(a,1),3896(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2181 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      (x \ 1) * L((x * x) * L(x,y,z),u,w) = (x \ 1) \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(939(a,1),3919(a,1,2,1))].">
      <j1 rule="para" parents="939 3919"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(4017(a,1),4064(a,1,2))].">
      <j1 rule="para" parents="4017 4064"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ 1) * u) = (1 / x) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(1020,a,4241,a),flip(a)].">
      <j1 rule="hyper" parents="1020 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) * ((1 / x) * (L(x,y,z) \ u)) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,4242,a(flip),b,940,a)].">
      <j1 rule="hyper" parents="129 4242 940"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      x * ((1 / x) * (L(x,y,z) \ u)) = L(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[para(4242(a,1),2203(a,1,2))].">
      <j1 rule="para" parents="4242 2203"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = x * (L(x,y,z) \ L(u,x,x))
    ]]></literal>
    <justification jstring="[para(4244(a,1),2083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4244 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      (x \ (x * x)) * L(L(x,y,z),u,w) = (x \ 1) \ L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4240,a(flip),b,4117,a),flip(a)].">
      <j1 rule="hyper" parents="60 4240 4117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      (x \ 1) \ L(L(x,y,z),u,w) = x * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      L(x,(y / (1 / z)) * R(y / (1 / z),z,z),u) = L(x,(y / z) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3395,a(flip),b,3651,a),flip(a)].">
      <j1 rule="hyper" parents="370 3395 3651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      L(x,(y * z) * (y / (1 / z)),u) = L(x,(y / z) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(2062(a,1),4249(a,1,2))].">
      <j1 rule="para" parents="2062 4249"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z \ 1) \ u)) = L(x,y,((z \ 1) \ u) * (z * u))
    ]]></literal>
    <justification jstring="[para(2082(a,1),3681(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2082 3681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z \ 1) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(4251(a,2),3577(a,1))].">
      <j1 rule="para" parents="4251 3577"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x,y,z)) = (1 / L(x \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,3871,a(flip),b,3898,a)].">
      <j1 rule="hyper" parents="60 3871 3898"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      x \ ((y * y) * (x \ ((y * y) * L((y * y) \ x,z,u)))) = L(((y * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(849(a,1),3849(a,1,2,2))].">
      <j1 rule="para" parents="849 3849"/>
    </justification>
  </clause>

  <clause id="4255">
    <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(3918(a,1),3821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3918 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (L(x,y,z) \ x),y,z) = L(x,y,z) \ ((x * x) * 1)
    ]]></literal>
    <justification jstring="[para(3985(a,1),4052(a,1,1,2))].">
      <j1 rule="para" parents="3985 4052"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (L(x,y,z) \ x),y,z) = L(x,y,z) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,177,a(flip),b,4256,a),flip(a)].">
      <j1 rule="hyper" parents="370 177 4256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (L(x,y,z) \ x),y,z) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,4257,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 4257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x \ 1,y,z) \ x),y,z) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(4026(a,1),4258(a,1,1))].">
      <j1 rule="para" parents="4026 4258"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ 1) = L(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3927,a,4078,a),flip(a)].">
      <j1 rule="hyper" parents="3927 4078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,u,w) \ L(x,y,z)) = L(x,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(3917,a,4078,a)].">
      <j1 rule="hyper" parents="3917 4078"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ x) = x * (L(x,u,w) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4260(a,1),2174(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4260 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,u,w) \ L(x,y,z))) = L(x,u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,4261,a,b,2169,a)].">
      <j1 rule="hyper" parents="129 4261 2169"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,u,w) \ L(x,y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) \ x = v5
    ]]></literal>
    <justification jstring="[para(4261(a,2),2175(a,1,2))].">
      <j1 rule="para" parents="4261 2175"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      x \ ((y * y) * (x \ L(x,z,u))) = L(((y * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3806(a,1),4254(a,1,2,2,2))].">
      <j1 rule="para" parents="3806 4254"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      x \ ((y * y) * (x \ L(x,z,u))) = L(x \ (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(578(a,1),4265(a,2,1))].">
      <j1 rule="para" parents="578 4265"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      ((x * x) \ y) * L(y \ (x * x),z,u) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,4266,a(flip),b,849,a)].">
      <j1 rule="hyper" parents="129 4266 849"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x \ 1) * L(((x \ 1) * y) \ ((x \ 1) * (x \ 1)),z,u) = ((x \ 1) * y) \ L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3410(a,2),4268(a,1,1))].">
      <j1 rule="para" parents="3410 4268"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,((x \ 1) * y) \ x,x * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3438,a(flip),b,3728,a)].">
      <j1 rule="hyper" parents="60 3438 3728"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,x * y) = (x \ 1) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3726,a(flip),b,4270,a)].">
      <j1 rule="hyper" parents="60 3726 4270"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * y) * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(798,a,4271,a),flip(a)].">
      <j1 rule="hyper" parents="798 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * z) * u) = (x * y) \ (x * (x \ ((x * z) * u)))
    ]]></literal>
    <justification jstring="[para(4272(a,1),1512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4272 1512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * z) * u) = (x * y) \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),4273(a,2,2))].">
      <j1 rule="para" parents="5 4273"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      (x \ (y * L(y \ (1 / x),z,u))) * ((1 / x) \ y) = L((x \ 1) * (x \ ((1 / x) \ y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,4116,a,b,4075,a),flip(a)].">
      <j1 rule="hyper" parents="370 4116 4075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      ((L(x,y,z) * L(x,y,z)) / x) * (L(x,y,z) \ u) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,576,a(flip),b,4243,a)].">
      <j1 rule="hyper" parents="60 576 4243"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      (x \ (y * L(y \ (1 / x),z,u))) * ((1 / x) \ y) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2071(a,1),4276(a,2,1))].">
      <j1 rule="para" parents="2071 4276"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      (x \ 1) \ L(x \ y,z,u) = x \ L((1 / x) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,4278,a(flip),b,4075,a(flip))].">
      <j1 rule="hyper" parents="125 4278 4075"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      L(x \ L((1 / x) \ (x \ y),z,u),x,x) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(4279(a,1),3913(a,1,1))].">
      <j1 rule="para" parents="4279 3913"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      L(x \ L(x \ ((x \ 1) \ y),z,u),x,x) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(945(a,1),4280(a,1,1,2,1))].">
      <j1 rule="para" parents="945 4280"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      (1 / x) * L(x \ ((x \ 1) \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(790,a,4281,a)].">
      <j1 rule="hyper" parents="790 4281"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      x \ L((x \ 1) * (x * y),z,u) = (1 / x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(64(a,1),4282(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="64 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      x \ L(x * ((1 / x) * y),z,u) = (1 / x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(951(a,1),4283(a,1,2,1))].">
      <j1 rule="para" parents="951 4283"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      L(x * ((1 / x) * y),z,u) = x * ((1 / x) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(156,a,4284,a),flip(a)].">
      <j1 rule="hyper" parents="156 4284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <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(17(a,2),2647(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4287">
    <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(274(a,1),4286(a,2,2))].">
      <j1 rule="para" parents="274 4286"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) / ((z \ 1) \ 1))),x,y) = (((1 / y) * x) * z) \ ((1 / y) * x)
    ]]></literal>
    <justification jstring="[para(1271(a,1),3493(a,1,1,2))].">
      <j1 rule="para" parents="1271 3493"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      (((1 / x) * y) * z) \ ((1 / x) * y) = (x * y) \ ((x * y) / ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,344,a(flip),b,4288,a),flip(a)].">
      <j1 rule="hyper" parents="60 344 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      (((1 / x) * y) * z) \ ((1 / x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(4289(a,2),3497(a,1))].">
      <j1 rule="para" parents="4289 3497"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z / ((1 / x) * (1 / x)))
    ]]></literal>
    <justification jstring="[para(4(a,1),3271(a,2,1))].">
      <j1 rule="para" parents="4 3271"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z / (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[para(320(a,1),4291(a,2,2,2))].">
      <j1 rule="para" parents="320 4291"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      T((x * ((x \ 1) \ y)) * z,(1 / x) \ ((1 / x) \ 1)) = y * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(1661(a,1),4292(a,2,2))].">
      <j1 rule="para" parents="1661 4292"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ ((1 / x) \ 1)) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(2078(a,1),4293(a,1,1,1))].">
      <j1 rule="para" parents="2078 4293"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,(1 / x) \ x) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(77(a,1),4294(a,1,2,2))].">
      <j1 rule="para" parents="77 4294"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) / ((y \ x) * (x \ y)) = R(x,y \ x,L(1 / (y \ x),y \ x,x))
    ]]></literal>
    <justification jstring="[para(4005(a,1),3435(a,1,1,2))].">
      <j1 rule="para" parents="4005 3435"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      L(x * (x * x),y,z) \ (x * (x * (L(x,y,z) * u))) = L(L(u,L(x,y,z),x),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3905(a,2),4172(a,1,1))].">
      <j1 rule="para" parents="3905 4172"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      (x * x) \ (L(x,y,z) \ (x * (x * (L(x,y,z) * u)))) = L(L(u,L(x,y,z),x),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3901,a,4297,a)].">
      <j1 rule="hyper" parents="3901 4297"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      (x * x) \ (x * (L(x,y,z) \ (x * (L(x,y,z) * u)))) = L(L(u,L(x,y,z),x),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2160(a,1),4298(a,1,2))].">
      <j1 rule="para" parents="2160 4298"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      L(L(x,L(y,z,u),y),y,y * L(y,z,u)) = (y * y) \ (y * (y * x))
    ]]></literal>
    <justification jstring="[para(2158(a,1),4299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2158 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      L(L(x,L(y,z,u),y),y,y * L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a,b,4300,a),flip(a)].">
      <j1 rule="hyper" parents="370 13 4300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      L(L(x,y,L(y,z,u)),y,y * L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(2390(a,1),4301(a,1,1))].">
      <j1 rule="para" parents="2390 4301"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      R(T(x / y,y \ L(y,z,u)),y,L(y \ 1,z,u)) = (y \ L(y,z,u)) \ (x * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3816(a,1),3828(a,2,1))].">
      <j1 rule="para" parents="3816 3828"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,L(1 / x,y,z),L(x,y,z)) = ((x \ 1) * (L(x \ 1,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(3804(a,1),4088(a,1,2))].">
      <j1 rule="para" parents="3804 4088"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,L(x,y,z),L(x,y,z)) = ((x \ 1) * (L(x \ 1,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(3805(a,1),4305(a,1,2))].">
      <j1 rule="para" parents="3805 4305"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,L(x,y,z),L(x,y,z)) = (L(1 / x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(4070(a,1),4306(a,2,1))].">
      <j1 rule="para" parents="4070 4306"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = x \ ((L(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4307 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      (x \ (1 / x)) * (((x \ 1) * (x \ y)) * ((1 / x) \ x)) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1224(a,1),1283(a,1,1))].">
      <j1 rule="para" parents="1224 1283"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      (x \ (1 / x)) * ((x \ 1) * ((x \ y) * ((1 / x) \ x))) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(4186(a,1),4309(a,1,2))].">
      <j1 rule="para" parents="4186 4309"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,(x \ 1) \ (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(1211(a,1),1316(a,2,2))].">
      <j1 rule="para" parents="1211 1316"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,(x \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),4311(a,2,2,2))].">
      <j1 rule="para" parents="74 4311"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (((x \ 1) \ 1) * ((x \ 1) \ 1)) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(311(a,1),4312(a,2,2))].">
      <j1 rule="para" parents="311 4312"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ (1 / (x \ 1))) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(1211(a,1),4314(a,1,2))].">
      <j1 rule="para" parents="1211 4314"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(74(a,1),4315(a,1,2,2))].">
      <j1 rule="para" parents="74 4315"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * (x * x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(311(a,1),4316(a,1,2))].">
      <j1 rule="para" parents="311 4316"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = (x \ 1) \ T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1664,a(flip),b,4318,a),flip(a)].">
      <j1 rule="hyper" parents="60 1664 4318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <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(1695(a,1),2908(a,2,2,1))].">
      <j1 rule="para" parents="1695 2908"/>
    </justification>
  </clause>

  <clause id="4321">
    <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(2598(a,1),4320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2598 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2921,a(flip),b,4321,a)].">
      <j1 rule="hyper" parents="60 2921 4321"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4322(a,1),1708(a,1))].">
      <j1 rule="para" parents="4322 1708"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4323,a,3202,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4323 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,1709,a(flip),b,4324,a),flip(a)].">
      <j1 rule="hyper" parents="31 1709 4324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4326">
    <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(308(a,1),4325(a,1,2))].">
      <j1 rule="para" parents="308 4325"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1945(a,1),4326(a,1,1))].">
      <j1 rule="para" parents="1945 4326"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,3245,a(flip),b,4327,a),flip(a)].">
      <j1 rule="hyper" parents="60 3245 4327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,4328,a),flip(a)].">
      <j1 rule="hyper" parents="215 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      1 / T((x \ 1) \ 1,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),4328(a,1,2,1))].">
      <j1 rule="para" parents="108 4328"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(417(a,1),4328(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="417 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      1 / T(1 / x,y) = T(x \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(1310(a,1),4328(a,1,2,1))].">
      <j1 rule="para" parents="1310 4328"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),4329(a,1,1))].">
      <j1 rule="para" parents="108 4329"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(1312(a,1),4330(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1312 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(221,a,4331,a)].">
      <j1 rule="hyper" parents="221 4331"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      x \ 1 != 1 / T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(4331(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4331 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1307,a,b,4332,a(flip))].">
      <j1 rule="hyper" parents="36 1307 4332"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,4333,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4333 17"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(109(a,1),4333(a,2,1,1))].">
      <j1 rule="para" parents="109 4333"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(z,T(x,y),T(x,y)) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(4333(a,2),2090(a,2,1))].">
      <j1 rule="para" parents="4333 2090"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      T(T(x,y),x \ 1) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(364(a,2),4335(a,1,1))].">
      <j1 rule="para" parents="364 4335"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(2100,a,4336,a)].">
      <j1 rule="hyper" parents="2100 4336"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      x * (1 / (1 / T(y,x))) = (1 / (1 / y)) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,4336,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4336 17"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) * T(1 / (1 / x),y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,4336,a(flip),b,1715,a)].">
      <j1 rule="hyper" parents="129 4336 1715"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = ((1 / T(x,y)) \ 1) * L(z,T(T(x,y),x \ 1),T(T(x,y),x \ 1))
    ]]></literal>
    <justification jstring="[para(4342(a,1),1326(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4342 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1057,a,4339,a)].">
      <j1 rule="hyper" parents="1057 4339"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),4339(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 4339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      ((R(x / y,y,z) \ 1) \ 1) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(711(a,1),4339(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="711 4339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1735,a,b,4347,a),flip(a)].">
      <j1 rule="hyper" parents="370 1735 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,4347,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2912,a,4350,a)].">
      <j1 rule="hyper" parents="2912 4350"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,4352,a)].">
      <j1 rule="hyper" parents="51 4352"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,4352,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 4352 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(125,a,4352,a(flip),b,2910,a)].">
      <j1 rule="hyper" parents="125 4352 2910"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4353(a,1),46(a,2))].">
      <j1 rule="para" parents="4353 46"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(4353(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4353 328"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      T(x,K(y,1 / y)) = x
    ]]></literal>
    <justification jstring="[para(1706(a,2),4353(a,1,2))].">
      <j1 rule="para" parents="1706 4353"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1716(a,2),4353(a,1,2))].">
      <j1 rule="para" parents="1716 4353"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(1724(a,1),4353(a,1,2))].">
      <j1 rule="para" parents="1724 4353"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(4000(a,1),4353(a,1,2))].">
      <j1 rule="para" parents="4000 4353"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(3284,a,4360,a),flip(a)].">
      <j1 rule="hyper" parents="3284 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(3284,a,4361,a),flip(a)].">
      <j1 rule="hyper" parents="3284 4361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,3714,a(flip),b,4361,a)].">
      <j1 rule="hyper" parents="60 3714 4361"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(51,a,4361,a)].">
      <j1 rule="hyper" parents="51 4361"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4361(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4361 328"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3284,a,4363,a),flip(a)].">
      <j1 rule="hyper" parents="3284 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4368(a,1),3355(a,1,1))].">
      <j1 rule="para" parents="4368 3355"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(3688,a,4354,a)].">
      <j1 rule="hyper" parents="3688 4354"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(3623,a,4354,a)].">
      <j1 rule="hyper" parents="3623 4354"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(3570,a,4354,a),flip(a)].">
      <j1 rule="hyper" parents="3570 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(3562,a,4354,a),flip(a)].">
      <j1 rule="hyper" parents="3562 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(3556,a,4354,a),flip(a)].">
      <j1 rule="hyper" parents="3556 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3673,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="370 3673 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3668,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="370 3668 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3663,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="370 3663 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3490,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="370 3490 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(370,a,3472,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="370 3472 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4196,a,b,4354,a)].">
      <j1 rule="hyper" parents="60 4196 4354"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,3559,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="60 3559 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(4354(a,1),3475(a,1,2))].">
      <j1 rule="para" parents="4354 3475"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(4354(a,2),3488(a,1))].">
      <j1 rule="para" parents="4354 3488"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(4354(a,1),3452(a,1,1))].">
      <j1 rule="para" parents="4354 3452"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4354(a,2),3655(a,1,1))].">
      <j1 rule="para" parents="4354 3655"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * (x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[para(4354(a,2),3658(a,1,1))].">
      <j1 rule="para" parents="4354 3658"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4354(a,2),3661(a,1,1))].">
      <j1 rule="para" parents="4354 3661"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (z * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(4354(a,1),3474(a,2,2))].">
      <j1 rule="para" parents="4354 3474"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(4354(a,1),3638(a,1,1))].">
      <j1 rule="para" parents="4354 3638"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ 1 = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4354(a,1),3690(a,1,1))].">
      <j1 rule="para" parents="4354 3690"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4354(a,1),3639(a,2,2))].">
      <j1 rule="para" parents="4354 3639"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4354(a,2),3678(a,1,1))].">
      <j1 rule="para" parents="4354 3678"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      R((K(x,x \ 1) * y) / z,z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(4354(a,2),3496(a,1,1,1))].">
      <j1 rule="para" parents="4354 3496"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3442,a,b,4364,a)].">
      <j1 rule="hyper" parents="60 3442 4364"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3749,a,4366,a)].">
      <j1 rule="hyper" parents="3749 4366"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(3748,a,4366,a)].">
      <j1 rule="hyper" parents="3748 4366"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(3612,a,4366,a)].">
      <j1 rule="hyper" parents="3612 4366"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(370,a,3705,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="370 3705 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3656,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="370 3656 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3654,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="370 3654 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2732,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="370 2732 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3450,a,b,4366,a)].">
      <j1 rule="hyper" parents="60 3450 4366"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,3622,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="60 3622 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,3603,a(flip),b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="60 3603 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(4366(a,2),3495(a,1))].">
      <j1 rule="para" parents="4366 3495"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4366(a,1),3445(a,1,1))].">
      <j1 rule="para" parents="4366 3445"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(4366(a,1),3621(a,1))].">
      <j1 rule="para" parents="4366 3621"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(4366(a,1),3637(a,1,1))].">
      <j1 rule="para" parents="4366 3637"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(4366(a,2),3652(a,1,1))].">
      <j1 rule="para" parents="4366 3652"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4366(a,1),3639(a,1,1))].">
      <j1 rule="para" parents="4366 3639"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(631(a,1),4373(a,1,1))].">
      <j1 rule="para" parents="631 4373"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2011,a,4340,a)].">
      <j1 rule="hyper" parents="2011 4340"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1147,a,4340,a)].">
      <j1 rule="hyper" parents="1147 4340"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,4340,a)].">
      <j1 rule="hyper" parents="316 4340"/>
    </justification>
  </clause>

  <clause id="4419">
    <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(2022(a,2),4340(a,1,1,1,1))].">
      <j1 rule="para" parents="2022 4340"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      (x / y) * (((y \ x) \ 1) \ 1) = (1 / (x / y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4340(a,1),2150(a,1,2))].">
      <j1 rule="para" parents="4340 2150"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),4416(a,1,2))].">
      <j1 rule="para" parents="6 4416"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),4416(a,1,2))].">
      <j1 rule="para" parents="74 4416"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4416(a,1),3645(a,2,2))].">
      <j1 rule="para" parents="4416 3645"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(109(a,1),4344(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 4344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(4344(a,1),3694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4344 3694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      ((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,4367,a(flip),b,2744,a),flip(a)].">
      <j1 rule="hyper" parents="128 4367 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2012(a,1),4367(a,1,1))].">
      <j1 rule="para" parents="2012 4367"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(4367(a,1),3652(a,1,1))].">
      <j1 rule="para" parents="4367 3652"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) * y) \ z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(4367(a,1),3470(a,1,2,1))].">
      <j1 rule="para" parents="4367 3470"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,4376,a(flip),b,3671,a)].">
      <j1 rule="hyper" parents="128 4376 3671"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      K(x,x \ 1) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(4376(a,1),3692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4376 3692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      (T(x,x \ 1) * y) * (x \ 1) = (x * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4377(a,1),3658(a,1,1))].">
      <j1 rule="para" parents="4377 3658"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(4378(a,1),3565(a,1,2))].">
      <j1 rule="para" parents="4378 3565"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3699,a,4379,a)].">
      <j1 rule="hyper" parents="3699 4379"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(275,a,4379,a(flip),b,3563,a(flip))].">
      <j1 rule="hyper" parents="275 4379 3563"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),4437(a,1,2))].">
      <j1 rule="para" parents="108 4437"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(417(a,1),4437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="417 4437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1310(a,1),4437(a,1,2))].">
      <j1 rule="para" parents="1310 4437"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,4441,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4441 17"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(129,a,4442,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4442 17"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,4443,a),flip(a)].">
      <j1 rule="hyper" parents="494 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      (1 / x) * T(y,x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,4443,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4443 17"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      T(x,L(y,z,u) \ ((y * y) * 1)) = T(x,1 / L(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(3800(a,2),4443(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3800 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      T(x * (y * y),y \ 1) = (1 / y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(855(a,1),4446(a,1,1))].">
      <j1 rule="para" parents="855 4446"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      (x \ (y * (x \ 1))) * x = T(y,x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1665,a(flip),b,4448,a)].">
      <j1 rule="hyper" parents="60 1665 4448"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      (x \ 1) * (x \ T(y,x \ 1)) = x \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(125,a,4448,a(flip),b,2070,a),flip(a)].">
      <j1 rule="hyper" parents="125 4448 2070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x \ 1) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(125,a,4381,a(flip),b,3647,a),flip(a)].">
      <j1 rule="hyper" parents="125 4381 3647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      (1 / x) * (y * (x \ 1)) = (x \ 1) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(4381(a,1),3565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4381 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,(x \ 1) \ 1) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(74(a,1),4384(a,1,1,1))].">
      <j1 rule="para" parents="74 4384"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4384(a,1),3658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4384 3658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(1317(a,2),4385(a,2,1))].">
      <j1 rule="para" parents="1317 4385"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      x * (y * a(x,x,x)) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(3947(a,1),4460(a,1,2,2))].">
      <j1 rule="para" parents="3947 4460"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3558(a,1),4388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3558 4388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3633(a,1),4388(a,1,1))].">
      <j1 rule="para" parents="3633 4388"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(3632(a,1),4389(a,1,1))].">
      <j1 rule="para" parents="3632 4389"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      (T(x,x \ 1) \ y) * T(x,x \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3557(a,1),4390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3557 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3678,a(flip),b,4393,a)].">
      <j1 rule="hyper" parents="60 3678 4393"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      (x \ (L(x \ 1,y,z) \ 1)) * K(x \ 1,x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3887,a(flip),b,4398,a),flip(a)].">
      <j1 rule="hyper" parents="370 3887 4398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      K(x \ 1,x) * ((y / (x \ 1)) * z) = (y / (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(4402(a,1),3445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4402 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / ((x \ 1) \ 1)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4403(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="4403 3604"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1716(a,1),4404(a,1,1))].">
      <j1 rule="para" parents="1716 4404"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (1 / x)) * z) = (y * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4404(a,1),3445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4404 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4413(a,1),3616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4413 3616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4422(a,1),3630(a,1,2))].">
      <j1 rule="para" parents="4422 3630"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(x,T(y \ (z \ y),z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(4422(a,2),4441(a,1,2))].">
      <j1 rule="para" parents="4422 4441"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ R(y,x,x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(125,a,1515,a(flip),b,4444,a)].">
      <j1 rule="hyper" parents="125 1515 4444"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      (x * x) \ ((1 / x) \ (y * x)) = x \ ((y * (x * x)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4451(a,1),941(a,1,2))].">
      <j1 rule="para" parents="4451 941"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4366,a(flip),b,4466,a)].">
      <j1 rule="hyper" parents="60 4366 4466"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      (1 / x) \ (y * (x \ 1)) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(125,a,4471,a(flip),b,3566,a)].">
      <j1 rule="hyper" parents="125 4471 3566"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      (1 / x) * (y * (1 / x)) = (x \ 1) * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4471(a,1),3565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4471 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3455(a,1),4358(a,1))].">
      <j1 rule="para" parents="3455 4358"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      ((x \ 1) \ 1) * R(y,x,x) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,1131,a(flip),b,4476,a)].">
      <j1 rule="hyper" parents="129 1131 4476"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      L(T(x * (y \ 1),y),y,y) = (y \ 1) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(4476(a,1),2120(a,1,1))].">
      <j1 rule="para" parents="4476 2120"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      (x \ 1) \ T(y * (x \ 1),x) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4476(a,1),1456(a,1,2))].">
      <j1 rule="para" parents="4476 1456"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      (1 / ((x \ 1) \ 1)) * (R(y,x,x) * (((x \ 1) \ 1) * ((x \ 1) \ 1))) = T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(4484(a,1),889(a,2,1))].">
      <j1 rule="para" parents="4484 889"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,2797,a,b,4348,a)].">
      <j1 rule="hyper" parents="60 2797 4348"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4348(a,1),2794(a,1,2))].">
      <j1 rule="para" parents="4348 2794"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(4370(a,1),4007(a,1,1))].">
      <j1 rule="para" parents="4370 4007"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(3476,a,4387,a),flip(a)].">
      <j1 rule="hyper" parents="3476 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[hyper(125,a,4354,a(flip),b,4387,a)].">
      <j1 rule="hyper" parents="125 4354 4387"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * (z * K(y,y \ 1))) = z
    ]]></literal>
    <justification jstring="[hyper(135,a,4391,a)].">
      <j1 rule="hyper" parents="135 4391"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3678,a(flip),b,4392,a),flip(a)].">
      <j1 rule="hyper" parents="60 3678 4392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1508(a,1),4392(a,2,2))].">
      <j1 rule="para" parents="1508 4392"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (1 / x)) = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,3678,a(flip),b,4496,a)].">
      <j1 rule="hyper" parents="60 3678 4496"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4369,a,4497,a)].">
      <j1 rule="hyper" parents="4369 4497"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(3621,a,4497,a)].">
      <j1 rule="hyper" parents="3621 4497"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      (x * (1 / y)) \ (y \ 1) = (x * (y \ 1)) \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3695,a(flip),b,4499,a)].">
      <j1 rule="hyper" parents="60 3695 4499"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      (x * (1 / y)) \ (z * K(y,y \ 1)) = (x * (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(4404(a,1),4394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4404 4394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4366,a(flip),b,4395,a),flip(a)].">
      <j1 rule="hyper" parents="370 4366 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(4195(a,1),4395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4195 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,170,a(flip),b,4397,a)].">
      <j1 rule="hyper" parents="128 170 4397"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      ((x * y) / z) * K(x \ 1,x) = ((1 / (1 / x)) * y) / z
    ]]></literal>
    <justification jstring="[para(3603(a,1),4406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3603 4406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(3473,a,4410,a),flip(a)].">
      <j1 rule="hyper" parents="3473 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <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(4410(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4410 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y * K(z \ 1,z),x)
    ]]></literal>
    <justification jstring="[para(4410(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4410 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(4382(a,1),4414(a,2,2))].">
      <j1 rule="para" parents="4382 4414"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4417(a,2,1,1))].">
      <j1 rule="para" parents="4 4417"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,2047,a(flip),b,4513,a)].">
      <j1 rule="hyper" parents="60 2047 4513"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,4514,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 4514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1942,a,4516,a(flip))].">
      <j1 rule="hyper" parents="1942 4516"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),4517(a,1,2,2))].">
      <j1 rule="para" parents="7 4517"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(4518(a,1),264(a,1,2,2))].">
      <j1 rule="para" parents="4518 264"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3511(a,2),4418(a,1,1,2))].">
      <j1 rule="para" parents="3511 4418"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[hyper(128,a,3686,a(flip),b,4424,a)].">
      <j1 rule="hyper" parents="128 3686 4424"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(215,a,4425,a)].">
      <j1 rule="hyper" parents="215 4425"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1496(a,1),4427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1496 4427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      ((1 / x) * (K(x,x \ 1) * y)) / (1 / x) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3565(a,1),4427(a,2,1))].">
      <j1 rule="para" parents="3565 4427"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(3301,a,4429,a),flip(a)].">
      <j1 rule="hyper" parents="3301 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      (((x \ 1) \ 1) * y) / L(x,x,x) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(1317(a,2),4432(a,1,2))].">
      <j1 rule="para" parents="1317 4432"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      (x * x) \ T(x * y,x \ 1) = (x \ 1) * (((x \ 1) \ y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,1577,a,b,4456,a)].">
      <j1 rule="hyper" parents="60 1577 4456"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      L(x,(1 / y) * ((y \ 1) * (z * (1 / y))),u) = L(x,L(z * (y \ 1),1 / y,1 / y),u)
    ]]></literal>
    <justification jstring="[para(4456(a,1),3390(a,1,2,2))].">
      <j1 rule="para" parents="4456 3390"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      x * ((x \ 1) * (y * (1 / x))) = L(y,x,x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4456(a,1),4076(a,1,2))].">
      <j1 rule="para" parents="4456 4076"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      ((1 / x) \ (x \ y)) * (1 / x) = (x \ ((1 / x) \ y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2104(a,1),4459(a,2,1))].">
      <j1 rule="para" parents="2104 4459"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      (T(x,x \ 1) \ ((x \ 1) \ y)) * T(x,x \ 1) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(945(a,2),4465(a,2,1))].">
      <j1 rule="para" parents="945 4465"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = y * (((y \ (x \ y)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4398,a,b,4474,a)].">
      <j1 rule="hyper" parents="370 4398 4474"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ 1 = x \ (((y \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(135,a,4474,a),flip(a)].">
      <j1 rule="hyper" parents="135 4474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(210(a,1),4474(a,1,2,1,1,2))].">
      <j1 rule="para" parents="210 4474"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      x \ T(y * x,x \ (x \ 1)) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,1562,a,b,4479,a)].">
      <j1 rule="hyper" parents="60 1562 4479"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      x * ((x \ 1) \ (y * (1 / x))) = T(y * x,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,4479,a(flip),b,1562,a)].">
      <j1 rule="hyper" parents="129 4479 1562"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      R((1 / x) * y,x,x) = (x \ 1) * R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1357,a(flip),b,4485,a)].">
      <j1 rule="hyper" parents="60 1357 4485"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4489(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4 4489"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(4358,a,4491,a)].">
      <j1 rule="hyper" parents="4358 4491"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ 1) = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(483,a,4491,a),flip(a)].">
      <j1 rule="hyper" parents="483 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      x * (K(y,y \ 1) * (x \ z)) = K(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,4491,a),flip(a)].">
      <j1 rule="hyper" parents="387 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <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(4491(a,2),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4491 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3559(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="3559 4491"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(3615(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="3615 4491"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z
    ]]></literal>
    <justification jstring="[para(4382(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="4382 4491"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4380(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="4380 4491"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(4381(a,1),4491(a,2,2))].">
      <j1 rule="para" parents="4381 4491"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4358,a,4541,a)].">
      <j1 rule="hyper" parents="4358 4541"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4492(a,1),1641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4492 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      x * (a(x,y,1 / y) * K(y,y \ 1)) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1721,a,4493,a),flip(a)].">
      <j1 rule="hyper" parents="1721 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,4492,a,b,4493,a)].">
      <j1 rule="hyper" parents="35 4492 4493"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4366,a(flip),b,4494,a),flip(a)].">
      <j1 rule="hyper" parents="370 4366 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * K(x \ 1,x) = ((x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3559(a,1),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3559 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4491(a,1),4503(a,1,1))].">
      <j1 rule="para" parents="4491 4503"/>
    </justification>
  </clause>

  <clause id="4558">
    <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(1209,a,4505,a)].">
      <j1 rule="hyper" parents="1209 4505"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      x * (K(y \ 1,y) * T(z,x)) = K(y \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(787,a,4508,a),flip(a)].">
      <j1 rule="hyper" parents="787 4508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(4366(a,1),4508(a,2,2))].">
      <j1 rule="para" parents="4366 4508"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      T(x,x \ y) = ((x \ y) * K(z \ 1,z)) \ (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a,b,4512,a)].">
      <j1 rule="hyper" parents="370 108 4512"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (((x / (x * L(x \ 1,y,z))) * (x * L(x \ 1,y,z))) / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(2928(a,2),4519(a,1,2))].">
      <j1 rule="para" parents="2928 4519"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(548,a,4520,a)].">
      <j1 rule="hyper" parents="548 4520"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2007,a,b,4566,a)].">
      <j1 rule="hyper" parents="370 2007 4566"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4566(a,1,2))].">
      <j1 rule="para" parents="4 4566"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4566(a,1),2729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4566 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(74(a,1),4522(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 4522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),4523(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 4523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,4568,a,b,4539,a)].">
      <j1 rule="hyper" parents="370 4568 4539"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(108(a,2),4572(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 4572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(215,a,4573,a)].">
      <j1 rule="hyper" parents="215 4573"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,1617,a(flip),b,4542,a),flip(a)].">
      <j1 rule="hyper" parents="125 1617 4542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4358,a,4575,a)].">
      <j1 rule="hyper" parents="4358 4575"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,359,a(flip),b,4576,a),flip(a)].">
      <j1 rule="hyper" parents="370 359 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(3488,a,4577,a)].">
      <j1 rule="hyper" parents="3488 4577"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4577(a,2),914(a,1))].">
      <j1 rule="para" parents="4577 914"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4577(a,1),4387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4577 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(4386,a,4546,a)].">
      <j1 rule="hyper" parents="4386 4546"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(478,a,4546,a),flip(a)].">
      <j1 rule="hyper" parents="478 4546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(4546(a,1),3453(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4546 3453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3747,a,4553,a)].">
      <j1 rule="hyper" parents="3747 4553"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,4553,a)].">
      <j1 rule="hyper" parents="2810 4553"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(831,a,4553,a)].">
      <j1 rule="hyper" parents="831 4553"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4586(a,1),48(a,2))].">
      <j1 rule="para" parents="4586 48"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),4586(a,1,3,2))].">
      <j1 rule="para" parents="77 4586"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(1706(a,2),4586(a,1,3))].">
      <j1 rule="para" parents="1706 4586"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(1716(a,2),4586(a,1,3))].">
      <j1 rule="para" parents="1716 4586"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[para(4590(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4590 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(1 / u,u))
    ]]></literal>
    <literal><![CDATA[
      K(1 / u,u) = z
    ]]></literal>
    <justification jstring="[para(4590(a,1),690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4590 690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(4590(a,1),726(a,1,1))].">
      <j1 rule="para" parents="4590 726"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4591(a,1),48(a,2))].">
      <j1 rule="para" parents="4591 48"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(4591(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4591 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3496,a(flip),b,4592,a),flip(a)].">
      <j1 rule="hyper" parents="60 3496 4592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4592(a,1),48(a,2))].">
      <j1 rule="para" parents="4592 48"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4592(a,1),675(a,1,1))].">
      <j1 rule="para" parents="4592 675"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,(u * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3998,a,b,4585,a),flip(a)].">
      <j1 rule="hyper" parents="370 3998 4585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(4602(a,2),3999(a,1))].">
      <j1 rule="para" parents="4602 3999"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4508(a,1),4554(a,1,2))].">
      <j1 rule="para" parents="4508 4554"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(4562(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4562 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,4570,a),flip(a)].">
      <j1 rule="hyper" parents="215 4570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,4571,a)].">
      <j1 rule="hyper" parents="215 4571"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(3747,a,4582,a)].">
      <j1 rule="hyper" parents="3747 4582"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4372,a(flip),b,4611,a)].">
      <j1 rule="hyper" parents="60 4372 4611"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      K((x * y) \ x,x \ (x * y)) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4182,a(flip),b,4611,a)].">
      <j1 rule="hyper" parents="60 4182 4611"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      L(x,y,z) != K(u \ 1,u)
    ]]></literal>
    <literal><![CDATA[
      K(u \ 1,u) = x
    ]]></literal>
    <justification jstring="[para(4611(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="4611 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1716,a(flip),b,4612,a),flip(a)].">
      <j1 rule="hyper" parents="370 1716 4612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),4613(a,1,2))].">
      <j1 rule="para" parents="4 4613"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4619(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,4620,a(flip),b,4400,a)].">
      <j1 rule="hyper" parents="129 4620 4400"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4620(a,1),3514(a,1,2))].">
      <j1 rule="para" parents="4620 3514"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) = K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(4620(a,1),4611(a,1,1))].">
      <j1 rule="para" parents="4620 4611"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4394,a,b,4587,a)].">
      <j1 rule="hyper" parents="60 4394 4587"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      (x \ (1 / (1 / y))) * K(y,y \ 1) = x \ y
    ]]></literal>
    <justification jstring="[para(2283(a,1),4587(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2283 4587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(4354(a,2),4587(a,1,2))].">
      <j1 rule="para" parents="4354 4587"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(4540(a,1),4587(a,1,2))].">
      <j1 rule="para" parents="4540 4587"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(4625(a,1),4387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4625 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4364,a,b,4597,a)].">
      <j1 rule="hyper" parents="60 4364 4597"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(3675(a,1),4598(a,2,2))].">
      <j1 rule="para" parents="3675 4598"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1496(a,1),4610(a,1,1,1,1))].">
      <j1 rule="para" parents="1496 4610"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      K(x \ y,y \ x) * y = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4370,a,b,4622,a)].">
      <j1 rule="hyper" parents="60 4370 4622"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(32,a,4423,a,b,4633,a)].">
      <j1 rule="hyper" parents="32 4423 4633"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4620,a,b,4634,a)].">
      <j1 rule="hyper" parents="370 4620 4634"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4000,a,b,4634,a)].">
      <j1 rule="hyper" parents="370 4000 4634"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3739,a,b,4634,a)].">
      <j1 rule="hyper" parents="60 3739 4634"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3642,a,b,4634,a)].">
      <j1 rule="hyper" parents="60 3642 4634"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4637(a,2),4622(a,1,2))].">
      <j1 rule="para" parents="4637 4622"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      (x / y) * K(x \ y,y \ x) = 1 / (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(129,a,4638,a(flip),b,2099,a)].">
      <j1 rule="hyper" parents="129 4638 2099"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      L(x * (1 / y),y,y) = L(x,y,y) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2079,a,4530,a)].">
      <j1 rule="hyper" parents="2079 4530"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4589,a,4551,a)].">
      <j1 rule="hyper" parents="4589 4551"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,u \ 1)) = z
    ]]></literal>
    <justification jstring="[para(4551(a,1),4589(a,1))].">
      <j1 rule="para" parents="4551 4589"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1716(a,2),4642(a,1,2,2))].">
      <j1 rule="para" parents="1716 4642"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3490(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="3490 4642"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3663(a,1),4642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3663 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      T(x,y * T(z,z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3668(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="3668 4642"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3673(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="3673 4642"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4354(a,2),4642(a,1,2))].">
      <j1 rule="para" parents="4354 4642"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4373(a,1),4642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4373 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4375(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="4375 4642"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4376(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="4376 4642"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(4384(a,1),4642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4384 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      T(x,y * (K(z,z \ 1) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4540(a,1),4642(a,1,2))].">
      <j1 rule="para" parents="4540 4642"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4398(a,1),4645(a,1,2))].">
      <j1 rule="para" parents="4398 4645"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4408(a,1),4645(a,1,2))].">
      <j1 rule="para" parents="4408 4645"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(4498(a,1),4645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4498 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(4503(a,2),4645(a,1,2))].">
      <j1 rule="para" parents="4503 4645"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      T(x,((1 / y) * z) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(3648(a,1),4650(a,1,2))].">
      <j1 rule="para" parents="3648 4650"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      T(x,(y * (1 / z)) \ u) = T(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3695(a,1),4650(a,1,2))].">
      <j1 rule="para" parents="3695 4650"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(4195(a,1),4650(a,1,2))].">
      <j1 rule="para" parents="4195 4650"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      T(x,(y \ 1) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2688,a(flip),b,4648,a)].">
      <j1 rule="hyper" parents="60 2688 4648"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      T(x,y / (y \ z)) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(3510(a,1),4649(a,1,2))].">
      <j1 rule="para" parents="3510 4649"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2805(a,2),4656(a,1,2,1))].">
      <j1 rule="para" parents="2805 4656"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,1318,a(flip),b,4658,a),flip(a)].">
      <j1 rule="hyper" parents="60 1318 4658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(4658(a,1),308(a,1,2))].">
      <j1 rule="para" parents="4658 308"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1317,a,b,4666,a),flip(a)].">
      <j1 rule="hyper" parents="370 1317 4666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) != y
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ 1 = y
    ]]></literal>
    <justification jstring="[para(4668(a,2),1328(a,1))].">
      <j1 rule="para" parents="4668 1328"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      T(x,y * ((1 / z) \ u)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3559(a,1),4655(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3559 4655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3567(a,1),4655(a,1,2,2))].">
      <j1 rule="para" parents="3567 4655"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      T(x,y * (((1 / z) * u) * w)) = T(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(3648(a,1),4655(a,1,2,2))].">
      <j1 rule="para" parents="3648 4655"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      T(x,y * (z * (1 / u))) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(4381(a,1),4655(a,1,2,2))].">
      <j1 rule="para" parents="4381 4655"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3558(a,1),4659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3558 4659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      T(x,((1 / y) \ z) \ u) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3559(a,1),4659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3559 4659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ u) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3567(a,1),4659(a,1,2,1))].">
      <j1 rule="para" parents="3567 4659"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(4643,a,4662,a)].">
      <j1 rule="hyper" parents="4643 4662"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,2312,a,b,4662,a)].">
      <j1 rule="hyper" parents="60 2312 4662"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),4662(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 4662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      T(x,R((y * K(z \ 1,z)) \ 1,u,w)) = T(x,R(K(z,z \ 1) / y,u,w))
    ]]></literal>
    <justification jstring="[para(4583(a,1),4662(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4583 4662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * y) * u)) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(1004(a,2),4677(a,1,2))].">
      <j1 rule="para" parents="1004 4677"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(4623(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="4623 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      T(x,R(y \ 1,(y \ 1) \ 1,x)) = (y * ((x * (y \ 1)) / x)) * x
    ]]></literal>
    <justification jstring="[para(2764(a,2),4679(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2764 4679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      K(x / y,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(4635(a,1),4684(a,1))].">
      <j1 rule="para" parents="4635 4684"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = w
    ]]></literal>
    <justification jstring="[para(4623(a,2),4684(a,1))].">
      <j1 rule="para" parents="4623 4684"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(4636(a,2),4686(a,1))].">
      <j1 rule="para" parents="4636 4686"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      a(x \ y,x \ y,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(3947(a,1),4688(a,1))].">
      <j1 rule="para" parents="3947 4688"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1967,a,4428,a)].">
      <j1 rule="hyper" parents="1967 4428"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) * u) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(4433(a,1),4655(a,1,2,2))].">
      <j1 rule="para" parents="4433 4655"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      T(a(x,x,x) * y,x \ 1) = (x \ 1) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(3947(a,1),4454(a,1,1,1))].">
      <j1 rule="para" parents="3947 4454"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1) = x \ ((x \ 1) \ (y * (1 / x)))
    ]]></literal>
    <justification jstring="[para(4454(a,1),4237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4454 4237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      T(x,(y / (1 / z)) * u) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(4469(a,1),4651(a,1,2))].">
      <j1 rule="para" parents="4469 4651"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      ((x * (y \ 1)) * z) * K(y,y \ 1) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[hyper(4409,a,4472,a)].">
      <j1 rule="hyper" parents="4409 4472"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      T(x,(y * (1 / z)) * u) = T(x,(y * (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(4472(a,1),4651(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4472 4651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11,a,b,4473,a),flip(a)].">
      <j1 rule="hyper" parents="370 11 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3614(a,1),4699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3614 4699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(3613(a,1),4699(a,1,1))].">
      <j1 rule="para" parents="3613 4699"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      T((x \ y) * x,x \ 1) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1295,a,4486,a)].">
      <j1 rule="hyper" parents="1295 4486"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      (x * (1 / y)) \ (z * (1 / y)) = (x * (y \ 1)) \ (z * (y \ 1))
    ]]></literal>
    <justification jstring="[para(3490(a,1),4502(a,1,2))].">
      <j1 rule="para" parents="3490 4502"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(((x \ y) \ y) \ 1,(x \ y) \ y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,3514,a,b,4533,a)].">
      <j1 rule="hyper" parents="31 3514 4533"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ T(R(x,y,z),x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(2017(a,1),4536(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2017 4536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      x \ ((x \ 1) \ (y * (1 / x))) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4536(a,1),2649(a,1,2))].">
      <j1 rule="para" parents="4536 2649"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * (((x \ 1) \ 1) \ (z * (1 / (x \ 1))))) = (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(4537(a,1),2142(a,2,2))].">
      <j1 rule="para" parents="4537 2142"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(4547(a,1),3570(a,1))].">
      <j1 rule="para" parents="4547 3570"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      T(x,y * (z * (u * (1 / w)))) = T(x,y * (z * (u * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(4548(a,1),4655(a,1,2,2))].">
      <j1 rule="para" parents="4548 4655"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(4411,a,4556,a)].">
      <j1 rule="hyper" parents="4411 4556"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(275,a,3445,a,b,4559,a)].">
      <j1 rule="hyper" parents="275 3445 4559"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4366,a(flip),b,4711,a),flip(a)].">
      <j1 rule="hyper" parents="370 4366 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x \ 1,x) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,4711,a,b,3617,a)].">
      <j1 rule="hyper" parents="129 4711 3617"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[para(3614(a,1),4711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3614 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      T(1 / x,y) * K(x \ 1,x) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1508(a,1),4712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1508 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2377(a,1),4712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2377 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4366(a,1),4712(a,1,1))].">
      <j1 rule="para" parents="4366 4712"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(4411,a,4715,a)].">
      <j1 rule="hyper" parents="4411 4715"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T(1 / x,y) * K(x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1716(a,1),4715(a,1,2))].">
      <j1 rule="para" parents="1716 4715"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4411,a,4716,a)].">
      <j1 rule="hyper" parents="4411 4716"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,4343,a,b,4716,a)].">
      <j1 rule="hyper" parents="31 4343 4716"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4716(a,1),3470(a,1,2,1))].">
      <j1 rule="para" parents="4716 3470"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * T(1 / (1 / x),z)
    ]]></literal>
    <justification jstring="[para(4716(a,1),4562(a,2,2))].">
      <j1 rule="para" parents="4716 4562"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,4721,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="129 4721 1156"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4721(a,1),1508(a,1,1))].">
      <j1 rule="para" parents="4721 1508"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,z)) = y * (1 / (1 / T(x,z)))
    ]]></literal>
    <justification jstring="[para(4721(a,1),4401(a,1,1))].">
      <j1 rule="para" parents="4721 4401"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z
    ]]></literal>
    <justification jstring="[para(4718(a,1),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4718 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z
    ]]></literal>
    <justification jstring="[para(4719(a,1),3692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4719 3692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,4345,a,b,4720,a)].">
      <j1 rule="hyper" parents="32 4345 4720"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,4730,a(flip),b,1709,a(flip))].">
      <j1 rule="hyper" parents="125 4730 1709"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1722,a,4731,a)].">
      <j1 rule="hyper" parents="1722 4731"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4355,a(flip),b,4731,a)].">
      <j1 rule="hyper" parents="60 4355 4731"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(155,a,4734,a)].">
      <j1 rule="hyper" parents="155 4734"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,1900,a,b,4734,a)].">
      <j1 rule="hyper" parents="34 1900 4734"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(155,a,4736,a)].">
      <j1 rule="hyper" parents="155 4736"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      x \ (x / T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,4736,a,b,1676,a)].">
      <j1 rule="hyper" parents="125 4736 1676"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,3263,a,b,4737,a)].">
      <j1 rule="hyper" parents="60 3263 4737"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(4739(a,1),3262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4739 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4735(a,1),1903(a,1))].">
      <j1 rule="para" parents="4735 1903"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(356,a,4741,a),flip(a)].">
      <j1 rule="hyper" parents="356 4741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4743,a)].">
      <j1 rule="hyper" parents="316 4743"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,4743,a)].">
      <j1 rule="hyper" parents="51 4743"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,4743,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 4743 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      L(K(x,y),z,u) * y = y * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4743(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4743 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,4745,a)].">
      <j1 rule="hyper" parents="167 4745"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(164,a,4745,a)].">
      <j1 rule="hyper" parents="164 4745"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(161,a,4745,a)].">
      <j1 rule="hyper" parents="161 4745"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4745(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4745 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      K(x,y) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4745(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4745 328"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4745(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4745 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4745(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4745 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4745(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4745 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4745(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="4745 488"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4745(a,1),534(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4745 534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1806(a,1),4745(a,1,2))].">
      <j1 rule="para" parents="1806 4745"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1809(a,1),4745(a,1,2))].">
      <j1 rule="para" parents="1809 4745"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(2224(a,1),4745(a,1,2))].">
      <j1 rule="para" parents="2224 4745"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,4751,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4751 17"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(109(a,1),4751(a,1,2,2))].">
      <j1 rule="para" parents="109 4751"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,4761,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4761 17"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4761(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4761 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4749(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4749 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3307,a,b,4744,a)].">
      <j1 rule="hyper" parents="60 3307 4744"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1849,a,b,4744,a)].">
      <j1 rule="hyper" parents="60 1849 4744"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(4744(a,1),673(a,1,1,1))].">
      <j1 rule="para" parents="4744 673"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      (((x / y) * K(z,x / y)) * y) / x = R(K(z,x / y),x / y,y)
    ]]></literal>
    <justification jstring="[para(4744(a,1),708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4744 708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2870,a,b,4746,a)].">
      <j1 rule="hyper" parents="60 2870 4746"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ ((x * (z * K(y,z))) * z) = L(z,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(4746(a,1),2487(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4746 2487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4774">
    <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(4752(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="4752 488"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * x = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(129,a,4762,a(flip),b,108,a(flip))].">
      <j1 rule="hyper" parents="129 4762 108"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4762(a,1),308(a,1,2))].">
      <j1 rule="para" parents="4762 308"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      (x * y) / x != z * y
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(4762(a,1),368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4762 368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(454,a,4768,a)].">
      <j1 rule="hyper" parents="454 4768"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,4768,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="125 4768 302"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,4778,a(flip),b,2069,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 4778 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,4778,a(flip),b,209,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 4778 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(4779(a,1),4654(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4779 4654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[para(4775(a,1),73(a,1,2,1))].">
      <j1 rule="para" parents="4775 73"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2291,a,b,4776,a)].">
      <j1 rule="hyper" parents="60 2291 4776"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      (x \ 1) \ ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = z
    ]]></literal>
    <justification jstring="[para(4776(a,1),2294(a,1))].">
      <j1 rule="para" parents="4776 2294"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,4724,a,b,1681,a)].">
      <j1 rule="hyper" parents="129 4724 1681"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / T(x,y)) = x \ (x / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,4738,a,b,4725,a),flip(a)].">
      <j1 rule="hyper" parents="370 4738 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(276,a,4748,a)].">
      <j1 rule="hyper" parents="276 4748"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(276,a,4755,a)].">
      <j1 rule="hyper" parents="276 4755"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      R(x,y,z) * u != K(w,x) * R(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      K(w,x) = u
    ]]></literal>
    <justification jstring="[para(4756(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="4756 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,4785,a,b,2248,a)].">
      <j1 rule="hyper" parents="275 4785 2248"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      x * (T((x \ y) * x,z) / x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3625,a(flip),b,4713,a)].">
      <j1 rule="hyper" parents="60 3625 4713"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4713,a(flip),b,3625,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 4713 3625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[para(3617(a,2),4713(a,1,2,1))].">
      <j1 rule="para" parents="3617 4713"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4796(a,1,2,1,1,1))].">
      <j1 rule="para" parents="4 4796"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(194(a,1),4796(a,1,2,1,1))].">
      <j1 rule="para" parents="194 4796"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(4796(a,1),78(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4796 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(78(a,1),4796(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="78 4796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,4802,a),flip(a)].">
      <j1 rule="hyper" parents="135 4802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(4802(a,1),78(a,1,1,2))].">
      <j1 rule="para" parents="4802 78"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1555(a,1),4802(a,1,2))].">
      <j1 rule="para" parents="1555 4802"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(2543,a,4805,a),flip(a)].">
      <j1 rule="hyper" parents="2543 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1847,a,4805,a)].">
      <j1 rule="hyper" parents="1847 4805"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1557,a,4805,a),flip(a)].">
      <j1 rule="hyper" parents="1557 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(33,a,308,a,b,4805,a)].">
      <j1 rule="hyper" parents="33 308 4805"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4805(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4805 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      K(x,y) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(4805(a,2),1072(a,2,1))].">
      <j1 rule="para" parents="4805 1072"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(4805(a,1),708(a,1,1))].">
      <j1 rule="para" parents="4805 708"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4805(a,1),1557(a,1))].">
      <j1 rule="para" parents="4805 1557"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1809(a,2),4812(a,1,2))].">
      <j1 rule="para" parents="1809 4812"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(4806(a,1),693(a,1,1,1))].">
      <j1 rule="para" parents="4806 693"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1615,a,b,4814,a)].">
      <j1 rule="hyper" parents="370 1615 4814"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1555(a,1),4814(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1555 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      K(x,y) / (x * K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,4820,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="128 4820 302"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2103,a,4810,a)].">
      <j1 rule="hyper" parents="2103 4810"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,4810,a,b,1539,a)].">
      <j1 rule="hyper" parents="275 4810 1539"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4824(a,1),284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4824 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4824(a,1),470(a,2,1))].">
      <j1 rule="para" parents="4824 470"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(4824(a,1),1810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4824 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1823,a,4818,a)].">
      <j1 rule="hyper" parents="1823 4818"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      R(x,x \ 1,K(x \ 1,y)) = 1 / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(816,a,4822,a)].">
      <j1 rule="hyper" parents="816 4822"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),4826(a,1,1)),flip(a)].">
      <j1 rule="para" parents="77 4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      1 / x = z
    ]]></literal>
    <justification jstring="[para(4826(a,2),956(a,1))].">
      <j1 rule="para" parents="4826 956"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      (x \ T(y,z)) / (1 / x) = T((x \ y) / (1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4797,a(flip),b,1379,a)].">
      <j1 rule="hyper" parents="128 4797 1379"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4797(a,1,1,1,1))].">
      <j1 rule="para" parents="4 4797"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,2),4797(a,1,1,1,1))].">
      <j1 rule="para" parents="11 4797"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4797(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4797 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(78(a,1),4797(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="78 4797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4213(a,1),4797(a,1,1,1))].">
      <j1 rule="para" parents="4213 4797"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      (x \ y) * (T(y,z) / (x \ y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4801(a,1,2,1,1))].">
      <j1 rule="para" parents="5 4801"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4801(a,1),78(a,1,1,2))].">
      <j1 rule="para" parents="4801 78"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      x * ((1 / x) * T((1 / x) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1548(a,2),4801(a,1,2))].">
      <j1 rule="para" parents="1548 4801"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,4803,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4803 17"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4803(a,2),41(a,1))].">
      <j1 rule="para" parents="4803 41"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(106(a,1),4803(a,2,1,2))].">
      <j1 rule="para" parents="106 4803"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      T((x \ y) * x,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4803(a,2),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4803 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(4803(a,2),89(a,1,1))].">
      <j1 rule="para" parents="4803 89"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      T(L(1 / x,x,y) * y,z) = (y \ T(y / x,z)) * y
    ]]></literal>
    <justification jstring="[para(3417(a,2),4803(a,1,1,1))].">
      <j1 rule="para" parents="3417 4803"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,4850,a)].">
      <j1 rule="hyper" parents="51 4850"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      T(x * y,y * x) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4855(a,1,2,1))].">
      <j1 rule="para" parents="4 4855"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,4804,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 4804 17"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      x \ T(x * (y / x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4804(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4804 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      x \ T(x * (y / x),z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) / x) / w = u
    ]]></literal>
    <justification jstring="[para(4804(a,2),722(a,1,2))].">
      <j1 rule="para" parents="4804 722"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(221,a,4829,a)].">
      <j1 rule="hyper" parents="221 4829"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(156,a,4829,a)].">
      <j1 rule="hyper" parents="156 4829"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1583,a,4835,a),flip(a)].">
      <j1 rule="hyper" parents="1583 4835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1551,a,4835,a)].">
      <j1 rule="hyper" parents="1551 4835"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,1378,a,b,4835,a)].">
      <j1 rule="hyper" parents="370 1378 4835"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2253,a,b,4835,a)].">
      <j1 rule="hyper" parents="60 2253 4835"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4835(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4835(a,1),109(a,1,1))].">
      <j1 rule="para" parents="4835 109"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4835(a,1),494(a,1,1))].">
      <j1 rule="para" parents="4835 494"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4835(a,1),4226(a,1,2))].">
      <j1 rule="para" parents="4835 4226"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4845(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4845 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      x \ T(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4845(a,1),389(a,1,2))].">
      <j1 rule="para" parents="4845 389"/>
    </justification>
  </clause>

  <clause id="4877">
    <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(1504(a,1),4861(a,1,1,1,1))].">
      <j1 rule="para" parents="1504 4861"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2596(a,1),4823(a,1,1,2))].">
      <j1 rule="para" parents="2596 4823"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      R(x,x \ 1,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,74,a(flip),b,4830,a),flip(a)].">
      <j1 rule="hyper" parents="370 74 4830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4880(a,1),1088(a,1,1,1))].">
      <j1 rule="para" parents="4880 1088"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      K(x \ (x / y),x) = (y \ 1) \ T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1806,a,b,4811,a)].">
      <j1 rule="hyper" parents="370 1806 4811"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4826(a,1),4828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4826 4828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,421,a(flip),b,4886,a),flip(a)].">
      <j1 rule="hyper" parents="370 421 4886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),4831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="77 4831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4443,a(flip),b,4890,a),flip(a)].">
      <j1 rule="hyper" parents="370 4443 4890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,2458,a,b,4891,a)].">
      <j1 rule="hyper" parents="60 2458 4891"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ L(x,y,z) = (L(x,y,z) \ (L(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(4892(a,1),3356(a,1,1,1))].">
      <j1 rule="para" parents="4892 3356"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),4848(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 4848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x \ y) * ((z \ ((x \ y) \ y)) * z) = ((z \ x) * z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),4848(a,1,2,1,2))].">
      <j1 rule="para" parents="108 4848"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(109(a,1),4857(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 4857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(262(a,1),4857(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="262 4857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (x \ 1),x) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1530(a,1),4867(a,1,1))].">
      <j1 rule="para" parents="1530 4867"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(4809(a,1),44(a,1))].">
      <j1 rule="para" parents="4809 44"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3581,a(flip),b,4821,a)].">
      <j1 rule="hyper" parents="60 3581 4821"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11,a(flip),b,4902,a)].">
      <j1 rule="hyper" parents="370 11 4902"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1588,a(flip),b,4902,a),flip(a)].">
      <j1 rule="hyper" parents="60 1588 4902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),4902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 4902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = K(T(x \ 1,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4332(a,1),4902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4332 4902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3757,a,b,4905,a)].">
      <j1 rule="hyper" parents="60 3757 4905"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      K(T(x \ y,y \ x),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3511(a,2),4905(a,1,1))].">
      <j1 rule="para" parents="3511 4905"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,4907,a)].">
      <j1 rule="hyper" parents="51 4907"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4907(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4907 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4909(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4909 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4909(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4909 328"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4909(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4909 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4909(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4909 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4909(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4909 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4909(a,1),4804(a,2,2,1))].">
      <j1 rule="para" parents="4909 4804"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,4911,a)].">
      <j1 rule="hyper" parents="51 4911"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      T(T(K(x,y),z),T(x,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4917(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4917 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4917(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4917 328"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      T(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4913(a,2),40(a,1))].">
      <j1 rule="para" parents="4913 40"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,4916,a)].">
      <j1 rule="hyper" parents="51 4916"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4922(a,1,2,2))].">
      <j1 rule="para" parents="6 4922"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(4923(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4923 328"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4903(a,1),396(a,1))].">
      <j1 rule="para" parents="4903 396"/>
    </justification>
  </clause>

  <clause id="4927">
    <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(1183,a,4910,a),flip(a)].">
      <j1 rule="hyper" parents="1183 4910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(276,a,4910,a)].">
      <j1 rule="hyper" parents="276 4910"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,4910,a,b,87,a),flip(a)].">
      <j1 rule="hyper" parents="124 4910 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      R(K(x,y),z,u) * L(x,w,v5) = L(x,w,v5) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4928(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="4928 273"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(276,a,4915,a)].">
      <j1 rule="hyper" parents="276 4915"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / (x \ y) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),4858(a,1,2,1,2))].">
      <j1 rule="para" parents="74 4858"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      L(x \ T(x * y,y),x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4865(a,1),2450(a,1,1))].">
      <j1 rule="para" parents="4865 2450"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(60,a,653,a(flip),b,4934,a)].">
      <j1 rule="hyper" parents="60 653 4934"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4409,a,4714,a),flip(a)].">
      <j1 rule="hyper" parents="4409 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4717(a,2),4600(a,1,2))].">
      <j1 rule="para" parents="4717 4600"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(276,a,4766,a)].">
      <j1 rule="hyper" parents="276 4766"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(4141,a,4788,a)].">
      <j1 rule="hyper" parents="4141 4788"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,3629,a,b,4789,a)].">
      <j1 rule="hyper" parents="31 3629 4789"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = T(x,z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1058,a,4799,a),flip(a)].">
      <j1 rule="hyper" parents="1058 4799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,z) = (x \ 1) * T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,4847,a(flip),b,3572,a)].">
      <j1 rule="hyper" parents="125 4847 3572"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,4863,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="128 4863 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4863(a,2),4858(a,1))].">
      <j1 rule="para" parents="4863 4858"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)),z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(2442(a,1),4864(a,2,1,1))].">
      <j1 rule="para" parents="2442 4864"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4864(a,2),4851(a,1))].">
      <j1 rule="para" parents="4864 4851"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,2267,a(flip),b,4866,a),flip(a)].">
      <j1 rule="hyper" parents="370 2267 4866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(147,a,4896,a)].">
      <j1 rule="hyper" parents="147 4896"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4223,a,b,4896,a)].">
      <j1 rule="hyper" parents="60 4223 4896"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(253(a,2),4896(a,1,1,1,2))].">
      <j1 rule="para" parents="253 4896"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * T(x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(4896(a,1),2432(a,1))].">
      <j1 rule="para" parents="4896 2432"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(251(a,2),4898(a,2,2,2,1))].">
      <j1 rule="para" parents="251 4898"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ y,z) * K(x,x \ 1) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3558(a,1),4936(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3558 4936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(32,a,4578,a,b,4939,a)].">
      <j1 rule="hyper" parents="32 4578 4939"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      T((x / y) * K(z,z \ 1),y) = (y \ x) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,1),4941(a,2,1))].">
      <j1 rule="para" parents="109 4941"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4950(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 4950"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4950(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4950 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(4580(a,1),3565(a,1,2))].">
      <j1 rule="para" parents="4580 3565"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,3632,a(flip),b,4628,a)].">
      <j1 rule="hyper" parents="60 3632 4628"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2283(a,1),4631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2283 4631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3610(a,1),4639(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3610 4639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,(y * z) \ (y * y))
    ]]></literal>
    <justification jstring="[para(3(a,1),4682(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 4682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4689,a,4233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4689 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[para(4722(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="4722 3604"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      K(x \ 1,x) * (y * ((x \ z) \ z)) = y * T(1 / (1 / x),x \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),4723(a,1,2,2))].">
      <j1 rule="para" parents="108 4723"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ z) \ z,u)) = y * (1 / (1 / T((x \ z) \ z,u)))
    ]]></literal>
    <justification jstring="[para(4704(a,1),4726(a,1,1))].">
      <j1 rule="para" parents="4704 4726"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,2321,a,b,4871,a)].">
      <j1 rule="hyper" parents="60 2321 4871"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      (((x \ 1) \ y) * x) * (1 / x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1338,a,4900,a)].">
      <j1 rule="hyper" parents="1338 4900"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      T(x,T(((y \ 1) \ 1) \ z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(4955(a,1),4642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4955 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      T(x,T((1 / y) \ z,u)) = T(x,T((y \ 1) \ z,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),4975(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 4975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4977">
    <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(4957(a,2),41(a,1))].">
      <j1 rule="para" parents="4957 41"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4688,a,4968,a)].">
      <j1 rule="hyper" parents="4688 4968"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) / y = u
    ]]></literal>
    <justification jstring="[para(2214(a,1),4946(a,1))].">
      <j1 rule="para" parents="2214 4946"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      x \ ((y * (x * x)) * (x \ 1)) = (1 / (1 / x)) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(1267,a,4477,a),flip(a)].">
      <j1 rule="hyper" parents="1267 4477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      x \ ((y * (x * x)) * (x \ 1)) = ((x \ 1) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1313(a,1),4982(a,2,1))].">
      <j1 rule="para" parents="1313 4982"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      x \ (y * ((x * x) * (x \ 1))) = ((x \ 1) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(29(a,1),4983(a,1,2))].">
      <j1 rule="para" parents="29 4983"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (y * x) = x \ (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(936(a,1),4984(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="936 4984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4490(a,2),239(a,1)),flip(b)].">
      <j1 rule="para" parents="4490 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * (x \ 1) = (x \ ((x \ 1) \ y)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(945(a,1),4531(a,1,1)),flip(a)].">
      <j1 rule="para" parents="945 4531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(13(a,2),4606(a,2,1))].">
      <j1 rule="para" parents="13 4606"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(4002(a,1),4621(a,1,2))].">
      <j1 rule="para" parents="4002 4621"/>
    </justification>
  </clause>

  <clause id="4990">
    <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(1029,a,4627,a),flip(a)].">
      <j1 rule="hyper" parents="1029 4627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * T(w,(1 / z) * u))) = T(x,y * (w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),4673(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 4673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4383(a,2),4678(a,1,2))].">
      <j1 rule="para" parents="4383 4678"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(4443(a,1),4904(a,2,1,1))].">
      <j1 rule="para" parents="4443 4904"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,2134,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="370 2134 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4897,a(flip),b,4962,a)].">
      <j1 rule="hyper" parents="60 4897 4962"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4959,a,4973,a)].">
      <j1 rule="hyper" parents="4959 4973"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * (1 / x) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,2116,a(flip),b,4987,a),flip(a)].">
      <j1 rule="hyper" parents="60 2116 4987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      x \ T(L(1 / (x \ 1),y,z) \ 1,x \ 1) = (x \ (L(x \ 1,y,z) \ (x \ 1))) * (1 / x)
    ]]></literal>
    <justification jstring="[para(3865(a,1),4997(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3865 4997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3455(a,1),4992(a,1,2,1))].">
      <j1 rule="para" parents="3455 4992"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4098,a(flip),b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="60 4098 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(155,a,5000,a)].">
      <j1 rule="hyper" parents="155 5000"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      x \ y != ((z \ (u * x)) * z) / x
    ]]></literal>
    <literal><![CDATA[
      (z \ (x * u)) * z = y
    ]]></literal>
    <justification jstring="[para(5000(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5000 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(5000(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5000 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) = K(x,y / x) * x
    ]]></literal>
    <justification jstring="[para(2591(a,1),4685(a,2,1))].">
      <j1 rule="para" parents="2591 4685"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * ((x * K(y,x)) \ 1))
    ]]></literal>
    <justification jstring="[para(4770(a,2),1533(a,1,1,2))].">
      <j1 rule="para" parents="4770 1533"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(536(a,1),4815(a,2,1))].">
      <j1 rule="para" parents="536 4815"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      T(x,R((y \ x) \ 1,((y \ x) \ 1) \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(5005(a,2),4912(a,1))].">
      <j1 rule="para" parents="5005 4912"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ T(x * y,x \ 1) = ((x \ 1) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1308,a,4528,a)].">
      <j1 rule="hyper" parents="1308 4528"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      x \ T(x,R(y,x,(y * x) \ x)) = L(K(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(2596(a,1),5010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2596 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5012(a,2),383(a,1))].">
      <j1 rule="para" parents="5012 383"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5013,a,300,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5013 300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2363,a,5014,a)].">
      <j1 rule="hyper" parents="2363 5014"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(5014(a,1),41(a,1))].">
      <j1 rule="para" parents="5014 41"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      (x \ K(x,y)) * L(z,x \ 1,K(x,y)) = K(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(5015(a,1),92(a,1,1))].">
      <j1 rule="para" parents="5015 92"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(5015(a,1),722(a,1,2))].">
      <j1 rule="para" parents="5015 722"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1713(a,1),4989(a,1,2))].">
      <j1 rule="para" parents="1713 4989"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      R(K(x,x \ 1) * (y / z),z,K(x \ 1,x)) = y / (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3456(a,1),4396(a,1,1))].">
      <j1 rule="para" parents="3456 4396"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(4593(a,1),4595(a,1,2))].">
      <j1 rule="para" parents="4593 4595"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(389,a,4881,a),flip(a)].">
      <j1 rule="hyper" parents="389 4881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(31,a,4808,a,b,5023,a)].">
      <j1 rule="hyper" parents="31 4808 5023"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5024(a,1),3321(a,1,1))].">
      <j1 rule="para" parents="5024 3321"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4614,a,5025,a)].">
      <j1 rule="hyper" parents="4614 5025"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(4201,a,5025,a),flip(a)].">
      <j1 rule="hyper" parents="4201 5025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5027(a,2),4372(a,1,1))].">
      <j1 rule="para" parents="5027 4372"/>
    </justification>
  </clause>

  <clause id="5031">
    <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(107(a,2),4927(a,2,1,1,1))].">
      <j1 rule="para" parents="107 4927"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4607,a(flip),b,4988,a)].">
      <j1 rule="hyper" parents="60 4607 4988"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3879,a,5032,a),flip(a)].">
      <j1 rule="hyper" parents="3879 5032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = K(y \ 1,y) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,4366,a,b,5032,a),flip(a)].">
      <j1 rule="hyper" parents="370 4366 5032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(4374(a,1),5033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4374 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,631,a(flip),b,5034,a),flip(a)].">
      <j1 rule="hyper" parents="370 631 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4409,a,5035,a),flip(a)].">
      <j1 rule="hyper" parents="4409 5035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      L(x * K(y \ z,(y \ z) \ 1),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(4000(a,1),5037(a,2,2))].">
      <j1 rule="para" parents="4000 5037"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5037(a,2),4587(a,1,2))].">
      <j1 rule="para" parents="5037 4587"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(4599,a,5021,a),flip(a)].">
      <j1 rule="hyper" parents="4599 5021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(4582(a,1),5041(a,1,2))].">
      <j1 rule="para" parents="4582 5041"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,5043,a,b,3618,a)].">
      <j1 rule="hyper" parents="129 5043 3618"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(4382(a,1),5044(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4382 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(4720(a,1),5045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4720 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[para(5046(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="5046 3604"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(4593(a,1),5022(a,1,2,2))].">
      <j1 rule="para" parents="4593 5022"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(629,a,5048,a)].">
      <j1 rule="hyper" parents="629 5048"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (1 / x) = x \ (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,4498,a,b,4467,a)].">
      <j1 rule="hyper" parents="32 4498 4467"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ ((L(x \ 1,y,z) \ 1) * K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4467(a,1),4563(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4467 4563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ K(y,y \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(4412(a,1),4681(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4412 4681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      T(x,R(y \ K(z,z \ 1),u,w)) = T(x,R(y \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,4999,a(flip),b,5053,a),flip(a)].">
      <j1 rule="hyper" parents="60 4999 5053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ ((x \ 1) \ y)) * (x \ 1) = T(T(y,x) / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4706,a(flip),b,4695,a),flip(a)].">
      <j1 rule="hyper" parents="370 4706 4695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ R(T(x,x \ (x \ 1)),y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),4705(a,2,2))].">
      <j1 rule="para" parents="22 4705"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ L(x,y,z) = T(1 / x,L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(2485(a,1),4894(a,2,1))].">
      <j1 rule="para" parents="2485 4894"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ L(x,y,z) = x * T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,536,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="370 536 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ L(x,y,z) = K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5024,a(flip),b,5062,a),flip(a)].">
      <j1 rule="hyper" parents="370 5024 5062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5026,a,b,5063,a),flip(a)].">
      <j1 rule="hyper" parents="370 5026 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,2036,a,b,5064,a),flip(a)].">
      <j1 rule="hyper" parents="36 2036 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(108(a,1),5065(a,1,1))].">
      <j1 rule="para" parents="108 5065"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      L(L(x,y,z),L(x,y,z),L(x,y,z)) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1317,a,b,5066,a)].">
      <j1 rule="hyper" parents="370 1317 5066"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),5066(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 5066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5066(a,2),1307(a,1,1))].">
      <j1 rule="para" parents="5066 1307"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1313(a,2),5066(a,1,1))].">
      <j1 rule="para" parents="1313 5066"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,5068,a)].">
      <j1 rule="hyper" parents="221 5068"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(5068(a,1),216(a,1,2,2))].">
      <j1 rule="para" parents="5068 216"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      1 / L(1 / x,y,z) = L(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(5068(a,1),1307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5068 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5068(a,1),4653(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5068 4653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1313(a,2),5069(a,1,1,1))].">
      <j1 rule="para" parents="1313 5069"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      (x \ 1) * (L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1)) = L(1 / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(5069(a,1),2170(a,2,1))].">
      <j1 rule="para" parents="5069 2170"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1313,a,b,5070,a),flip(a)].">
      <j1 rule="hyper" parents="370 1313 5070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      1 / L(x \ 1,y,z \ 1) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1492(a,1),5071(a,2,1))].">
      <j1 rule="para" parents="1492 5071"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x,y,z)) = (L(1 / x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5071(a,1),4253(a,2,1))].">
      <j1 rule="para" parents="5071 4253"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      T(x,L(y,z,u) \ ((y * y) * 1)) = T(x,L(y \ 1,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5073(a,1),4450(a,2,2))].">
      <j1 rule="para" parents="5073 4450"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      L(1 / (1 / (x \ y)),x,1 / x) = 1 / (1 / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(654(a,1),5077(a,2,2,2))].">
      <j1 rule="para" parents="654 5077"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      L(L(1 / x,y,z),L(x,y,z),L(1 / x,y,z)) = L(((1 / x) \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3805,a(flip),b,5067,a)].">
      <j1 rule="hyper" parents="60 3805 5067"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      (1 / x) \ (1 / (1 / ((1 / x) * y))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(125,a,5081,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="125 5081 302"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) \ 1) = T(x,L(y,z,u) \ (y * y))
    ]]></literal>
    <justification jstring="[para(3(a,1),5080(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 5080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) \ 1) = T(x,y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(2160(a,1),5084(a,2,2))].">
      <j1 rule="para" parents="2160 5084"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ (y \ 1),z) = (x \ T(x * K(y \ 1,y),z)) / y
    ]]></literal>
    <justification jstring="[para(301(a,2),4944(a,2,1,2,1,2))].">
      <j1 rule="para" parents="301 4944"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(4000(a,1),5039(a,1,1,2))].">
      <j1 rule="para" parents="4000 5039"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ R(L(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(4668(a,1),5059(a,2,2,1))].">
      <j1 rule="para" parents="4668 5059"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = x \ L(R(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(24(a,1),5089(a,2,2))].">
      <j1 rule="para" parents="24 5089"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) * (1 / x)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2072,a(flip),b,5090,a),flip(a)].">
      <j1 rule="hyper" parents="370 2072 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      (x \ 1) \ R(1 / x,y,z) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2043(a,1),5091(a,1,2))].">
      <j1 rule="para" parents="2043 5091"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      (x \ 1) \ R(1 / x,y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1863,a(flip),b,5092,a),flip(a)].">
      <j1 rule="hyper" parents="370 1863 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(4211(a,2),4952(a,1,1))].">
      <j1 rule="para" parents="4211 4952"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4898,a(flip),b,4954,a),flip(a)].">
      <j1 rule="hyper" parents="60 4898 4954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(1 / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(4083(a,1),5076(a,1,2))].">
      <j1 rule="para" parents="4083 5076"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      L(1 / L(x,y,z),x,x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3922,a,5096,a),flip(a)].">
      <j1 rule="hyper" parents="3922 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (L(x,y,z) \ u) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,3899,a(flip),b,5079,a),flip(a)].">
      <j1 rule="hyper" parents="60 3899 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      L(L(1 / x,y,z),L(x,y,z),L(1 / x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),5082(a,2,1,1))].">
      <j1 rule="para" parents="77 5082"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,5094,a),flip(a)].">
      <j1 rule="hyper" parents="327 5094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      x * ((y * x) * T((y * x) \ 1,x)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(4953,a,5100,a)].">
      <j1 rule="hyper" parents="4953 5100"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      x * (y * (x * T(x \ (y \ 1),x))) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(1352(a,1),5101(a,1,2))].">
      <j1 rule="para" parents="1352 5101"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      (((x \ (1 / y)) * x) * y) * x = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[para(107(a,1),5102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 5102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(3965(a,2),5095(a,1,2))].">
      <j1 rule="para" parents="3965 5095"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(336,a,5104,a),flip(a)].">
      <j1 rule="hyper" parents="336 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5106">
    <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(370,a,522,a,b,4464,a)].">
      <j1 rule="hyper" parents="370 522 4464"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * (1 / (T(x,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4330(a,1),4972(a,2,2,2))].">
      <j1 rule="para" parents="4330 4972"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),5107(a,2,2))].">
      <j1 rule="para" parents="74 5107"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(3696(a,1),5020(a,2,1))].">
      <j1 rule="para" parents="3696 5020"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(5110(a,1),3702(a,1,1))].">
      <j1 rule="para" parents="5110 3702"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1534(a,1),5111(a,2,1,2))].">
      <j1 rule="para" parents="1534 5111"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,4215,a(flip),b,5112,a)].">
      <j1 rule="hyper" parents="60 4215 5112"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(4(a,1),5113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 5113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(147,a,5114,a),flip(a)].">
      <j1 rule="hyper" parents="147 5114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(128,a,5,a(flip),b,5114,a),flip(a)].">
      <j1 rule="hyper" parents="128 5 5114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,5115,a)].">
      <j1 rule="hyper" parents="135 5115"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,263,a(flip),b,5115,a)].">
      <j1 rule="hyper" parents="125 263 5115"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,4765,a,b,5115,a)].">
      <j1 rule="hyper" parents="60 4765 5115"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,4784,a,b,5115,a)].">
      <j1 rule="hyper" parents="31 4784 5115"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5115(a,1),1543(a,1,2))].">
      <j1 rule="para" parents="5115 1543"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5115(a,1),3298(a,1,1))].">
      <j1 rule="para" parents="5115 3298"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4901,a,5117,a)].">
      <j1 rule="hyper" parents="4901 5117"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4786,a,5117,a)].">
      <j1 rule="hyper" parents="4786 5117"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(5117(a,1),657(a,1,1))].">
      <j1 rule="para" parents="5117 657"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[para(5117(a,1),2542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5117 2542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(5008,a,5123,a),flip(a)].">
      <j1 rule="hyper" parents="5008 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      (x * y) / x != z * y
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5119(a,1),41(a,1))].">
      <j1 rule="para" parents="5119 41"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(5119(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="5119 210"/>
    </justification>
  </clause>

  <clause id="5132">
    <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(4229(a,2),5119(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4229 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <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(5122(a,1),629(a,1,1))].">
      <j1 rule="para" parents="5122 629"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(5128(a,2),40(a,1))].">
      <j1 rule="para" parents="5128 40"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(263(a,1),5125(a,2,2)),flip(a)].">
      <j1 rule="para" parents="263 5125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5126(a,2),4813(a,1))].">
      <j1 rule="para" parents="5126 4813"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(4931(a,1),5136(a,1))].">
      <j1 rule="para" parents="4931 5136"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2590,a,5124,a)].">
      <j1 rule="hyper" parents="2590 5124"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(5124(a,1),2590(a,1))].">
      <j1 rule="para" parents="5124 2590"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(5124(a,1),2884(a,1,1))].">
      <j1 rule="para" parents="5124 2884"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(5124(a,1),3221(a,2,2,1))].">
      <j1 rule="para" parents="5124 3221"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(5124(a,1),3234(a,2,2,1))].">
      <j1 rule="para" parents="5124 3234"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(108(a,2),5134(a,1,2,1))].">
      <j1 rule="para" parents="108 5134"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5140,a(flip),b,5143,a),flip(a)].">
      <j1 rule="hyper" parents="370 5140 5143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <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(4827(a,1),5147(a,2,2,2,1))].">
      <j1 rule="para" parents="4827 5147"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      (x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(5140(a,1),5144(a,1,1))].">
      <j1 rule="para" parents="5140 5144"/>
    </justification>
  </clause>

  <clause id="5151">
    <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(60,a,4584,a(flip),b,4510,a)].">
      <j1 rule="hyper" parents="60 4584 4510"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      L(x,(y \ 1) * ((1 / y) * (z * (1 / y))),u) = L(x,L(z * (y \ 1),1 / y,1 / y),u)
    ]]></literal>
    <justification jstring="[para(1796(a,1),4529(a,1,2))].">
      <j1 rule="para" parents="1796 4529"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((x * y) * T((x * y) \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(1153(a,1),5132(a,2,1))].">
      <j1 rule="para" parents="1153 5132"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(2316(a,1),5153(a,2,1))].">
      <j1 rule="para" parents="2316 5153"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5103,a(flip),b,5154,a),flip(a)].">
      <j1 rule="hyper" parents="370 5103 5154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(4896(a,2),5155(a,2,2))].">
      <j1 rule="para" parents="4896 5155"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      ((1 / (x * y)) * x) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(4229(a,1),5156(a,1,1))].">
      <j1 rule="para" parents="4229 5156"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4427,a(flip),b,5157,a)].">
      <j1 rule="hyper" parents="60 4427 5157"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(5158(a,2),40(a,1))].">
      <j1 rule="para" parents="5158 40"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(4545(a,1),5151(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4545 5151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a,b,5160,a),flip(a)].">
      <j1 rule="hyper" parents="370 13 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4366(a,2),5161(a,1,2))].">
      <j1 rule="para" parents="4366 5161"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      L(x,T(1 / y,z) \ u,w) = L(x,T(y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(4728(a,1),5161(a,1,2))].">
      <j1 rule="para" parents="4728 5161"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      L(x,T((y \ 1) \ 1,z) \ u,w) = L(x,T(y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),5164(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 5164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      x \ T(L(1 / (x \ 1),y,z) \ 1,x \ 1) = (x \ (L(x,y,z) \ x)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4079(a,1),4998(a,2,1,2))].">
      <j1 rule="para" parents="4079 4998"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      x \ T(L(1 / (x \ 1),y,z) \ 1,x \ 1) = (L(x,y,z) \ 1) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2169(a,1),5167(a,2,1))].">
      <j1 rule="para" parents="2169 5167"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      x \ T(L(x,y,z) \ 1,x \ 1) = (L(x,y,z) \ 1) * (1 / x)
    ]]></literal>
    <justification jstring="[para(74(a,1),5169(a,1,2,1,1,1))].">
      <j1 rule="para" parents="74 5169"/>
    </justification>
  </clause>

  <clause id="5172">
    <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(4410(a,1),4509(a,1,2,1))].">
      <j1 rule="para" parents="4410 4509"/>
    </justification>
  </clause>

  <clause id="5173">
    <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(3452(a,1),4543(a,1,1,2))].">
      <j1 rule="para" parents="3452 4543"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,z,K(y,y \ 1) * u)
    ]]></literal>
    <justification jstring="[para(4491(a,2),4990(a,1,1,1,2))].">
      <j1 rule="para" parents="4491 4990"/>
    </justification>
  </clause>

  <clause id="5175">
    <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(3445(a,1),5172(a,1,2))].">
      <j1 rule="para" parents="3445 5172"/>
    </justification>
  </clause>

  <clause id="5176">
    <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(3452(a,1),5173(a,1,2))].">
      <j1 rule="para" parents="3452 5173"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4557(a,1),5174(a,1,1))].">
      <j1 rule="para" parents="4557 5174"/>
    </justification>
  </clause>

  <clause id="5178">
    <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(1201,a,5175,a)].">
      <j1 rule="hyper" parents="1201 5175"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3449,a,5178,a),flip(a)].">
      <j1 rule="hyper" parents="3449 5178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      a(T(1 / x,y),z,u) = a(T(x \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[para(4715(a,1),5179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4715 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5182">
    <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(60,a,4626,a(flip),b,5176,a)].">
      <j1 rule="hyper" parents="60 4626 5176"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,2),5177(a,1,1,1))].">
      <j1 rule="para" parents="9 5177"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(3489,a,5183,a),flip(a)].">
      <j1 rule="hyper" parents="3489 5183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4990,a,b,5184,a)].">
      <j1 rule="hyper" parents="60 4990 5184"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      a(x,y,z * (u * (1 / w))) = a(x,y,z * (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(4548(a,1),5184(a,1,3))].">
      <j1 rule="para" parents="4548 5184"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4354(a,1),5186(a,1,1,1,2,2))].">
      <j1 rule="para" parents="4354 5186"/>
    </justification>
  </clause>

  <clause id="5190">
    <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(4557(a,1),5182(a,1,1))].">
      <j1 rule="para" parents="4557 5182"/>
    </justification>
  </clause>

  <clause id="5191">
    <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(9(a,2),5190(a,1,1,1))].">
      <j1 rule="para" parents="9 5190"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3489,a,5191,a),flip(a)].">
      <j1 rule="hyper" parents="3489 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(4382(a,1),5192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4382 5192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(1 / x,(1 / x) \ 1)) = (x \ 1) * (L(x \ 1,y,z) \ (x \ ((x \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[para(1313(a,1),3183(a,2,2,2,2))].">
      <j1 rule="para" parents="1313 3183"/>
    </justification>
  </clause>

  <clause id="5196">
    <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(3823(a,1),3852(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="3823 3852"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(1 / x,(1 / x) \ 1)) = (x \ 1) * (L(x \ 1,y,z) \ K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1734(a,1),5195(a,2,2,2))].">
      <j1 rule="para" parents="1734 5195"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(1 / x,(1 / x) \ 1)) = (x \ 1) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(4090(a,1),5197(a,2,2))].">
      <j1 rule="para" parents="4090 5197"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(x \ 1,x)) = (x \ 1) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1731(a,1),5198(a,1,2,2))].">
      <j1 rule="para" parents="1731 5198"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ K(x,x \ 1)) = (x \ 1) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1716(a,1),5199(a,1,2,2))].">
      <j1 rule="para" parents="1716 5199"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      (x \ 1) * (L(1 / x,y,z) \ 1) = L(x \ 1,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1712(a,1),5200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1712 5200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      (x \ 1) * (L(1 / x,y,z) \ 1) = x \ (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5051,a(flip),b,5201,a),flip(a)].">
      <j1 rule="hyper" parents="370 5051 5201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5203">
    <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(68(a,1),5196(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="68 5196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      (x \ y) \ L(L(x \ y,z,u),w,v5) = x \ (y * L(L(y \ x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(4039,a,5203,a)].">
      <j1 rule="hyper" parents="4039 5203"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z
    ]]></literal>
    <justification jstring="[para(1052(a,1),2409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1052 2409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z
    ]]></literal>
    <justification jstring="[para(1405(a,1),5206(a,2,1,2))].">
      <j1 rule="para" parents="1405 5206"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[para(88(a,1),5207(a,2,1,2))].">
      <j1 rule="para" parents="88 5207"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[para(3920(a,2),5208(a,1,2))].">
      <j1 rule="para" parents="3920 5208"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(336,a,5209,a)].">
      <j1 rule="hyper" parents="336 5209"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      (x * K(y \ z,y)) * y = x * (y * K(y \ z,y))
    ]]></literal>
    <justification jstring="[para(4772(a,1),5210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4772 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),5211(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 5211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),5212(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 5212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(809,a,5213,a)].">
      <j1 rule="hyper" parents="809 5213"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ ((x * (y * K(z,y))) * y) = L(y,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5213(a,1),4773(a,1,1))].">
      <j1 rule="para" parents="5213 4773"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(386,a,5216,a),flip(a)].">
      <j1 rule="hyper" parents="386 5216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      L(x,K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5216(a,1),386(a,1))].">
      <j1 rule="para" parents="5216 386"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5217(a,1),20(a,2,1))].">
      <j1 rule="para" parents="5217 20"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(5217(a,1),531(a,1,2,1))].">
      <j1 rule="para" parents="5217 531"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5217(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="5217 528"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5217(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="5217 529"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(691,a,5221,a)].">
      <j1 rule="hyper" parents="691 5221"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5224(a,1),48(a,2))].">
      <j1 rule="para" parents="5224 48"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(106(a,1),5224(a,1,3))].">
      <j1 rule="para" parents="106 5224"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = K(y,x) * x
    ]]></literal>
    <justification jstring="[para(5226(a,1),724(a,1,1))].">
      <j1 rule="para" parents="5226 724"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,4935,a(flip),b,5227,a)].">
      <j1 rule="hyper" parents="60 4935 5227"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,4935,a(flip),b,5227,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 4935 5227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5130,a,5228,a),flip(a)].">
      <j1 rule="hyper" parents="5130 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(4777,a,5228,a),flip(a)].">
      <j1 rule="hyper" parents="4777 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(382,a,5228,a),flip(a)].">
      <j1 rule="hyper" parents="382 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4746,a(flip),b,5228,a),flip(a)].">
      <j1 rule="hyper" parents="370 4746 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1480,a,b,5228,a(flip))].">
      <j1 rule="hyper" parents="128 1480 5228"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      x / y != K(y,z) * z
    ]]></literal>
    <literal><![CDATA[
      y * z = x
    ]]></literal>
    <justification jstring="[para(5228(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5228 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(5228(a,1),262(a,1,1))].">
      <j1 rule="para" parents="5228 262"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      ((x * y) / x) / y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5228(a,2),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5228 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5228(a,2),4753(a,1))].">
      <j1 rule="para" parents="5228 4753"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5137,a,5230,a)].">
      <j1 rule="hyper" parents="5137 5230"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      x * ((x \ 1) \ (y * (z * (x \ (1 / x))))) = T(y * z,x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(3225,a,5230,a)].">
      <j1 rule="hyper" parents="3225 5230"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5147,a,b,5230,a)].">
      <j1 rule="hyper" parents="370 5147 5230"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5124,a,b,5230,a)].">
      <j1 rule="hyper" parents="370 5124 5230"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5122,a,b,5230,a),flip(a)].">
      <j1 rule="hyper" parents="370 5122 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4883,a,b,5230,a)].">
      <j1 rule="hyper" parents="370 4883 5230"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4810,a,b,5230,a),flip(a)].">
      <j1 rule="hyper" parents="370 4810 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,4805,a,b,5230,a),flip(a)].">
      <j1 rule="hyper" parents="370 4805 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1539,a,b,5230,a),flip(a)].">
      <j1 rule="hyper" parents="370 1539 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4811,a(flip),b,5230,a)].">
      <j1 rule="hyper" parents="370 4811 5230"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1153,a(flip),b,5230,a)].">
      <j1 rule="hyper" parents="370 1153 5230"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,5230,a,b,5118,a)].">
      <j1 rule="hyper" parents="129 5230 5118"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5230,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="129 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(125,a,5230,a,b,5124,a)].">
      <j1 rule="hyper" parents="125 5230 5124"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,5230,a,b,5122,a)].">
      <j1 rule="hyper" parents="125 5230 5122"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5230,a,b,4810,a),flip(a)].">
      <j1 rule="hyper" parents="125 5230 4810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5230,a,b,4811,a(flip))].">
      <j1 rule="hyper" parents="125 5230 4811"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,4902,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 4902 5230"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(20(a,2),5230(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),5230(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      K(x,y) != x \ z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5230(a,2),44(a,1))].">
      <j1 rule="para" parents="5230 44"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5230(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5230 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      L(x \ K(y,z),x,y) = (y * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5230(a,2),344(a,1,1,2))].">
      <j1 rule="para" parents="5230 344"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(5230(a,2),1816(a,1,1))].">
      <j1 rule="para" parents="5230 1816"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2686(a,1),5230(a,2,2))].">
      <j1 rule="para" parents="2686 5230"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = w
    ]]></literal>
    <justification jstring="[para(5230(a,2),3363(a,1,3))].">
      <j1 rule="para" parents="5230 3363"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(4443(a,1),5230(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4443 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4642(a,1),5230(a,2,2))].">
      <j1 rule="para" parents="4642 5230"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(5230(a,2),4806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5230 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5230(a,2),4813(a,1,1))].">
      <j1 rule="para" parents="5230 4813"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(5230(a,2),4816(a,1))].">
      <j1 rule="para" parents="5230 4816"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(5230(a,2),5114(a,1,1,2))].">
      <j1 rule="para" parents="5230 5114"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(5230(a,2),5116(a,1,2))].">
      <j1 rule="para" parents="5230 5116"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4746(a,1),5236(a,1,1))].">
      <j1 rule="para" parents="4746 5236"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1206,a,5249,a(flip))].">
      <j1 rule="hyper" parents="1206 5249"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      R(T(x,y),z,u) / R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),5249(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      x \ (y * x) = y * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(504,a,5256,a)].">
      <j1 rule="hyper" parents="504 5256"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5256,a,b,341,a),flip(a)].">
      <j1 rule="hyper" parents="129 5256 341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      T(x * y,z) / a(x,y,K(x * y,z)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,5256,a,b,82,a)].">
      <j1 rule="hyper" parents="128 5256 82"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      x * K(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4443,a(flip),b,5256,a),flip(a)].">
      <j1 rule="hyper" parents="60 4443 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5256(a,2),40(a,1))].">
      <j1 rule="para" parents="5256 40"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5256(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5256 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      R(x / y,y,K(x,z)) = T(x,z) / (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(5256(a,2),104(a,2,1))].">
      <j1 rule="para" parents="5256 104"/>
    </justification>
  </clause>

  <clause id="5295">
    <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(5256(a,2),691(a,2,2))].">
      <j1 rule="para" parents="5256 691"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      x * (K(x,y) * L(K(x,y) \ (x \ z),u,w)) = T(x,y) * L((x * K(x,y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5256(a,2),1598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5256 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5256(a,2),2601(a,1,1))].">
      <j1 rule="para" parents="5256 2601"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(5256(a,2),5213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5256 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(1146,a,5275,a),flip(a)].">
      <j1 rule="hyper" parents="1146 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      (x \ y) \ y = K(x,x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(505,a,5275,a)].">
      <j1 rule="hyper" parents="505 5275"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x / y,y) * (x / y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,5275,a),flip(a)].">
      <j1 rule="hyper" parents="494 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a,b,5275,a),flip(a)].">
      <j1 rule="hyper" parents="60 20 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(129,a,5275,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 5275 17"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5275(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5275 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5275(a,2),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5275 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5275(a,2),94(a,2,2))].">
      <j1 rule="para" parents="5275 94"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * (z * x)) = L(T(z,x),x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5275(a,2),270(a,1,1))].">
      <j1 rule="para" parents="5275 270"/>
    </justification>
  </clause>

  <clause id="5309">
    <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(5275(a,2),822(a,1,2))].">
      <j1 rule="para" parents="5275 822"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      T(x * y,z) * a(K(x * y,z),y,T(x,y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5275(a,2),1028(a,1,1))].">
      <j1 rule="para" parents="5275 1028"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(T(x,y),a(K(x,y),z,z \ x)) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(5275(a,2),1400(a,1,2,1))].">
      <j1 rule="para" parents="5275 1400"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(5275(a,2),2627(a,1,1))].">
      <j1 rule="para" parents="5275 2627"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5275(a,2),4912(a,1))].">
      <j1 rule="para" parents="5275 4912"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y,z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(557,a,5280,a)].">
      <j1 rule="hyper" parents="557 5280"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(416,a,5280,a)].">
      <j1 rule="hyper" parents="416 5280"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5280(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5280(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="5280 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      (x * K(y,x)) \ (y * x) = y
    ]]></literal>
    <justification jstring="[para(5280(a,1),264(a,1,2,2))].">
      <j1 rule="para" parents="5280 264"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(5280(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5280(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5280(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * y) = L(x,y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5280(a,1),891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      ((x * K(y * z,x)) * y) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5280(a,1),879(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (1 / (x * K(y,x))) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5280(a,1),3177(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),4336(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5280 4336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5280(a,1),4444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5280 4444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),4848(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5280 4848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2291,a,b,5229,a),flip(a)].">
      <j1 rule="hyper" parents="370 2291 5229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5231(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(y / x,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),5231(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(5231(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5231 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5231(a,2),172(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5231 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = u
    ]]></literal>
    <justification jstring="[para(5231(a,2),1685(a,1,2,2))].">
      <j1 rule="para" parents="5231 1685"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K((x * y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5159,a,5233,a)].">
      <j1 rule="hyper" parents="5159 5233"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      K(x,1 / y) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,3302,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="370 3302 5233"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5233,a,b,2402,a)].">
      <j1 rule="hyper" parents="125 5233 2402"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4524,a(flip),b,5233,a),flip(a)].">
      <j1 rule="hyper" parents="60 4524 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = y * K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1098,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="60 1098 5233"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      L(x,x,(x \ 1) * y) = ((x \ 1) * y) \ (y * K(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,5233,a(flip),b,2480,a),flip(a)].">
      <j1 rule="hyper" parents="125 5233 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      (x * y) / x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5233(a,2),40(a,1))].">
      <j1 rule="para" parents="5233 40"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5233(a,1),334(a,1))].">
      <j1 rule="para" parents="5233 334"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5233(a,1),390(a,1,1))].">
      <j1 rule="para" parents="5233 390"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(103(a,1),5233(a,1,1))].">
      <j1 rule="para" parents="103 5233"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5233(a,1),104(a,1,1))].">
      <j1 rule="para" parents="5233 104"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(5233(a,1),382(a,1))].">
      <j1 rule="para" parents="5233 382"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5233(a,2),676(a,1,2))].">
      <j1 rule="para" parents="5233 676"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5233(a,1),706(a,1,1))].">
      <j1 rule="para" parents="5233 706"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      T(x * K(y,x),x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),896(a,1,1))].">
      <j1 rule="para" parents="5233 896"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(5233(a,1),556(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5233 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5233(a,1),986(a,1,1,1))].">
      <j1 rule="para" parents="5233 986"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),1141(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5233 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5233(a,1),1233(a,1,1))].">
      <j1 rule="para" parents="5233 1233"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5233(a,1),1236(a,1,1))].">
      <j1 rule="para" parents="5233 1236"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5233(a,2),86(a,1,2))].">
      <j1 rule="para" parents="5233 86"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      R(T(x,y * K(z,y)),y,K(z,y)) = ((z * y) / z) \ ((x * y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(5233(a,2),880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5233 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),900(a,1,1))].">
      <j1 rule="para" parents="5233 900"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),1397(a,1,1,1))].">
      <j1 rule="para" parents="5233 1397"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5233(a,1),1234(a,1,1))].">
      <j1 rule="para" parents="5233 1234"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(5233(a,1),2290(a,2,1,2))].">
      <j1 rule="para" parents="5233 2290"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      L(T(x * K(y * z,x),z),z,y) = (y * (x * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5233(a,1),2443(a,1,1,1))].">
      <j1 rule="para" parents="5233 2443"/>
    </justification>
  </clause>

  <clause id="5367">
    <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(2466(a,1),5233(a,1,1))].">
      <j1 rule="para" parents="2466 5233"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5233(a,1),2491(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5233 2491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5369">
    <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(2623(a,1),5233(a,1,1))].">
      <j1 rule="para" parents="2623 5233"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x / K(z,y)
    ]]></literal>
    <justification jstring="[para(5233(a,2),5214(a,1,2))].">
      <j1 rule="para" parents="5233 5214"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(435,a,5250,a(flip))].">
      <j1 rule="hyper" parents="435 5250"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(5250(a,2),629(a,1,2,2))].">
      <j1 rule="para" parents="5250 629"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5250(a,2),1544(a,1))].">
      <j1 rule="para" parents="5250 1544"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * ((T(x,y) \ 1) \ z)) = ((T(x,y) \ 1) * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5250(a,2),1512(a,1,1))].">
      <j1 rule="para" parents="5250 1512"/>
    </justification>
  </clause>

  <clause id="5376">
    <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(32,a,2631,a,b,5278,a),flip(a)].">
      <j1 rule="hyper" parents="32 2631 5278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      ((x * y) * z) * a(z * K(x * y,z),x,y) = ((z * K(x * y,z)) * x) * y
    ]]></literal>
    <justification jstring="[para(5278(a,1),82(a,1,1))].">
      <j1 rule="para" parents="5278 82"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4781(a,1),5278(a,1,1))].">
      <j1 rule="para" parents="4781 5278"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5278(a,1),4964(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5278 4964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(4902(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="4902 5265"/>
    </justification>
  </clause>

  <clause id="5381">
    <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(20(a,2),5290(a,1,2))].">
      <j1 rule="para" parents="20 5290"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      x \ L(x,x,x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x * x) = y
    ]]></literal>
    <justification jstring="[para(110(a,1),5290(a,1,2))].">
      <j1 rule="para" parents="110 5290"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(891(a,2),5290(a,1,2))].">
      <j1 rule="para" parents="891 5290"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1534(a,2),5290(a,1))].">
      <j1 rule="para" parents="1534 5290"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4811(a,1),5290(a,1))].">
      <j1 rule="para" parents="4811 5290"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(5124(a,2),5290(a,1))].">
      <j1 rule="para" parents="5124 5290"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5242(a,2),5290(a,1))].">
      <j1 rule="para" parents="5242 5290"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3757(a,1),5387(a,1))].">
      <j1 rule="para" parents="3757 5387"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(1911(a,1),5246(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1911 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5246(a,1),5373(a,1))].">
      <j1 rule="para" parents="5246 5373"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3330,a,5247,a)].">
      <j1 rule="hyper" parents="3330 5247"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(T(x,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2843,a,5247,a)].">
      <j1 rule="hyper" parents="2843 5247"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3319,a,b,5247,a)].">
      <j1 rule="hyper" parents="60 3319 5247"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2234,a(flip),b,5247,a)].">
      <j1 rule="hyper" parents="60 2234 5247"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2215,a(flip),b,5247,a)].">
      <j1 rule="hyper" parents="60 2215 5247"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5247,a(flip),b,2215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 5247 2215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5247(a,1,1,2))].">
      <j1 rule="para" parents="6 5247"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5247(a,1),2233(a,1,1))].">
      <j1 rule="para" parents="5247 2233"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5247(a,1),2218(a,1,2))].">
      <j1 rule="para" parents="5247 2218"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      (x / y) * K(y \ 1,x) = L(1 / y,y,x) * x
    ]]></literal>
    <justification jstring="[para(5247(a,1),3423(a,1,2))].">
      <j1 rule="para" parents="5247 3423"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) / y = u
    ]]></literal>
    <justification jstring="[para(5247(a,1),4981(a,1,2))].">
      <j1 rule="para" parents="5247 4981"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1381,a,5251,a)].">
      <j1 rule="hyper" parents="1381 5251"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5251,a(flip),b,1352,a(flip))].">
      <j1 rule="hyper" parents="125 5251 1352"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5251(a,1),1052(a,2,2))].">
      <j1 rule="para" parents="5251 1052"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5251(a,1),1390(a,2,2))].">
      <j1 rule="para" parents="5251 1390"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5251(a,1),1815(a,1,1))].">
      <j1 rule="para" parents="5251 1815"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5251(a,1),2340(a,2,1))].">
      <j1 rule="para" parents="5251 2340"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5251(a,1),2349(a,2,1))].">
      <j1 rule="para" parents="5251 2349"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      (x * y) * (y * T(y \ 1,z)) = (x * K(y \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(5251(a,1),2547(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5251 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5251(a,1),2367(a,2,1))].">
      <j1 rule="para" parents="5251 2367"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(5251(a,1),3247(a,2,1,2))].">
      <j1 rule="para" parents="5251 3247"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2231,a(flip),b,5252,a)].">
      <j1 rule="hyper" parents="60 2231 5252"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5290,a,5273,a),flip(a)].">
      <j1 rule="hyper" parents="5290 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(5142,a,5273,a)].">
      <j1 rule="hyper" parents="5142 5273"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(125,a,5273,a(flip),b,5124,a)].">
      <j1 rule="hyper" parents="125 5273 5124"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(5273(a,1),5290(a,1))].">
      <j1 rule="para" parents="5273 5290"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),5423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 5423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),5423(a,2,2))].">
      <j1 rule="para" parents="77 5423"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(5423(a,1),3302(a,2,1))].">
      <j1 rule="para" parents="5423 3302"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5423(a,2),4781(a,2,2))].">
      <j1 rule="para" parents="5423 4781"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4700,a,b,5428,a)].">
      <j1 rule="hyper" parents="60 4700 5428"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1701(a,2),5428(a,1,2))].">
      <j1 rule="para" parents="1701 5428"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2007(a,2),5428(a,1,2))].">
      <j1 rule="para" parents="2007 5428"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(2807(a,1),5428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2807 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(4338(a,1),5428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4338 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4566(a,2),5428(a,1,2))].">
      <j1 rule="para" parents="4566 5428"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,(x \ 1) \ 1) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5428(a,1),4781(a,2,2))].">
      <j1 rule="para" parents="5428 4781"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(5068(a,1),5428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5068 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,803,a(flip),b,5281,a),flip(a)].">
      <j1 rule="hyper" parents="128 803 5281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(31,a,5128,a(flip),b,5288,a),flip(a)].">
      <j1 rule="hyper" parents="31 5128 5288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5298(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5298 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      L((x * K(y,x)) \ z,x * K(y,x),y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5298(a,1),94(a,2,1))].">
      <j1 rule="para" parents="5298 94"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(5233(a,2),5298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5233 5298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5279(a,1),5298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5279 5298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(5315(a,2),2401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5315 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(5317,a,5316,a)].">
      <j1 rule="hyper" parents="5317 5316"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(557,a,5316,a)].">
      <j1 rule="hyper" parents="557 5316"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5316(a,1),46(a,2)),flip(b)].">
      <j1 rule="para" parents="5316 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      L(x,y,T(z * K(u * u,z),w)) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(5316(a,1),3548(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5316 3548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,5424,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="129 5424 90"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      x * K(y,1 / (x \ z)) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(5424(a,1),2881(a,1,2))].">
      <j1 rule="para" parents="5424 2881"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(3314(a,2),5432(a,1,1))].">
      <j1 rule="para" parents="3314 5432"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1686,a,5448,a)].">
      <j1 rule="hyper" parents="1686 5448"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1678,a,5448,a),flip(a)].">
      <j1 rule="hyper" parents="1678 5448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,2296,a,b,5448,a)].">
      <j1 rule="hyper" parents="32 2296 5448"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,T(z,y) * (z * ((z * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(5448(a,1),3390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5448 3390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,2265,a(flip),b,5464,a)].">
      <j1 rule="hyper" parents="60 2265 5464"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(125,a,5464,a(flip),b,2264,a)].">
      <j1 rule="hyper" parents="125 5464 2264"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),5464(a,1,2,2))].">
      <j1 rule="para" parents="74 5464"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(216(a,1),5464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="216 5464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      T(x,(y \ 1) \ x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(2456,a,5468,a),flip(a)].">
      <j1 rule="hyper" parents="2456 5468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      T(x,y \ x) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,5468,a(flip),b,2261,a)].">
      <j1 rule="hyper" parents="128 5468 2261"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      x \ T(y,x \ y) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(125,a,5468,a(flip),b,2262,a)].">
      <j1 rule="hyper" parents="125 5468 2262"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(5468(a,1),2259(a,1,1,1))].">
      <j1 rule="para" parents="5468 2259"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(363(a,2),5469(a,1,2))].">
      <j1 rule="para" parents="363 5469"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(275,a,1908,a,b,5462,a)].">
      <j1 rule="hyper" parents="275 1908 5462"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(275,a,1894,a(flip),b,5462,a)].">
      <j1 rule="hyper" parents="275 1894 5462"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,175,a(flip),b,5462,a)].">
      <j1 rule="hyper" parents="125 175 5462"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(88(a,1),5462(a,1,2))].">
      <j1 rule="para" parents="88 5462"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5462(a,1),629(a,1,1))].">
      <j1 rule="para" parents="5462 629"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5462(a,1),4769(a,1,1,1))].">
      <j1 rule="para" parents="5462 4769"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5475(a,1),284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5475 284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(275,a,5466,a,b,1688,a)].">
      <j1 rule="hyper" parents="275 5466 1688"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4663,a(flip),b,5470,a),flip(a)].">
      <j1 rule="hyper" parents="60 4663 5470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,893,a,b,5485,a)].">
      <j1 rule="hyper" parents="370 893 5485"/>
    </justification>
  </clause>

  <clause id="5487">
    <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(60,a,22,a,b,5485,a)].">
      <j1 rule="hyper" parents="60 22 5485"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5485,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="129 5485 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      x \ T(x,x * y) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5485,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 5485 5256"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5485(a,2,2))].">
      <j1 rule="para" parents="5 5485"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(5485(a,1),18(a,1,1))].">
      <j1 rule="para" parents="5485 18"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(5485(a,2),18(a,1,1))].">
      <j1 rule="para" parents="5485 18"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(5485(a,2),895(a,1,2))].">
      <j1 rule="para" parents="5485 895"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5485(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="5485 1165"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5490(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="5490 1165"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4845(a,1),5490(a,1,2))].">
      <j1 rule="para" parents="4845 5490"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,5316,a,b,5486,a)].">
      <j1 rule="hyper" parents="37 5316 5486"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(5486(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="5486 273"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a(flip),b,5495,a)].">
      <j1 rule="hyper" parents="60 22 5495"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      T(x,y) * K(x * y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5317,a,5500,a)].">
      <j1 rule="hyper" parents="5317 5500"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,5316,a,b,5500,a)].">
      <j1 rule="hyper" parents="37 5316 5500"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      (T(x,y \ x) / y) * x = x * (x / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5473,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 5473 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a,b,5476,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      T(x,T(x \ y,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5504(a,1,2,2))].">
      <j1 rule="para" parents="5 5504"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5485(a,1),5504(a,1,2))].">
      <j1 rule="para" parents="5485 5504"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(5506(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="5506 489"/>
    </justification>
  </clause>

  <clause id="5508">
    <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(5506(a,1),490(a,1,2,1))].">
      <j1 rule="para" parents="5506 490"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5481,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 5481 17"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(5481(a,2),1063(a,1,2,2))].">
      <j1 rule="para" parents="5481 1063"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5290,a,5489,a),flip(a)].">
      <j1 rule="hyper" parents="5290 5489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(5489(a,1),5290(a,1))].">
      <j1 rule="para" parents="5489 5290"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),5512(a,2,2))].">
      <j1 rule="para" parents="82 5512"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x * x,y) = z
    ]]></literal>
    <justification jstring="[para(853(a,1),5240(a,1))].">
      <j1 rule="para" parents="853 5240"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(77(a,1),5390(a,1,1,1))].">
      <j1 rule="para" parents="77 5390"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(74(a,1),5427(a,1,2))].">
      <j1 rule="para" parents="74 5427"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(1924,a,5494,a)].">
      <j1 rule="hyper" parents="1924 5494"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1923,a,5494,a)].">
      <j1 rule="hyper" parents="1923 5494"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(1922,a,5494,a)].">
      <j1 rule="hyper" parents="1922 5494"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      L(x,y,(y * x) / y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(1415,a,5494,a)].">
      <j1 rule="hyper" parents="1415 5494"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      (L(x,y,x) * y) * x = x * (y * x)
    ]]></literal>
    <justification jstring="[para(5494(a,1),1892(a,1,1))].">
      <j1 rule="para" parents="5494 1892"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      L(x,y,x * K(y,x)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),5523(a,1,3))].">
      <j1 rule="para" parents="5233 5523"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,5496,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5502(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5502 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(5521(a,1),680(a,1,1))].">
      <j1 rule="para" parents="5521 680"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,5532,a)].">
      <j1 rule="hyper" parents="60 24 5532"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2448,a,5533,a)].">
      <j1 rule="hyper" parents="2448 5533"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(672,a,5533,a)].">
      <j1 rule="hyper" parents="672 5533"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[para(5535(a,1),2258(a,1,2))].">
      <j1 rule="para" parents="5535 2258"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(4875,a,5536,a)].">
      <j1 rule="hyper" parents="4875 5536"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      T(x * y,x) / R(x,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(221,a,5536,a)].">
      <j1 rule="hyper" parents="221 5536"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),5536(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      (x * y) \ T(L(y,x,x),1 / x) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(579(a,1),5536(a,1,2,1))].">
      <j1 rule="para" parents="579 5536"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(5536(a,1),94(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5536 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(5537(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5537 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      T(x,y) / R(y,y \ x,y) = y \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),5539(a,1,1,1))].">
      <j1 rule="para" parents="5 5539"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2492,a,5522,a)].">
      <j1 rule="hyper" parents="2492 5522"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      ((x * (y * x)) / x) / T(x,x * y) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,5522,a,b,895,a)].">
      <j1 rule="hyper" parents="128 5522 895"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(5522(a,1),262(a,1,1))].">
      <j1 rule="para" parents="5522 262"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5522(a,2),1399(a,1))].">
      <j1 rule="para" parents="5522 1399"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5546(a,1),315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5546 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,5550,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 5550 17"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      x \ T(x * y,y) = y * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,5502,a,b,5538,a),flip(a)].">
      <j1 rule="hyper" parents="37 5502 5538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,3310,a(flip),b,5245,a)].">
      <j1 rule="hyper" parents="60 3310 5245"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ 1))) / z)) = K(z,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1842,a(flip),b,5245,a)].">
      <j1 rule="hyper" parents="60 1842 5245"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5245,a(flip),b,2883,a(flip))].">
      <j1 rule="hyper" parents="129 5245 2883"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(5245(a,1),3231(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5245 3231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,5271,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 5271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,5274,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5274(a,2),5290(a,1))].">
      <j1 rule="para" parents="5274 5290"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1716(a,2),5562(a,1,2,2))].">
      <j1 rule="para" parents="1716 5562"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3490(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="3490 5562"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3663(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3663 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3668(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="3668 5562"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3673(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="3673 5562"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      K(x,y / (1 / (1 / z))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3707(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="3707 5562"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4354(a,2),5562(a,1,2))].">
      <j1 rule="para" parents="4354 5562"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4373(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4373 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4375(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="4375 5562"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4376(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="4376 5562"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4377(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="4377 5562"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(4384(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4384 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,y * (K(z,z \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(4540(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="4540 5562"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(4624(a,2),5562(a,1,2))].">
      <j1 rule="para" parents="4624 5562"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(4626(a,2),5562(a,1,2))].">
      <j1 rule="para" parents="4626 5562"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(4415(a,1),5562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4415 5562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4457(a,1),5562(a,1,2))].">
      <j1 rule="para" parents="4457 5562"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4941(a,2),5562(a,1,2))].">
      <j1 rule="para" parents="4941 5562"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(4406(a,2),5564(a,1,2))].">
      <j1 rule="para" parents="4406 5564"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(4503(a,2),5564(a,1,2))].">
      <j1 rule="para" parents="4503 5564"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      K(x,((1 / (1 / y)) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4506(a,1),5564(a,1,2))].">
      <j1 rule="para" parents="4506 5564"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x,((1 / y) \ z) \ u) = K(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(4556(a,1),5564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4556 5564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1706(a,2),5570(a,1,2,1))].">
      <j1 rule="para" parents="1706 5570"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3695(a,1),5570(a,1,2))].">
      <j1 rule="para" parents="3695 5570"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(4544(a,1),5570(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4544 5570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(4548(a,1),5570(a,1,2))].">
      <j1 rule="para" parents="4548 5570"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(3679(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="3679 5571"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(4430(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="4430 5571"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x,(y / (1 / z)) * u) = K(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(4469(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="4469 5571"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4504(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="4504 5571"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(5045(a,2),5571(a,1,2))].">
      <j1 rule="para" parents="5045 5571"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3443(a,1),5586(a,1,2))].">
      <j1 rule="para" parents="3443 5586"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      T(x * K(1 / y,x),y) = (((y * y) \ x) * y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,1276,a,b,5320,a),flip(a)].">
      <j1 rule="hyper" parents="128 1276 5320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(32,a,2631,a,b,5320,a),flip(a)].">
      <j1 rule="hyper" parents="32 2631 5320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,5354,a,b,5233,a(flip))].">
      <j1 rule="hyper" parents="125 5354 5233"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T((y * x) / y,z) = u
    ]]></literal>
    <justification jstring="[para(5354(a,2),559(a,1))].">
      <j1 rule="para" parents="5354 559"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(5354(a,2),5240(a,1))].">
      <j1 rule="para" parents="5354 5240"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x / K(y,z)
    ]]></literal>
    <justification jstring="[hyper(2299,a,5370,a)].">
      <j1 rule="hyper" parents="2299 5370"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,x * x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(5382,a,3953,a)].">
      <j1 rule="hyper" parents="5382 3953"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(5449(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5449 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5453,a,b,xx)].">
      <j1 rule="hyper" parents="129 5453"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(5463(a,1),262(a,1,1))].">
      <j1 rule="para" parents="5463 262"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      T(1 / x,(1 / x) \ y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,554,a,b,5477,a),flip(a)].">
      <j1 rule="hyper" parents="370 554 5477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      ((x \ y) \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),5477(a,1,1))].">
      <j1 rule="para" parents="108 5477"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(1146,a,5492,a),flip(a)].">
      <j1 rule="hyper" parents="1146 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(5493(a,1),1146(a,1))].">
      <j1 rule="para" parents="5493 1146"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      (((1 / x) * ((y * (x * x)) * (1 / x))) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(889(a,1),5547(a,1,2,2))].">
      <j1 rule="para" parents="889 5547"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      x * T(y,z) != y * L(z,y,z)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(5551(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="5551 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5560,a(flip),b,5568,a)].">
      <j1 rule="hyper" parents="60 5560 5568"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5512,a,b,5614,a),flip(a)].">
      <j1 rule="hyper" parents="370 5512 5614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(5615(a,2),5513(a,1))].">
      <j1 rule="para" parents="5615 5513"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      K(x,y / L(1 / z,u,w)) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5072(a,1),5569(a,1,2,2))].">
      <j1 rule="para" parents="5072 5569"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) * w) = K(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5068(a,1),5573(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5068 5573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ w) = K(x,L(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(5068(a,1),5580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5068 5580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      (x * ((y * z) / y)) / K(y,z) = x * z
    ]]></literal>
    <justification jstring="[para(6(a,1),5601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(5609(a,2),1146(a,1))].">
      <j1 rule="para" parents="5609 1146"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      (x / y) * ((z * y) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(377,a,5620,a),flip(a)].">
      <j1 rule="hyper" parents="377 5620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(155,a,5620,a)].">
      <j1 rule="hyper" parents="155 5620"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      (x * (y * K(z,y))) / K(z,y) = x * y
    ]]></literal>
    <justification jstring="[para(5233(a,1),5620(a,1,1,2))].">
      <j1 rule="para" parents="5233 5620"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(401,a,5623,a),flip(a)].">
      <j1 rule="hyper" parents="401 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),5623(a,1,2,1))].">
      <j1 rule="para" parents="5 5623"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      L(x,(y / z) * ((u * u) * z),w) = L(x,y * K(u * u,z),w)
    ]]></literal>
    <justification jstring="[para(5623(a,1),3777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5623 3777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      K(x,y) * ((z * x) / z) = T(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5249(a,2),5623(a,1,1))].">
      <j1 rule="para" parents="5249 5623"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5335,a(flip),b,5624,a),flip(a)].">
      <j1 rule="hyper" parents="370 5335 5624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5624(a,2,2,1))].">
      <j1 rule="para" parents="5 5624"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(751,a,5625,a),flip(a)].">
      <j1 rule="hyper" parents="751 5625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(627,a,5625,a)].">
      <j1 rule="hyper" parents="627 5625"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2778,a,5632,a)].">
      <j1 rule="hyper" parents="2778 5632"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(2761,a,5632,a)].">
      <j1 rule="hyper" parents="2761 5632"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      x \ (y * K(z,x \ y)) = (x \ y) * K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(5632(a,1),675(a,1,1))].">
      <j1 rule="para" parents="5632 675"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5632(a,1),327(a,1,1))].">
      <j1 rule="para" parents="5632 327"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5632(a,1),2773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5632 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5633,a,b,5633,a)].">
      <j1 rule="hyper" parents="370 5633 5633"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,5633,a)].">
      <j1 rule="hyper" parents="50 5633"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5633,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 5633 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      L(x,y,z) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(5633(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="5633 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y \ 1,u) = z
    ]]></literal>
    <justification jstring="[para(5633(a,1),3531(a,1))].">
      <j1 rule="para" parents="5633 3531"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5635(a,1),48(a,2))].">
      <j1 rule="para" parents="5635 48"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5640(a,1),645(a,1)),flip(b)].">
      <j1 rule="para" parents="5640 645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      L(1 / x,x,x * y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(3420,a,5341,a)].">
      <j1 rule="hyper" parents="3420 5341"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5121,a(flip),b,5341,a)].">
      <j1 rule="hyper" parents="60 5121 5341"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5657(a,1),2556(a,1,1,2))].">
      <j1 rule="para" parents="5657 2556"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2213(a,1),5385(a,1))].">
      <j1 rule="para" parents="2213 5385"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(3320(a,1),5385(a,1))].">
      <j1 rule="para" parents="3320 5385"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(3331(a,1),5385(a,1))].">
      <j1 rule="para" parents="3331 5385"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5120(a,1),5480(a,1,1))].">
      <j1 rule="para" parents="5120 5480"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5644,a,5664,a)].">
      <j1 rule="hyper" parents="5644 5664"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5135,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="60 5135 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,5665,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 5665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(T(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5665(a,2),5290(a,1))].">
      <j1 rule="para" parents="5665 5290"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5667,a(flip),b,5231,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 5667 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),5667(a,1,1))].">
      <j1 rule="para" parents="17 5667"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,1),5667(a,1,1))].">
      <j1 rule="para" parents="108 5667"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(1163(a,1),5667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1163 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      K(x,y) * T(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5667(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5667 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5280(a,1),5667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,5674,a,b,88,a)].">
      <j1 rule="hyper" parents="129 5674 88"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5332,a,b,5674,a)].">
      <j1 rule="hyper" parents="60 5332 5674"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5674,a(flip),b,5332,a),flip(a)].">
      <j1 rule="hyper" parents="129 5674 5332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      x \ (y * K(y \ x,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(5674(a,1),2401(a,1,2,2))].">
      <j1 rule="para" parents="5674 2401"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(5674(a,1),5301(a,1,1))].">
      <j1 rule="para" parents="5674 5301"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      K(x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y / x,x) = z
    ]]></literal>
    <justification jstring="[para(109(a,1),5669(a,1,1))].">
      <j1 rule="para" parents="109 5669"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K((x \ y) * (x * x),x * x) != z
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,x * x) = z
    ]]></literal>
    <justification jstring="[para(950(a,1),5669(a,1,1))].">
      <j1 rule="para" parents="950 5669"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5669,a,5666,a)].">
      <j1 rule="hyper" parents="5669 5666"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      T(x,T(y,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5666,a(flip),b,5665,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 5666 5665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),5688(a,1,2))].">
      <j1 rule="para" parents="17 5688"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),5688(a,1,2))].">
      <j1 rule="para" parents="20 5688"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(286(a,1),5688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="286 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5280(a,1),5688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5280 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[para(5688(a,1),5254(a,1,2))].">
      <j1 rule="para" parents="5688 5254"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(928,a,5696,a)].">
      <j1 rule="hyper" parents="928 5696"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(147,a,5696,a),flip(a)].">
      <j1 rule="hyper" parents="147 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(135,a,5696,a),flip(a)].">
      <j1 rule="hyper" parents="135 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(60,a,4754,a(flip),b,5696,a)].">
      <j1 rule="hyper" parents="60 4754 5696"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5696,a(flip),b,4754,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 5696 4754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,5696,a(flip),b,4754,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 5696 4754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      T(x,y) * (x \ K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,5696,a(flip),b,1672,a),flip(a)].">
      <j1 rule="hyper" parents="124 5696 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      x * K(y,z) != z
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(5696(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="5696 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(109(a,1),5696(a,1,1))].">
      <j1 rule="para" parents="109 5696"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5696(a,1),159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5696 159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5696(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5696 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5696(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5696 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5429(a,1),5698(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5429 5698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(5373,a,5699,a),flip(a)].">
      <j1 rule="hyper" parents="5373 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5277,a,5699,a),flip(a)].">
      <j1 rule="hyper" parents="5277 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,4735,a,b,5699,a),flip(a)].">
      <j1 rule="hyper" parents="370 4735 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1676,a,b,5699,a),flip(a)].">
      <j1 rule="hyper" parents="370 1676 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5699,a,b,4735,a)].">
      <j1 rule="hyper" parents="128 5699 4735"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5699,a,b,1676,a),flip(a)].">
      <j1 rule="hyper" parents="125 5699 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5665,a(flip),b,5699,a),flip(a)].">
      <j1 rule="hyper" parents="60 5665 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5699,a(flip),b,5231,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 5699 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),5699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),5699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(2687(a,1),5699(a,2,1))].">
      <j1 rule="para" parents="2687 5699"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5699(a,2),4742(a,1))].">
      <j1 rule="para" parents="5699 4742"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(5699(a,1),5280(a,1,1,2))].">
      <j1 rule="para" parents="5699 5280"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(109(a,1),5700(a,1,2))].">
      <j1 rule="para" parents="109 5700"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5700(a,1),152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5700 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5700(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5700 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5700(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5700 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(5700(a,1),5221(a,2,2))].">
      <j1 rule="para" parents="5700 5221"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = z / T(z,x)
    ]]></literal>
    <justification jstring="[para(4642(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="4642 5701"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(5701(a,2),4940(a,1,2))].">
      <j1 rule="para" parents="5701 4940"/>
    </justification>
  </clause>

  <clause id="5739">
    <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(5703(a,2),3358(a,1,2,1))].">
      <j1 rule="para" parents="5703 3358"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(5665(a,1),5703(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5665 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,5689,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5689(a,2),5265(a,1))].">
      <j1 rule="para" parents="5689 5265"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(818,a,5741,a),flip(a)].">
      <j1 rule="hyper" parents="818 5741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5466,a,b,5741,a)].">
      <j1 rule="hyper" parents="60 5466 5741"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5741,a(flip),b,5466,a)].">
      <j1 rule="hyper" parents="128 5741 5466"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,5741,a(flip),b,1688,a)].">
      <j1 rule="hyper" parents="128 5741 1688"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5741,a(flip),b,1688,a),flip(a)].">
      <j1 rule="hyper" parents="125 5741 1688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5741 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),5741(a,1,2))].">
      <j1 rule="para" parents="18 5741"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),5741(a,1,2))].">
      <j1 rule="para" parents="20 5741"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 5741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),272(a,1,2,1))].">
      <j1 rule="para" parents="5741 272"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="5741 273"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),274(a,1,2,1))].">
      <j1 rule="para" parents="5741 274"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      T((x \ y) \ y,T(z,x)) = T(T(x,z),x \ y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5741 364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5758">
    <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(5741(a,1),488(a,1,2,1))].">
      <j1 rule="para" parents="5741 488"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5280(a,1),5741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5280 5741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      R(T(x,T(x * y,x)),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5741(a,2),5495(a,1,1))].">
      <j1 rule="para" parents="5741 5495"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5741(a,1),5535(a,1,3))].">
      <j1 rule="para" parents="5741 5535"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(5548(a,1),5741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5548 5741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5741(a,1),5666(a,1,1))].">
      <j1 rule="para" parents="5741 5666"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,90,a,b,5692,a)].">
      <j1 rule="hyper" parents="60 90 5692"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5692,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="129 5692 90"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(147,a,5705,a),flip(a)].">
      <j1 rule="hyper" parents="147 5705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5705(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5705 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5718(a,2),211(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5718 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5719(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5719 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5719(a,2),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5719 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y)) = (K(y,x) / x) * z
    ]]></literal>
    <justification jstring="[para(5720(a,2),586(a,2,1))].">
      <j1 rule="para" parents="5720 586"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,4780,a,b,5721,a)].">
      <j1 rule="hyper" parents="370 4780 5721"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(5721(a,1),3195(a,1,2,1))].">
      <j1 rule="para" parents="5721 3195"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(5721(a,1),4351(a,1,2))].">
      <j1 rule="para" parents="5721 4351"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5721(a,2),5266(a,1,1))].">
      <j1 rule="para" parents="5721 5266"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = L(R(x,z,x),z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5533,a,b,5730,a),flip(a)].">
      <j1 rule="hyper" parents="370 5533 5730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(323,a,5746,a)].">
      <j1 rule="hyper" parents="323 5746"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5741,a(flip),b,5746,a)].">
      <j1 rule="hyper" parents="128 5741 5746"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      (x / y) / T(y,x / y) = (y \ x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,109,a(flip),b,5746,a),flip(a)].">
      <j1 rule="hyper" parents="128 109 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1887,a,b,5746,a)].">
      <j1 rule="hyper" parents="60 1887 5746"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[para(5746(a,1),211(a,1,1,1))].">
      <j1 rule="para" parents="5746 211"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(5746(a,1),1889(a,1,1))].">
      <j1 rule="para" parents="5746 1889"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(5490(a,1),5746(a,1,1,2))].">
      <j1 rule="para" parents="5490 5746"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      L(1 / T(x,y),T(x,y),y) = y \ (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5747,a,b,3403,a),flip(a)].">
      <j1 rule="hyper" parents="125 5747 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(54,a,5747,a)].">
      <j1 rule="hyper" parents="54 5747"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,5747,a(flip),b,4840,a),flip(a)].">
      <j1 rule="hyper" parents="129 5747 4840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      T(x,y / x) / (y / x) = x / (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),5747(a,2,2))].">
      <j1 rule="para" parents="109 5747"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      T(x,T(y,x) \ x) / T(y,x) = (x * (T(x,y) / y)) / x
    ]]></literal>
    <justification jstring="[para(5747(a,2),5471(a,2,1,2))].">
      <j1 rule="para" parents="5747 5471"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),5748(a,1,2,1))].">
      <j1 rule="para" parents="18 5748"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[para(5748(a,1),219(a,1,2,1))].">
      <j1 rule="para" parents="5748 219"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(1692,a,5749,a)].">
      <j1 rule="hyper" parents="1692 5749"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5749(a,2),88(a,1,2,1))].">
      <j1 rule="para" parents="5749 88"/>
    </justification>
  </clause>

  <clause id="5796">
    <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(5749(a,1),84(a,1,1,2,1))].">
      <j1 rule="para" parents="5749 84"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(5749(a,1),3193(a,1,2,1))].">
      <j1 rule="para" parents="5749 3193"/>
    </justification>
  </clause>

  <clause id="5798">
    <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(5749(a,1),2927(a,1,2,1))].">
      <j1 rule="para" parents="5749 2927"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,5753,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5753,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 5753 17"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      (x * (y / x)) / T(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(5753(a,1),214(a,1,2))].">
      <j1 rule="para" parents="5753 214"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      T(T(x / y,(x / y) \ z),y) = T(y \ x,z / (x / y))
    ]]></literal>
    <justification jstring="[para(5753(a,1),284(a,1,1))].">
      <j1 rule="para" parents="5753 284"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5753(a,1),1175(a,2,2))].">
      <j1 rule="para" parents="5753 1175"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(5753(a,1),1340(a,1,2,2))].">
      <j1 rule="para" parents="5753 1340"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(5753(a,1),4804(a,2,2,1))].">
      <j1 rule="para" parents="5753 4804"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      L(T(x,y),K(y,x) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * (K(y,x) / x)) \ z = u
    ]]></literal>
    <justification jstring="[para(5770(a,2),668(a,1,1))].">
      <j1 rule="para" parents="5770 668"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,5783,a)].">
      <j1 rule="hyper" parents="215 5783"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),5783(a,1,2))].">
      <j1 rule="para" parents="22 5783"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5783(a,1),1908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5783 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      x / T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / y = z
    ]]></literal>
    <justification jstring="[para(5784(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5784 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5785,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="129 5785 210"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <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(5785(a,1),625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),1670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5785 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5491(a,1),5793(a,1,1))].">
      <j1 rule="para" parents="5491 5793"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),5799(a,1,2))].">
      <j1 rule="para" parents="6 5799"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(5799(a,1),1175(a,2,2))].">
      <j1 rule="para" parents="5799 1175"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(1 / x,y / (x \ 1)) = x * (((x \ 1) \ y) \ y)
    ]]></literal>
    <justification jstring="[para(5799(a,1),5252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5799 5252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      ((x \ y) \ y) * K(y / x,x) = x
    ]]></literal>
    <justification jstring="[para(5799(a,1),5696(a,1,1))].">
      <j1 rule="para" parents="5799 5696"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      T(x,y) \ z != T(y,x)
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(5808(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5808 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,x)) = z
    ]]></literal>
    <justification jstring="[para(5808(a,1),492(a,1))].">
      <j1 rule="para" parents="5808 492"/>
    </justification>
  </clause>

  <clause id="5830">
    <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(20(a,2),5710(a,1,1))].">
      <j1 rule="para" parents="20 5710"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(22(a,2),5710(a,1,1))].">
      <j1 rule="para" parents="22 5710"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5699,a(flip),b,5682,a),flip(a)].">
      <j1 rule="hyper" parents="129 5699 5682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,5231,a(flip),b,5682,a)].">
      <j1 rule="hyper" parents="35 5231 5682"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      x / (x / y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,4746,a,b,5683,a),flip(a)].">
      <j1 rule="hyper" parents="370 4746 5683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      T(x,(y / (y / (1 / z))) * u) = T(x,((z \ 1) * K((1 / z) \ y,1 / z)) * u)
    ]]></literal>
    <justification jstring="[para(5683(a,2),4660(a,1,2,1))].">
      <j1 rule="para" parents="5683 4660"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(5683(a,2),5280(a,1,1))].">
      <j1 rule="para" parents="5683 5280"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5683(a,2),5362(a,1,1))].">
      <j1 rule="para" parents="5683 5362"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5683(a,2),5678(a,1,1))].">
      <j1 rule="para" parents="5683 5678"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(77(a,1),5839(a,1,2))].">
      <j1 rule="para" parents="77 5839"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,T(x,y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,5722,a,b,5117,a),flip(a)].">
      <j1 rule="hyper" parents="129 5722 5117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1907,a,5736,a)].">
      <j1 rule="hyper" parents="1907 5736"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(808,a,5736,a),flip(a)].">
      <j1 rule="hyper" parents="808 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,5736,a)].">
      <j1 rule="hyper" parents="135 5736"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      K(x,x \ y) * K(z,x \ y) = (y / x) / T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5232,a(flip),b,5736,a),flip(a)].">
      <j1 rule="hyper" parents="128 5232 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,7,a(flip),b,5736,a),flip(a)].">
      <j1 rule="hyper" parents="128 7 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5,a(flip),b,5736,a)].">
      <j1 rule="hyper" parents="128 5 5736"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,5275,a,b,5736,a),flip(a)].">
      <j1 rule="hyper" parents="126 5275 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      (x * K(y \ z,y)) * ((y \ z) \ z) = x * y
    ]]></literal>
    <justification jstring="[hyper(60,a,361,a(flip),b,5736,a)].">
      <j1 rule="hyper" parents="60 361 5736"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      (T(x,y) * z) * K(y,T(x,z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(32,a,1930,a(flip),b,5736,a),flip(a)].">
      <j1 rule="hyper" parents="32 1930 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(32,a,1886,a(flip),b,5736,a),flip(a)].">
      <j1 rule="hyper" parents="32 1886 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      (x * y) / T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5736(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5736 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      T(x,y) * T(x,y) = x * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5254(a,1),5736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5254 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      (x / y) * T(y \ x,y) = (y \ x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(5279(a,1),5736(a,1,1))].">
      <j1 rule="para" parents="5279 5736"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(4063,a,5857,a)].">
      <j1 rule="hyper" parents="4063 5857"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(147,a,5857,a)].">
      <j1 rule="hyper" parents="147 5857"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,5857,a,b,63,a)].">
      <j1 rule="hyper" parents="129 5857 63"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5857,a(flip),b,5623,a),flip(a)].">
      <j1 rule="hyper" parents="128 5857 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5857(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="5857 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5857(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5857 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5857(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5857 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      K(x,y) \ 1 != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5857(a,1),383(a,1,2))].">
      <j1 rule="para" parents="5857 383"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      K(T(x,y),y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(5667(a,2),5857(a,1,1))].">
      <j1 rule="para" parents="5667 5857"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5688,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="370 5688 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      K(x,y) \ 1 = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(y,x),w) = L((w * K(y,x)) \ w,z,u)
    ]]></literal>
    <justification jstring="[para(5865(a,1),463(a,1,1,1))].">
      <j1 rule="para" parents="5865 463"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5865(a,1),1492(a,1,3))].">
      <j1 rule="para" parents="5865 1492"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (z / u)) = (K(x,y) * (K(y,x) \ z)) / u
    ]]></literal>
    <justification jstring="[para(5865(a,1),1791(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5865 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <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(5865(a,1),2945(a,2,1,2,1))].">
      <j1 rule="para" parents="5865 2945"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(5865(a,1),3401(a,1,2))].">
      <j1 rule="para" parents="5865 3401"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z * K(w,u))
    ]]></literal>
    <justification jstring="[para(5865(a,1),3426(a,1,3,2))].">
      <j1 rule="para" parents="5865 3426"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5865(a,1),3522(a,1,3))].">
      <j1 rule="para" parents="5865 3522"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(5865(a,1),3530(a,1,2))].">
      <j1 rule="para" parents="5865 3530"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5865(a,1),5250(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5865 5250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5251(a,2),5865(a,1,1))].">
      <j1 rule="para" parents="5251 5865"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(K(y,x),K(x,y),K(x,y)),z,u) = w
    ]]></literal>
    <justification jstring="[para(5867(a,1),2976(a,1,1))].">
      <j1 rule="para" parents="5867 2976"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5873(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5873 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(4811(a,1),5740(a,1,1))].">
      <j1 rule="para" parents="4811 5740"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      ((x \ y) \ y) * T(x \ y,x) = y
    ]]></literal>
    <justification jstring="[hyper(129,a,5745,a,b,xx)].">
      <j1 rule="hyper" parents="129 5745"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      T(x \ y,x) != z \ y
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(5745(a,2),45(a,1))].">
      <j1 rule="para" parents="5745 45"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(5745(a,1),1076(a,1,1))].">
      <j1 rule="para" parents="5745 1076"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      T(T(x,y),L(T(z,x),u,w)) = T(T(x,L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(20(a,2),5750(a,1,2))].">
      <j1 rule="para" parents="20 5750"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(5741(a,1),5751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5741 5751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(5766(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5766 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      K(x,x \ y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,x \ y)) = z
    ]]></literal>
    <justification jstring="[para(5766(a,1),276(a,2))].">
      <j1 rule="para" parents="5766 276"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5766(a,1),675(a,1,2))].">
      <j1 rule="para" parents="5766 675"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5775(a,1),5213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5775 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5777(a,1),308(a,1,2))].">
      <j1 rule="para" parents="5777 308"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5538,a(flip),b,5794,a),flip(a)].">
      <j1 rule="hyper" parents="370 5538 5794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      T(x * y,T(y,x)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(5821(a,2),5469(a,1,2))].">
      <j1 rule="para" parents="5821 5469"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * K(1 / x,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5825(a,1),5049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5825 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5844,a)].">
      <j1 rule="hyper" parents="316 5844"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(5844(a,1),1091(a,1,1))].">
      <j1 rule="para" parents="5844 1091"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(323,a,5850,a)].">
      <j1 rule="hyper" parents="323 5850"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(147,a,5850,a)].">
      <j1 rule="hyper" parents="147 5850"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(5850(a,1),389(a,1,2))].">
      <j1 rule="para" parents="5850 389"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / T(z,y),z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5850(a,1),694(a,1,1))].">
      <j1 rule="para" parents="5850 694"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5851(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5851 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      (x / y) * K(z,y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5851(a,1),379(a,1,1))].">
      <j1 rule="para" parents="5851 379"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      a(x * K(y,x),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5853(a,1),2988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5853 2988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      a(x,y * K(z,y),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5853(a,1),3066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5853 3066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(5853(a,1),3458(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5853 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(5853(a,1),3532(a,1,3))].">
      <j1 rule="para" parents="5853 3532"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,214,a(flip),b,5855,a),flip(a)].">
      <j1 rule="hyper" parents="125 214 5855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      (x \ 1) * (x \ K(y,x)) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,5855,a(flip),b,2070,a),flip(a)].">
      <j1 rule="hyper" parents="125 5855 2070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * K(z,y) = x / T((y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5428(a,1),5855(a,1,2))].">
      <j1 rule="para" parents="5428 5855"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4860,a,b,5929,a),flip(a)].">
      <j1 rule="hyper" parents="370 4860 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2251,a,b,5929,a),flip(a)].">
      <j1 rule="hyper" parents="370 2251 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5929,a,b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="125 5929 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,5699,a(flip),b,5929,a),flip(a)].">
      <j1 rule="hyper" parents="60 5699 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      T((x * y) / x,z) \ T(y,z) = K(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(556(a,1),5929(a,2,1)),flip(a)].">
      <j1 rule="para" parents="556 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(5929(a,2),4861(a,1,1))].">
      <j1 rule="para" parents="5929 4861"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),5938(a,1,2,1))].">
      <j1 rule="para" parents="82 5938"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(5699(a,1),5938(a,1,1))].">
      <j1 rule="para" parents="5699 5938"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,5860,a)].">
      <j1 rule="hyper" parents="125 5 5860"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(5860(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="5860 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(108(a,1),5860(a,1,1,2))].">
      <j1 rule="para" parents="108 5860"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = (((x * y) * T(z,u)) * K(u,z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5860(a,1),685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5860 685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5233(a,1),5868(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5233 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(5218,a,5883,a),flip(a)].">
      <j1 rule="hyper" parents="5218 5883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5220,a(flip),b,5883,a),flip(a)].">
      <j1 rule="hyper" parents="370 5220 5883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      L(x,K(y,z),u) * w = L(x,K(z,y),u) * w
    ]]></literal>
    <justification jstring="[hyper(54,a,5883,a)].">
      <j1 rule="hyper" parents="54 5883"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5948(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="5948 528"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(5948(a,1),3931(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5948 3931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5949(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5949 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5955">
    <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(5949(a,1),1186(a,1,2,1))].">
      <j1 rule="para" parents="5949 1186"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      L(x,((y \ z) \ z) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = w
    ]]></literal>
    <justification jstring="[para(5893(a,1),3544(a,1,2,2))].">
      <j1 rule="para" parents="5893 3544"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      (x * K(y,z / y)) / (z / y) = x / (y \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),5912(a,2,2))].">
      <j1 rule="para" parents="109 5912"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      T(x / T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5912(a,1),494(a,1,1))].">
      <j1 rule="para" parents="5912 494"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      R(x,y,z) * (x * (((u * R(x,y,z)) / u) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5934(a,2),1947(a,2,2))].">
      <j1 rule="para" parents="5934 1947"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      ((1 / x) * y) \ K((1 / x) * y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(1243(a,1),5935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1243 5935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      L(x,y * (z \ K(z,u)),w) = L(x,y * ((u * z) / u),w)
    ]]></literal>
    <justification jstring="[para(5935(a,1),3778(a,1,2,2))].">
      <j1 rule="para" parents="5935 3778"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5935(a,1),4513(a,1,2))].">
      <j1 rule="para" parents="5935 4513"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5233(a,1),5935(a,1,1))].">
      <j1 rule="para" parents="5233 5935"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(5522(a,1),5935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5522 5935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5966">
    <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(5936(a,1),1758(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5936 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      x * ((y * z) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(5941(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="5941 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,5947,a)].">
      <j1 rule="hyper" parents="215 5947"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(4902(a,2),5947(a,2,1))].">
      <j1 rule="para" parents="4902 5947"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      K(x,y) / ((x \ 1) \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5963(a,1),308(a,1,2))].">
      <j1 rule="para" parents="5963 308"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5963(a,1),272(a,1,2,1))].">
      <j1 rule="para" parents="5963 272"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      1 / (x \ K(x,y)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(221,a,5964,a)].">
      <j1 rule="hyper" parents="221 5964"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5761(a,1),274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5761 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5485,a(flip),b,5763,a),flip(a)].">
      <j1 rule="hyper" parents="370 5485 5763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(898(a,1),5763(a,1,2))].">
      <j1 rule="para" parents="898 5763"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      (x / y) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / y = z
    ]]></literal>
    <justification jstring="[para(5855(a,2),5813(a,1))].">
      <j1 rule="para" parents="5855 5813"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(5842(a,2),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5842 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),5842(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ (x * K(y,z)),z)
    ]]></literal>
    <justification jstring="[para(5912(a,1),5842(a,1,1,2))].">
      <j1 rule="para" parents="5912 5842"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5865(a,1),5891(a,1))].">
      <j1 rule="para" parents="5865 5891"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(17(a,1),5980(a,1,2))].">
      <j1 rule="para" parents="17 5980"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K(x,R(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(22(a,2),5980(a,1,2))].">
      <j1 rule="para" parents="22 5980"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5667(a,2),5980(a,1))].">
      <j1 rule="para" parents="5667 5980"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5974(a,1),1926(a,1,1))].">
      <j1 rule="para" parents="5974 1926"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5672(a,1),875(a,1,1,1))].">
      <j1 rule="para" parents="5672 875"/>
    </justification>
  </clause>

  <clause id="5988">
    <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(5672(a,1),2930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5672 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1498(a,1),5691(a,1,2))].">
      <j1 rule="para" parents="1498 5691"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      (T(x,y \ 1) \ x) \ (y * (T(y \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y \ 1,x),y) = u
    ]]></literal>
    <justification jstring="[para(5717(a,2),629(a,1,1))].">
      <j1 rule="para" parents="5717 629"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5699,a,b,5727,a),flip(a)].">
      <j1 rule="hyper" parents="370 5699 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(74(a,1),5992(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 5992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(5935(a,1),5993(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5935 5993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,5737,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 5737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3490(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="3490 5995"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3663(a,1),5995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3663 5995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3673(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="3673 5995"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3703(a,1),5995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3703 5995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4354(a,2),5995(a,1,1))].">
      <j1 rule="para" parents="4354 5995"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4373(a,1),5995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4373 5995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(4375(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="4375 5995"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4376(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="4376 5995"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(4384(a,1),5995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4384 5995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(4587(a,2),5995(a,1,1))].">
      <j1 rule="para" parents="4587 5995"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(4626(a,2),5995(a,1,1))].">
      <j1 rule="para" parents="4626 5995"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4457(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="4457 5995"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3339(a,1),6000(a,1,1))].">
      <j1 rule="para" parents="3339 6000"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      K(R(1 / x,y,z),u) = K(R(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(4195(a,1),6000(a,1,1))].">
      <j1 rule="para" parents="4195 6000"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4499(a,1),6000(a,1,1))].">
      <j1 rule="para" parents="4499 6000"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      K(x * ((1 / y) \ z),u) = K(x * ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(4544(a,1),6000(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4544 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      K(x * (y * (1 / z)),u) = K(x * (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(4548(a,1),6000(a,1,1))].">
      <j1 rule="para" parents="4548 6000"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(4395(a,2),6001(a,1,1))].">
      <j1 rule="para" parents="4395 6001"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4430(a,1),6001(a,1,1))].">
      <j1 rule="para" parents="4430 6001"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      K((x / (1 / y)) * z,u) = K((x / (y \ 1)) * z,u)
    ]]></literal>
    <justification jstring="[para(4469(a,1),6001(a,1,1))].">
      <j1 rule="para" parents="4469 6001"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      K(x / (K(y,y \ 1) * z),u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(5045(a,2),6001(a,1,1))].">
      <j1 rule="para" parents="5045 6001"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(221,a,5738,a)].">
      <j1 rule="hyper" parents="221 5738"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5280(a,1),5752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 5752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(323,a,5823,a)].">
      <j1 rule="hyper" parents="323 5823"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),5834(a,2,2,1,2))].">
      <j1 rule="para" parents="4 5834"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      ((x * T(T(x,y),y)) \ z) * T(x,y) = (1 / T(x,y)) * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(5863(a,1),1276(a,1,1,1))].">
      <j1 rule="para" parents="5863 1276"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      x * (y * T(T(y,y \ 1),y \ 1)) = (x * T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5863(a,1),860(a,1,2))].">
      <j1 rule="para" parents="5863 860"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(5904(a,1),3662(a,1,1))].">
      <j1 rule="para" parents="5904 3662"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(5904(a,1),3665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5904 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(5909(a,1),1237(a,1,1))].">
      <j1 rule="para" parents="5909 1237"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      a((a(x,x,x) * y) * K(x \ 1,a(x,x,x) * y),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(4694(a,1),5921(a,2,1))].">
      <j1 rule="para" parents="4694 5921"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5254(a,1),5923(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5254 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      L(x,y,T(z \ u,z)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5279(a,1),5923(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5279 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      L(x,y,T(T(z,z * u),u)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(893(a,1),6032(a,1,3,1))].">
      <j1 rule="para" parents="893 6032"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u * z)) = L(x,y,R(z,u,z))
    ]]></literal>
    <justification jstring="[para(1163(a,1),6032(a,1,3,1))].">
      <j1 rule="para" parents="1163 6032"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1378(a,1),5942(a,1,1))].">
      <j1 rule="para" parents="1378 5942"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(1352(a,1),5942(a,1,1))].">
      <j1 rule="para" parents="1352 5942"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(2286(a,1),5942(a,1,1))].">
      <j1 rule="para" parents="2286 5942"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(917,a,5970,a)].">
      <j1 rule="hyper" parents="917 5970"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5993,a(flip),b,5998,a)].">
      <j1 rule="hyper" parents="60 5993 5998"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x * T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(4338(a,1),5998(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4338 5998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(4421(a,2),5998(a,1,1,2))].">
      <j1 rule="para" parents="4421 5998"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      K((1 / (1 / x)) * (x \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(407(a,1),6002(a,2,1))].">
      <j1 rule="para" parents="407 6002"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5947(a,1),6002(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5947 6002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6010(a,2),5427(a,1))].">
      <j1 rule="para" parents="6010 5427"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(5720(a,2),6021(a,1,2))].">
      <j1 rule="para" parents="5720 6021"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1716(a,2),5563(a,1,2,2))].">
      <j1 rule="para" parents="1716 5563"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1735(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="1735 5563"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(2283(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="2283 5563"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3490(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="3490 5563"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (1 / z)) = u
    ]]></literal>
    <justification jstring="[para(3663(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="3663 5563"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3673(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="3673 5563"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      K(x,y / (1 / (1 / z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3707(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="3707 5563"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4354(a,2),5563(a,1,2))].">
      <j1 rule="para" parents="4354 5563"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) * z) = u
    ]]></literal>
    <justification jstring="[para(4375(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="4375 5563"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4376(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="4376 5563"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      K(x,y \ K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4549(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="4549 5563"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4457(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="4457 5563"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(4697(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="4697 5563"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(77(a,1),6052(a,1,2,1))].">
      <j1 rule="para" parents="77 6052"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2007(a,2),6052(a,1,2))].">
      <j1 rule="para" parents="2007 6052"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6001(a,2),6052(a,1))].">
      <j1 rule="para" parents="6001 6052"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(214(a,1),5917(a,1,1))].">
      <j1 rule="para" parents="214 5917"/>
    </justification>
  </clause>

  <clause id="6074">
    <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(5664(a,2),5984(a,1))].">
      <j1 rule="para" parents="5664 5984"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (1 / z)) = u
    ]]></literal>
    <justification jstring="[para(2732(a,1),6051(a,1,2))].">
      <j1 rule="para" parents="2732 6051"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(4366(a,2),6051(a,1,2))].">
      <j1 rule="para" parents="4366 6051"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(4407(a,1),6051(a,1,2))].">
      <j1 rule="para" parents="4407 6051"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      K(x,(1 / (1 / y)) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4408(a,1),6051(a,1,2))].">
      <j1 rule="para" parents="4408 6051"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(3695(a,1),6058(a,1,2))].">
      <j1 rule="para" parents="3695 6058"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(4548(a,1),6058(a,1,2))].">
      <j1 rule="para" parents="4548 6058"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(4430(a,1),6076(a,1,2))].">
      <j1 rule="para" parents="4430 6076"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(4504(a,1),6076(a,1,2))].">
      <j1 rule="para" parents="4504 6076"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(5230(a,2),5244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5230 5244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(77(a,1),6084(a,2,1,2))].">
      <j1 rule="para" parents="77 6084"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(6084(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="6084 5265"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5428(a,1),6084(a,2,1))].">
      <j1 rule="para" parents="5428 6084"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(6064,a,6087,a)].">
      <j1 rule="hyper" parents="6064 6087"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(4331(a,1),6087(a,1,2))].">
      <j1 rule="para" parents="4331 6087"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(6087(a,1),4929(a,1,2,1))].">
      <j1 rule="para" parents="6087 4929"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      T(x,y) != K(z,1 / T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,1 / u) = x
    ]]></literal>
    <justification jstring="[para(6091(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="6091 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,5278,a,b,5321,a)].">
      <j1 rule="hyper" parents="32 5278 5321"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      L(L(x,y,z) * K(u,L(x,y,z)),w,v5) * u = u * L(L(x,w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,1),5321(a,2,2))].">
      <j1 rule="para" parents="25 5321"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,5278,a,b,5322,a)].">
      <j1 rule="hyper" parents="32 5278 5322"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5947(a,1),5327(a,1,1,2))].">
      <j1 rule="para" parents="5947 5327"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(129,a,6101,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 6101 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(1426,a,5343,a)].">
      <j1 rule="hyper" parents="1426 5343"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      a(x,y,T(1 / z,u \ (u \ 1))) = a(x,y,z * K(u * u,1 / z))
    ]]></literal>
    <justification jstring="[para(6103(a,2),3079(a,1,3))].">
      <j1 rule="para" parents="6103 3079"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,5357,a,b,5228,a(flip))].">
      <j1 rule="hyper" parents="128 5357 5228"/>
    </justification>
  </clause>

  <clause id="6106">
    <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(5357(a,2),5237(a,1,1))].">
      <j1 rule="para" parents="5357 5237"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5357(a,2),5933(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5357 5933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,5358,a,b,5233,a(flip))].">
      <j1 rule="hyper" parents="125 5358 5233"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5358(a,2),5929(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5358 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(5251(a,1),5394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5251 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(77(a,1),6110(a,2,1,1))].">
      <j1 rule="para" parents="77 6110"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4905(a,1),6110(a,2,1))].">
      <j1 rule="para" parents="4905 6110"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(4331(a,1),6111(a,1,1))].">
      <j1 rule="para" parents="4331 6111"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6112(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6112 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(6113(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="6113 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[para(1582(a,1),5396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1582 5396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1352(a,1),5396(a,1,1))].">
      <j1 rule="para" parents="1352 5396"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1352(a,1),5397(a,1,2))].">
      <j1 rule="para" parents="1352 5397"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2395(a,1),5397(a,1,2))].">
      <j1 rule="para" parents="2395 5397"/>
    </justification>
  </clause>

  <clause id="6120">
    <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(3188(a,1),5397(a,1,2))].">
      <j1 rule="para" parents="3188 5397"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(1058,a,5399,a),flip(a)].">
      <j1 rule="hyper" parents="1058 5399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2316,a(flip),b,5399,a)].">
      <j1 rule="hyper" parents="60 2316 5399"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5399,a(flip),b,1378,a(flip))].">
      <j1 rule="hyper" parents="129 5399 1378"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5399,a(flip),b,536,a)].">
      <j1 rule="hyper" parents="128 5399 536"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K((T(y,x) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5749(a,2),5399(a,2,2,1,1))].">
      <j1 rule="para" parents="5749 5399"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,1582,a(flip),b,5402,a),flip(a)].">
      <j1 rule="hyper" parents="370 1582 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1535,a(flip),b,5402,a),flip(a)].">
      <j1 rule="hyper" parents="370 1535 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5402(a,2,2,1))].">
      <j1 rule="para" parents="4 5402"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1548(a,1),5419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1548 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(5430(a,1),5280(a,1,1))].">
      <j1 rule="para" parents="5430 5280"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(5430(a,1),5356(a,1,1))].">
      <j1 rule="para" parents="5430 5356"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(5443(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5443 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6137">
    <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(5454(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5454 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      T(T(x,(x * K(y,x)) * z) * K(y,T(x,(x * K(y,x)) * z)),u) = T(T(x * K(y,x),u),z * (x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(5454(a,2),5492(a,1,1))].">
      <j1 rule="para" parents="5454 5492"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T((x \ 1) * y,x),x)
    ]]></literal>
    <justification jstring="[para(3567(a,1),5461(a,1,1,1))].">
      <j1 rule="para" parents="3567 5461"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5484,a(flip),b,5228,a(flip))].">
      <j1 rule="hyper" parents="128 5484 5228"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      x \ T(x * y,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5484(a,1),5345(a,1))].">
      <j1 rule="para" parents="5484 5345"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      R(K(x * (y / (z * y)),y / (z * y)),R(1 / z,z,y),z * y) = ((x \ T(x * (y / (z * y)),y / (z * y))) * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(6141(a,1),1094(a,1,1))].">
      <j1 rule="para" parents="6141 1094"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,5558,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 5558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5256,a,b,5558,a)].">
      <j1 rule="hyper" parents="128 5256 5558"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(323,a,6144,a)].">
      <j1 rule="hyper" parents="323 6144"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4899,a(flip),b,6144,a)].">
      <j1 rule="hyper" parents="60 4899 6144"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6144,a(flip),b,4898,a(flip))].">
      <j1 rule="hyper" parents="125 6144 4898"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6145(a,1,1,2))].">
      <j1 rule="para" parents="77 6145"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(6145(a,2),251(a,2,1))].">
      <j1 rule="para" parents="6145 251"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(719,a,6149,a)].">
      <j1 rule="hyper" parents="719 6149"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,6149,a,b,5449,a)].">
      <j1 rule="hyper" parents="125 6149 5449"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6149(a,2,2,1))].">
      <j1 rule="para" parents="77 6149"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(468(a,2),6149(a,2,2)),flip(a)].">
      <j1 rule="para" parents="468 6149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      x * R(y \ 1,y,x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(2786(a,2),6149(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2786 6149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      K(x,y * (z * ((1 / z) * u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1741(a,1),5576(a,1,2,2))].">
      <j1 rule="para" parents="1741 5576"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(3558(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3558 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(3648(a,1),5576(a,1,2,2))].">
      <j1 rule="para" parents="3648 5576"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      K(x,y * (z * ((1 / u) \ w))) = K(x,y * (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(4544(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4544 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      K(x,y * (z * (u * (1 / w)))) = K(x,y * (z * (u * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(4548(a,1),5576(a,1,2,2))].">
      <j1 rule="para" parents="4548 5576"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      K(x,y * (T(1 / z,u) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(4729(a,1),5576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4729 5576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      K(x,(y \ (1 / z)) \ u) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(4497(a,1),5577(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4497 5577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1741(a,1),5578(a,1,2,2))].">
      <j1 rule="para" parents="1741 5578"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(4375(a,1),5581(a,1,2,1))].">
      <j1 rule="para" parents="4375 5581"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      K(x,(y / ((z \ 1) \ 1)) / u) = K(x,(y / z) / u)
    ]]></literal>
    <justification jstring="[para(4403(a,1),5582(a,1,2,1))].">
      <j1 rule="para" parents="4403 5582"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(4433(a,1),5583(a,1,2,1))].">
      <j1 rule="para" parents="4433 5583"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(4547(a,1),5583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4547 5583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(3454(a,1),5594(a,1,2,2))].">
      <j1 rule="para" parents="3454 5594"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      K(x,y / ((1 / z) \ u)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3559(a,1),5594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3559 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      K(x,y / ((1 / z) * u)) = K(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3567(a,1),5594(a,1,2,2))].">
      <j1 rule="para" parents="3567 5594"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(4381(a,1),5594(a,1,2,2))].">
      <j1 rule="para" parents="4381 5594"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3229,a(flip),b,5626,a)].">
      <j1 rule="hyper" parents="370 3229 5626"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4385,a,b,5639,a)].">
      <j1 rule="hyper" parents="60 4385 5639"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5785,a(flip),b,5754,a)].">
      <j1 rule="hyper" parents="128 5785 5754"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5785,a(flip),b,5754,a)].">
      <j1 rule="hyper" parents="125 5785 5754"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(18(a,1),5754(a,1,2))].">
      <j1 rule="para" parents="18 5754"/>
    </justification>
  </clause>

  <clause id="6184">
    <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(20(a,2),6182(a,1,1))].">
      <j1 rule="para" parents="20 6182"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      R(T(T(x,y),x \ 1),x \ 1,T(y,x)) = T(y,x) \ ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[para(5757(a,1),2877(a,1,1))].">
      <j1 rule="para" parents="5757 2877"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,z,y),z,y)
    ]]></literal>
    <justification jstring="[para(5849(a,2),5779(a,1,1))].">
      <j1 rule="para" parents="5849 5779"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(5741(a,1),5792(a,1,2,1))].">
      <j1 rule="para" parents="5741 5792"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ z)) = L(x,y,(u \ z) * u)
    ]]></literal>
    <justification jstring="[para(353(a,1),5884(a,1,3)),flip(a)].">
      <j1 rule="para" parents="353 5884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5751,a(flip),b,5897,a),flip(a)].">
      <j1 rule="hyper" parents="370 5751 5897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,5335,a,b,5903,a)].">
      <j1 rule="hyper" parents="60 5335 5903"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      K(x,y) \ (y * ((y \ 1) \ z)) = (y \ (1 / T(y,x))) \ z
    ]]></literal>
    <justification jstring="[para(5930(a,1),1511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5930 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(5721(a,2),5930(a,1,2))].">
      <j1 rule="para" parents="5721 5930"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(T(x,z),u),y)
    ]]></literal>
    <justification jstring="[para(5354(a,2),5937(a,1,1,1))].">
      <j1 rule="para" parents="5354 5937"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5490,a(flip),b,5975,a),flip(a)].">
      <j1 rule="hyper" parents="370 5490 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6194(a,1),1918(a,1,1))].">
      <j1 rule="para" parents="6194 1918"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(352(a,1),6005(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="352 6005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      K(x \ ((1 / y) * z),u) = K(x \ ((y \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(4375(a,1),6005(a,1,1,2))].">
      <j1 rule="para" parents="4375 6005"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(4384(a,1),6005(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4384 6005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(4195(a,1),6006(a,1,1,2))].">
      <j1 rule="para" parents="4195 6006"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3558(a,1),6017(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3558 6017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3650(a,1),6017(a,1,1,1))].">
      <j1 rule="para" parents="3650 6017"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(4491(a,1),6017(a,1,1,1))].">
      <j1 rule="para" parents="4491 6017"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(4710(a,1),6017(a,1,1,1))].">
      <j1 rule="para" parents="4710 6017"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x / ((1 / y) * z),u) = K(x / ((y \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6020(a,1,1,2))].">
      <j1 rule="para" parents="3567 6020"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      K(x / (y * (1 / z)),u) = K(x / (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(4381(a,1),6020(a,1,1,2))].">
      <j1 rule="para" parents="4381 6020"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,5789,a(flip),b,6023,a),flip(a)].">
      <j1 rule="hyper" parents="60 5789 6023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,2279,a(flip),b,6024,a)].">
      <j1 rule="hyper" parents="60 2279 6024"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6028,a(flip),b,4587,a),flip(a)].">
      <j1 rule="hyper" parents="129 6028 4587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(5721(a,2),6029(a,2,1))].">
      <j1 rule="para" parents="5721 6029"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = ((y / z) \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),6037(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 6037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6089,a(flip),b,6114,a),flip(a)].">
      <j1 rule="hyper" parents="60 6089 6114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(215,a,6212,a)].">
      <j1 rule="hyper" parents="215 6212"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(6212(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6212 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6212(a,1),5718(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6212 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,6213,a(flip),b,5721,a(flip))].">
      <j1 rule="hyper" parents="129 6213 5721"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,5888,a(flip),b,6216,a)].">
      <j1 rule="hyper" parents="60 5888 6216"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,6218,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 6218 5230"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,6218,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 6218 5230"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(6218(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6218 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6218(a,1),5871(a,1,1))].">
      <j1 rule="para" parents="6218 5871"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5350,a,6219,a),flip(a)].">
      <j1 rule="hyper" parents="5350 6219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5346,a,6219,a),flip(a)].">
      <j1 rule="hyper" parents="5346 6219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5334,a,6219,a)].">
      <j1 rule="hyper" parents="5334 6219"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(6219(a,1),5278(a,1,1))].">
      <j1 rule="para" parents="6219 5278"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6219(a,1),5347(a,1,1))].">
      <j1 rule="para" parents="6219 5347"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6219(a,1),5334(a,1))].">
      <j1 rule="para" parents="6219 5334"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6219(a,1),5346(a,1))].">
      <j1 rule="para" parents="6219 5346"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(6219(a,1),5498(a,1,1))].">
      <j1 rule="para" parents="6219 5498"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2900,a,6224,a),flip(a)].">
      <j1 rule="hyper" parents="2900 6224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2895,a,6224,a),flip(a)].">
      <j1 rule="hyper" parents="2895 6224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(6224(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="6224 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      K(x,y) * z != u * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6224(a,1),277(a,1,2))].">
      <j1 rule="para" parents="6224 277"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6231,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 6231 17"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6231(a,1),328(a,1,2))].">
      <j1 rule="para" parents="6231 328"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      K(x,y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6232(a,1),328(a,1,2))].">
      <j1 rule="para" parents="6232 328"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5280(a,1),6227(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5280 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5402(a,1),6225(a,1,1))].">
      <j1 rule="para" parents="5402 6225"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5865(a,1),6222(a,1))].">
      <j1 rule="para" parents="5865 6222"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(125,a,6150,a,b,xx)].">
      <j1 rule="hyper" parents="125 6150"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(1850,a,6154,a)].">
      <j1 rule="hyper" parents="1850 6154"/>
    </justification>
  </clause>

  <clause id="6246">
    <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(129,a,6183,a(flip),b,1070,a),flip(a)].">
      <j1 rule="hyper" parents="129 6183 1070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = L(R(y,z,y),z,y)
    ]]></literal>
    <justification jstring="[para(5484(a,1),6186(a,1,1))].">
      <j1 rule="para" parents="5484 6186"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x \ 1,T(x,y) \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(329,a,6192,a)].">
      <j1 rule="hyper" parents="329 6192"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(215,a,6207,a)].">
      <j1 rule="hyper" parents="215 6207"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6207(a,1),2214(a,2,2,1,2))].">
      <j1 rule="para" parents="6207 2214"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      K(x,y) = (T(y,x) \ 1) * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5943,a,6209,a),flip(a)].">
      <j1 rule="hyper" parents="5943 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      (T(x,y) \ 1) \ K(y,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,6251,a,b,xx)].">
      <j1 rule="hyper" parents="125 6251"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5280(a,1),6252(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 6252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(5753(a,2),6244(a,1,2,1))].">
      <j1 rule="para" parents="5753 6244"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(5723(a,2),6249(a,1,1))].">
      <j1 rule="para" parents="5723 6249"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y
    ]]></literal>
    <justification jstring="[para(5723(a,1),6257(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5723 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6259">
    <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(5358(a,2),6257(a,1,1))].">
      <j1 rule="para" parents="5358 6257"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2020(a,1),5263(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2020 5263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      (R(T(x,y),z,u) * (z * u)) / ((x * z) * u) = R(K(R(x,z,u),y),R(x,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(5282(a,1),716(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5282 716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5648,a,5291,a),flip(a)].">
      <j1 rule="hyper" parents="5648 5291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5775(a,1),6262(a,1,2))].">
      <j1 rule="para" parents="5775 6262"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(6263(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6263 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(370,a,5948,a(flip),b,5304,a),flip(a)].">
      <j1 rule="hyper" parents="370 5948 5304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5948,a(flip),b,5304,a)].">
      <j1 rule="hyper" parents="129 5948 5304"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1910,a,6267,a)].">
      <j1 rule="hyper" parents="1910 6267"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1899,a,6267,a),flip(a)].">
      <j1 rule="hyper" parents="1899 6267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(221,a,6267,a)].">
      <j1 rule="hyper" parents="221 6267"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6267(a,1),146(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="6267 146"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6267(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6267 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[para(6267(a,1),374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6267 374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4754,a,b,6268,a),flip(a)].">
      <j1 rule="hyper" parents="370 4754 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(323,a,6268,a)].">
      <j1 rule="hyper" parents="323 6268"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,5248,a,b,6268,a),flip(a)].">
      <j1 rule="hyper" parents="128 5248 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(32,a,1930,a,b,6268,a),flip(a)].">
      <j1 rule="hyper" parents="32 1930 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,5736,a(flip),b,6268,a),flip(a)].">
      <j1 rule="hyper" parents="32 5736 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      (x * (y / z)) * K(y / z,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(32,a,1898,a(flip),b,6268,a),flip(a)].">
      <j1 rule="hyper" parents="32 1898 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6268(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6268 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6268(a,1),251(a,2,1))].">
      <j1 rule="para" parents="6268 251"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),6268(a,1,1))].">
      <j1 rule="para" parents="5014 6268"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(5624(a,1),6268(a,1,1))].">
      <j1 rule="para" parents="5624 6268"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(5630(a,1),6268(a,1,1))].">
      <j1 rule="para" parents="5630 6268"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5775(a,1),6268(a,1,1))].">
      <j1 rule="para" parents="5775 6268"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5860(a,1),6268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5860 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(378,a,6281,a),flip(a)].">
      <j1 rule="hyper" parents="378 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,6281,a)].">
      <j1 rule="hyper" parents="135 6281"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,108,a,b,6281,a)].">
      <j1 rule="hyper" parents="125 108 6281"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(32,a,6226,a,b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="32 6226 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(32,a,5631,a,b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="32 5631 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,5014,a,b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="32 5014 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,2894,a,b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="32 2894 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6281(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="6281 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6281(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6281 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6281(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6281 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6307">
    <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(6281(a,1),1029(a,1,1,2))].">
      <j1 rule="para" parents="6281 1029"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,6226,a(flip),b,6291,a),flip(a)].">
      <j1 rule="hyper" parents="370 6226 6291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5370,a,b,6291,a)].">
      <j1 rule="hyper" parents="60 5370 6291"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6291(a,1),290(a,1,1))].">
      <j1 rule="para" parents="6291 290"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6291(a,1),291(a,1,1))].">
      <j1 rule="para" parents="6291 291"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6291(a,1),349(a,1,1))].">
      <j1 rule="para" parents="6291 349"/>
    </justification>
  </clause>

  <clause id="6314">
    <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(6291(a,1),815(a,1,1,1))].">
      <j1 rule="para" parents="6291 815"/>
    </justification>
  </clause>

  <clause id="6315">
    <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(6291(a,1),815(a,1,1))].">
      <j1 rule="para" parents="6291 815"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(6291(a,1),2579(a,1,1,2))].">
      <j1 rule="para" parents="6291 2579"/>
    </justification>
  </clause>

  <clause id="6317">
    <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(6291(a,1),4558(a,1,1,2))].">
      <j1 rule="para" parents="6291 4558"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      x / (K(y,z) \ 1) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(5865(a,2),6291(a,1,2))].">
      <j1 rule="para" parents="5865 6291"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,6037,a,b,6294,a)].">
      <j1 rule="hyper" parents="36 6037 6294"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5942,a,b,6294,a)].">
      <j1 rule="hyper" parents="36 5942 6294"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      ((x * K(y,z)) * R((x * K(y,z)) \ u,w,v5)) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(6294(a,1),2586(a,1,2))].">
      <j1 rule="para" parents="6294 2586"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      ((x / T(y,z)) * y) \ x = K(y,z)
    ]]></literal>
    <justification jstring="[para(5850(a,2),6294(a,1,1))].">
      <j1 rule="para" parents="5850 6294"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5860(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="5860 6294"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(762,a,6269,a)].">
      <j1 rule="hyper" parents="762 6269"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(275,a,5459,a(flip),b,6269,a)].">
      <j1 rule="hyper" parents="275 5459 6269"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,6269,a)].">
      <j1 rule="hyper" parents="135 6269"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,361,a(flip),b,6269,a)].">
      <j1 rule="hyper" parents="60 361 6269"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,6269,a(flip),b,539,a)].">
      <j1 rule="hyper" parents="128 6269 539"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      T(x,y) * z != u * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(u / x,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(6269(a,1),276(a,2))].">
      <j1 rule="para" parents="6269 276"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = (x * y) * T(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(213(a,1),6269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="213 6269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6336">
    <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(6269(a,1),1530(a,1,2,1))].">
      <j1 rule="para" parents="6269 1530"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5249(a,2),6269(a,1,1))].">
      <j1 rule="para" parents="5249 6269"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5701(a,2),6269(a,1,1))].">
      <j1 rule="para" parents="5701 6269"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6268,a,b,6270,a)].">
      <j1 rule="hyper" parents="370 6268 6270"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,5286,a,b,6270,a)].">
      <j1 rule="hyper" parents="31 5286 6270"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(6270(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * x,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6270(a,1),389(a,1,2))].">
      <j1 rule="para" parents="6270 389"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6270(a,1),378(a,1))].">
      <j1 rule="para" parents="6270 378"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      (x / (y * y)) * K(y \ 1,z) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1105(a,1),6270(a,1,1))].">
      <j1 rule="para" parents="1105 6270"/>
    </justification>
  </clause>

  <clause id="6347">
    <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(6270(a,1),724(a,1,2))].">
      <j1 rule="para" parents="6270 724"/>
    </justification>
  </clause>

  <clause id="6348">
    <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(6270(a,1),685(a,1,1))].">
      <j1 rule="para" parents="6270 685"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) * y)) * K((1 / x) * y,z) = (1 / x) * T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(3745(a,1),6270(a,1,1))].">
      <j1 rule="para" parents="3745 6270"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6270(a,1),5213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5256(a,2),6270(a,1,1))].">
      <j1 rule="para" parents="5256 6270"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      ((x * y) / x) * K(x \ y,z) = T(x,y) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5462(a,1),6270(a,1,1))].">
      <j1 rule="para" parents="5462 6270"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      (x * y) * K(y,z / y) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(5799(a,1),6270(a,2,2))].">
      <j1 rule="para" parents="5799 6270"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      L(K(x \ 1,y),x,z) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3530,a,6340,a)].">
      <j1 rule="hyper" parents="3530 6340"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,5865,a,b,6340,a),flip(a)].">
      <j1 rule="hyper" parents="370 5865 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      a(x,y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,6340,a)].">
      <j1 rule="hyper" parents="50 6340"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6340,a(flip),b,2075,a)].">
      <j1 rule="hyper" parents="125 6340 2075"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      a(x,y,K(y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(3058,a,6357,a)].">
      <j1 rule="hyper" parents="3058 6357"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6355(a,2),5871(a,1))].">
      <j1 rule="para" parents="6355 5871"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6272(a,1),494(a,1,1))].">
      <j1 rule="para" parents="6272 494"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      (x * T(y \ z,u)) / T(z / y,u) = x * K(T(z / y,u),y)
    ]]></literal>
    <justification jstring="[para(284(a,1),6272(a,1,1,2))].">
      <j1 rule="para" parents="284 6272"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,2375,a,b,6279,a)].">
      <j1 rule="hyper" parents="60 2375 6279"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(6299(a,1),104(a,2,2))].">
      <j1 rule="para" parents="6299 104"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6325(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6325 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5370(a,2),6304(a,1))].">
      <j1 rule="para" parents="5370 6304"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6225(a,1),6304(a,1))].">
      <j1 rule="para" parents="6225 6304"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4780(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="4780 6305"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5624(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="5624 6305"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(4384(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4384 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      (x * y) * K(y \ 1,z) = x * (y * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6354,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 6354 13"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4745(a,1),6280(a,1,2,1))].">
      <j1 rule="para" parents="4745 6280"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      ((x \ y) \ y) * z = (x * z) * K(T(x,z),y / x)
    ]]></literal>
    <justification jstring="[para(5799(a,1),6280(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5799 6280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(125,a,92,a(flip),b,6290,a)].">
      <j1 rule="hyper" parents="125 92 6290"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,z / y) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(109(a,1),6290(a,1,1,2))].">
      <j1 rule="para" parents="109 6290"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1982(a,1),6290(a,1,1))].">
      <j1 rule="para" parents="1982 6290"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      (T(x,y) * y) * x = (x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),6290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 6290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      T(x,K(y,z)) != (K(z,y) * u) * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6296(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="6296 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6308(a,1),5784(a,1,1))].">
      <j1 rule="para" parents="6308 5784"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(491,a,6309,a)].">
      <j1 rule="hyper" parents="491 6309"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(4948,a,6322,a),flip(a)].">
      <j1 rule="hyper" parents="4948 6322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(1757,a,6322,a)].">
      <j1 rule="hyper" parents="1757 6322"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(1537,a,6322,a)].">
      <j1 rule="hyper" parents="1537 6322"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      x * (y * K((x \ 1) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,6322,a(flip),b,1378,a(flip))].">
      <j1 rule="hyper" parents="129 6322 1378"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,2395,a(flip),b,6322,a(flip))].">
      <j1 rule="hyper" parents="125 2395 6322"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,5399,a(flip),b,6322,a(flip))].">
      <j1 rule="hyper" parents="31 5399 6322"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6322(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6322 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6322(a,2),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6322 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      (x * K(y \ x,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(y \ x,z) \ u,T(y \ x,z),y) = w
    ]]></literal>
    <justification jstring="[para(6322(a,1),822(a,1,1))].">
      <j1 rule="para" parents="6322 822"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6322(a,1),1573(a,1,1))].">
      <j1 rule="para" parents="6322 1573"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6322(a,1),2856(a,2,1))].">
      <j1 rule="para" parents="6322 2856"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T((L(x,y,z) \ x) \ x,u) = x * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3939(a,1),6322(a,2,2,1))].">
      <j1 rule="para" parents="3939 6322"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6322(a,1),4948(a,1))].">
      <j1 rule="para" parents="6322 4948"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      R(K(x \ (y / z),y / z),y / z,z) = ((x * T(x \ (y / z),y / z)) * z) / y
    ]]></literal>
    <justification jstring="[para(6322(a,2),4771(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6322 4771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5517,a,6410,a)].">
      <j1 rule="hyper" parents="5517 6410"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,933,a(flip),b,6410,a),flip(a)].">
      <j1 rule="hyper" parents="370 933 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      T(x,y \ z) * K((z \ y) \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,6410,a,b,5699,a(flip))].">
      <j1 rule="hyper" parents="129 6410 5699"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6410(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6410(a,1,1,1))].">
      <j1 rule="para" parents="17 6410"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u)
    ]]></literal>
    <justification jstring="[para(94(a,2),6410(a,1,1,1))].">
      <j1 rule="para" parents="94 6410"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(6410(a,1),5703(a,2,1))].">
      <j1 rule="para" parents="6410 5703"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(z \ y,x) \ 1
    ]]></literal>
    <justification jstring="[para(6410(a,1),5865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6410 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6422(a,1),4925(a,1))].">
      <j1 rule="para" parents="6422 4925"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6423,a(flip),b,5251,a),flip(a)].">
      <j1 rule="hyper" parents="125 6423 5251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(6423(a,1),5261(a,1,2))].">
      <j1 rule="para" parents="6423 5261"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      T(x,(y * z) \ y) = 1 / (x \ K(z \ 1,x))
    ]]></literal>
    <justification jstring="[para(6425(a,1),5767(a,2,2,2))].">
      <j1 rule="para" parents="6425 5767"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      (x \ y) * K(x \ ((x \ 1) \ y),z) = (1 / x) * T(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,6327,a(flip),b,1264,a(flip))].">
      <j1 rule="hyper" parents="129 6327 1264"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4913,a(flip),b,6337,a)].">
      <j1 rule="hyper" parents="370 4913 6337"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      K(x,y) * T(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6337(a,2),4921(a,1))].">
      <j1 rule="para" parents="6337 4921"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(6302,a,6400,a(flip))].">
      <j1 rule="hyper" parents="6302 6400"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6400(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5233(a,1),6400(a,1,2))].">
      <j1 rule="para" parents="5233 6400"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5835(a,1),6400(a,1,2))].">
      <j1 rule="para" parents="5835 6400"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5706,a,6424,a)].">
      <j1 rule="hyper" parents="5706 6424"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,6446,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 6446 17"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6446(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6446(a,2,2))].">
      <j1 rule="para" parents="4 6446"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6446(a,1,2,1))].">
      <j1 rule="para" parents="17 6446"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      x \ ((y \ z) \ T(x,z \ y)) = ((y \ z) \ x) / x
    ]]></literal>
    <justification jstring="[para(6446(a,1),6152(a,1,2,2))].">
      <j1 rule="para" parents="6446 6152"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(505,a,6448,a),flip(a)].">
      <j1 rule="hyper" parents="505 6448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      T(x * y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x * y) \ x) \ x = z
    ]]></literal>
    <justification jstring="[para(6448(a,1),505(a,1))].">
      <j1 rule="para" parents="6448 505"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,(1 / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3412(a,2),6448(a,1,2))].">
      <j1 rule="para" parents="3412 6448"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(251(a,2),6449(a,1,2,1))].">
      <j1 rule="para" parents="251 6449"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6449(a,1),4448(a,1,2))].">
      <j1 rule="para" parents="6449 4448"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6112,a(flip),b,6426,a),flip(a)].">
      <j1 rule="hyper" parents="60 6112 6426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6429(a,2),5735(a,1))].">
      <j1 rule="para" parents="6429 5735"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5865,a(flip),b,6430,a),flip(a)].">
      <j1 rule="hyper" parents="370 5865 6430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6430(a,2),5871(a,1))].">
      <j1 rule="para" parents="6430 5871"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6064,a,6463,a)].">
      <j1 rule="hyper" parents="6064 6463"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5633,a,b,6463,a)].">
      <j1 rule="hyper" parents="370 5633 6463"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      K((x \ y) \ 1,(z \ u) \ 1) = K(y \ x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6410,a(flip),b,6463,a),flip(a)].">
      <j1 rule="hyper" parents="370 6410 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6463(a,2,2))].">
      <j1 rule="para" parents="4 6463"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,2),6463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(77(a,1),6463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(511(a,1),6463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="511 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1040(a,1),6463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1040 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6463(a,1),5634(a,1,3))].">
      <j1 rule="para" parents="6463 5634"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(6474(a,1),675(a,1,1))].">
      <j1 rule="para" parents="6474 675"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),6465(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13 6465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,6468,a(flip),b,5765,a),flip(a)].">
      <j1 rule="hyper" parents="129 6468 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      K(x,y \ 1) / ((z * y) \ z) = 1 / T((z * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,6468,a(flip),b,5718,a(flip))].">
      <j1 rule="hyper" parents="128 6468 5718"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,((u * y) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5633,a,b,6469,a)].">
      <j1 rule="hyper" parents="370 5633 6469"/>
    </justification>
  </clause>

  <clause id="6482">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(426,a,6438,a)].">
      <j1 rule="hyper" parents="426 6438"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6441(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6441"/>
    </justification>
  </clause>

  <clause id="6484">
    <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(6441(a,1),1407(a,2,1,2))].">
      <j1 rule="para" parents="6441 1407"/>
    </justification>
  </clause>

  <clause id="6485">
    <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(6441(a,1),4862(a,1,2,1))].">
      <j1 rule="para" parents="6441 4862"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      x / T(y * x,T(y,x) \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(6451(a,2),308(a,1,2))].">
      <j1 rule="para" parents="6451 308"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,457,a,b,6454,a)].">
      <j1 rule="hyper" parents="370 457 6454"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(77(a,1),6454(a,1,2))].">
      <j1 rule="para" parents="77 6454"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      T(x * y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ x = z
    ]]></literal>
    <justification jstring="[para(6454(a,2),800(a,1))].">
      <j1 rule="para" parents="6454 800"/>
    </justification>
  </clause>

  <clause id="6490">
    <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(5912(a,1),6343(a,1,1))].">
      <j1 rule="para" parents="5912 6343"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * T(y * z,u) = w
    ]]></literal>
    <justification jstring="[para(103(a,1),6372(a,1,1))].">
      <j1 rule="para" parents="103 6372"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      x * K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(5700(a,1),6372(a,1,1))].">
      <j1 rule="para" parents="5700 6372"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),6456(a,2,2))].">
      <j1 rule="para" parents="77 6456"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3401(a,1),6494(a,1,2))].">
      <j1 rule="para" parents="3401 6494"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      T(x * (1 / y),y * y) = (y \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6495(a,1),2825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6495 2825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      T(x,(y / (z * z)) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ 1) \ (z / y)) = u
    ]]></literal>
    <justification jstring="[para(1297(a,1),6462(a,1,2,1))].">
      <j1 rule="para" parents="1297 6462"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),6464(a,1,2,1))].">
      <j1 rule="para" parents="17 6464"/>
    </justification>
  </clause>

  <clause id="6501">
    <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(94(a,2),6464(a,1,2,1))].">
      <j1 rule="para" parents="94 6464"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(1671(a,1),6464(a,1,2,1))].">
      <j1 rule="para" parents="1671 6464"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5423(a,2),6464(a,1))].">
      <j1 rule="para" parents="5423 6464"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6480(a,1),645(a,1)),flip(b)].">
      <j1 rule="para" parents="6480 645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(221,a,6487,a)].">
      <j1 rule="hyper" parents="221 6487"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      T(x * (y \ 1),T(y,y \ 1)) = L((y \ 1) \ 1,y \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(108(a,2),6487(a,2,2)),flip(a)].">
      <j1 rule="para" parents="108 6487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * T(y * x,x \ 1)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(6487(a,1),2159(a,1,2,2))].">
      <j1 rule="para" parents="6487 2159"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      T(x,x \ 1) * K(y,x) = (x * (K(y,x) / x)) * x
    ]]></literal>
    <justification jstring="[para(6208(a,1),6276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6208 6276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      T(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6276(a,1),6274(a,1))].">
      <j1 rule="para" parents="6276 6274"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = (x * y) * R(K(x * y,z),y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,4927,a,b,6287,a),flip(a)].">
      <j1 rule="hyper" parents="370 4927 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(128,a,6288,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="128 6288 103"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ z) \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(6298(a,1),5858(a,1,1))].">
      <j1 rule="para" parents="6298 5858"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(4932,a,6321,a)].">
      <j1 rule="hyper" parents="4932 6321"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      (T(x,y) / z) / K((z \ 1) \ (x / z),y) = x / z
    ]]></literal>
    <justification jstring="[hyper(4859,a,6321,a)].">
      <j1 rule="hyper" parents="4859 6321"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      (x / y) * K((y \ 1) \ (x / y),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(4858,a,6321,a),flip(a)].">
      <j1 rule="hyper" parents="4858 6321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6321(a,1),4867(a,1,1))].">
      <j1 rule="para" parents="6321 4867"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      T(x / (x / y),z) != u / (x / y)
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6332(a,1),43(a,1))].">
      <j1 rule="para" parents="6332 43"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      T(x * K(x \ y,x),z) = (y * K(x,z)) / (y / x)
    ]]></literal>
    <justification jstring="[para(5683(a,1),6332(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5683 6332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4774,a,6338,a)].">
      <j1 rule="hyper" parents="4774 6338"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6436(a,2),5768(a,1))].">
      <j1 rule="para" parents="6436 5768"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      T(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),6528(a,1,2,1))].">
      <j1 rule="para" parents="5 6528"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6528(a,1,2,1))].">
      <j1 rule="para" parents="7 6528"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      T(x,(y * z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),6528(a,1,2,1))].">
      <j1 rule="para" parents="107 6528"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      T(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(189(a,1),6528(a,1,2))].">
      <j1 rule="para" parents="189 6528"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      (x / (y / (y / z))) / (y / z) = (x / z) / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,6444,a,b,5627,a)].">
      <j1 rule="hyper" parents="128 6444 5627"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      (((x * y) * (1 / x)) \ (x * y)) \ (x * y) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3281,a(flip),b,6488,a),flip(a)].">
      <j1 rule="hyper" parents="60 3281 6488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      T(x * (1 / y),y) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(3398(a,2),6488(a,2,1))].">
      <j1 rule="para" parents="3398 6488"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      x * (L(x,x,y) \ y) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,6537,a(flip),b,2061,a(flip))].">
      <j1 rule="hyper" parents="129 6537 2061"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      (x \ 1) * T(x \ ((x \ 1) \ y),x) = T(x \ T(y,x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(4997(a,1),6496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4997 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      R(x * K(y,x),y,x) = x * K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5233,a(flip),b,5349,a),flip(a)].">
      <j1 rule="hyper" parents="370 5233 5349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      K(x * (y * y),y * y) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(697,a,6542,a)].">
      <j1 rule="hyper" parents="697 6542"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(5368(a,2),5520(a,1,1))].">
      <j1 rule="para" parents="5368 5520"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      T((x / y) * K(y \ 1,x),L(1 / y,y,x)) = x * R(L(1 / y,y,x),x,L(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(5404(a,2),5537(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5404 5537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,22,a,b,5529,a),flip(a)].">
      <j1 rule="hyper" parents="370 22 5529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      x * ((y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5233(a,2),5638(a,1,2))].">
      <j1 rule="para" parents="5233 5638"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) = R(x,u,w) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(2020(a,1),5725(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2020 5725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),5953(a,2,1))].">
      <j1 rule="para" parents="4 5953"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(129,a,6550,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 6550 13"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      T(T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)),u) = L(T(z,u),z \ (x * K(y,z)),z)
    ]]></literal>
    <justification jstring="[para(5912(a,1),5977(a,1,1,1,2))].">
      <j1 rule="para" parents="5912 5977"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u * z)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(5492(a,1),6034(a,1,3))].">
      <j1 rule="para" parents="5492 6034"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(5072(a,1),6078(a,1,2,1))].">
      <j1 rule="para" parents="5072 6078"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(6142,a,6321,a),flip(a)].">
      <j1 rule="hyper" parents="6142 6321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(6142,a,5553,a)].">
      <j1 rule="hyper" parents="6142 5553"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),6557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 6557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(6557(a,1),5598(a,1,2,1,2))].">
      <j1 rule="para" parents="6557 5598"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6556,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 6556 5230"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),6556(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 6556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),6155(a,2,2,2))].">
      <j1 rule="para" parents="77 6155"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1406(a,1),6412(a,1,2))].">
      <j1 rule="para" parents="1406 6412"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(1352(a,1),6412(a,1,2))].">
      <j1 rule="para" parents="1352 6412"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5397(a,1),6412(a,1))].">
      <j1 rule="para" parents="5397 6412"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,6466,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 6466 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6466(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6466 20"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6035,a(flip),b,6553,a)].">
      <j1 rule="hyper" parents="60 6035 6553"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(32,a,5278,a,b,5329,a)].">
      <j1 rule="hyper" parents="32 5278 5329"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6375,a,5365,a),flip(a)].">
      <j1 rule="hyper" parents="6375 5365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,(z * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      ((z * y) / z) \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(5365(a,1),494(a,1,1))].">
      <j1 rule="para" parents="5365 494"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      (x / (y / (y / z))) * z = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5683(a,2),6574(a,1,1,2))].">
      <j1 rule="para" parents="5683 6574"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (x \ y) / (y / (y / x)) = (y / x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,5279,a(flip),b,6576,a),flip(a)].">
      <j1 rule="hyper" parents="128 5279 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(5912(a,1),6576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5912 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = ((x * T(x \ 1,u)) * y) * z
    ]]></literal>
    <justification jstring="[para(5393(a,1),103(a,1,1))].">
      <j1 rule="para" parents="5393 103"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5251(a,1),5393(a,1,1))].">
      <j1 rule="para" parents="5251 5393"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),6582(a,2,1,1))].">
      <j1 rule="para" parents="104 6582"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4905(a,1),6582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4905 6582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5251(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="5251 5395"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5252(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="5252 5395"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5029,a(flip),b,6586,a),flip(a)].">
      <j1 rule="hyper" parents="60 5029 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,u) = x * (y * K(z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,6586,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 6586 13"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(2558(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2558 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4905(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4905 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6111(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6111 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6112(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6112 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6410(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6410 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4902,a,b,6587,a),flip(a)].">
      <j1 rule="hyper" parents="370 4902 6587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(6591(a,1),5865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6591 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * K(1 / z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,6596,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 6596 13"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(787,a,5406,a)].">
      <j1 rule="hyper" parents="787 5406"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2407,a(flip),b,5406,a)].">
      <j1 rule="hyper" parents="60 2407 5406"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),5406(a,1,2,2,1,2))].">
      <j1 rule="para" parents="77 5406"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      x \ K((x * ((1 / y) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,5086,a(flip),b,5408,a),flip(a)].">
      <j1 rule="hyper" parents="370 5086 5408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,5408,a,b,1378,a(flip))].">
      <j1 rule="hyper" parents="129 5408 1378"/>
    </justification>
  </clause>

  <clause id="6605">
    <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(304(a,1),5411(a,1,1,1))].">
      <j1 rule="para" parents="304 5411"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      K(x,y) * ((1 / x) \ z) = z * T(z \ ((1 / x) \ z),y)
    ]]></literal>
    <justification jstring="[para(77(a,1),5412(a,1,1,1))].">
      <j1 rule="para" parents="77 5412"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(4887(a,1),5412(a,1,1))].">
      <j1 rule="para" parents="4887 5412"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      (x * y) \ (K(x \ 1,z) * y) = T((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,5413,a)].">
      <j1 rule="hyper" parents="135 5413"/>
    </justification>
  </clause>

  <clause id="6614">
    <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(60,a,2811,a,b,5436,a)].">
      <j1 rule="hyper" parents="60 2811 5436"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(135,a,5460,a)].">
      <j1 rule="hyper" parents="135 5460"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(155,a,5555,a)].">
      <j1 rule="hyper" parents="155 5555"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1842(a,1),5555(a,1,1))].">
      <j1 rule="para" parents="1842 5555"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(3240(a,1),5555(a,1,1))].">
      <j1 rule="para" parents="3240 5555"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ z)) = K(x,y * (z * z))
    ]]></literal>
    <justification jstring="[para(311(a,1),5588(a,2,2,2))].">
      <j1 rule="para" parents="311 5588"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2821(a,2),5588(a,1,2,2))].">
      <j1 rule="para" parents="2821 5588"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5935(a,2),5588(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5935 5588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      K(x,(y * L(1 / z,u,w)) \ v5) = K(x,(y * L(z \ 1,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(5068(a,1),5590(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5068 5590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(891(a,1),5755(a,1,2))].">
      <j1 rule="para" parents="891 5755"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5551,a(flip),b,6626,a),flip(a)].">
      <j1 rule="hyper" parents="370 5551 6626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5485(a,2),6627(a,1,2))].">
      <j1 rule="para" parents="5485 6627"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,899,a,b,6629,a)].">
      <j1 rule="hyper" parents="60 899 6629"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5613,a,6630,a),flip(a)].">
      <j1 rule="hyper" parents="5613 6630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5521,a,b,6632,a)].">
      <j1 rule="hyper" parents="370 5521 6632"/>
    </justification>
  </clause>

  <clause id="6634">
    <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(5756(a,1),266(a,1,1,2))].">
      <j1 rule="para" parents="5756 266"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,4803,a(flip),b,5786,a),flip(a)].">
      <j1 rule="hyper" parents="32 4803 5786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(5862,a,6635,a)].">
      <j1 rule="hyper" parents="5862 6635"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6636(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6636(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6636 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      K(x,y) = (x \ T(y,x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(6636(a,1),6294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6636 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      x * (y * K(x * y,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(156,a,6637,a)].">
      <j1 rule="hyper" parents="156 6637"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,6321,a(flip),b,6637,a(flip))].">
      <j1 rule="hyper" parents="31 6321 6637"/>
    </justification>
  </clause>

  <clause id="6642">
    <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(6637(a,2),5771(a,1,1))].">
      <j1 rule="para" parents="6637 5771"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      K((1 / x) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6004,a,b,6641,a)].">
      <j1 rule="hyper" parents="60 6004 6641"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6007,a(flip),b,6641,a),flip(a)].">
      <j1 rule="hyper" parents="60 6007 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      x * (y * K(y * x,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(6557(a,2),6640(a,1,2,2))].">
      <j1 rule="para" parents="6557 6640"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6557,a,b,6644,a)].">
      <j1 rule="hyper" parents="60 6557 6644"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,4804,a,b,5806,a),flip(a)].">
      <j1 rule="hyper" parents="370 4804 5806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2331(a,1),5819(a,1,2))].">
      <j1 rule="para" parents="2331 5819"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(6649(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="6649 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5747(a,1),6649(a,1,2))].">
      <j1 rule="para" parents="5747 6649"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(6651(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="6651 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = x * (((x \ 1) \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(6055,a,5824,a)].">
      <j1 rule="hyper" parents="6055 5824"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(6302,a,5907,a)].">
      <j1 rule="hyper" parents="6302 5907"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      K(x * (((y \ 1) \ 1) \ z),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(74(a,1),6013(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      K(x * ((x \ 1) \ y),z) = K((x * x) * y,z)
    ]]></literal>
    <justification jstring="[para(553(a,1),6013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="553 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(1496(a,1),6018(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1496 6018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K((x / (1 / y)) \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(5251(a,1),6019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5251 6019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5865(a,1),6123(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="5865 6123"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(31,a,1532,a,b,6148,a)].">
      <j1 rule="hyper" parents="31 1532 6148"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,y * (z \ ((z \ 1) \ u)))
    ]]></literal>
    <justification jstring="[para(2114(a,1),6160(a,1,2,2))].">
      <j1 rule="para" parents="2114 6160"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / u) = K(x,(y / z) / u)
    ]]></literal>
    <justification jstring="[para(220(a,1),6169(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="220 6169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(6208(a,1),6180(a,1,2))].">
      <j1 rule="para" parents="6208 6180"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      x * (T(x,y) \ (x * (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,6663,a(flip),b,1673,a),flip(a)].">
      <j1 rule="hyper" parents="125 6663 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,z * (u / z))
    ]]></literal>
    <justification jstring="[para(5766(a,1),6188(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5766 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      L(x,y,z * ((z * u) / z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6666(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      L(x,y,((1 / z) \ (z \ u)) * z) = L(x,y,z * (((z \ 1) \ u) / z))
    ]]></literal>
    <justification jstring="[para(945(a,2),6666(a,1,3,1))].">
      <j1 rule="para" parents="945 6666"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      L(x,y,z * (((z \ 1) \ u) / z)) = L(x,y,(z \ 1) \ T(u,z))
    ]]></literal>
    <justification jstring="[para(2874(a,1),6666(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2874 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      L(x,y,T(z,u) * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(263(a,1),6667(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="263 6667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      L(x,y,z * ((T(z,u \ 1) / u) / z)) = L(x,y,((z / u) / z) * z)
    ]]></literal>
    <justification jstring="[para(6145(a,2),6667(a,1,3,2,1))].">
      <j1 rule="para" parents="6145 6667"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      x / T(x,y \ ((z \ 1) \ u)) = K(y \ ((1 / z) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a(flip),b,6198,a)].">
      <j1 rule="hyper" parents="370 5701 6198"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) \ z,u) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(2114(a,1),6200(a,1,1,1))].">
      <j1 rule="para" parents="2114 6200"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(6245(a,1),565(a,1,2))].">
      <j1 rule="para" parents="6245 565"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(691,a,6387,a)].">
      <j1 rule="hyper" parents="691 6387"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6302,a,6402,a)].">
      <j1 rule="hyper" parents="6302 6402"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(5000(a,1),6407(a,1,2))].">
      <j1 rule="para" parents="5000 6407"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(251(a,2),6432(a,1,1,1))].">
      <j1 rule="para" parents="251 6432"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(6012(a,1),6517(a,2,2))].">
      <j1 rule="para" parents="6012 6517"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = (x * y) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4887(a,1),6610(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4887 6610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6682">
    <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(467(a,1),6615(a,1,2,2,1,2))].">
      <j1 rule="para" parents="467 6615"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5557,a,b,6618,a),flip(a)].">
      <j1 rule="hyper" parents="370 5557 6618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(6654(a,1),4629(a,2,2))].">
      <j1 rule="para" parents="6654 4629"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,4462,a(flip),b,6660,a),flip(a)].">
      <j1 rule="hyper" parents="60 4462 6660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(409,a,6677,a),flip(a)].">
      <j1 rule="hyper" parents="409 6677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6403,a(flip),b,6678,a),flip(a)].">
      <j1 rule="hyper" parents="60 6403 6678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6410,a(flip),b,6687,a),flip(a)].">
      <j1 rule="hyper" parents="370 6410 6687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,934,a(flip),b,6687,a),flip(a)].">
      <j1 rule="hyper" parents="60 934 6687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6689(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 6689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5935(a,1),6683(a,1,1,2))].">
      <j1 rule="para" parents="5935 6683"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(249(a,2),6685(a,1,2))].">
      <j1 rule="para" parents="249 6685"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,6695,a(flip),b,1235,a),flip(a)].">
      <j1 rule="hyper" parents="128 6695 1235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5499(a,1),2657(a,1,1))].">
      <j1 rule="para" parents="5499 2657"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5511,a,6327,a),flip(a)].">
      <j1 rule="hyper" parents="5511 6327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,933,a(flip),b,6698,a),flip(a)].">
      <j1 rule="hyper" parents="60 933 6698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,933,a(flip),b,6699,a),flip(a)].">
      <j1 rule="hyper" parents="60 933 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5485(a,2),6700(a,1,2))].">
      <j1 rule="para" parents="5485 6700"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(y * y,x) = z
    ]]></literal>
    <justification jstring="[para(1421(a,1),5516(a,1))].">
      <j1 rule="para" parents="1421 5516"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5549,a,4958,a),flip(a)].">
      <j1 rule="hyper" parents="5549 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5233(a,1),6704(a,1,1,2))].">
      <j1 rule="para" parents="5233 6704"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      (((x * y) / x) \ x) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(6257(a,2),6704(a,1,1))].">
      <j1 rule="para" parents="6257 6704"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      ((x * y) / x) \ x = (y \ x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,6268,a,b,6706,a),flip(a)].">
      <j1 rule="hyper" parents="32 6268 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      ((x * y) / x) \ x != K(y,x) * z
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(6708(a,2),276(a,2)),flip(a)].">
      <j1 rule="para" parents="6708 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6710">
    <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(253(a,1),5597(a,2,3))].">
      <j1 rule="para" parents="253 5597"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(3198,a,5658,a)].">
      <j1 rule="hyper" parents="3198 5658"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,5778,a(flip),b,6711,a)].">
      <j1 rule="hyper" parents="60 5778 6711"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,6711,a(flip),b,5778,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 6711 5778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(221,a,6712,a)].">
      <j1 rule="hyper" parents="221 6712"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      (x * y) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ x = z
    ]]></literal>
    <justification jstring="[para(6713(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6713 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),6714(a,1,2,1))].">
      <j1 rule="para" parents="7 6714"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5459,a,b,6716,a),flip(a)].">
      <j1 rule="hyper" parents="370 5459 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ y = z
    ]]></literal>
    <justification jstring="[para(5778(a,2),6715(a,1))].">
      <j1 rule="para" parents="5778 6715"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(2316(a,1),5661(a,1,2))].">
      <j1 rule="para" parents="2316 5661"/>
    </justification>
  </clause>

  <clause id="6720">
    <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(3023(a,1),5809(a,1,2,1))].">
      <j1 rule="para" parents="3023 5809"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,5973,a,b,6396,a(flip))].">
      <j1 rule="hyper" parents="125 5973 6396"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,5542,a(flip),b,6721,a)].">
      <j1 rule="hyper" parents="60 5542 6721"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5428(a,1),6067(a,1))].">
      <j1 rule="para" parents="5428 6067"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3613(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="3613 6724"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3622(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="3622 6724"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3679(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="3679 6724"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4401(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="4401 6724"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (1 / y),z) = u
    ]]></literal>
    <justification jstring="[para(4404(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="4404 6724"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      K(x \ (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (1 / y),z) = u
    ]]></literal>
    <justification jstring="[para(4497(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="4497 6724"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(4430(a,1),6724(a,1,1))].">
      <j1 rule="para" parents="4430 6724"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),6728(a,1,1,2,2))].">
      <j1 rule="para" parents="74 6728"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      K(x * L(1 / y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * L(y \ 1,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(5072(a,1),6728(a,1,1,2))].">
      <j1 rule="para" parents="5072 6728"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (1 / y),z * u) = w
    ]]></literal>
    <justification jstring="[para(5567(a,2),6730(a,1))].">
      <j1 rule="para" parents="5567 6730"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(31,a,5087,a(flip),b,6096,a),flip(a)].">
      <j1 rule="hyper" parents="31 5087 6096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,5049,a(flip),b,6096,a),flip(a)].">
      <j1 rule="hyper" parents="31 5049 6096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x,L(x \ 1,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(31,a,5037,a(flip),b,6096,a),flip(a)].">
      <j1 rule="hyper" parents="31 5037 6096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = 1 / T(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,6738,a(flip),b,5718,a(flip))].">
      <j1 rule="hyper" parents="128 6738 5718"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(6738(a,1),6596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6738 6596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(655(a,1),6737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="655 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      R(x / (x / y),z,u) = R(y,z,u) * K(y \ x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5683(a,2),6099(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5683 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6745">
    <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(6099(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="6099 6305"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) \ 1,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5399(a,2),6137(a,1,2,1))].">
      <j1 rule="para" parents="5399 6137"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      K(x,y * L((1 / z) * u,z,z)) = K(x,y * L((z \ 1) * u,z,z))
    ]]></literal>
    <justification jstring="[para(3746(a,1),6159(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3746 6159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(5225,a,6312,a),flip(a)].">
      <j1 rule="hyper" parents="5225 6312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(4718(a,1),6749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4718 6749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6595,a(flip),b,6428,a)].">
      <j1 rule="hyper" parents="60 6595 6428"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6196,a(flip),b,6752,a),flip(a)].">
      <j1 rule="hyper" parents="370 6196 6752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6752(a,2,1,1))].">
      <j1 rule="para" parents="5 6752"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6752(a,2,1,2))].">
      <j1 rule="para" parents="5 6752"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6752(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 6752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(94(a,2),6752(a,2,1))].">
      <j1 rule="para" parents="94 6752"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6641(a,1),6752(a,1,1))].">
      <j1 rule="para" parents="6641 6752"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(1497(a,1),6757(a,2,1))].">
      <j1 rule="para" parents="1497 6757"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(2660(a,2),6757(a,2,1))].">
      <j1 rule="para" parents="2660 6757"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(5650,a,6754,a)].">
      <j1 rule="hyper" parents="5650 6754"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6754(a,1),5650(a,1))].">
      <j1 rule="para" parents="6754 5650"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(96(a,2),6756(a,1,1))].">
      <j1 rule="para" parents="96 6756"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a(flip),b,6763,a),flip(a)].">
      <j1 rule="hyper" parents="370 13 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),6763(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(6763(a,1),5865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6763 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z / x,u)) = w
    ]]></literal>
    <justification jstring="[para(6763(a,1),5871(a,1,1))].">
      <j1 rule="para" parents="6763 5871"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      x * K(y,L(z,u / z,w)) = x / L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6763(a,1),6291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6763 6291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(5650,a,6765,a),flip(a)].">
      <j1 rule="hyper" parents="5650 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,6765,a(flip),b,355,a)].">
      <j1 rule="hyper" parents="129 6765 355"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5512,a(flip),b,6769,a),flip(a)].">
      <j1 rule="hyper" parents="370 5512 6769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6769(a,2),5513(a,1))].">
      <j1 rule="para" parents="6769 5513"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4687,a,6759,a),flip(a)].">
      <j1 rule="hyper" parents="4687 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6002,a(flip),b,6759,a),flip(a)].">
      <j1 rule="hyper" parents="370 6002 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(74(a,1),6773(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 6773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(6302,a,6770,a)].">
      <j1 rule="hyper" parents="6302 6770"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[para(6770(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="6770 6294"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6770(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6770 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,z) = L(K(x \ y,z),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,6774,a)].">
      <j1 rule="hyper" parents="370 5230 6774"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(499(a,2),6476(a,1,2))].">
      <j1 rule="para" parents="499 6476"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4612,a(flip),b,6588,a),flip(a)].">
      <j1 rule="hyper" parents="370 4612 6588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,6782,a(flip),b,301,a(flip))].">
      <j1 rule="hyper" parents="128 6782 301"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      K(x,x \ 1) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1716(a,1),6786(a,1,1))].">
      <j1 rule="para" parents="1716 6786"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1732(a,2),6786(a,1,1))].">
      <j1 rule="para" parents="1732 6786"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,1725,a,b,6788,a)].">
      <j1 rule="hyper" parents="34 1725 6788"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6790,a(flip),b,1709,a(flip))].">
      <j1 rule="hyper" parents="125 6790 1709"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,6791,a(flip),b,2202,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 6791 2202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ K(L(x,u,w),L(x,u,w) \ 1) = 1 / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,1),6791(a,1,1))].">
      <j1 rule="para" parents="25 6791"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2558(a,1),6679(a,2,2))].">
      <j1 rule="para" parents="2558 6679"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x * K(y,x)),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5760(a,1),6697(a,2,2))].">
      <j1 rule="para" parents="5760 6697"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6596,a(flip),b,6741,a),flip(a)].">
      <j1 rule="hyper" parents="370 6596 6741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,6755,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 6755 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6641(a,1),6755(a,1,1))].">
      <j1 rule="para" parents="6641 6755"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6687(a,1),6755(a,1,1))].">
      <j1 rule="para" parents="6687 6755"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6764(a,2),629(a,1))].">
      <j1 rule="para" parents="6764 629"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      K(L(x \ y,x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ y,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(74(a,1),6800(a,1,1,2))].">
      <j1 rule="para" parents="74 6800"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * y) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(L(z,y,x) \ u,w),u,x * y) = v5
    ]]></literal>
    <justification jstring="[para(669(a,1),6801(a,1,1))].">
      <j1 rule="para" parents="669 6801"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(691,a,5222,a)].">
      <j1 rule="hyper" parents="691 5222"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(691,a,5223,a)].">
      <j1 rule="hyper" parents="691 5223"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6312,a(flip),b,6804,a)].">
      <j1 rule="hyper" parents="60 6312 6804"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ ((x \ 1) \ y)) * y = z
    ]]></literal>
    <justification jstring="[para(5270(a,2),328(a,1))].">
      <j1 rule="para" parents="5270 328"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5270(a,2),5414(a,1,2))].">
      <j1 rule="para" parents="5270 5414"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5295,a,6270,a)].">
      <j1 rule="hyper" parents="5295 6270"/>
    </justification>
  </clause>

  <clause id="6810">
    <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(6808(a,1),4287(a,1,1,1))].">
      <j1 rule="para" parents="6808 4287"/>
    </justification>
  </clause>

  <clause id="6811">
    <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(22(a,2),5403(a,2,2))].">
      <j1 rule="para" parents="22 5403"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5251(a,1),5415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5251 5415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(135,a,6813,a)].">
      <j1 rule="hyper" parents="135 6813"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,170,a(flip),b,6813,a)].">
      <j1 rule="hyper" parents="128 170 6813"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6815(a,1),1641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6815 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(5696(a,1),6816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5696 6816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,6818,a)].">
      <j1 rule="hyper" parents="135 6818"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4993,a,b,6819,a)].">
      <j1 rule="hyper" parents="60 4993 6819"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),6820(a,1,2,2))].">
      <j1 rule="para" parents="6 6820"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(6077,a,6821,a)].">
      <j1 rule="hyper" parents="6077 6821"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(129,a,6822,a(flip),b,5765,a),flip(a)].">
      <j1 rule="hyper" parents="129 6822 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(4708,a,6823,a)].">
      <j1 rule="hyper" parents="4708 6823"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      x * K((y \ 1) \ 1,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4470,a(flip),b,6823,a),flip(a)].">
      <j1 rule="hyper" parents="60 4470 6823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,6823,a(flip),b,2072,a)].">
      <j1 rule="hyper" parents="129 6823 2072"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      L(y / (x \ 1),x,x) = z
    ]]></literal>
    <justification jstring="[para(6823(a,1),2079(a,1,2))].">
      <j1 rule="para" parents="6823 2079"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(4902(a,2),6824(a,2,2))].">
      <j1 rule="para" parents="4902 6824"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6410(a,1),6824(a,2,2))].">
      <j1 rule="para" parents="6410 6824"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      x * K(y,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(4905(a,1),6825(a,1,2))].">
      <j1 rule="para" parents="4905 6825"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(31,a,5766,a,b,6830,a),flip(a)].">
      <j1 rule="hyper" parents="31 5766 6830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      T(x,y * (x \ 1)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(275,a,6830,a(flip),b,6269,a),flip(a)].">
      <j1 rule="hyper" parents="275 6830 6269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6830(a,1,2,2))].">
      <j1 rule="para" parents="7 6830"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(6075,a,6831,a)].">
      <j1 rule="hyper" parents="6075 6831"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y * x) = z
    ]]></literal>
    <justification jstring="[para(6831(a,1),6056(a,1))].">
      <j1 rule="para" parents="6831 6056"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4646,a,b,6832,a)].">
      <j1 rule="hyper" parents="60 4646 6832"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(6835(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6835 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,6838,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 6838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(6734,a,6840,a)].">
      <j1 rule="hyper" parents="6734 6840"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5674,a,b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="370 5674 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),6840(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,6841,a,b,88,a)].">
      <j1 rule="hyper" parents="129 6841 88"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(6728,a,6842,a),flip(a)].">
      <j1 rule="hyper" parents="6728 6842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6844(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="77 6844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6469,a(flip),b,6843,a),flip(a)].">
      <j1 rule="hyper" parents="370 6469 6843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(566,a,6828,a)].">
      <j1 rule="hyper" parents="566 6828"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      x * (((x \ 1) \ y) \ y) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6653,a(flip),b,6849,a)].">
      <j1 rule="hyper" parents="60 6653 6849"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(31,a,5252,a,b,6850,a)].">
      <j1 rule="hyper" parents="31 5252 6850"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),6851(a,1,2))].">
      <j1 rule="para" parents="5 6851"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6465(a,1),6847(a,2,2))].">
      <j1 rule="para" parents="6465 6847"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),5556(a,1,2,2,1))].">
      <j1 rule="para" parents="5 5556"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = (((y * y) \ x) * y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(4902(a,1),5596(a,1,1,2))].">
      <j1 rule="para" parents="4902 5596"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,(y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(982,a,5802,a),flip(a)].">
      <j1 rule="hyper" parents="982 5802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      K(x,y \ z) * K(y,y \ z) = (z / y) / T(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6237,a,5854,a)].">
      <j1 rule="hyper" parents="6237 5854"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(5431(a,1),5969(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5431 5969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),6039(a,1,1,2))].">
      <j1 rule="para" parents="107 6039"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1352(a,1),6039(a,1,1,2))].">
      <j1 rule="para" parents="1352 6039"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(2395(a,1),6039(a,1,1,2))].">
      <j1 rule="para" parents="2395 6039"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(36,a,6294,a,b,6859,a)].">
      <j1 rule="hyper" parents="36 6294 6859"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5964(a,1),6046(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5964 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6201,a(flip),b,6116,a)].">
      <j1 rule="hyper" parents="60 6201 6116"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(4223(a,1),6119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4223 6119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4959,a,6122,a),flip(a)].">
      <j1 rule="hyper" parents="4959 6122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3650(a,1),6202(a,1,1,1,2))].">
      <j1 rule="para" parents="3650 6202"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(370,a,5533,a(flip),b,6247,a),flip(a)].">
      <j1 rule="hyper" parents="370 5533 6247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      T(x,x \ T(x * y,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6869(a,1),5505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6869 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      T(x,y) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(6870(a,1),5905(a,1,1))].">
      <j1 rule="para" parents="6870 5905"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),6871(a,1,1))].">
      <j1 rule="para" parents="17 6871"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,63,a(flip),b,6260,a),flip(a)].">
      <j1 rule="hyper" parents="370 63 6260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      x * ((y * y) \ K(y \ 1,z)) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1025,a,6345,a)].">
      <j1 rule="hyper" parents="1025 6345"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,6393,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6417,a(flip),b,6322,a(flip))].">
      <j1 rule="hyper" parents="125 6417 6322"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(77(a,1),6877(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),y \ 1,z * y)) = K(x,a(z,y,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4144(a,2),6473(a,1,2))].">
      <j1 rule="para" parents="4144 6473"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,3517,a(flip),b,6479,a),flip(a)].">
      <j1 rule="hyper" parents="370 3517 6479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(4482,a,6880,a)].">
      <j1 rule="hyper" parents="4482 6880"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(6549(a,2),237(a,1))].">
      <j1 rule="para" parents="6549 237"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6137,a,6559,a),flip(a)].">
      <j1 rule="hyper" parents="6137 6559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5391,a(flip),b,6601,a),flip(a)].">
      <j1 rule="hyper" parents="60 5391 6601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5399(a,1),6601(a,1,1))].">
      <j1 rule="para" parents="5399 6601"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((x \ 1) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6018,a(flip),b,6602,a),flip(a)].">
      <j1 rule="hyper" parents="370 6018 6602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(1378(a,1),6602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1378 6602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(6884(a,1),6604(a,1,2,2))].">
      <j1 rule="para" parents="6884 6604"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(6888(a,1),2668(a,2,2,1))].">
      <j1 rule="para" parents="6888 2668"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(6607(a,2),5414(a,1,2))].">
      <j1 rule="para" parents="6607 5414"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(3701,a,6609,a),flip(a)].">
      <j1 rule="hyper" parents="3701 6609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((y \ 1) \ z),u) = w
    ]]></literal>
    <justification jstring="[para(6672(a,1),5734(a,1))].">
      <j1 rule="para" parents="6672 5734"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6610,a(flip),b,6681,a),flip(a)].">
      <j1 rule="hyper" parents="370 6610 6681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6694(a,2,2,2,1))].">
      <j1 rule="para" parents="4 6694"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      1 / T(L(x,y,z),1 / x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6789,a(flip),b,6740,a),flip(a)].">
      <j1 rule="hyper" parents="60 6789 6740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4337,a,6896,a(flip))].">
      <j1 rule="hyper" parents="4337 6896"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6897(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6897 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6750(a,1),4412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6750 4412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(6750(a,1),5161(a,1,2))].">
      <j1 rule="para" parents="6750 5161"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      K(x * y,y \ (x \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4978,a(flip),b,6775,a),flip(a)].">
      <j1 rule="hyper" parents="60 4978 6775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,6775,a(flip),b,4005,a)].">
      <j1 rule="hyper" parents="125 6775 4005"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = (y * y) \ ((x * y) / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,1000,a(flip),b,6855,a),flip(a)].">
      <j1 rule="hyper" parents="370 1000 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6410(a,1),6867(a,1,2))].">
      <j1 rule="para" parents="6410 6867"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,6862,a,b,6904,a)].">
      <j1 rule="hyper" parents="31 6862 6904"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6905(a,1),5866(a,1,2))].">
      <j1 rule="para" parents="6905 5866"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(5870,a,6906,a),flip(a)].">
      <j1 rule="hyper" parents="5870 6906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      (x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),6876(a,2,1))].">
      <j1 rule="para" parents="5280 6876"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,6881,a(flip),b,6330,a)].">
      <j1 rule="hyper" parents="128 6881 6330"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(1535(a,1),6886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1535 6886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,858,a(flip),b,6903,a),flip(a)].">
      <j1 rule="hyper" parents="370 858 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5599,a,6911,a)].">
      <j1 rule="hyper" parents="5599 6911"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(6410(a,1),6911(a,1,1,2))].">
      <j1 rule="para" parents="6410 6911"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      T((K(x \ 1,x) * y) / (x \ 1),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(3607(a,1),6912(a,1,1,1))].">
      <j1 rule="para" parents="3607 6912"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5312,a,4843,a)].">
      <j1 rule="hyper" parents="5312 4843"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      L(x,x,x * y) = ((x \ 1) * y) \ (y * K(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3438,a(flip),b,5344,a)].">
      <j1 rule="hyper" parents="60 3438 5344"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(5251(a,1),5662(a,1,1))].">
      <j1 rule="para" parents="5251 5662"/>
    </justification>
  </clause>

  <clause id="6920">
    <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(5251(a,1),5663(a,1,1))].">
      <j1 rule="para" parents="5251 5663"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3200,a,b,5772,a)].">
      <j1 rule="hyper" parents="60 3200 5772"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,1172,a(flip),b,5815,a),flip(a)].">
      <j1 rule="hyper" parents="32 1172 5815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5762,a(flip),b,6922,a)].">
      <j1 rule="hyper" parents="60 5762 6922"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(y,x),w) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6294(a,1),5879(a,2,1))].">
      <j1 rule="para" parents="6294 5879"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,984,a(flip),b,5910,a),flip(a)].">
      <j1 rule="hyper" parents="370 984 5910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(5909(a,2),6926(a,1,2))].">
      <j1 rule="para" parents="5909 6926"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1004(a,2),6082(a,1,2))].">
      <j1 rule="para" parents="1004 6082"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(5996(a,1),6135(a,1,1,1))].">
      <j1 rule="para" parents="5996 6135"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,6765,a(flip),b,6341,a)].">
      <j1 rule="hyper" parents="129 6765 6341"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      K(L(x,y,z),u) \ ((z * (y * T(x,u))) / (z * (y * x))) = K(z * (y * x),K(L(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(6930(a,1),5231(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6930 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(6930(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="6930 6294"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(6930(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="6930 6305"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(670(a,2),6470(a,1,2))].">
      <j1 rule="para" parents="670 6470"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6678(a,1),6566(a,1))].">
      <j1 rule="para" parents="6678 6566"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,6084,a,b,6571,a),flip(a)].">
      <j1 rule="hyper" parents="370 6084 6571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6688(a,1),6583(a,1,1))].">
      <j1 rule="para" parents="6688 6583"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),6938(a,2,1,1,2))].">
      <j1 rule="para" parents="7 6938"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u \ 1,w))
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x) \ 1,w) = z
    ]]></literal>
    <justification jstring="[para(6589(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="6589 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      K(1 / L(x,y,z),x) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(4594,a,6599,a),flip(a)].">
      <j1 rule="hyper" parents="4594 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6796,a,b,6941,a)].">
      <j1 rule="hyper" parents="60 6796 6941"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,6942,a(flip),b,5332,a)].">
      <j1 rule="hyper" parents="129 6942 5332"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = z
    ]]></literal>
    <justification jstring="[para(1572(a,2),6892(a,1))].">
      <j1 rule="para" parents="1572 6892"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2721,a(flip),b,6929,a),flip(a)].">
      <j1 rule="hyper" parents="370 2721 6929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6646(a,1),6946(a,1,1,1))].">
      <j1 rule="para" parents="6646 6946"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(2627,a,5348,a),flip(a)].">
      <j1 rule="hyper" parents="2627 5348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6284(a,2),5372(a,1))].">
      <j1 rule="para" parents="6284 5372"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5328(a,1),5379(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5328 5379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2538(a,1),6950(a,2,2))].">
      <j1 rule="para" parents="2538 6950"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4855(a,1),5478(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4855 5478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      (x * y) \ T(L(y,x,x),x \ 1) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(4443(a,1),5541(a,1,2))].">
      <j1 rule="para" parents="4443 5541"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      L(x,(y / z) * z,u) = L(x,y * K(w * w,z),u)
    ]]></literal>
    <justification jstring="[hyper(4132,a,5628,a)].">
      <j1 rule="hyper" parents="4132 5628"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      L(x,y * K(z * z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),6955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6959">
    <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(5812(a,2),5758(a,1))].">
      <j1 rule="para" parents="5812 5758"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(77(a,1),6040(a,1,1,1,2,1))].">
      <j1 rule="para" parents="77 6040"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(2412(a,1),6117(a,1,1))].">
      <j1 rule="para" parents="2412 6117"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      x * K((T(x,y) \ y) \ 1,z) = T(y * T(y \ x,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2856,a(flip),b,6126,a),flip(a)].">
      <j1 rule="hyper" parents="60 2856 6126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) != y * u
    ]]></literal>
    <literal><![CDATA[
      K((T(y,x) \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6962(a,1),40(a,1))].">
      <j1 rule="para" parents="6962 40"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(6102(a,1),6161(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ L(1 / u,w,v5)))) = K(x,y * (z * (u \ L(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(3798(a,1),6162(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3798 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1485(a,1),6620(a,1,1,1))].">
      <j1 rule="para" parents="1485 6620"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5399(a,2),6659(a,1,2))].">
      <j1 rule="para" parents="5399 6659"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(6121(a,1),6659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6121 6659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      L(x,y,z * (((z \ 1) \ u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6669(a,2),3576(a,1))].">
      <j1 rule="para" parents="6669 3576"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6328(a,1),6717(a,1,1))].">
      <j1 rule="para" parents="6328 6717"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(77(a,1),6971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 6971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6973">
    <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(6797(a,2),6305(a,1,1))].">
      <j1 rule="para" parents="6797 6305"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4905(a,1),6807(a,2,1))].">
      <j1 rule="para" parents="4905 6807"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ 1) \ (x \ y)) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(125,a,5232,a(flip),b,6974,a),flip(a)].">
      <j1 rule="hyper" parents="125 5232 6974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6974(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),6974(a,1,2,2))].">
      <j1 rule="para" parents="17 6974"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(6976(a,2),632(a,1,2))].">
      <j1 rule="para" parents="6976 632"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(6806,a,6975,a)].">
      <j1 rule="hyper" parents="6806 6975"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(435,a,6885,a)].">
      <j1 rule="hyper" parents="435 6885"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6601,a,b,6887,a)].">
      <j1 rule="hyper" parents="60 6601 6887"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(77(a,1),6890(a,2,1,1))].">
      <j1 rule="para" parents="77 6890"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6982(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,6983,a,b,107,a)].">
      <j1 rule="hyper" parents="125 6983 107"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      T((K(x,x \ 1) * y) / (x \ 1),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(1716(a,1),6914(a,1,1,1,1))].">
      <j1 rule="para" parents="1716 6914"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5676(a,1),6948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5676 6948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      (x * y) \ (x * (y * (x \ 1))) = R(1 / x,x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(2119(a,1),6954(a,1,2))].">
      <j1 rule="para" parents="2119 6954"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      R(1 / x,x * y,1 / x) = L(x \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(629,a,6989,a),flip(a)].">
      <j1 rule="hyper" parents="629 6989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,6968,a)].">
      <j1 rule="hyper" parents="135 6968"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      T(z,u) * K(y,x) = w
    ]]></literal>
    <justification jstring="[para(6969(a,2),40(a,1))].">
      <j1 rule="para" parents="6969 40"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      T(K(x,x \ 1) * (y / (x \ 1)),x) = T((1 / x) \ y,x * x)
    ]]></literal>
    <justification jstring="[para(3456(a,1),6987(a,1,1))].">
      <j1 rule="para" parents="3456 6987"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6991(a,1),4845(a,1,1))].">
      <j1 rule="para" parents="6991 4845"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6994(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) != w * K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(z,u) = w
    ]]></literal>
    <justification jstring="[para(6995(a,2),41(a,1))].">
      <j1 rule="para" parents="6995 41"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6350(a,1),5446(a,1,1))].">
      <j1 rule="para" parents="6350 5446"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(693,a,6997,a),flip(a)].">
      <j1 rule="hyper" parents="693 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      K((x \ 1) \ y,x * x) = K(x \ y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5687,a,6543,a)].">
      <j1 rule="hyper" parents="5687 6543"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      T(x * (y \ 1),T(y,y \ 1)) = L((y \ 1) \ 1,y,x) \ x
    ]]></literal>
    <justification jstring="[para(3401(a,1),6506(a,2,1))].">
      <j1 rule="para" parents="3401 6506"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y) \ y = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4437,a(flip),b,7000,a),flip(a)].">
      <j1 rule="hyper" parents="60 4437 7000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      ((x \ 1) * y) / ((y * x) * (x \ 1)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6507(a,1,2))].">
      <j1 rule="para" parents="107 6507"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      ((x \ 1) * y) / R(y,x,x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(1111(a,1),7002(a,1,2))].">
      <j1 rule="para" parents="1111 7002"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6268(a,1),6512(a,1,2))].">
      <j1 rule="para" parents="6268 6512"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(693,a,7004,a),flip(a)].">
      <j1 rule="hyper" parents="693 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(5279(a,1),7005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5279 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2769(a,1),6562(a,1,2))].">
      <j1 rule="para" parents="2769 6562"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,u,w)) * (y * z) = (K(x \ 1,x) * y) * z
    ]]></literal>
    <justification jstring="[para(2049(a,1),6581(a,2,1,1))].">
      <j1 rule="para" parents="2049 6581"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,439,a(flip),b,6590,a),flip(a)].">
      <j1 rule="hyper" parents="370 439 6590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1769(a,1),7009(a,1,2))].">
      <j1 rule="para" parents="1769 7009"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(53,a,7011,a)].">
      <j1 rule="hyper" parents="53 7011"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,7012,a)].">
      <j1 rule="hyper" parents="51 7012"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1771(a,2),7013(a,1,1))].">
      <j1 rule="para" parents="1771 7013"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(6674,a,5765,a)].">
      <j1 rule="hyper" parents="6674 5765"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(6866(a,2),6719(a,1))].">
      <j1 rule="para" parents="6866 6719"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(6779(a,1),5290(a,1))].">
      <j1 rule="para" parents="6779 5290"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(6759(a,1),7017(a,1))].">
      <j1 rule="para" parents="6759 7017"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6755,a(flip),b,6799,a),flip(a)].">
      <j1 rule="hyper" parents="60 6755 6799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7019(a,2,1,1))].">
      <j1 rule="para" parents="5 7019"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,5233,a),flip(a)].">
      <j1 rule="hyper" parents="6959 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6988,a,b,7021,a)].">
      <j1 rule="hyper" parents="60 6988 7021"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x
    ]]></literal>
    <justification jstring="[para(5(a,1),7022(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(7016,a,6410,a)].">
      <j1 rule="hyper" parents="7016 6410"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6569,a,7024,a),flip(a)].">
      <j1 rule="hyper" parents="6569 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5490(a,1),7023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5490 7023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5509,a(flip),b,7026,a),flip(a)].">
      <j1 rule="hyper" parents="370 5509 7026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(32,a,6705,a,b,7027,a),flip(a)].">
      <j1 rule="hyper" parents="32 6705 7027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      x * ((x \ 1) \ (y * (z * (x \ (1 / x))))) = T(y * z,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,4658,a(flip),b,5243,a),flip(a)].">
      <j1 rule="hyper" parents="370 4658 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (x / z)) = (K(x,y) * T(x,y)) / z
    ]]></literal>
    <justification jstring="[para(5703(a,2),5881(a,2,1,2))].">
      <j1 rule="para" parents="5703 5881"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ 1) \ (x / z)) = T(T(x,y),y) / z
    ]]></literal>
    <justification jstring="[para(5677(a,1),7030(a,2,1))].">
      <j1 rule="para" parents="5677 7030"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      ((x * T(T(x,x \ 1),x \ 1)) \ y) * T(x,x \ 1) = (x \ 1) * T(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(308(a,1),6026(a,2,1))].">
      <j1 rule="para" parents="308 6026"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / (y \ 1) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(1336(a,1),6027(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1336 6027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      (x \ 1) \ (y * T(x,x \ 1)) = T(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(7033(a,1),109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      (x \ 1) \ (y * T(x,x \ 1)) = (1 / x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4451,a(flip),b,7034,a),flip(a)].">
      <j1 rule="hyper" parents="370 4451 7034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      (x \ 1) \ (y * ((x \ 1) \ 1)) = (1 / x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(108(a,1),7035(a,1,2,2))].">
      <j1 rule="para" parents="108 7035"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      T(x,y \ 1) * (1 / (y \ 1)) = ((1 / y) \ (x * y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7036(a,1),4452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7036 4452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      ((1 / x) \ (y * x)) * (x \ 1) = T(y,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(74(a,1),7037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,(1 / z) / (u * u))
    ]]></literal>
    <justification jstring="[hyper(3120,a,6104,a),flip(a)].">
      <j1 rule="hyper" parents="3120 6104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,1 / ((u * u) * z))
    ]]></literal>
    <justification jstring="[para(524(a,1),7040(a,2,3))].">
      <j1 rule="para" parents="524 7040"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3078,a(flip),b,7041,a),flip(a)].">
      <j1 rule="hyper" parents="370 3078 7041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      a(x,y,z * K(u * u,1 / z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3074,a(flip),b,7042,a),flip(a)].">
      <j1 rule="hyper" parents="370 3074 7042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      a(x,y,z * K(u * u,z \ 1)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5423(a,1),7043(a,1,3,2))].">
      <j1 rule="para" parents="5423 7043"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(6189(a,1),6187(a,1,1))].">
      <j1 rule="para" parents="6189 6187"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5792,a(flip),b,7046,a),flip(a)].">
      <j1 rule="hyper" parents="60 5792 7046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,7047,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 7047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(282(a,1),7047(a,1,2,2))].">
      <j1 rule="para" parents="282 7047"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5289,a,7049,a)].">
      <j1 rule="hyper" parents="5289 7049"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7049(a,2),5265(a,1))].">
      <j1 rule="para" parents="7049 5265"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,R(z / T(x,y),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(286(a,1),7055(a,1,2))].">
      <j1 rule="para" parents="286 7055"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      T(T(T(x,y) / (T(x,y) / y),x),z) = L(T(y,z),y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(7051(a,1),5977(a,1,1))].">
      <j1 rule="para" parents="7051 5977"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) \ 1) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5695(a,1),6254(a,2,2))].">
      <j1 rule="para" parents="5695 6254"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(505,a,7059,a)].">
      <j1 rule="hyper" parents="505 7059"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5964(a,1),7059(a,1,2))].">
      <j1 rule="para" parents="5964 7059"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5964(a,1),7060(a,1,1))].">
      <j1 rule="para" parents="5964 7060"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6291(a,1),6316(a,2,2))].">
      <j1 rule="para" parents="6291 6316"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = x \ T(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3571,a(flip),b,6539,a),flip(a)].">
      <j1 rule="hyper" parents="60 3571 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),6619(a,1,1,2,2,1))].">
      <j1 rule="para" parents="5 6619"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1675(a,1),6664(a,1,2))].">
      <j1 rule="para" parents="1675 6664"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z \ 1))
    ]]></literal>
    <justification jstring="[para(5056(a,1),6668(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5056 6668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      L(x,y,z * ((T(z,u \ 1) / u) / z)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),6671(a,2,3))].">
      <j1 rule="para" parents="7 6671"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5392,a,6696,a)].">
      <j1 rule="hyper" parents="5392 6696"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(60,a,6779,a(flip),b,7070,a)].">
      <j1 rule="hyper" parents="60 6779 7070"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),7071(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 7071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7072(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 7072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(5000(a,1),6861(a,1,1,2))].">
      <j1 rule="para" parents="5000 6861"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,6475,a(flip),b,6921,a)].">
      <j1 rule="hyper" parents="129 6475 6921"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(5719(a,2),6951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5719 6951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5715,a(flip),b,7076,a),flip(a)].">
      <j1 rule="hyper" parents="370 5715 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(4956(a,1),7077(a,1,2))].">
      <j1 rule="para" parents="4956 7077"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(215,a,7078,a)].">
      <j1 rule="hyper" parents="215 7078"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6269(a,1),6960(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6269 6960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(129,a,7080,a,b,xx)].">
      <j1 rule="hyper" parents="129 7080"/>
    </justification>
  </clause>

  <clause id="7082">
    <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(5952(a,1),7080(a,2,1))].">
      <j1 rule="para" parents="5952 7080"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(7081(a,1),6294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7081 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      (x * y) \ ((x * K(z \ x,u)) * y) = K((z * y) \ (x * y),u)
    ]]></literal>
    <justification jstring="[para(74(a,1),7084(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 7084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      (x * y) * K((z * y) \ (x * y),u) = (x * K(z \ x,u)) * y
    ]]></literal>
    <justification jstring="[hyper(156,a,7085,a)].">
      <j1 rule="hyper" parents="156 7085"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,6985,a)].">
      <j1 rule="hyper" parents="1068 6985"/>
    </justification>
  </clause>

  <clause id="7089">
    <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(7088(a,1),6593(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7088 6593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6111,a(flip),b,7089,a),flip(a)].">
      <j1 rule="hyper" parents="370 6111 7089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7091">
    <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(7090(a,1),1031(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7090 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,u,w)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,3445,a(flip),b,7008,a),flip(a)].">
      <j1 rule="hyper" parents="32 3445 7008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,u,w)) = K(x \ 1,R(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,4692,a,b,7092,a),flip(a)].">
      <j1 rule="hyper" parents="370 4692 7092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(7092(a,1),4498(a,1,2))].">
      <j1 rule="para" parents="7092 4498"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      R(x,y,z) * K(x \ 1,R(x,u,w)) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,7093,a(flip),b,5682,a)].">
      <j1 rule="hyper" parents="129 7093 5682"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) \ 1 = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7093(a,1),1717(a,1,1))].">
      <j1 rule="para" parents="7093 1717"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6744,a,b,7096,a)].">
      <j1 rule="hyper" parents="60 6744 7096"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,7098,a(flip))].">
      <j1 rule="hyper" parents="215 7098"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),7098(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 7098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4336(a,1),7099(a,1,1,1))].">
      <j1 rule="para" parents="4336 7099"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(7100(a,1),220(a,1,1,1))].">
      <j1 rule="para" parents="7100 220"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(7100(a,1),5999(a,1,1,2))].">
      <j1 rule="para" parents="7100 5999"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      R(x \ 1,y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      R(1 / x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(7102(a,1),45(a,1))].">
      <j1 rule="para" parents="7102 45"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),7102(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 7102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      1 / R(1 / x,y,z) = R(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(7102(a,1),1307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7102 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(7102(a,1),6062(a,1,2,1))].">
      <j1 rule="para" parents="7102 6062"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(706(a,1),7105(a,2,1,1))].">
      <j1 rule="para" parents="706 7105"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      L(R((x \ 1) \ 1,y,z) \ u,R(x,y,z),R(x,y,z)) = 1 \ ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(7105(a,2),2123(a,1,1,1))].">
      <j1 rule="para" parents="7105 2123"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2727(a,1),7105(a,2,1,1))].">
      <j1 rule="para" parents="2727 7105"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(7105(a,2),4349(a,1,1))].">
      <j1 rule="para" parents="7105 4349"/>
    </justification>
  </clause>

  <clause id="7112">
    <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(7105(a,2),4419(a,1,1))].">
      <j1 rule="para" parents="7105 4419"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1056(a,1),7101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1056 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      R(x,y,z) \ K(R(x,u,w),x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5872,a,7097,a)].">
      <j1 rule="hyper" parents="5872 7097"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(448(a,1),7114(a,1,2,1))].">
      <j1 rule="para" parents="448 7114"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,7115,a)].">
      <j1 rule="hyper" parents="156 7115"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,4569,a,b,7110,a)].">
      <j1 rule="hyper" parents="60 4569 7110"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5866(a,1),7118(a,1,2,2))].">
      <j1 rule="para" parents="5866 7118"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(x,y) \ K(z,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6235(a,1),7119(a,2,1,1))].">
      <j1 rule="para" parents="6235 7119"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6384,a,7095,a)].">
      <j1 rule="hyper" parents="6384 7095"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2769(a,1),7113(a,1,2))].">
      <j1 rule="para" parents="2769 7113"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3608(a,1),7122(a,1,2,1))].">
      <j1 rule="para" parents="3608 7122"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      T((x \ 1) * y,x \ (x \ 1)) = x * (y * (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(742,a,7029,a),flip(a)].">
      <j1 rule="hyper" parents="742 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (x * x)) = x * ((x \ y) * (x \ (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,2540,a(flip),b,7124,a)].">
      <j1 rule="hyper" parents="60 2540 7124"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (x * x)) = y * (x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(370,a,1431,a(flip),b,7125,a),flip(a)].">
      <j1 rule="hyper" parents="370 1431 7125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(156,a,7063,a)].">
      <j1 rule="hyper" parents="156 7063"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      R(T(x,y * K(z,y)),y,K(z,y)) = ((z * y) / z) \ (x * (y * K(z,y)))
    ]]></literal>
    <justification jstring="[para(5630(a,1),5361(a,2,2))].">
      <j1 rule="para" parents="5630 5361"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5367(a,1),1141(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5367 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7131">
    <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(5600,a,7130,a)].">
      <j1 rule="hyper" parents="5600 7130"/>
    </justification>
  </clause>

  <clause id="7132">
    <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(5369(a,1),1523(a,1,1,1))].">
      <j1 rule="para" parents="5369 1523"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      (x * y) * (z \ T(z * L(y \ (z \ 1),y,x),u)) = (x * K(y \ 1,u)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(1378(a,1),5417(a,1,2))].">
      <j1 rule="para" parents="1378 5417"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,z * (T(z,y) * ((z * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(1668(a,1),5465(a,2,2))].">
      <j1 rule="para" parents="1668 5465"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      R(x,y,z) * (x * (R((u * x) / u,y,z) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1236(a,2),5960(a,1,2,2,1))].">
      <j1 rule="para" parents="1236 5960"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      L(L(x * K(y,x),z,u),w,v5) * y = y * L(L(x,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(6096(a,1),6097(a,1,1,1))].">
      <j1 rule="para" parents="6096 6097"/>
    </justification>
  </clause>

  <clause id="7137">
    <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(6414(a,2),6568(a,1))].">
      <j1 rule="para" parents="6414 6568"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      T(L(x,y,z),u) * (L(x,y,z) \ x) = x * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(925,a,6418,a)].">
      <j1 rule="hyper" parents="925 6418"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ x) = x * K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(20(a,2),7138(a,1,1))].">
      <j1 rule="para" parents="20 7138"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(6747,a,6120,a),flip(a)].">
      <j1 rule="hyper" parents="6747 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6410,a(flip),b,7140,a),flip(a)].">
      <j1 rule="hyper" parents="370 6410 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6569,a,7141,a)].">
      <j1 rule="hyper" parents="6569 7141"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      x / K(y \ x,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7142(a,1),5709(a,1,2))].">
      <j1 rule="para" parents="7142 5709"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(7142(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7142 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,7144,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 7144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(6322(a,2),6973(a,1,1,2))].">
      <j1 rule="para" parents="6322 6973"/>
    </justification>
  </clause>

  <clause id="7147">
    <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(1406(a,1),7146(a,1,1,2))].">
      <j1 rule="para" parents="1406 7146"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3182(a,1),7135(a,1,2))].">
      <j1 rule="para" parents="3182 7135"/>
    </justification>
  </clause>

  <clause id="7149">
    <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(6270(a,1),6348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 6348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <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(7149(a,2),693(a,1))].">
      <j1 rule="para" parents="7149 693"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      R(x,y,T(z,y * z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7150,a,5632,a)].">
      <j1 rule="hyper" parents="7150 5632"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7150,a,26,a),flip(a)].">
      <j1 rule="hyper" parents="7150 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(6868(a,1),6603(a,1,2))].">
      <j1 rule="para" parents="6868 6603"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(6358(a,1),6623(a,2,2,2))].">
      <j1 rule="para" parents="6358 6623"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(6203(a,1),6680(a,2,2))].">
      <j1 rule="para" parents="6203 6680"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(6504,a,6848,a)].">
      <j1 rule="hyper" parents="6504 6848"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),6860(a,1,1,2,2))].">
      <j1 rule="para" parents="107 6860"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(4096(a,2),7158(a,1,1))].">
      <j1 rule="para" parents="4096 7158"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(6022(a,1),6908(a,1,1,2))].">
      <j1 rule="para" parents="6022 6908"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5298(a,1),7160(a,1,2,2))].">
      <j1 rule="para" parents="5298 7160"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),6980(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6410(a,1),7162(a,1,2))].">
      <j1 rule="para" parents="6410 7162"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(31,a,4399,a,b,7163,a)].">
      <j1 rule="hyper" parents="31 4399 7163"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6012(a,1),7163(a,1,2))].">
      <j1 rule="para" parents="6012 7163"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(74(a,1),7164(a,2,1,2))].">
      <j1 rule="para" parents="74 7164"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1548(a,1),6981(a,1,1))].">
      <j1 rule="para" parents="1548 6981"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,z)) = (x \ T(y,z)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(4797(a,1),7167(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4797 7167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4937(a,1),7153(a,2,1))].">
      <j1 rule="para" parents="4937 7153"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(370,a,7165,a(flip),b,7155,a),flip(a)].">
      <j1 rule="hyper" parents="370 7165 7155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4949(a,1),7168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4949 7168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5330,a,b,7171,a)].">
      <j1 rule="hyper" parents="370 5330 7171"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7172(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(5230(a,2),7169(a,2,1,1))].">
      <j1 rule="para" parents="5230 7169"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = K(y,z) / T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5912,a(flip),b,7174,a),flip(a)].">
      <j1 rule="hyper" parents="370 5912 7174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,360,a(flip),b,7175,a),flip(a)].">
      <j1 rule="hyper" parents="129 360 7175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      ((x * y) * z) * a(z * K(x * y,z),x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5325,a(flip),b,5377,a),flip(a)].">
      <j1 rule="hyper" parents="370 5325 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      ((x * y) * z) * a(z * K(x * y,z),x,y) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      R(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(7177(a,2),40(a,1))].">
      <j1 rule="para" parents="7177 40"/>
    </justification>
  </clause>

  <clause id="7179">
    <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(6402(a,1),5604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6402 5604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,T(x / T(z,y),z),z)
    ]]></literal>
    <justification jstring="[para(5911(a,2),5979(a,2,2))].">
      <j1 rule="para" parents="5911 5979"/>
    </justification>
  </clause>

  <clause id="7181">
    <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(5701(a,2),6246(a,2,1))].">
      <j1 rule="para" parents="5701 6246"/>
    </justification>
  </clause>

  <clause id="7182">
    <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(5701(a,2),7181(a,1,1,3))].">
      <j1 rule="para" parents="5701 7181"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6511(a,2),40(a,1))].">
      <j1 rule="para" parents="6511 40"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),6927(a,2,1,2))].">
      <j1 rule="para" parents="77 6927"/>
    </justification>
  </clause>

  <clause id="7185">
    <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(4(a,1),7132(a,2,1,1))].">
      <j1 rule="para" parents="4 7132"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7147,a,7074,a),flip(a)].">
      <j1 rule="hyper" parents="7147 7074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7186(a,2,2,1))].">
      <j1 rule="para" parents="5 7186"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(74(a,1),7186(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="74 7186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(436(a,1),7188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="436 7188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5850(a,1),7189(a,1,2,1))].">
      <j1 rule="para" parents="5850 7189"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5697(a,1),7190(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5697 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,x / T(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6632,a(flip),b,7180,a),flip(a)].">
      <j1 rule="hyper" parents="370 6632 7180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (K(x,y) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5947(a,1),5326(a,2,1))].">
      <j1 rule="para" parents="5947 5326"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5280(a,1),7193(a,1,1,1))].">
      <j1 rule="para" parents="5280 7193"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,7194,a)].">
      <j1 rule="hyper" parents="215 7194"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ L(R(x,y,x),y,x) = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(5533(a,1),7195(a,1,1,2))].">
      <j1 rule="para" parents="5533 7195"/>
    </justification>
  </clause>

  <clause id="7197">
    <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(6213(a,1),5882(a,1,2,1))].">
      <j1 rule="para" parents="6213 5882"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,2394,a(flip),b,6250,a),flip(a)].">
      <j1 rule="hyper" parents="60 2394 6250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),7198(a,2,1,2))].">
      <j1 rule="para" parents="107 7198"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(6258(a,1),7199(a,1,2,1))].">
      <j1 rule="para" parents="6258 7199"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      K(((x * y) / x) \ x,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,6952,a(flip),b,7200,a),flip(a)].">
      <j1 rule="hyper" parents="31 6952 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      K(x \ ((x * y) / x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(6257(a,1),7201(a,1,1))].">
      <j1 rule="para" parents="6257 7201"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(263(a,1),7202(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="263 7202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5795,a,b,7203,a)].">
      <j1 rule="hyper" parents="60 5795 7203"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,7203,a(flip),b,5682,a),flip(a)].">
      <j1 rule="hyper" parents="129 7203 5682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      (T(x,y) \ y) * x != z * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(7204(a,1),146(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="7204 146"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(7205(a,1),7058(a,1,1,1))].">
      <j1 rule="para" parents="7205 7058"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(7206,a,5944,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7206 5944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(5362(a,1),7207(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5362 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,7209,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 7209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = R(L(T(x,y),x \ w,x),z,u)
    ]]></literal>
    <justification jstring="[para(7210(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7210 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = L(R(T(x,y),z,u),x \ w,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,24,a(flip),b,7211,a),flip(a)].">
      <j1 rule="hyper" parents="370 24 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7213">
    <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(6944(a,1),6682(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6944 6682"/>
    </justification>
  </clause>

  <clause id="7214">
    <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(5430(a,1),6710(a,1,1))].">
      <j1 rule="para" parents="5430 6710"/>
    </justification>
  </clause>

  <clause id="7215">
    <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(7103(a,1),7214(a,1,1,1))].">
      <j1 rule="para" parents="7103 7214"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ K(x,x \ 1) = 1 / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(6790(a,1),6793(a,1,2))].">
      <j1 rule="para" parents="6790 6793"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5968(a,1),6964(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5968 6964"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(5278(a,1),7218(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5278 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(294,a,6720,a),flip(a)].">
      <j1 rule="hyper" parents="294 6720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(5279(a,1),7220(a,1,2,1))].">
      <j1 rule="para" parents="5279 7220"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,7111,a),flip(a)].">
      <j1 rule="hyper" parents="327 7111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(4348(a,1),7223(a,2,1))].">
      <j1 rule="para" parents="4348 7223"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,4535,a(flip),b,7224,a)].">
      <j1 rule="hyper" parents="60 4535 7224"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      (x * y) * L(z \ T(z * (y \ (z \ 1)),z),y,x) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(2611(a,2),7133(a,1,2))].">
      <j1 rule="para" parents="2611 7133"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(7105(a,2),7225(a,1,1))].">
      <j1 rule="para" parents="7105 7225"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(336,a,7226,a)].">
      <j1 rule="hyper" parents="336 7226"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5416(a,1),7228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5416 7228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(4965(a,1),7227(a,2,1))].">
      <j1 rule="para" parents="4965 7227"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      (((x * (y \ 1)) \ 1) \ 1) \ (((x / y) * y) * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7108(a,1),7230(a,1,1))].">
      <j1 rule="para" parents="7108 7230"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      x * (K(x,y) * L(K(x,y) \ (x \ z),u,w)) = T(x,y) * L(T(x,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5256(a,2),5296(a,2,2,1,1))].">
      <j1 rule="para" parents="5256 5296"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5860(a,1),5946(a,2,1))].">
      <j1 rule="para" parents="5860 5946"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15,a,b,7233,a),flip(a)].">
      <j1 rule="hyper" parents="370 15 7233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      R(R(x,y \ z,T(y,y \ z)),z,K(y \ z,y)) = R(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(257(a,1),7234(a,1,2))].">
      <j1 rule="para" parents="257 7234"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(7006(a,1),7236(a,1,1))].">
      <j1 rule="para" parents="7006 7236"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      R(K(R(x,y,z),u),R(x,y,z),y * z) = ((T(x,u) * y) * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(103(a,1),6261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="103 6261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <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(370,a,4803,a,b,6336,a)].">
      <j1 rule="hyper" parents="370 4803 6336"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      ((x * x) \ y) * T(x,x \ 1) = (x \ 1) * T(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1336(a,1),7032(a,1,1,1,2))].">
      <j1 rule="para" parents="1336 7032"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      ((x * x) \ y) * T(x,x \ 1) = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4437(a,1),7240(a,2,2))].">
      <j1 rule="para" parents="4437 7240"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,x) = (x \ y) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(940(a,1),7241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="940 7241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      (x \ y) * T(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(7242(a,1),1579(a,1))].">
      <j1 rule="para" parents="7242 1579"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(6245(a,1),7239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(4596,a,6317,a)].">
      <j1 rule="hyper" parents="4596 6317"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(6944(a,1),7245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6944 7245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(7007(a,1),6614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7007 6614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ ((y \ 1) \ x),y) = z
    ]]></literal>
    <justification jstring="[para(7248(a,2),6945(a,1))].">
      <j1 rule="para" parents="7248 6945"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      T((x / y) * K(y \ 1,x),L(1 / y,y,x)) = x * R(L(1 / y,y,x),x,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(3802(a,1),6545(a,2,2))].">
      <j1 rule="para" parents="3802 6545"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      T((x / y) * K(y \ 1,x),L(1 / y,y,x)) = x * L(R(1 / y,x,L(y,y,x)),y,x)
    ]]></literal>
    <justification jstring="[para(24(a,1),7251(a,2,2))].">
      <j1 rule="para" parents="24 7251"/>
    </justification>
  </clause>

  <clause id="7253">
    <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(1949(a,1),6634(a,1,1))].">
      <j1 rule="para" parents="1949 6634"/>
    </justification>
  </clause>

  <clause id="7254">
    <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(1837(a,1),7253(a,1,2))].">
      <j1 rule="para" parents="1837 7253"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(1029,a,7254,a),flip(a)].">
      <j1 rule="hyper" parents="1029 7254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(5533(a,1),7196(a,1,2))].">
      <j1 rule="para" parents="5533 7196"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6099,a(flip),b,7258,a),flip(a)].">
      <j1 rule="hyper" parents="370 6099 7258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      (((1 / x) * (y * ((x * x) * (1 / x)))) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(29(a,1),5612(a,1,1,1,2))].">
      <j1 rule="para" parents="29 5612"/>
    </justification>
  </clause>

  <clause id="7261">
    <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(3277(a,1),5966(a,1,1))].">
      <j1 rule="para" parents="3277 5966"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(107(a,1),7261(a,1,1,1,2))].">
      <j1 rule="para" parents="107 7261"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(5936(a,1),7262(a,1,2))].">
      <j1 rule="para" parents="5936 7262"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4803(a,2),7263(a,1,1,1,2))].">
      <j1 rule="para" parents="4803 7263"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(263(a,1),7264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 7264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(5699(a,2),7265(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5699 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5699(a,2),7267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5699 7267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,6339,a,b,7268,a),flip(a)].">
      <j1 rule="hyper" parents="32 6339 7268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(156,a,7270,a)].">
      <j1 rule="hyper" parents="156 7270"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      x * ((x \ y) * K(x \ 1,z)) = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1251,a(flip),b,7271,a)].">
      <j1 rule="hyper" parents="60 1251 7271"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7271(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3747,a,7273,a)].">
      <j1 rule="hyper" parents="3747 7273"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,7273,a)].">
      <j1 rule="hyper" parents="2810 7273"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6390,a(flip),b,7273,a),flip(a)].">
      <j1 rule="hyper" parents="60 6390 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,7273,a(flip),b,82,a),flip(a)].">
      <j1 rule="hyper" parents="124 7273 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7273(a,1),6268(a,1,1))].">
      <j1 rule="para" parents="7273 6268"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7275(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7275 22"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7275(a,1),687(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7275(a,1),688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7275(a,1),689(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7275(a,1),7152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a,b,7274,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 7274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6765,a(flip),b,7274,a)].">
      <j1 rule="hyper" parents="60 6765 7274"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7287,a(flip),b,5262,a)].">
      <j1 rule="hyper" parents="129 7287 5262"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7287(a,1),5698(a,2,2))].">
      <j1 rule="para" parents="7287 5698"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5842(a,2),7287(a,1,1))].">
      <j1 rule="para" parents="5842 7287"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7287(a,1),5302(a,1,1))].">
      <j1 rule="para" parents="7287 5302"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      K(T(x / y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(5978(a,1),7287(a,1,1))].">
      <j1 rule="para" parents="5978 7287"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6723(a,1),7287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6723 7287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7294,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 7294 5230"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5540(a,1),7294(a,1,1))].">
      <j1 rule="para" parents="5540 7294"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7294(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7294 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(7294(a,1),7259(a,1,1,1,1))].">
      <j1 rule="para" parents="7294 7259"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = T(R(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(7284(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7284 22"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),7284(a,1,3)),flip(a)].">
      <j1 rule="para" parents="109 7284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7279(a,1),7152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7279 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5698,a,b,7290,a),flip(a)].">
      <j1 rule="hyper" parents="370 5698 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6291,a(flip),b,7290,a),flip(a)].">
      <j1 rule="hyper" parents="370 6291 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7290(a,2),5709(a,1))].">
      <j1 rule="para" parents="7290 5709"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,7306,a),flip(a)].">
      <j1 rule="hyper" parents="494 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7306,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 7306 17"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(5978(a,1),7306(a,1,2))].">
      <j1 rule="para" parents="5978 7306"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6723(a,1),7306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6723 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,7315,a),flip(a)].">
      <j1 rule="hyper" parents="494 7315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7315,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 7315 17"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      T(x,T(y,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5985(a,1),7315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5985 7315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6195(a,1),7315(a,1,2))].">
      <j1 rule="para" parents="6195 7315"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(7184(a,1),7315(a,1,2))].">
      <j1 rule="para" parents="7184 7315"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,7295,a(flip),b,7148,a),flip(a)].">
      <j1 rule="hyper" parents="125 7295 7148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,7298,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 7298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7298(a,2),5870(a,1))].">
      <j1 rule="para" parents="7298 5870"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7322,a(flip),b,6108,a),flip(a)].">
      <j1 rule="hyper" parents="129 7322 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5985(a,1),7322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5985 7322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6195(a,1),7322(a,1,2))].">
      <j1 rule="para" parents="6195 7322"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5289,a,7307,a)].">
      <j1 rule="hyper" parents="5289 7307"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(5978(a,1),7327(a,1,2))].">
      <j1 rule="para" parents="5978 7327"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(216(a,1),7291(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="216 7291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1317(a,1),7308(a,1,2))].">
      <j1 rule="para" parents="1317 7308"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5978(a,1),7308(a,1,2))].">
      <j1 rule="para" parents="5978 7308"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(74(a,1),7314(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 7314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7314(a,1),7055(a,1))].">
      <j1 rule="para" parents="7314 7055"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6195(a,1),7323(a,1,2))].">
      <j1 rule="para" parents="6195 7323"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5980,a,7325,a),flip(a)].">
      <j1 rule="hyper" parents="5980 7325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7338">
    <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(2157(a,1),7325(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2157 7325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(2686(a,1),7325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2686 7325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5485(a,2),7325(a,1,2))].">
      <j1 rule="para" parents="5485 7325"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x * y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(7325(a,1),5980(a,1))].">
      <j1 rule="para" parents="7325 5980"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5688,a(flip),b,7326,a),flip(a)].">
      <j1 rule="hyper" parents="370 5688 7326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(108(a,1),7326(a,1,2))].">
      <j1 rule="para" parents="108 7326"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),7342(a,1,2))].">
      <j1 rule="para" parents="108 7342"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(77(a,1),7344(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 7344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(709(a,1),7329(a,1,2))].">
      <j1 rule="para" parents="709 7329"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) \ 1) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6529,a,7334,a)].">
      <j1 rule="hyper" parents="6529 7334"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,7334,a),flip(a)].">
      <j1 rule="hyper" parents="494 7334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7337(a,1),5501(a,1,2))].">
      <j1 rule="para" parents="7337 5501"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7286(a,2),385(a,1)),flip(b)].">
      <j1 rule="para" parents="7286 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6765(a,1),7351(a,1))].">
      <j1 rule="para" parents="6765 7351"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(638(a,1),7354(a,1,1))].">
      <j1 rule="para" parents="638 7354"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(6723(a,1),7354(a,1,1))].">
      <j1 rule="para" parents="6723 7354"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6510,a,7350,a)].">
      <j1 rule="hyper" parents="6510 7350"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = R(x,y,x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,7350,a(flip),b,6276,a),flip(a)].">
      <j1 rule="hyper" parents="128 7350 6276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7350(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7350 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),7355(a,1,1,2))].">
      <j1 rule="para" parents="7 7355"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(7360(a,1),6749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7360 6749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5500,a(flip),b,7302,a),flip(a)].">
      <j1 rule="hyper" parents="370 5500 7302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      K(x,T(R(y,z,y),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7302(a,1),7322(a,1,2))].">
      <j1 rule="para" parents="7302 7322"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(1925,a,7367,a)].">
      <j1 rule="hyper" parents="1925 7367"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5485,a,b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="370 5485 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),7369(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5280 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      K(x,R(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(22(a,2),7368(a,1,2))].">
      <j1 rule="para" parents="22 7368"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,5527,a(flip),b,7305,a),flip(a)].">
      <j1 rule="hyper" parents="370 5527 7305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <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(7305(a,1),1983(a,1,1))].">
      <j1 rule="para" parents="7305 1983"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      R(T(x * K(y,x),y),z,x * K(y,x)) = R(x,z,T(x * K(y,x),u))
    ]]></literal>
    <justification jstring="[para(5280(a,1),7305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 7305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7309,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 7309 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),7311(a,1,2))].">
      <j1 rule="para" parents="109 7311"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7316,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 7316 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(6575,a,7320,a),flip(a)].">
      <j1 rule="hyper" parents="6575 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6446(a,1),7339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6446 7339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),7336(a,1,2))].">
      <j1 rule="para" parents="108 7336"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(919(a,2),7336(a,1))].">
      <j1 rule="para" parents="919 7336"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2014,a(flip),b,7361,a),flip(a)].">
      <j1 rule="hyper" parents="370 2014 7361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(7361(a,2),2023(a,1))].">
      <j1 rule="para" parents="7361 2023"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7378(a,1),7368(a,1,2,1))].">
      <j1 rule="para" parents="7378 7368"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2902,a,7391,a)].">
      <j1 rule="hyper" parents="2902 7391"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7391(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(7391(a,1),2902(a,1))].">
      <j1 rule="para" parents="7391 2902"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7391(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="7391 6294"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(6557(a,2),7391(a,1,1))].">
      <j1 rule="para" parents="6557 7391"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7394(a,1),2896(a,1))].">
      <j1 rule="para" parents="7394 2896"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6463(a,1),7394(a,1,1))].">
      <j1 rule="para" parents="6463 7394"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6557(a,2),7394(a,1,2))].">
      <j1 rule="para" parents="6557 7394"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(7398(a,1),2902(a,1))].">
      <j1 rule="para" parents="7398 2902"/>
    </justification>
  </clause>

  <clause id="7403">
    <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(6268(a,1),7401(a,1,2,1))].">
      <j1 rule="para" parents="6268 7401"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7276(a,2),6510(a,1))].">
      <j1 rule="para" parents="7276 6510"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7278(a,1),6283(a,1,2))].">
      <j1 rule="para" parents="7278 6283"/>
    </justification>
  </clause>

  <clause id="7406">
    <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(370,a,5627,a,b,7324,a)].">
      <j1 rule="hyper" parents="370 5627 7324"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4756,a(flip),b,7324,a),flip(a)].">
      <j1 rule="hyper" parents="370 4756 7324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      R(x * K(R(y \ 1,z,u) \ 1,x),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6584(a,1),7324(a,2,2))].">
      <j1 rule="para" parents="6584 7324"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7407(a,2),6805(a,1,2))].">
      <j1 rule="para" parents="7407 6805"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(7366(a,1),6268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7366 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3747,a,7281,a)].">
      <j1 rule="hyper" parents="3747 7281"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (z * K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(7417(a,1),336(a,1,2))].">
      <j1 rule="para" parents="7417 336"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),7392(a,1,1,1))].">
      <j1 rule="para" parents="5 7392"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(2894(a,2),7392(a,1))].">
      <j1 rule="para" parents="2894 7392"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(6940,a,7416,a)].">
      <j1 rule="hyper" parents="6940 7416"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,7416,a)].">
      <j1 rule="hyper" parents="2810 7416"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7422(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7422 22"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(6723(a,1),7421(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6723 7421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6817,a(flip),b,7424,a),flip(a)].">
      <j1 rule="hyper" parents="60 6817 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7427,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 7427 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6584,a(flip),b,7426,a)].">
      <j1 rule="hyper" parents="60 6584 7426"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,7429,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 7429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(x \ 1,y * K(x,z)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(4905(a,1),7431(a,1,2,2))].">
      <j1 rule="para" parents="4905 7431"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6281(a,1),7431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6281 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6424(a,1),7431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6424 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6463(a,1),7433(a,1,2,2))].">
      <j1 rule="para" parents="6463 7433"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(87(a,1),7432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="87 7432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      x * T(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(5277,a,7436,a)].">
      <j1 rule="hyper" parents="5277 7436"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(7436(a,1),6826(a,1,2,2))].">
      <j1 rule="para" parents="7436 6826"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4905,a(flip),b,7430,a),flip(a)].">
      <j1 rule="hyper" parents="370 4905 7430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7430(a,2),5390(a,1))].">
      <j1 rule="para" parents="7430 5390"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2741,a,7439,a)].">
      <j1 rule="hyper" parents="2741 7439"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(7439(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7439 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7441(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7441 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      K(x,y) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * x = u
    ]]></literal>
    <justification jstring="[para(7441(a,1),327(a,1,1))].">
      <j1 rule="para" parents="7441 327"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      R(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2711(a,1),7440(a,1))].">
      <j1 rule="para" parents="2711 7440"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3747,a,7444,a)].">
      <j1 rule="hyper" parents="3747 7444"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7444(a,1),251(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7444 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(5885,a,7447,a)].">
      <j1 rule="hyper" parents="5885 7447"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      L(x,y,K(R(x,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(168,a,7447,a(flip))].">
      <j1 rule="hyper" parents="168 7447"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7447(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7447 20"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[para(7447(a,1),727(a,1,2))].">
      <j1 rule="para" parents="7447 727"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      (K(x,y) * z) * L(x,u,w) = K(x,y) * (z * L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7447(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="7447 528"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7447(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="7447 529"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7447(a,1),6763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7447 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,7449,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 7449 5160"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7449(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7449 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7449(a,1),6763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7449 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,L(x,w,K(R(x,y,z),u))) = (K(R(x,y,z),u) * (w * x)) / (w * x)
    ]]></literal>
    <justification jstring="[para(7450(a,1),623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7450 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      (K(x,y) * z) / T(x,u) = K(x,y) * (z / T(x,u))
    ]]></literal>
    <justification jstring="[para(7451(a,1),727(a,1,2))].">
      <j1 rule="para" parents="7451 727"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(7451(a,1),7182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7451 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      T(x / (x / K(y,z)),x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5842,a,b,7455,a)].">
      <j1 rule="hyper" parents="60 5842 7455"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,7455,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 7455 5160"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(7455(a,1),5548(a,1,1,1))].">
      <j1 rule="para" parents="7455 5548"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      T((T(x,y) / z) / (x / z),T(x,y) / z) = K((z \ 1) \ (x / z),y)
    ]]></literal>
    <justification jstring="[para(6518(a,1),7462(a,1,1,2))].">
      <j1 rule="para" parents="6518 7462"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(5235,a,7452,a),flip(a)].">
      <j1 rule="hyper" parents="5235 7452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5692(a,1),7466(a,1,1))].">
      <j1 rule="para" parents="5692 7466"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(5901,a,7467,a)].">
      <j1 rule="hyper" parents="5901 7467"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      T(K(x,x \ y),y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(275,a,7467,a,b,5766,a)].">
      <j1 rule="hyper" parents="275 7467 5766"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,4804,a,b,7467,a)].">
      <j1 rule="hyper" parents="128 4804 7467"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7467(a,1),6325(a,1,1))].">
      <j1 rule="para" parents="7467 6325"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(5690(a,1),7468(a,1,2))].">
      <j1 rule="para" parents="5690 7468"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(506,a,7474,a)].">
      <j1 rule="hyper" parents="506 7474"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(7474(a,1),357(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7474 357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(782,a,7475,a)].">
      <j1 rule="hyper" parents="782 7475"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(406,a,7475,a)].">
      <j1 rule="hyper" parents="406 7475"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(384,a,7475,a)].">
      <j1 rule="hyper" parents="384 7475"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      x / ((y \ x) * y) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(381,a,7475,a)].">
      <j1 rule="hyper" parents="381 7475"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(156,a,7475,a)].">
      <j1 rule="hyper" parents="156 7475"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(7475(a,1),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7475 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(7476(a,1),5708(a,1)),flip(a)].">
      <j1 rule="para" parents="7476 5708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      (x * y) / T(y * x,z) = K(x,y) * K(z,y * x)
    ]]></literal>
    <justification jstring="[para(7476(a,2),5855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7476 5855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(7476(a,2),6269(a,1,1))].">
      <j1 rule="para" parents="7476 6269"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,y * x,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7481(a,1),625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7481 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(7481(a,1),4836(a,1,1,1))].">
      <j1 rule="para" parents="7481 4836"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[para(5699(a,1),7481(a,1,1))].">
      <j1 rule="para" parents="5699 7481"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      (x * y) / T(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(z,y * x) = u
    ]]></literal>
    <justification jstring="[para(7481(a,1),5862(a,1,1))].">
      <j1 rule="para" parents="7481 5862"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(7479(a,1),2878(a,2,2))].">
      <j1 rule="para" parents="7479 2878"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      x / L((y \ ((z \ 1) \ (z \ x))) * y,z \ 1,z) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4097(a,2),7480(a,1,2))].">
      <j1 rule="para" parents="4097 7480"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(275,a,7491,a,b,87,a),flip(a)].">
      <j1 rule="hyper" parents="275 7491 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5716(a,1),7496(a,2,1))].">
      <j1 rule="para" parents="5716 7496"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5147,a(flip),b,7498,a)].">
      <j1 rule="hyper" parents="370 5147 7498"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(6398,a,7464,a),flip(a)].">
      <j1 rule="hyper" parents="6398 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6233,a,7464,a)].">
      <j1 rule="hyper" parents="6233 7464"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),7464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      T(x,K(y,z)) != u * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * u = x
    ]]></literal>
    <justification jstring="[para(7464(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7464 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7464(a,1),6227(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7464 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(787,a,7500,a)].">
      <j1 rule="hyper" parents="787 7500"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,7500,a),flip(a)].">
      <j1 rule="hyper" parents="387 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = K(w,v5) * (K(v5,w) * a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5194,a,b,7500,a)].">
      <j1 rule="hyper" parents="370 5194 7500"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(338,a,7500,a),flip(a)].">
      <j1 rule="hyper" parents="338 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(275,a,6275,a,b,7500,a)].">
      <j1 rule="hyper" parents="275 6275 7500"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(x,y) * (z / (K(y,x) \ 1)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(275,a,6319,a(flip),b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="275 6319 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(147,a,7500,a)].">
      <j1 rule="hyper" parents="147 7500"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(31,a,7467,a,b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="31 7467 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(31,a,5015,a,b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="31 5015 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,x)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,2894,a,b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="31 2894 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(31,a,1041,a,b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="31 1041 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,2894,a(flip),b,7500,a),flip(a)].">
      <j1 rule="hyper" parents="31 2894 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,7500,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="129 7500 210"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(7500(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="7500 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(7500(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="7500 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7500(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7500 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(7500(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7500 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(7500(a,1),94(a,2,2))].">
      <j1 rule="para" parents="7500 94"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7500(a,1),787(a,1))].">
      <j1 rule="para" parents="7500 787"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      (K(x,y) \ 1) * (K(x,y) * z) = z
    ]]></literal>
    <justification jstring="[para(5865(a,2),7500(a,1,1))].">
      <j1 rule="para" parents="5865 7500"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(7500(a,1),6425(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 6425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(7500(a,1),6468(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7500 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(7500(a,1),6504(a,1,2,1,1))].">
      <j1 rule="para" parents="7500 6504"/>
    </justification>
  </clause>

  <clause id="7528">
    <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(7500(a,1),6752(a,2,1,1))].">
      <j1 rule="para" parents="7500 6752"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(7500(a,1),5899(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 5899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5019,a,7506,a)].">
      <j1 rule="hyper" parents="5019 7506"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(3065,a,7506,a),flip(a)].">
      <j1 rule="hyper" parents="3065 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4759,a,b,7506,a),flip(a)].">
      <j1 rule="hyper" parents="370 4759 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x \ y,x) \ y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7467,a(flip),b,7506,a),flip(a)].">
      <j1 rule="hyper" parents="370 7467 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(125,a,7506,a,b,107,a)].">
      <j1 rule="hyper" parents="125 7506 107"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6237,a,7506,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6237 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(7506(a,1),297(a,1,2))].">
      <j1 rule="para" parents="7506 297"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(7506(a,1),298(a,1,2))].">
      <j1 rule="para" parents="7506 298"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(7506(a,1),344(a,1,1))].">
      <j1 rule="para" parents="7506 344"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(7506(a,1),801(a,1,2))].">
      <j1 rule="para" parents="7506 801"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7506(a,1),430(a,1,1,3))].">
      <j1 rule="para" parents="7506 430"/>
    </justification>
  </clause>

  <clause id="7545">
    <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(7506(a,1),2022(a,1,1))].">
      <j1 rule="para" parents="7506 2022"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      (K(x,y) \ 1) \ z = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5865(a,2),7506(a,1,1))].">
      <j1 rule="para" parents="5865 7506"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6294(a,2),7506(a,1,1))].">
      <j1 rule="para" parents="6294 7506"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(7506(a,1),6464(a,1,2,1))].">
      <j1 rule="para" parents="7506 6464"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(7506(a,1),6569(a,1,1,1))].">
      <j1 rule="para" parents="7506 6569"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6584(a,1),7506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6584 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6591(a,1),7506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6591 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6763(a,1),7506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6763 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) * v5 = L(T(K(y,x),z),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(6594(a,1),7506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6594 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7506(a,1),7173(a,1,2))].">
      <j1 rule="para" parents="7506 7173"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(7508(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7508 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(5402(a,1),7511(a,1,2))].">
      <j1 rule="para" parents="5402 7511"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(6976(a,1),7511(a,1,2))].">
      <j1 rule="para" parents="6976 7511"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(7513(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7513 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      (K(x,y) \ 1) * (z * K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(787,a,7524,a)].">
      <j1 rule="hyper" parents="787 7524"/>
    </justification>
  </clause>

  <clause id="7562">
    <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(7535(a,1),2554(a,1,2,2,1))].">
      <j1 rule="para" parents="7535 2554"/>
    </justification>
  </clause>

  <clause id="7563">
    <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(7535(a,1),2571(a,1,2,2,1))].">
      <j1 rule="para" parents="7535 2571"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * (K(x,y) * u)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[para(7546(a,1),1512(a,1,2,2))].">
      <j1 rule="para" parents="7546 1512"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (x / z)) = T(T(x,y),y) / z
    ]]></literal>
    <justification jstring="[para(7546(a,1),7031(a,1,2))].">
      <j1 rule="para" parents="7546 7031"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,(y / x) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5402(a,1),7520(a,1,2))].">
      <j1 rule="para" parents="5402 7520"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7501(a,1),6227(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7501 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      x \ K(y,z) != K(y,z) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7536(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="7536 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7536(a,1),7120(a,1,2))].">
      <j1 rule="para" parents="7536 7120"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(7547(a,1),7330(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7547 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(5631(a,1),7435(a,1,2))].">
      <j1 rule="para" parents="5631 7435"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(31,a,5251,a,b,7437,a),flip(a)].">
      <j1 rule="hyper" parents="31 5251 7437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,6851,a(flip),b,7578,a),flip(a)].">
      <j1 rule="hyper" parents="60 6851 7578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7580">
    <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(7578(a,1),3195(a,1,2,1,1))].">
      <j1 rule="para" parents="7578 3195"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(7578(a,2),3195(a,1,1))].">
      <j1 rule="para" parents="7578 3195"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ x = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4228,a,7579,a),flip(a)].">
      <j1 rule="hyper" parents="4228 7579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(221,a,7579,a(flip))].">
      <j1 rule="hyper" parents="221 7579"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      x / T(y \ 1,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ x = z
    ]]></literal>
    <justification jstring="[para(7579(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7579 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      T(x,T(y \ 1,y * z)) = T(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(7579(a,2),7334(a,1,2))].">
      <j1 rule="para" parents="7579 7334"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K(x,T(y \ 1,y * z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(7579(a,2),7343(a,1,2))].">
      <j1 rule="para" parents="7579 7343"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ z) = a(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(7582(a,1),3082(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7582 3082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      L(x,y,z * R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ z) = v5
    ]]></literal>
    <justification jstring="[para(7582(a,1),3576(a,1,3))].">
      <j1 rule="para" parents="7582 3576"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      ((x / (y \ 1)) \ z) / T(y \ 1,y * ((x / (y \ 1)) \ z)) = (1 / (y \ 1)) \ ((x / (1 / (y \ 1))) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1260,a,b,7583,a),flip(a)].">
      <j1 rule="hyper" parents="370 1260 7583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      (1 / K(x,y)) * (z / (K(x,y) \ 1)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5866(a,2),7510(a,1,1))].">
      <j1 rule="para" parents="5866 7510"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(7525(a,1),6110(a,2,1))].">
      <j1 rule="para" parents="7525 6110"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      K(x,T(y \ 1,y \ z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7586(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 7586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(6270(a,1),7504(a,1,1))].">
      <j1 rule="para" parents="6270 7504"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(6557(a,2),7420(a,1,2))].">
      <j1 rule="para" parents="6557 7420"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3747,a,7442,a)].">
      <j1 rule="hyper" parents="3747 7442"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(275,a,7442,a,b,6977,a)].">
      <j1 rule="hyper" parents="275 7442 6977"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(7602(a,1),1345(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7602 1345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      T(K(x,y) * (z / T(x,u)),T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) \ (K(x,y) * z) = w
    ]]></literal>
    <justification jstring="[para(7460(a,1),494(a,1,1))].">
      <j1 rule="para" parents="7460 494"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(4924,a,7487,a(flip))].">
      <j1 rule="hyper" parents="4924 7487"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(155,a,7490,a)].">
      <j1 rule="hyper" parents="155 7490"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      x \ T(T(y,z),u) != T(T(y,z),u) * K(w,y)
    ]]></literal>
    <literal><![CDATA[
      K(y,w) = x
    ]]></literal>
    <justification jstring="[para(7533(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="7533 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7500(a,1),7559(a,1,2,2))].">
      <j1 rule="para" parents="7500 7559"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(7577(a,2),6829(a,2,2))].">
      <j1 rule="para" parents="7577 6829"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      T(x * K(y,z),z \ 1) = T(x,z \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6992,a,7603,a),flip(a)].">
      <j1 rule="hyper" parents="6992 7603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(7606(a,1),6551(a,2,2))].">
      <j1 rule="para" parents="7606 6551"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      T(x * K(y,x),x \ 1) = (x * (K(y,x) / x)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,6509,a(flip),b,7611,a),flip(a)].">
      <j1 rule="hyper" parents="370 6509 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      (x * (K(y,x) / x)) * x = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3303,a,7614,a),flip(a)].">
      <j1 rule="hyper" parents="3303 7614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * x = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5720(a,1),7615(a,1,1,2))].">
      <j1 rule="para" parents="5720 7615"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(6490,a,7415,a)].">
      <j1 rule="hyper" parents="6490 7415"/>
    </justification>
  </clause>

  <clause id="7618">
    <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(7506(a,1),7522(a,1,1))].">
      <j1 rule="para" parents="7506 7522"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      L(K(x \ 1,y) * ((1 / x) \ z),K(y,x \ 1),1 / x) = (K(y,x \ 1) / x) \ z
    ]]></literal>
    <justification jstring="[para(4526(a,1),7539(a,2,1))].">
      <j1 rule="para" parents="4526 7539"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3747,a,7282,a)].">
      <j1 rule="hyper" parents="3747 7282"/>
    </justification>
  </clause>

  <clause id="7621">
    <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(7282(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="7282 6305"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,6765,a(flip),b,7620,a)].">
      <j1 rule="hyper" parents="60 6765 7620"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * K(x,u) = R(x,y,z) \ K(x,u)
    ]]></literal>
    <justification jstring="[hyper(486,a,7283,a),flip(a)].">
      <j1 rule="hyper" parents="486 7283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,7623,a)].">
      <j1 rule="hyper" parents="135 7623"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(6915(a,1),7299(a,1,1))].">
      <j1 rule="para" parents="6915 7299"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      R(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2810,a,7453,a)].">
      <j1 rule="hyper" parents="2810 7453"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2810,a,7454,a)].">
      <j1 rule="hyper" parents="2810 7454"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(7481(a,1),7454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7481 7454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      R((x / R(K(y,z),u,u \ 1)) * K(y,z),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7515(a,1),6312(a,2,2))].">
      <j1 rule="para" parents="7515 6312"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5236(a,1),7592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5236 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7632,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 7632 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2623(a,2),7630(a,1,2))].">
      <j1 rule="para" parents="2623 7630"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      K(x,R(T(y,z * u),y \ z,u)) = K(x,((y \ z) * u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(74(a,1),7346(a,1,2,1,1))].">
      <j1 rule="para" parents="74 7346"/>
    </justification>
  </clause>

  <clause id="7636">
    <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(6226(a,1),7379(a,1,2,1))].">
      <j1 rule="para" parents="6226 7379"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x * K(y,x),u * x),z)
    ]]></literal>
    <justification jstring="[para(7375(a,1),5492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7375 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(7507(a,2),7537(a,1)),flip(b)].">
      <j1 rule="para" parents="7507 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1716(a,1),7638(a,1,2,2))].">
      <j1 rule="para" parents="1716 7638"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7500,a(flip),b,7612,a),flip(a)].">
      <j1 rule="hyper" parents="370 7500 7612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,7607,a,b,7641,a)].">
      <j1 rule="hyper" parents="32 7607 7641"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7405(a,1),1029(a,1))].">
      <j1 rule="para" parents="7405 1029"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7604,a(flip),b,7448,a),flip(a)].">
      <j1 rule="hyper" parents="60 7604 7448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(5280(a,1),7380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),7646(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5280 7646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5279(a,1),7647(a,1,3))].">
      <j1 rule="para" parents="5279 7647"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(6574(a,1),7386(a,1,1))].">
      <j1 rule="para" parents="6574 7386"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5993(a,1),7400(a,1,2))].">
      <j1 rule="para" parents="5993 7400"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6761(a,1),7650(a,1,2))].">
      <j1 rule="para" parents="6761 7650"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6584(a,1),7408(a,1,1,2))].">
      <j1 rule="para" parents="6584 7408"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) != T(w,z)
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),u * x) = w
    ]]></literal>
    <justification jstring="[para(7637(a,2),46(a,1))].">
      <j1 rule="para" parents="7637 46"/>
    </justification>
  </clause>

  <clause id="7654">
    <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(273(a,1),7562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="273 7562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7655">
    <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(5865(a,1),7654(a,1,1,2,1))].">
      <j1 rule="para" parents="5865 7654"/>
    </justification>
  </clause>

  <clause id="7656">
    <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(274(a,1),7563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="274 7563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7657">
    <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(5865(a,1),7656(a,1,1,2,1))].">
      <j1 rule="para" parents="5865 7656"/>
    </justification>
  </clause>

  <clause id="7658">
    <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(2014(a,1),7406(a,1,1))].">
      <j1 rule="para" parents="2014 7406"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5279(a,1),7658(a,2,1))].">
      <j1 rule="para" parents="5279 7658"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,L(x,w,K(R(x,y,z),u))) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6,a(flip),b,7459,a),flip(a)].">
      <j1 rule="hyper" parents="370 6 7459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      R(K(R(x,y,z),u),w,x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7450(a,1),7660(a,1,3))].">
      <j1 rule="para" parents="7450 7660"/>
    </justification>
  </clause>

  <clause id="7663">
    <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(6808(a,1),6810(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6808 6810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7664">
    <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(4(a,1),7663(a,2,1,2,1))].">
      <j1 rule="para" parents="4 7663"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      (x * R(y,z,u)) * K(y,w) = x * (R(y,z,u) * K(y,w))
    ]]></literal>
    <justification jstring="[para(6808(a,1),7664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6808 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(625,a,7665,a)].">
      <j1 rule="hyper" parents="625 7665"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      (((x * (y \ 1)) \ 1) \ 1) \ (x * (y \ 1)) = (y * K((x / y) \ 1,x / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),7231(a,1,2,1))].">
      <j1 rule="para" parents="7 7231"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2037,a,7667,a),flip(a)].">
      <j1 rule="hyper" parents="2037 7667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,7166,a(flip),b,7668,a),flip(a)].">
      <j1 rule="hyper" parents="370 7166 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4638(a,1),7670(a,1,1,2))].">
      <j1 rule="para" parents="4638 7670"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4986,a,7671,a),flip(a)].">
      <j1 rule="hyper" parents="4986 7671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      K(x \ (y \ 1),x * T(y,y \ 1)) = K(x \ (y \ 1),(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(108(a,2),7672(a,1,2,2))].">
      <j1 rule="para" parents="108 7672"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(6736,a,7673,a),flip(a)].">
      <j1 rule="hyper" parents="6736 7673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6742,a(flip),b,7674,a),flip(a)].">
      <j1 rule="hyper" parents="60 6742 7674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7164,a,b,7675,a)].">
      <j1 rule="hyper" parents="60 7164 7675"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      (((1 / x) * (y * x)) / (1 / x)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(254(a,1),7260(a,1,1,1,2,2))].">
      <j1 rule="para" parents="254 7260"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      (((x \ 1) * (y * x)) / (x \ 1)) / T(1 / x,T(x * y,x * x)) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(4427(a,1),7677(a,1,1))].">
      <j1 rule="para" parents="4427 7677"/>
    </justification>
  </clause>

  <clause id="7679">
    <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(304(a,1),6605(a,1,2))].">
      <j1 rule="para" parents="304 6605"/>
    </justification>
  </clause>

  <clause id="7680">
    <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(304(a,1),7679(a,2,2,2))].">
      <j1 rule="para" parents="304 7679"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(y,z) \ (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(1602(a,1),6323(a,1,1))].">
      <j1 rule="para" parents="1602 6323"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5258(a,1),6484(a,1,2,2,1))].">
      <j1 rule="para" parents="5258 6484"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(6190(a,1),7682(a,1,2,2))].">
      <j1 rule="para" parents="6190 7682"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(191,a,7684,a)].">
      <j1 rule="hyper" parents="191 7684"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(62(a,1),7685(a,2,1))].">
      <j1 rule="para" parents="62 7685"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(125,a,4793,a(flip),b,7686,a)].">
      <j1 rule="hyper" parents="125 4793 7686"/>
    </justification>
  </clause>

  <clause id="7688">
    <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(1769(a,1),7580(a,2,1))].">
      <j1 rule="para" parents="1769 7580"/>
    </justification>
  </clause>

  <clause id="7689">
    <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(60,a,7688,a(flip),b,7581,a),flip(a)].">
      <j1 rule="hyper" parents="60 7688 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1769(a,1),7689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1769 7689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      ((x / (y \ 1)) \ z) / T(y \ 1,y * ((x / (y \ 1)) \ z)) = y \ ((x / (1 / (y \ 1))) \ z)
    ]]></literal>
    <justification jstring="[para(74(a,1),7589(a,2,1))].">
      <j1 rule="para" parents="74 7589"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      ((x / (y \ 1)) \ z) / T(y \ 1,y * ((x / (y \ 1)) \ z)) = y \ ((x / y) \ z)
    ]]></literal>
    <justification jstring="[para(74(a,1),7691(a,2,2,1,2))].">
      <j1 rule="para" parents="74 7691"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      (x \ 1) \ ((y / (x \ 1)) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7584,a,7694,a)].">
      <j1 rule="hyper" parents="7584 7694"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      x \ ((R(y,x,x) / x) \ z) = (x \ 1) \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(1112(a,1),7696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1112 7696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      L(x \ ((y / x) \ z),x,x) = x * ((y / (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(7696(a,1),2082(a,1,1))].">
      <j1 rule="para" parents="7696 2082"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ z) = x \ ((y * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(2057(a,1),7697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2057 7697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      (x \ 1) \ (((x \ R(x,y,z)) * x) \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2043(a,1),7699(a,2,2,1))].">
      <j1 rule="para" parents="2043 7699"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ z) = x * ((y / (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(790,a,7698,a)].">
      <j1 rule="hyper" parents="790 7698"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2017(a,1),7700(a,1,2,1))].">
      <j1 rule="para" parents="2017 7700"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * ((x * K(y,z)) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(7506(a,1),7681(a,1,1,2,2,1))].">
      <j1 rule="para" parents="7506 7681"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,y) * (x \ u),w,v5))) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(6294(a,1),7703(a,2,2,1,2,2))].">
      <j1 rule="para" parents="6294 7703"/>
    </justification>
  </clause>

  <clause id="7706">
    <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(6(a,1),4877(a,1,1,1))].">
      <j1 rule="para" parents="6 4877"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(5967,a,7706,a),flip(a)].">
      <j1 rule="hyper" parents="5967 7706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3538,a,7707,a)].">
      <j1 rule="hyper" parents="3538 7707"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(3608(a,1),7709(a,2,1))].">
      <j1 rule="para" parents="3608 7709"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7073,a(flip),b,7710,a),flip(a)].">
      <j1 rule="hyper" parents="60 7073 7710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7485,a,7711,a),flip(a)].">
      <j1 rule="hyper" parents="7485 7711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2875(a,1),7712(a,1,2))].">
      <j1 rule="para" parents="2875 7712"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(7712(a,1),7123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7712 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5742,a,7713,a)].">
      <j1 rule="hyper" parents="5742 7713"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4652,a,b,7715,a)].">
      <j1 rule="hyper" parents="60 4652 7715"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(7715(a,1),7499(a,1,2,2,1))].">
      <j1 rule="para" parents="7715 7499"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(7716(a,2),308(a,1,2))].">
      <j1 rule="para" parents="7716 308"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      x / T(1 / y,y * x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(4657(a,1),7718(a,1,2))].">
      <j1 rule="para" parents="4657 7718"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      T(1 / x,x * y) = ((1 / x) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,7719,a),flip(a)].">
      <j1 rule="hyper" parents="215 7719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      T(1 / x,x * y) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2140,a,b,7720,a),flip(a)].">
      <j1 rule="hyper" parents="370 2140 7720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      T(1 / (x / y),x) = ((1 / (x / y)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7(a,1),7720(a,1,2))].">
      <j1 rule="para" parents="7 7720"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      T(x \ 1,x \ (x \ y)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7721(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 7721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      T(x \ 1,x \ T(y,x)) = T(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7721(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      L(T(x \ 1,y),x \ 1,x) = T(x \ 1,x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,1216,a,b,7723,a)].">
      <j1 rule="hyper" parents="370 1216 7723"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,7717,a),flip(a)].">
      <j1 rule="hyper" parents="156 7717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5146,a,7726,a)].">
      <j1 rule="hyper" parents="5146 7726"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(7250,a,7727,a)].">
      <j1 rule="hyper" parents="7250 7727"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(7727(a,1),7466(a,1,1))].">
      <j1 rule="para" parents="7727 7466"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5428,a(flip),b,7728,a),flip(a)].">
      <j1 rule="hyper" parents="370 5428 7728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6198,a,b,7730,a)].">
      <j1 rule="hyper" parents="60 6198 7730"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      K((x \ 1) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7730(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7731(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 7731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      K((1 / x) \ y,1 / x) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6049,a,7733,a),flip(a)].">
      <j1 rule="hyper" parents="6049 7733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6840,a,b,7733,a),flip(a)].">
      <j1 rule="hyper" parents="370 6840 7733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(17(a,2),7733(a,2,1))].">
      <j1 rule="para" parents="17 7733"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      ((1 / x) * y) \ K(x \ y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(7733(a,1),5961(a,1,2))].">
      <j1 rule="para" parents="7733 5961"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5999,a(flip),b,7735,a),flip(a)].">
      <j1 rule="hyper" parents="370 5999 7735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(1066(a,1),7736(a,1,1))].">
      <j1 rule="para" parents="1066 7736"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,6149,a,b,7729,a)].">
      <j1 rule="hyper" parents="128 6149 7729"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6140,a(flip),b,7739,a)].">
      <j1 rule="hyper" parents="60 6140 7739"/>
    </justification>
  </clause>

  <clause id="7742">
    <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(6329(a,1),7740(a,1,2))].">
      <j1 rule="para" parents="6329 7740"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(7741(a,1),5874(a,1,1))].">
      <j1 rule="para" parents="7741 5874"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5891,a,7743,a),flip(a)].">
      <j1 rule="hyper" parents="5891 7743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,((x / (y * x)) \ 1) \ z) = K((x / (y * x)) \ 1,R(y \ 1,y,x) * z)
    ]]></literal>
    <justification jstring="[para(2805(a,2),7744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2805 7744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(7744(a,2),7467(a,1,1))].">
      <j1 rule="para" parents="7744 7467"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5572(a,2),7746(a,1,1))].">
      <j1 rule="para" parents="5572 7746"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5989(a,1),7747(a,1,1))].">
      <j1 rule="para" parents="5989 7747"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6045,a(flip),b,7738,a),flip(a)].">
      <j1 rule="hyper" parents="60 6045 7738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      T(1 / x,x \ (x \ y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2126,a,b,7725,a)].">
      <j1 rule="hyper" parents="38 2126 7725"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      T(1 / x,x \ y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),7750(a,1,2,2))].">
      <j1 rule="para" parents="4 7750"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      T(1 / x,x \ y) = T(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7578,a,b,7751,a),flip(a)].">
      <j1 rule="hyper" parents="370 7578 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),7748(a,2,2))].">
      <j1 rule="para" parents="6 7748"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7482,a,7753,a),flip(a)].">
      <j1 rule="hyper" parents="7482 7753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(7244(a,1),7742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7244 7742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,7470,a(flip),b,7755,a),flip(a)].">
      <j1 rule="hyper" parents="370 7470 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,R(y \ 1,y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z * (x / (y * x))) = u
    ]]></literal>
    <justification jstring="[para(7745(a,1),6836(a,1))].">
      <j1 rule="para" parents="7745 6836"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(x \ 1,y,z) \ K(x \ 1,x)) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4478(a,1),5052(a,1,2))].">
      <j1 rule="para" parents="4478 5052"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = T(x,x \ (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4086(a,1),7759(a,1,2))].">
      <j1 rule="para" parents="4086 7759"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = (T(y,z) * x) * R((T(y,z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(272(a,1),2462(a,2,2,1,1))].">
      <j1 rule="para" parents="272 2462"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      x * (T(T(y,x),z) * R(T(T(y,x),z) \ (x \ u),w,v5)) = T(y,z) * (x * R(x \ (T(y,z) \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,1602,a(flip),b,7761,a),flip(a)].">
      <j1 rule="hyper" parents="370 1602 7761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7763">
    <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(2561(a,1),2946(a,2,1))].">
      <j1 rule="para" parents="2561 2946"/>
    </justification>
  </clause>

  <clause id="7764">
    <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(370,a,1965,a(flip),b,7763,a),flip(a)].">
      <j1 rule="hyper" parents="370 1965 7763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1965(a,1),7764(a,1,1))].">
      <j1 rule="para" parents="1965 7764"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ R(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,7766,a)].">
      <j1 rule="hyper" parents="51 7766"/>
    </justification>
  </clause>

  <clause id="7768">
    <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(370,a,6570,a(flip),b,5988,a),flip(a)].">
      <j1 rule="hyper" parents="370 6570 5988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5233(a,1),7768(a,1,1))].">
      <j1 rule="para" parents="5233 7768"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(92(a,1),2211(a,1,2,1,1))].">
      <j1 rule="para" parents="92 2211"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * ((y * z) * R((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(1603,a,7770,a),flip(a)].">
      <j1 rule="hyper" parents="1603 7770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(721,a,7770,a)].">
      <j1 rule="hyper" parents="721 7770"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * (y * (z * R(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(1600(a,1),7771(a,2,2))].">
      <j1 rule="para" parents="1600 7771"/>
    </justification>
  </clause>

  <clause id="7774">
    <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(625,a,7773,a),flip(a)].">
      <j1 rule="hyper" parents="625 7773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7775">
    <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(60,a,1774,a(flip),b,7774,a),flip(a)].">
      <j1 rule="hyper" parents="60 1774 7774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      L(x * R(x \ 1,x,1 / x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7774(a,1),2747(a,1,1))].">
      <j1 rule="para" parents="7774 2747"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      L(x * T(1 * (x \ 1),x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2722(a,1),7776(a,1,1,1,2))].">
      <j1 rule="para" parents="2722 7776"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      L(x * T(x \ 1,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),7777(a,1,1,1,2,1))].">
      <j1 rule="para" parents="2 7777"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(5252(a,1),7778(a,1,1,1))].">
      <j1 rule="para" parents="5252 7778"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      K(1 / L(x,y,z),x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6596(a,1),7779(a,1,1))].">
      <j1 rule="para" parents="6596 7779"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6941(a,1),7780(a,1,1))].">
      <j1 rule="para" parents="6941 7780"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6789,a(flip),b,7781,a),flip(a)].">
      <j1 rule="hyper" parents="60 6789 7781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3938(a,1),7782(a,1,1))].">
      <j1 rule="para" parents="3938 7782"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(435,a,7784,a)].">
      <j1 rule="hyper" parents="435 7784"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,7784,a)].">
      <j1 rule="hyper" parents="135 7784"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = K(x \ 1,x) * (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(7784(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7784 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <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(2562(a,1),7775(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2562 7775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,3322,a(flip),b,7788,a),flip(a)].">
      <j1 rule="hyper" parents="32 3322 7788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,7789,a)].">
      <j1 rule="hyper" parents="215 7789"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(77(a,1),7789(a,1,1))].">
      <j1 rule="para" parents="77 7789"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ (1 / L(x,y,z))) * u) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(7790(a,1),1787(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7790 1787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1354(a,1),7791(a,1,2))].">
      <j1 rule="para" parents="1354 7791"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ u)) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(1214(a,1),7793(a,1,2))].">
      <j1 rule="para" parents="1214 7793"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      x \ ((L(1 / x,y,z) \ 1) * (L(x,y,z) \ u)) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,4308,a(flip),b,7795,a)].">
      <j1 rule="hyper" parents="60 4308 7795"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      x \ ((L(x,y,z) * L(x \ 1,y,z)) \ u) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(5098(a,1),7796(a,1,2))].">
      <j1 rule="para" parents="5098 7796"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ L(x,y,z))) \ u) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(156,a,7797,a)].">
      <j1 rule="hyper" parents="156 7797"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = L(x \ 1,y,z) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4466,a(flip),b,7787,a),flip(a)].">
      <j1 rule="hyper" parents="370 4466 7787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * T(1 / (1 / x),x \ 1) = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2200,a(flip),b,7799,a),flip(a)].">
      <j1 rule="hyper" parents="370 2200 7799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * x = (x \ 1) * (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1939(a,1),7800(a,1,2))].">
      <j1 rule="para" parents="1939 7800"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) \ (L(1 / x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(125,a,4070,a(flip),b,7801,a)].">
      <j1 rule="hyper" parents="125 4070 7801"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,7760,a(flip),b,7802,a)].">
      <j1 rule="hyper" parents="60 7760 7802"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(251(a,1),7803(a,1,2,2,1))].">
      <j1 rule="para" parents="251 7803"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(7805(a,1),4667(a,1,2))].">
      <j1 rule="para" parents="7805 4667"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ R(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,1987,a(flip),b,7772,a),flip(a)].">
      <j1 rule="hyper" parents="370 1987 7772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(24(a,1),7807(a,2,2))].">
      <j1 rule="para" parents="24 7807"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1601(a,1),7808(a,1,2))].">
      <j1 rule="para" parents="1601 7808"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * R(z \ 1,u,w)))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1600(a,1),7809(a,1,2,2))].">
      <j1 rule="para" parents="1600 7809"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1987(a,1),7810(a,1,2,2,2))].">
      <j1 rule="para" parents="1987 7810"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(629,a,7811,a),flip(a)].">
      <j1 rule="hyper" parents="629 7811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ R(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(7811(a,1),629(a,1))].">
      <j1 rule="para" parents="7811 629"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x,y,z) \ R(L(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(24(a,1),7812(a,1,2,1))].">
      <j1 rule="para" parents="24 7812"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x,y,z) \ L(R(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(24(a,1),7814(a,2,1,2))].">
      <j1 rule="para" parents="24 7814"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x \ R(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7812(a,1),7815(a,2,1))].">
      <j1 rule="para" parents="7812 7815"/>
    </justification>
  </clause>

  <clause id="7817">
    <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(370,a,3232,a(flip),b,3233,a),flip(a)].">
      <j1 rule="hyper" parents="370 3232 3233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7818">
    <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(4222(a,2),7817(a,1,1))].">
      <j1 rule="para" parents="4222 7817"/>
    </justification>
  </clause>

  <clause id="7819">
    <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(7818(a,1),327(a,1))].">
      <j1 rule="para" parents="7818 327"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7819,a,5145,a)].">
      <j1 rule="hyper" parents="7819 5145"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(7819,a,4898,a),flip(a)].">
      <j1 rule="hyper" parents="7819 4898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(6144(a,1),7820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6144 7820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(4441(a,1),7822(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4441 7822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4441(a,1),7823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4441 7823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7824(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(1384,a,7825,a)].">
      <j1 rule="hyper" parents="1384 7825"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(742,a,7825,a),flip(a)].">
      <j1 rule="hyper" parents="742 7825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(1086,a,7826,a)].">
      <j1 rule="hyper" parents="1086 7826"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(5230(a,2),7828(a,1,2))].">
      <j1 rule="para" parents="5230 7828"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7829(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7829 22"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(7829(a,1),688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7829 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7832">
    <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(7830(a,1),689(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7830 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(1060,a,7827,a)].">
      <j1 rule="hyper" parents="1060 7827"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(31,a,1672,a,b,7827,a),flip(a)].">
      <j1 rule="hyper" parents="31 1672 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,1668,a(flip),b,7827,a),flip(a)].">
      <j1 rule="hyper" parents="31 1668 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(5230(a,2),7827(a,1,2,1))].">
      <j1 rule="para" parents="5230 7827"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(5230(a,2),7833(a,1,2))].">
      <j1 rule="para" parents="5230 7833"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(5886,a,7841,a)].">
      <j1 rule="hyper" parents="5886 7841"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      a(x,K(x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7841,a)].">
      <j1 rule="hyper" parents="50 7841"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      L(x,K(y,z),1 / z) = x
    ]]></literal>
    <justification jstring="[hyper(3526,a,7842,a)].">
      <j1 rule="hyper" parents="3526 7842"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,7842,a),flip(a)].">
      <j1 rule="hyper" parents="1838 7842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7539,a(flip),b,7842,a)].">
      <j1 rule="hyper" parents="60 7539 7842"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7842(a,1),47(a,2))].">
      <j1 rule="para" parents="7842 47"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      ((1 / x) * (K(x,y) * z)) * 1 = (K(x,y) * (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(7843(a,1),3034(a,1,2))].">
      <j1 rule="para" parents="7843 3034"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) \ z = K(x,y) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7539,a(flip),b,7844,a)].">
      <j1 rule="hyper" parents="60 7539 7844"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(7539(a,1),7847(a,1))].">
      <j1 rule="para" parents="7539 7847"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(6978,a,7839,a)].">
      <j1 rule="hyper" parents="6978 7839"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(811,a,7839,a),flip(a)].">
      <j1 rule="hyper" parents="811 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(787,a,7839,a),flip(a)].">
      <j1 rule="hyper" parents="787 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) = T(x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(323,a,7839,a),flip(a)].">
      <j1 rule="hyper" parents="323 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,7839,a)].">
      <j1 rule="hyper" parents="135 7839"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,1699,a,b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="31 1699 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,1672,a,b,7839,a)].">
      <j1 rule="hyper" parents="31 1672 7839"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,1670,a,b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="31 1670 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,6629,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="31 6629 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,6627,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="31 6627 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,1668,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="31 1668 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ (T(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,7839,a(flip),b,121,a),flip(a)].">
      <j1 rule="hyper" parents="125 7839 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(7839(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7839 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      (x / y) * (K(x / y,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(109(a,1),7839(a,2,1))].">
      <j1 rule="para" parents="109 7839"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(7839(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7839 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(7500(a,1),7839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      T(x,y) * (y \ K(y,x)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(7513(a,1),7839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7513 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(7521,a,7853,a)].">
      <j1 rule="hyper" parents="7521 7853"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      T(x / y,z) \ x = K(x / y,z) \ y
    ]]></literal>
    <justification jstring="[para(77(a,1),7853(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(7853(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7853 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,7857,a(flip),b,1671,a(flip))].">
      <j1 rule="hyper" parents="125 7857 1671"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(7857(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7857 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(7857(a,1),1687(a,1))].">
      <j1 rule="para" parents="7857 1687"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(T(x,u),y,z) \ w) = R(x,y,z) \ w
    ]]></literal>
    <justification jstring="[para(22(a,2),7858(a,1,2,1))].">
      <j1 rule="para" parents="22 7858"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),40(a,1))].">
      <j1 rule="para" parents="7858 40"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(108(a,1),7858(a,1,2,1))].">
      <j1 rule="para" parents="108 7858"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      T(x,y) \ z != u * (x \ z)
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),7519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7858 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1384,a,7860,a)].">
      <j1 rule="hyper" parents="1384 7860"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(928,a,7860,a)].">
      <j1 rule="hyper" parents="928 7860"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(832,a,7860,a)].">
      <j1 rule="hyper" parents="832 7860"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(810,a,7860,a),flip(a)].">
      <j1 rule="hyper" parents="810 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6235,a,b,7860,a),flip(a)].">
      <j1 rule="hyper" parents="370 6235 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,7500,a(flip),b,7860,a),flip(a)].">
      <j1 rule="hyper" parents="125 7500 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,7292,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="125 7292 7860"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,7839,a,b,7860,a)].">
      <j1 rule="hyper" parents="60 7839 7860"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3840,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="60 3840 7860"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      x \ (K(x,y) * z) = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,7860,a(flip),b,7839,a)].">
      <j1 rule="hyper" parents="125 7860 7839"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),7860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(y / x,x) * z
    ]]></literal>
    <justification jstring="[para(109(a,1),7860(a,1,1))].">
      <j1 rule="para" parents="109 7860"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      T(x,y) * ((1 / x) \ z) = K(x,y) * ((x * x) * z)
    ]]></literal>
    <justification jstring="[para(554(a,1),7860(a,1,2))].">
      <j1 rule="para" parents="554 7860"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(7860(a,1),742(a,1))].">
      <j1 rule="para" parents="7860 742"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(L(x,y,y),z) * x
    ]]></literal>
    <justification jstring="[para(1362(a,1),7860(a,1,2))].">
      <j1 rule="para" parents="1362 7860"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      L(x,y,T(z \ 1,u) * (z \ w)) = L(x,y,K(z \ 1,u) * w)
    ]]></literal>
    <justification jstring="[para(7860(a,1),4110(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7860 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(7860(a,2),7526(a,1,2,1))].">
      <j1 rule="para" parents="7860 7526"/>
    </justification>
  </clause>

  <clause id="7905">
    <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(7860(a,1),7179(a,2,2))].">
      <j1 rule="para" parents="7860 7179"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * u) = T(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(7857(a,1),7860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7857 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(7556,a,7864,a)].">
      <j1 rule="hyper" parents="7556 7864"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(7518,a,7864,a)].">
      <j1 rule="hyper" parents="7518 7864"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(275,a,7864,a,b,6280,a)].">
      <j1 rule="hyper" parents="275 7864 6280"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,107,a(flip),b,7864,a)].">
      <j1 rule="hyper" parents="125 107 7864"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = R(K(x,y),x * z,u)
    ]]></literal>
    <justification jstring="[para(7864(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(22(a,2),7864(a,2,1))].">
      <j1 rule="para" parents="22 7864"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      K(x,y) * ((x * x) * z) = (T(x,y) * x) * z
    ]]></literal>
    <justification jstring="[para(7864(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(7864(a,1),387(a,1))].">
      <j1 rule="para" parents="7864 387"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(273(a,1),7864(a,1,2))].">
      <j1 rule="para" parents="273 7864"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(274(a,1),7864(a,1,2))].">
      <j1 rule="para" parents="274 7864"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      T(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * x) = u
    ]]></literal>
    <justification jstring="[para(7864(a,1),787(a,1))].">
      <j1 rule="para" parents="7864 787"/>
    </justification>
  </clause>

  <clause id="7921">
    <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(7864(a,1),621(a,1,1))].">
      <j1 rule="para" parents="7864 621"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5275(a,1),7864(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5275 7864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5667(a,1),7864(a,1,1))].">
      <j1 rule="para" parents="5667 7864"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(6218(a,1),7864(a,1,1))].">
      <j1 rule="para" parents="6218 7864"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(7864(a,1),7452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 7452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7864(a,1),7511(a,1,2))].">
      <j1 rule="para" parents="7864 7511"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(7864(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7864 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6652,a,7871,a),flip(a)].">
      <j1 rule="hyper" parents="6652 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(6650,a,7871,a),flip(a)].">
      <j1 rule="hyper" parents="6650 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(1738,a,7871,a)].">
      <j1 rule="hyper" parents="1738 7871"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1689,a,7871,a)].">
      <j1 rule="hyper" parents="1689 7871"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(147,a,7871,a)].">
      <j1 rule="hyper" parents="147 7871"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(135,a,7871,a)].">
      <j1 rule="hyper" parents="135 7871"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      x / (K(y,x * K(z,u)) * K(u,z)) = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(128,a,6281,a(flip),b,7871,a)].">
      <j1 rule="hyper" parents="128 6281 7871"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5256,a,b,7871,a)].">
      <j1 rule="hyper" parents="125 5256 7871"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,5696,a(flip),b,7871,a),flip(a)].">
      <j1 rule="hyper" parents="125 5696 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7871(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7871 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(7871(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7871 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      (x * T(y,z)) * ((K(z,y) * K(z,y)) * u) = (x * (y * K(z,y))) * u
    ]]></literal>
    <justification jstring="[para(7871(a,1),122(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7871 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      a(x,y * K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(7871(a,1),3123(a,1,2))].">
      <j1 rule="para" parents="7871 3123"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3219(a,1),7871(a,1,2))].">
      <j1 rule="para" parents="3219 7871"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      L(x,y * K(z,y),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7871(a,1),3776(a,1,2))].">
      <j1 rule="para" parents="7871 3776"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      T(x,y) * (K(y,T(x,y)) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5688(a,2),7871(a,1,2,1))].">
      <j1 rule="para" parents="5688 7871"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),7871(a,1,2))].">
      <j1 rule="para" parents="7864 7871"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),7873(a,2,1)),flip(a)].">
      <j1 rule="para" parents="108 7873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5688(a,1),7873(a,1,1))].">
      <j1 rule="para" parents="5688 7873"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(7873(a,1),7229(a,2,2))].">
      <j1 rule="para" parents="7873 7229"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * y) = (T(y,x) \ z) * y
    ]]></literal>
    <justification jstring="[para(7873(a,1),7456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 7456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      L(K(x,y),x,z) = (T(x,y) * u) / (x * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6340,a,b,7885,a)].">
      <j1 rule="hyper" parents="370 6340 7885"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,7885,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      ((T(x,y) \ 1) * (x \ 1)) \ z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5374,a(flip),b,7887,a)].">
      <j1 rule="hyper" parents="60 5374 7887"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5230(a,1),7887(a,1,1))].">
      <j1 rule="para" parents="5230 7887"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7536,a(flip),b,7888,a),flip(a)].">
      <j1 rule="hyper" parents="370 7536 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,7873,a,b,7890,a)].">
      <j1 rule="hyper" parents="129 7873 7890"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,7890,a(flip),b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="129 7890 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),z,u) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(129,a,4205,a(flip),b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="129 4205 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = x \ (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[para(108(a,1),7890(a,2,1)),flip(a)].">
      <j1 rule="para" parents="108 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      L(x,y,z * (T(z \ 1,u) \ w)) = L(x,y,K(u,z \ 1) * w)
    ]]></literal>
    <justification jstring="[para(7890(a,1),3372(a,1,3,2))].">
      <j1 rule="para" parents="7890 3372"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(1 / y,z,u)) * v5)) = K(x,T(L(1 / y,z,u),w) \ v5)
    ]]></literal>
    <justification jstring="[para(7890(a,1),5619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7890 5619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7964">
    <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="[para(5739(a,1),7890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5739 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),7890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(1414,a,7907,a)].">
      <j1 rule="hyper" parents="1414 7907"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7871,a(flip),b,7907,a)].">
      <j1 rule="hyper" parents="129 7871 7907"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(60,a,7860,a,b,7908,a)].">
      <j1 rule="hyper" parents="60 7860 7908"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(7908(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7908 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <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(7908(a,1),621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7908 621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5699(a,1),7908(a,1,1))].">
      <j1 rule="para" parents="5699 7908"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7910(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 7910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      K(x,y) * (x / y) = (x / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5855,a,b,7929,a),flip(a)].">
      <j1 rule="hyper" parents="370 5855 7929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(7929(a,1),92(a,1,1))].">
      <j1 rule="para" parents="7929 92"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(7929(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="7929 210"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4733,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="60 4733 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      x * (((x \ y) \ y) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(108(a,1),7932(a,1,2,1))].">
      <j1 rule="para" parents="108 7932"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      x \ (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(7932(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7932 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(5780(a,1),7932(a,1,2,1))].">
      <j1 rule="para" parents="5780 7932"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(7934(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7934 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (L(x,z,u) * w) = K(y,L(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(20(a,2),7935(a,1,1))].">
      <j1 rule="para" parents="20 7935"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(7935(a,1),1690(a,1))].">
      <j1 rule="para" parents="7935 1690"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(108(a,1),7973(a,1,1))].">
      <j1 rule="para" parents="108 7973"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,7977,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 7977 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7330,a(flip),b,7986,a)].">
      <j1 rule="hyper" parents="60 7330 7986"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),7986(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5821(a,2),7986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5821 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6220,a,b,7989,a)].">
      <j1 rule="hyper" parents="370 6220 7989"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      K(T(x,y \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3215,a(flip),b,7989,a),flip(a)].">
      <j1 rule="hyper" parents="370 3215 7989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2892,a(flip),b,7989,a),flip(a)].">
      <j1 rule="hyper" parents="370 2892 7989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,7989,a,b,7535,a)].">
      <j1 rule="hyper" parents="129 7989 7535"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,7989,a,b,6399,a)].">
      <j1 rule="hyper" parents="129 7989 6399"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,7989,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 7989 17"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7989(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7989 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7989(a,1),5865(a,1,1))].">
      <j1 rule="para" parents="7989 5865"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6410,a,b,7990,a),flip(a)].">
      <j1 rule="hyper" parents="370 6410 7990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4791,a(flip),b,7990,a)].">
      <j1 rule="hyper" parents="60 4791 7990"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7990,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 7990 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      T(K(x,y),(x \ z) * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7973,a(flip),b,7991,a),flip(a)].">
      <j1 rule="hyper" parents="370 7973 7991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7608,a,7995,a(flip))].">
      <j1 rule="hyper" parents="7608 7995"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x,T(y,K(z,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7573,a,7995,a(flip))].">
      <j1 rule="hyper" parents="7573 7995"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6224(a,1),8008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6224 8008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      K(x,R(T(y,K(x,z)),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),8009(a,1,2))].">
      <j1 rule="para" parents="22 8009"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6302,a,7996,a)].">
      <j1 rule="hyper" parents="6302 7996"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7996(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7996 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      K(x,K(x \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7996(a,1),7433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7996 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(6302,a,7997,a)].">
      <j1 rule="hyper" parents="6302 7997"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),7997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 7997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(262(a,1),7997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 7997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7997(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="7997 6294"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      (K(x,y) * z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7997(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="7997 6305"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(6214,a,8000,a),flip(a)].">
      <j1 rule="hyper" parents="6214 8000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8000,a(flip),b,5721,a(flip))].">
      <j1 rule="hyper" parents="129 8000 5721"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8000(a,1),6214(a,1))].">
      <j1 rule="para" parents="8000 6214"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(7341,a,8019,a),flip(a)].">
      <j1 rule="hyper" parents="7341 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7989,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 7989 8019"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7986,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 7986 8019"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7973,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 7973 8019"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,6221,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 6221 8019"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,6220,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 6220 8019"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6110,a,b,8019,a)].">
      <j1 rule="hyper" parents="370 6110 8019"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,6084,a,b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="370 6084 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7990,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="370 7990 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      K(x,y) * K(K(x,y),z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,8019,a)].">
      <j1 rule="hyper" parents="370 5256 8019"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4931,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="370 4931 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(129,a,8019,a,b,4,a)].">
      <j1 rule="hyper" parents="129 8019 4"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7343,a,b,8019,a)].">
      <j1 rule="hyper" parents="60 7343 8019"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,7340,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="60 7340 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7329,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="60 7329 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,7325,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="60 7325 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8019,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8019 5230"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),8019(a,1,2))].">
      <j1 rule="para" parents="18 8019"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) = T(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8019(a,2),20(a,1,1))].">
      <j1 rule="para" parents="8019 20"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) = T(K(x,L(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(20(a,2),8019(a,1,2))].">
      <j1 rule="para" parents="20 8019"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      T(x,y) != K(z,T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(8019(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8019 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(8019(a,2),259(a,1,2,2))].">
      <j1 rule="para" parents="8019 259"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8019(a,2),273(a,1,2,1))].">
      <j1 rule="para" parents="8019 273"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(8019(a,2),787(a,1,2,2))].">
      <j1 rule="para" parents="8019 787"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(8019(a,2),869(a,1,2,2))].">
      <j1 rule="para" parents="8019 869"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8019(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="8019 5265"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      T(x,K(y,T(z,x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8019(a,2),5742(a,1,2))].">
      <j1 rule="para" parents="8019 5742"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8019(a,2),6226(a,1,1))].">
      <j1 rule="para" parents="8019 6226"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(8019(a,2),6937(a,1,1))].">
      <j1 rule="para" parents="8019 6937"/>
    </justification>
  </clause>

  <clause id="8055">
    <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(8019(a,2),7197(a,1,1))].">
      <j1 rule="para" parents="8019 7197"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8019(a,2),8000(a,1,1))].">
      <j1 rule="para" parents="8019 8000"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),8019(a,1,2))].">
      <j1 rule="para" parents="8019 8019"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7329,a(flip),b,8024,a),flip(a)].">
      <j1 rule="hyper" parents="370 7329 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8024,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8024 5230"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,7991,a,b,8024,a)].">
      <j1 rule="hyper" parents="60 7991 8024"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6294,a,b,8024,a)].">
      <j1 rule="hyper" parents="60 6294 8024"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(T(x,z),T(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6193,a,b,8024,a)].">
      <j1 rule="hyper" parents="60 6193 8024"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7973,a(flip),b,8024,a),flip(a)].">
      <j1 rule="hyper" parents="60 7973 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,y) = z * K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8024,a(flip),b,5231,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8024 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      T(x,y) * K(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8024,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8024 5230"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,8024,a(flip),b,5719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 8024 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(18(a,1),8024(a,2,2))].">
      <j1 rule="para" parents="18 8024"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      K(R(T(x,y),z,u),w) = K(R(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),8024(a,1,1))].">
      <j1 rule="para" parents="22 8024"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),8024(a,2,2))].">
      <j1 rule="para" parents="109 8024"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(262(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="262 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(245(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="245 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,x \ y))
    ]]></literal>
    <justification jstring="[para(365(a,1),8024(a,1,1))].">
      <j1 rule="para" parents="365 8024"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1593(a,1),8024(a,2,2))].">
      <j1 rule="para" parents="1593 8024"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,T(y,K(z,L(x,u,w)))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4750(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4750 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(8024(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8024 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8024(a,1),5280(a,1,1,2))].">
      <j1 rule="para" parents="8024 5280"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      x * K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8024(a,2),5265(a,1,2))].">
      <j1 rule="para" parents="8024 5265"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(8024(a,1),5299(a,1,1))].">
      <j1 rule="para" parents="8024 5299"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(8024(a,1),5642(a,1,3))].">
      <j1 rule="para" parents="8024 5642"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(8024(a,1),5635(a,1,3))].">
      <j1 rule="para" parents="8024 5635"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8024(a,1),5698(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8024 5698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (x * z) = T(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(8024(a,1),5853(a,1,1,2))].">
      <j1 rule="para" parents="8024 5853"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      1 / (x \ K(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8024(a,1),5768(a,1,2,2))].">
      <j1 rule="para" parents="8024 5768"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      T(x / T(y,T(z,u)),y) = y \ (x * K(z,T(y,u)))
    ]]></literal>
    <justification jstring="[para(8024(a,1),5911(a,2,2,2))].">
      <j1 rule="para" parents="8024 5911"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(8024(a,1),6291(a,1,2))].">
      <j1 rule="para" parents="8024 6291"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8024(a,1),6302(a,1,2))].">
      <j1 rule="para" parents="8024 6302"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8024(a,1),6304(a,1,2))].">
      <j1 rule="para" parents="8024 6304"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      x / (y * K(z,T(y,u))) = (x / y) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8024(a,1),6443(a,1,2,2))].">
      <j1 rule="para" parents="8024 6443"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7468(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7468 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y,T(x,z)) * u) = u
    ]]></literal>
    <justification jstring="[para(8024(a,1),7500(a,1,1))].">
      <j1 rule="para" parents="8024 7500"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8024(a,1),7506(a,1,1))].">
      <j1 rule="para" parents="8024 7506"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      K(x,T(y,z)) * (y \ u) = T(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(8024(a,1),7873(a,1,1))].">
      <j1 rule="para" parents="8024 7873"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) = T(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8024(a,1),7907(a,1,1))].">
      <j1 rule="para" parents="8024 7907"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(49,a,8080,a)].">
      <j1 rule="hyper" parents="49 8080"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 8033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5280(a,1),8081(a,1,3,2))].">
      <j1 rule="para" parents="5280 8081"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(8007(a,1),5275(a,2,1))].">
      <j1 rule="para" parents="8007 5275"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6073,a,8011,a)].">
      <j1 rule="hyper" parents="6073 8011"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,7873,a(flip),b,8011,a),flip(a)].">
      <j1 rule="hyper" parents="370 7873 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[hyper(129,a,8011,a,b,7506,a)].">
      <j1 rule="hyper" parents="129 8011 7506"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,8011,a,b,7932,a)].">
      <j1 rule="hyper" parents="125 8011 7932"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(31,a,6683,a(flip),b,8011,a),flip(a)].">
      <j1 rule="hyper" parents="31 6683 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = R(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[para(8011(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8011 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),8011(a,1,2,2))].">
      <j1 rule="para" parents="18 8011"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) = K(y,L(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(20(a,2),8011(a,1,2,2))].">
      <j1 rule="para" parents="20 8011"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8011(a,1),40(a,1))].">
      <j1 rule="para" parents="8011 40"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      K(x,y * z) * (z * y) = (z * y) * K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4856(a,1),8011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4856 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7325(a,1),8011(a,1,2))].">
      <j1 rule="para" parents="7325 8011"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(8019(a,2),8011(a,1,2,2))].">
      <j1 rule="para" parents="8019 8011"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      K(x,T(y,x \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7873(a,1),8013(a,1,2))].">
      <j1 rule="para" parents="7873 8013"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(8014(a,1),7427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8014 7427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8024,a(flip),b,8026,a)].">
      <j1 rule="hyper" parents="60 8024 8026"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5799(a,2),8035(a,1,2))].">
      <j1 rule="para" parents="5799 8035"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8035(a,1),7388(a,1))].">
      <j1 rule="para" parents="8035 7388"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a(flip),b,8036,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 8036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,6463,a,b,8037,a),flip(a)].">
      <j1 rule="hyper" parents="370 6463 8037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(8037(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8037 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8038(a,1),6217(a,1,2))].">
      <j1 rule="para" parents="8038 6217"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6088,a,8039,a),flip(a)].">
      <j1 rule="hyper" parents="6088 8039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6351,a,b,8039,a)].">
      <j1 rule="hyper" parents="60 6351 8039"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8056(a,1),5871(a,1))].">
      <j1 rule="para" parents="8056 5871"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(245(a,1),8058(a,1,1))].">
      <j1 rule="para" parents="245 8058"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K(x,L(L(x,y,z),u,w) / v5) = K(x,v5 \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(247(a,1),8058(a,1,1))].">
      <j1 rule="para" parents="247 8058"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      K(x,y \ z) * T(x,z) = T(T(x,z),z / y)
    ]]></literal>
    <justification jstring="[para(8058(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8058 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      L(x,K(y,z \ u),u / z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(8058(a,1),7847(a,1,2))].">
      <j1 rule="para" parents="8058 7847"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(6493,a,8059,a)].">
      <j1 rule="hyper" parents="6493 8059"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      (x / y) * K(y \ x,z) = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8059(a,1,2,1))].">
      <j1 rule="para" parents="109 8059"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7973(a,1),8059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7973 8059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8026(a,1),8059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8026 8059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8019,a,b,8060,a)].">
      <j1 rule="hyper" parents="60 8019 8060"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8060,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 8060 17"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x / y,y \ z) = K(y \ x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8069(a,1,2))].">
      <j1 rule="para" parents="109 8069"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x / y,T(y,z)) = K(y \ x,T(y,z))
    ]]></literal>
    <justification jstring="[para(203(a,1),8069(a,1,2))].">
      <j1 rule="para" parents="203 8069"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(204(a,1),8069(a,1,2))].">
      <j1 rule="para" parents="204 8069"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(8069(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8069 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="8069 5276"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(8069(a,2),7355(a,1))].">
      <j1 rule="para" parents="8069 7355"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,y / L(x,z,u)) = K(x,L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(201(a,1),8070(a,1,1))].">
      <j1 rule="para" parents="201 8070"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[para(8070(a,1),5855(a,1,2))].">
      <j1 rule="para" parents="8070 5855"/>
    </justification>
  </clause>

  <clause id="8148">
    <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(8070(a,1),5917(a,1,2))].">
      <j1 rule="para" parents="8070 5917"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(8070(a,1),7995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8070 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(8071(a,1),5218(a,1,2))].">
      <j1 rule="para" parents="8071 5218"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(8071(a,1),5642(a,1,3))].">
      <j1 rule="para" parents="8071 5642"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(8071(a,1),6803(a,1,2))].">
      <j1 rule="para" parents="8071 6803"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,8151,a)].">
      <j1 rule="hyper" parents="49 8151"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7362,a,b,8153,a)].">
      <j1 rule="hyper" parents="60 7362 8153"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(u,y),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      x * (T(y,z) * L(K(u,y),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(8153(a,1),1186(a,1,2,1))].">
      <j1 rule="para" parents="8153 1186"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      T(x,T(y,z) \ T(x,z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7143,a,8083,a)].">
      <j1 rule="hyper" parents="7143 8083"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5423(a,2),8119(a,1,2,1))].">
      <j1 rule="para" parents="5423 8119"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8120(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6448(a,1),8120(a,1,2))].">
      <j1 rule="para" parents="6448 8120"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      T(K(x,y),z / y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8019,a(flip),b,8121,a)].">
      <j1 rule="hyper" parents="60 8019 8121"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,7287,a,b,8138,a)].">
      <j1 rule="hyper" parents="370 7287 8138"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),8138(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      K(L(x,y,z),T(u,z * (y * x))) = K(L(x,y,z),T(u,z * y))
    ]]></literal>
    <justification jstring="[para(92(a,1),8138(a,1,2,2))].">
      <j1 rule="para" parents="92 8138"/>
    </justification>
  </clause>

  <clause id="8165">
    <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(82(a,1),8138(a,1,2,2))].">
      <j1 rule="para" parents="82 8138"/>
    </justification>
  </clause>

  <clause id="8166">
    <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(8152(a,1),725(a,1,1))].">
      <j1 rule="para" parents="8152 725"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(8158(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="8158 5701"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      T(x,y * x) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4757,a,7862,a)].">
      <j1 rule="hyper" parents="4757 7862"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(K(x,y) * z,y) * T(y,K(x,y) * (z * y)) = L(y,K(x,y) * z,y)
    ]]></literal>
    <justification jstring="[para(7456(a,1),7862(a,1,2,2))].">
      <j1 rule="para" parents="7456 7862"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4757,a,7863,a)].">
      <j1 rule="hyper" parents="4757 7863"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7863,a(flip),b,4754,a),flip(a)].">
      <j1 rule="hyper" parents="125 7863 4754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7863(a,1),6749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7863 6749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      T(x,y) != K(z,L(T(u,y),w,v5))
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,w,v5)) = x
    ]]></literal>
    <justification jstring="[para(20(a,2),8043(a,2,2))].">
      <j1 rule="para" parents="20 8043"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (x * z),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,8099,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 8099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5964(a,1),8101(a,1,2))].">
      <j1 rule="para" parents="5964 8101"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6370,a(flip),b,8177,a)].">
      <j1 rule="hyper" parents="60 6370 8177"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7986(a,2),8122(a,1))].">
      <j1 rule="para" parents="7986 8122"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7989(a,2),8122(a,1))].">
      <j1 rule="para" parents="7989 8122"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(K(x,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8123(a,2),8122(a,1))].">
      <j1 rule="para" parents="8123 8122"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8019(a,1),8129(a,1))].">
      <j1 rule="para" parents="8019 8129"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,8168,a(flip),b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="125 8168 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,8170,a(flip),b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="125 8170 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,8170,a(flip),b,6390,a)].">
      <j1 rule="hyper" parents="125 8170 6390"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      T(x,y \ x) * K(y \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2686(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="2686 8170"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      T(x,x * T(y,K(x,z))) * K(y,x) = L(x,T(y,K(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7994(a,1),8170(a,1,2))].">
      <j1 rule="para" parents="7994 8170"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8171(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8171 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),8181(a,1,1))].">
      <j1 rule="para" parents="20 8181"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(7145(a,2),8181(a,1))].">
      <j1 rule="para" parents="7145 8181"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7991(a,2),8181(a,1))].">
      <j1 rule="para" parents="7991 8181"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5150,a(flip),b,7836,a),flip(a)].">
      <j1 rule="hyper" parents="60 5150 7836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(7837(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7837 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(2746,a,7845,a)].">
      <j1 rule="hyper" parents="2746 7845"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6416,a(flip),b,7845,a),flip(a)].">
      <j1 rule="hyper" parents="60 6416 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (z * u)) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(7845(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7845 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * (w \ 1))) = L(x,y,(z * K(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(7845(a,1),3426(a,1,3))].">
      <j1 rule="para" parents="7845 3426"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5233(a,2),7845(a,1,1))].">
      <j1 rule="para" parents="5233 7845"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5279(a,1),7845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5279 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5683(a,2),7845(a,1,1))].">
      <j1 rule="para" parents="5683 7845"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7845(a,1),5325(a,1,1))].">
      <j1 rule="para" parents="7845 5325"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      T(T(x,x * (K(y,x) * z)) * K(y,T(x,(x * K(y,x)) * z)),u) = T(T(x * K(y,x),u),z * (x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(7845(a,1),6138(a,1,1,1,2))].">
      <j1 rule="para" parents="7845 6138"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(8198(a,1),689(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8198 689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      K(x \ 1,y) * ((x \ 1) \ z) = (x \ K(y,x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(4781(a,1),7846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4781 7846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5233(a,2),7846(a,1,1))].">
      <j1 rule="para" parents="5233 7846"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(5279(a,1),7846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5279 7846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,x / y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5315(a,2),7846(a,1,1))].">
      <j1 rule="para" parents="5315 7846"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x * K(y,x),y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(7846(a,1),5447(a,1,1))].">
      <j1 rule="para" parents="7846 5447"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,5412,a,b,7859,a),flip(a)].">
      <j1 rule="hyper" parents="32 5412 7859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,5402,a,b,7859,a)].">
      <j1 rule="hyper" parents="32 5402 7859"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,5413,a(flip),b,7859,a),flip(a)].">
      <j1 rule="hyper" parents="32 5413 7859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K((x * y) / x,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7859(a,2,2,1))].">
      <j1 rule="para" parents="4 7859"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(7859(a,1),7511(a,1,2))].">
      <j1 rule="para" parents="7859 7511"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(7859(a,1),7520(a,1,2))].">
      <j1 rule="para" parents="7859 7520"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y \ x) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(8214(a,1),5680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8214 5680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5517,a,8215,a)].">
      <j1 rule="hyper" parents="5517 8215"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K((x / y) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6690,a(flip),b,8215,a),flip(a)].">
      <j1 rule="hyper" parents="370 6690 8215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6865,a(flip),b,8215,a),flip(a)].">
      <j1 rule="hyper" parents="60 6865 8215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),8215(a,2,1))].">
      <j1 rule="para" parents="6 8215"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      T(x * K(y / z,x),z / y) = T(x,(z / y) * (z / y))
    ]]></literal>
    <justification jstring="[para(8215(a,1),6911(a,1,1,2))].">
      <j1 rule="para" parents="8215 6911"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K((1 / y) / x,z),u)
    ]]></literal>
    <justification jstring="[para(8215(a,1),6658(a,2,1))].">
      <j1 rule="para" parents="8215 6658"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(8216(a,2),5517(a,1))].">
      <j1 rule="para" parents="8216 5517"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(8216(a,1),5680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8216 5680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z * (x / (y * x))) = K(y,R(y \ 1,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(7758,a,8224,a)].">
      <j1 rule="hyper" parents="7758 8224"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(7445,a,7861,a)].">
      <j1 rule="hyper" parents="7445 7861"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(7861(a,2),7461(a,1,2))].">
      <j1 rule="para" parents="7861 7461"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,y) * (x \ (y \ z)) = x \ (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,7873,a(flip),b,7892,a),flip(a)].">
      <j1 rule="hyper" parents="125 7873 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,4746,a(flip),b,7892,a)].">
      <j1 rule="hyper" parents="125 4746 7892"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      x \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(7892(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7892 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2746,a,7923,a)].">
      <j1 rule="hyper" parents="2746 7923"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,7923,a)].">
      <j1 rule="hyper" parents="625 7923"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5885,a,8240,a)].">
      <j1 rule="hyper" parents="5885 8240"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3531,a,8240,a)].">
      <j1 rule="hyper" parents="3531 8240"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8240(a,1),47(a,2))].">
      <j1 rule="para" parents="8240 47"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1838,a,8241,a),flip(a)].">
      <j1 rule="hyper" parents="1838 8241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,8241,a)].">
      <j1 rule="hyper" parents="50 8241"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(8241(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="8241 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(8071(a,1),8241(a,1,3))].">
      <j1 rule="para" parents="8071 8241"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5135,a(flip),b,8239,a),flip(a)].">
      <j1 rule="hyper" parents="370 5135 8239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7238,a(flip),b,8239,a)].">
      <j1 rule="hyper" parents="60 7238 8239"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8242(a,1),5018(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8242 5018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1838,a,8247,a),flip(a)].">
      <j1 rule="hyper" parents="1838 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      L(x,T(T(y,z),u),K(w,y)) = x
    ]]></literal>
    <justification jstring="[para(8071(a,1),8247(a,1,3))].">
      <j1 rule="para" parents="8071 8247"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      L(x,y,K(z,y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5865(a,2),8243(a,1,3))].">
      <j1 rule="para" parents="5865 8243"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      L(x,T(T(y,z),u),K(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(8253(a,1),47(a,2))].">
      <j1 rule="para" parents="8253 47"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(1378(a,1),7931(a,1,2))].">
      <j1 rule="para" parents="1378 7931"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[para(1535(a,1),7931(a,1,2))].">
      <j1 rule="para" parents="1535 7931"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * ((y * (u \ z)) * T(L(T(u,u \ z),u \ z,y),x)) = y * z
    ]]></literal>
    <justification jstring="[para(412(a,2),7931(a,1,2,2,1))].">
      <j1 rule="para" parents="412 7931"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2894,a,b,7937,a),flip(a)].">
      <j1 rule="hyper" parents="370 2894 7937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5233(a,2),7944(a,1,2))].">
      <j1 rule="para" parents="5233 7944"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      L(x,T(y \ z,y),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(5279(a,1),7944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5279 7944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      T(x,y) * (T(x,y) * z) = x * (T(T(x,y),y) * z)
    ]]></literal>
    <justification jstring="[para(7908(a,1),7945(a,1,2))].">
      <j1 rule="para" parents="7908 7945"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = (x * y) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,92,a,b,7946,a),flip(a)].">
      <j1 rule="hyper" parents="370 92 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(7946(a,1),5816(a,1,1))].">
      <j1 rule="para" parents="7946 5816"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,T(z,x)) * u) = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),7946(a,1,2,1))].">
      <j1 rule="para" parents="8019 7946"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4819,a,7952,a)].">
      <j1 rule="hyper" parents="4819 7952"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5007,a(flip),b,8266,a)].">
      <j1 rule="hyper" parents="60 5007 8266"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(129,a,617,a(flip),b,7965,a)].">
      <j1 rule="hyper" parents="129 617 7965"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(7967(a,1),103(a,2,1))].">
      <j1 rule="para" parents="7967 103"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(7967(a,1),387(a,1))].">
      <j1 rule="para" parents="7967 387"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7967(a,1),7444(a,1,1))].">
      <j1 rule="para" parents="7967 7444"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = w
    ]]></literal>
    <justification jstring="[para(7969(a,1),7355(a,1,1,2))].">
      <j1 rule="para" parents="7969 7355"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      (T(x,y) \ x) \ z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,7972,a)].">
      <j1 rule="hyper" parents="125 5 7972"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(6234,a,7974,a)].">
      <j1 rule="hyper" parents="6234 7974"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(8278(a,2),7303(a,1,1))].">
      <j1 rule="para" parents="8278 7303"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,7987,a,b,107,a)].">
      <j1 rule="hyper" parents="125 7987 107"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,1 / T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(7987(a,2),94(a,2,1))].">
      <j1 rule="para" parents="7987 94"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8002(a,2),6569(a,1))].">
      <j1 rule="para" parents="8002 6569"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      K((x * T(x \ y,z)) / T(y / x,z),u) * (x * T(x \ y,z)) = (x * T(x \ y,z)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(546(a,1),8004(a,2,2,1))].">
      <j1 rule="para" parents="546 8004"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(6499,a,8030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6499 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(8019(a,1),8040(a,2,1))].">
      <j1 rule="para" parents="8019 8040"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(8040(a,2),8122(a,1))].">
      <j1 rule="para" parents="8040 8122"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,8065,a(flip),b,6337,a)].">
      <j1 rule="hyper" parents="125 8065 6337"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(4907(a,1),8065(a,1,2,2))].">
      <j1 rule="para" parents="4907 8065"/>
    </justification>
  </clause>

  <clause id="8295">
    <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(8066(a,1),2916(a,1,2))].">
      <j1 rule="para" parents="8066 2916"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(8094(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8094 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,8102,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 8102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5280(a,1),8298(a,1,2,2,1))].">
      <j1 rule="para" parents="5280 8298"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7306(a,1),8103(a,1,2,1))].">
      <j1 rule="para" parents="7306 8103"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8124(a,2),6464(a,1))].">
      <j1 rule="para" parents="8124 6464"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x \ 1,T(x \ 1,y)) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(8127(a,2),6248(a,1,2))].">
      <j1 rule="para" parents="8127 6248"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      K(x \ 1,y) * ((1 / x) \ z) = (K(y,x \ 1) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(8133,a,7619,a)].">
      <j1 rule="hyper" parents="8133 7619"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      L(T(T(x,y),z) \ (K(x,y) * u),T(T(x,y),z),K(y,x)) = T(x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[para(8134(a,1),7522(a,2,1))].">
      <j1 rule="para" parents="8134 7522"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8039,a(flip),b,8136,a),flip(a)].">
      <j1 rule="hyper" parents="370 8039 8136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),8308(a,2,2))].">
      <j1 rule="para" parents="106 8308"/>
    </justification>
  </clause>

  <clause id="8310">
    <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(8308(a,1),5262(a,1,2,1))].">
      <j1 rule="para" parents="8308 5262"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      T(x,T(x * y,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8309(a,1,2,2))].">
      <j1 rule="para" parents="4 8309"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8137(a,2),5265(a,1))].">
      <j1 rule="para" parents="8137 5265"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      K(T(x / y,z),y) = K(y \ x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8129,a,8141,a)].">
      <j1 rule="hyper" parents="8129 8141"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7874,a,b,8149,a)].">
      <j1 rule="hyper" parents="60 7874 8149"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,7874,a,b,8149,a(flip))].">
      <j1 rule="hyper" parents="125 7874 8149"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(5883(a,1),8150(a,1))].">
      <j1 rule="para" parents="5883 8150"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,8167,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 8167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),8317(a,1,1,1,2))].">
      <j1 rule="para" parents="74 8317"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5423(a,1),8317(a,1,1,1))].">
      <j1 rule="para" parents="5423 8317"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(6127(a,1),8317(a,1,1))].">
      <j1 rule="para" parents="6127 8317"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6128(a,1),8319(a,1,1))].">
      <j1 rule="para" parents="6128 8319"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(7015(a,1),8319(a,1,1,1))].">
      <j1 rule="para" parents="7015 8319"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      K(T(x,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(7858(a,1),8319(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 8319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(8016(a,1),8319(a,1,1))].">
      <j1 rule="para" parents="8016 8319"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6463(a,1),8325(a,1,1,2))].">
      <j1 rule="para" parents="6463 8325"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5976,a,8202,a),flip(a)].">
      <j1 rule="hyper" parents="5976 8202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(721,a,8202,a)].">
      <j1 rule="hyper" parents="721 8202"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(485,a,8202,a),flip(a)].">
      <j1 rule="hyper" parents="485 8202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,7967,a,b,8202,a)].">
      <j1 rule="hyper" parents="370 7967 8202"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,7958,a(flip),b,8202,a),flip(a)].">
      <j1 rule="hyper" parents="370 7958 8202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K((y * z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,8202,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="125 8202 87"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(7929(a,1),8202(a,2,2))].">
      <j1 rule="para" parents="7929 8202"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6709,a,8209,a)].">
      <j1 rule="hyper" parents="6709 8209"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,173,a(flip),b,8209,a),flip(a)].">
      <j1 rule="hyper" parents="370 173 8209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6708,a(flip),b,8209,a),flip(a)].">
      <j1 rule="hyper" parents="60 6708 8209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      T((x * (y \ 1)) \ x,K(x * (y \ 1),x)) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,3494,a(flip),b,8335,a),flip(a)].">
      <j1 rule="hyper" parents="370 3494 8335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7566,a,8218,a)].">
      <j1 rule="hyper" parents="7566 8218"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      x / (y * (z * T(z \ (y \ x),u))) = K(u,x / (y * z))
    ]]></literal>
    <justification jstring="[para(1352(a,1),8218(a,1,2))].">
      <j1 rule="para" parents="1352 8218"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      x / (((y \ (x / z)) * y) * z) = K(y,x / (y * z))
    ]]></literal>
    <justification jstring="[para(2316(a,1),8218(a,1,2))].">
      <j1 rule="para" parents="2316 8218"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(2395(a,1),8218(a,1,2))].">
      <j1 rule="para" parents="2395 8218"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6064,a,8340,a)].">
      <j1 rule="hyper" parents="6064 8340"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7065,a,b,8340,a)].">
      <j1 rule="hyper" parents="60 7065 8340"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),8340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 8340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),8340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 8340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(x,y \ K(y,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(5935(a,1),8340(a,1,2))].">
      <j1 rule="para" parents="5935 8340"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(6(a,1),8345(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 8345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6291(a,1),8345(a,2,2))].">
      <j1 rule="para" parents="6291 8345"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,6471,a,b,8347,a)].">
      <j1 rule="hyper" parents="370 6471 8347"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(8347(a,1),5732(a,1,1))].">
      <j1 rule="para" parents="8347 5732"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      x * K(y,x \ (z \ x)) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[para(8348(a,1),8112(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8348 8112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(8350(a,2),5427(a,1))].">
      <j1 rule="para" parents="8350 5427"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      ((x * y) \ y) * K(x * y,1 / x) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(8350(a,1),5707(a,1,2))].">
      <j1 rule="para" parents="8350 5707"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(275,a,8233,a,b,7839,a)].">
      <j1 rule="hyper" parents="275 8233 7839"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(7860(a,2),8233(a,1,1))].">
      <j1 rule="para" parents="7860 8233"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7846,a,b,8237,a)].">
      <j1 rule="hyper" parents="370 7846 8237"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2746,a,8244,a)].">
      <j1 rule="hyper" parents="2746 8244"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5232(a,1),8244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5232 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      K(x \ y,x) * (x * z) = (y / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(5837(a,2),8244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5837 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6920,a,8363,a)].">
      <j1 rule="hyper" parents="6920 8363"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2761,a,8363,a)].">
      <j1 rule="hyper" parents="2761 8363"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,8340,a,b,8363,a),flip(a)].">
      <j1 rule="hyper" parents="370 8340 8363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,8347,a(flip),b,8363,a),flip(a)].">
      <j1 rule="hyper" parents="370 8347 8363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(8363(a,1),2709(a,1))].">
      <j1 rule="para" parents="8363 2709"/>
    </justification>
  </clause>

  <clause id="8371">
    <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(1093(a,1),8366(a,1,1,1))].">
      <j1 rule="para" parents="1093 8366"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(5839(a,1),8259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5839 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y)
    ]]></literal>
    <justification jstring="[hyper(5991,a,8277,a),flip(a)].">
      <j1 rule="hyper" parents="5991 8277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      T(x,y) != K(z,T(T(u,y),w))
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),w) = x
    ]]></literal>
    <justification jstring="[para(8291(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8291 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      L(T(x,T(y,z)),K(x,z),z * x) = (x * z) \ ((T(x,y) * z) * x)
    ]]></literal>
    <justification jstring="[para(8293(a,1),1826(a,1,1))].">
      <j1 rule="para" parents="8293 1826"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      (x * T(y \ z,u)) / T(z / y,u) = x * K(y \ z,T(y,u))
    ]]></literal>
    <justification jstring="[para(8313(a,1),6366(a,2,2))].">
      <j1 rule="para" parents="8313 6366"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,5856,a,b,8314,a)].">
      <j1 rule="hyper" parents="370 5856 8314"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ z),y \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(z / (y \ 1),x) \ z) = u
    ]]></literal>
    <justification jstring="[para(8315(a,1),667(a,1,1))].">
      <j1 rule="para" parents="8315 667"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      K((x \ y) * x,x \ 1) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(7479(a,1),8318(a,1,1))].">
      <j1 rule="para" parents="7479 8318"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      K(T(x / (y / (y / z)),1 / u) / (y / z),u) = K((x / z) / (z \ y),u)
    ]]></literal>
    <justification jstring="[para(6534(a,1),8320(a,2,1))].">
      <j1 rule="para" parents="6534 8320"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),8328(a,1,2,1,1))].">
      <j1 rule="para" parents="5 8328"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),8329(a,1,2,1,1))].">
      <j1 rule="para" parents="5 8329"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(7518,a,8330,a)].">
      <j1 rule="hyper" parents="7518 8330"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,7864,a(flip),b,8331,a)].">
      <j1 rule="hyper" parents="125 7864 8331"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),8331(a,1,1,1))].">
      <j1 rule="para" parents="5 8331"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(8331(a,1),6967(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8331 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7860,a,b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="370 7860 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      (x / (x / y)) \ (y * z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(5835(a,1),8336(a,1,1))].">
      <j1 rule="para" parents="5835 8336"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      L(K(x,y) * ((y \ x) \ z),K(y,x),y \ x) = (K(y,x) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(8337(a,2),7539(a,2,1))].">
      <j1 rule="para" parents="8337 7539"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      K(x,y / (y * z)) * y = y * K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(8349(a,1),6894(a,1,1))].">
      <j1 rule="para" parents="8349 6894"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6992,a,8359,a),flip(a)].">
      <j1 rule="hyper" parents="6992 8359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),8359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 8359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x) = K(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),8359(a,2,2))].">
      <j1 rule="para" parents="20 8359"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,7028,a,b,8362,a)].">
      <j1 rule="hyper" parents="370 7028 8362"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,8377,a)].">
      <j1 rule="hyper" parents="215 8377"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(74(a,1),8377(a,2,1,1))].">
      <j1 rule="para" parents="74 8377"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),8377(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 8377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),8385(a,1,2,1,1))].">
      <j1 rule="para" parents="5 8385"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      T(x * K(y,z),z) * z = T(x,z) * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(8393(a,2),5213(a,1,1))].">
      <j1 rule="para" parents="8393 5213"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1058,a,8394,a),flip(a)].">
      <j1 rule="hyper" parents="1058 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8394,a(flip),b,6991,a),flip(a)].">
      <j1 rule="hyper" parents="129 8394 6991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,8394,a(flip),b,1623,a),flip(a)].">
      <j1 rule="hyper" parents="125 8394 1623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(74(a,1),8398(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 8398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8398(a,1),7343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8398 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(108(a,2),8399(a,1,2,1))].">
      <j1 rule="para" parents="108 8399"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(221,a,8400,a)].">
      <j1 rule="hyper" parents="221 8400"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(5842(a,1),8400(a,1,1))].">
      <j1 rule="para" parents="5842 8400"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(6050(a,1),8400(a,1,1,1))].">
      <j1 rule="para" parents="6050 8400"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6365,a,8404,a)].">
      <j1 rule="hyper" parents="6365 8404"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6269,a,b,8404,a)].">
      <j1 rule="hyper" parents="370 6269 8404"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      T(x * K(y,z),y) * y = T(x,y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(8404(a,2),6268(a,1,1))].">
      <j1 rule="para" parents="8404 6268"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(7394(a,1),8405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7394 8405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      T((x \ y) \ y,x \ z) = (((x \ z) \ z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(108(a,1),8407(a,2,1,1))].">
      <j1 rule="para" parents="108 8407"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(8407(a,2),7388(a,1,2))].">
      <j1 rule="para" parents="8407 7388"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      T(x / (x / (y / z)),z) = x / (x / (z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8411(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      T(x * K(x \ y,x),z) = y / (y / T(x,z))
    ]]></literal>
    <justification jstring="[para(5683(a,1),8411(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5683 8411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(8404(a,2),7868(a,1,2))].">
      <j1 rule="para" parents="8404 7868"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      K(x,y \ z) * K(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ z,x) \ (z / y) = u
    ]]></literal>
    <justification jstring="[para(5331(a,1),7883(a,1,2))].">
      <j1 rule="para" parents="5331 7883"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * ((x * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(944(a,1),7900(a,1,2))].">
      <j1 rule="para" parents="944 7900"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8095(a,2),7900(a,1))].">
      <j1 rule="para" parents="8095 7900"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K(x,y) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(7871(a,1),7928(a,1,2))].">
      <j1 rule="para" parents="7871 7928"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8024(a,1),7939(a,1,2,1))].">
      <j1 rule="para" parents="8024 7939"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      T(L(K(x,y),x,z),x * u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (T(x,y) * u) = w
    ]]></literal>
    <justification jstring="[para(7951(a,2),494(a,1,1))].">
      <j1 rule="para" parents="7951 494"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) \ z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * ((x \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(6191(a,1),7970(a,1))].">
      <j1 rule="para" parents="6191 7970"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,u) \ (K(x,u) * y) = z
    ]]></literal>
    <justification jstring="[para(7500(a,1),7979(a,1,2))].">
      <j1 rule="para" parents="7500 7979"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(8011(a,2),7979(a,1,2))].">
      <j1 rule="para" parents="8011 7979"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),8145(a,1,1,1))].">
      <j1 rule="para" parents="5 8145"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8162(a,1),7354(a,1))].">
      <j1 rule="para" parents="8162 7354"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x,T(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8019(a,2),8182(a,1))].">
      <j1 rule="para" parents="8019 8182"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(4743(a,1),8283(a,1))].">
      <j1 rule="para" parents="4743 8283"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8019(a,2),8283(a,1))].">
      <j1 rule="para" parents="8019 8283"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      K(R(x / y,y,x \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y * (x \ z)) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(428(a,2),8459(a,1,1))].">
      <j1 rule="para" parents="428 8459"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x,x / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ x) = z
    ]]></literal>
    <justification jstring="[para(4907(a,1),8303(a,1))].">
      <j1 rule="para" parents="4907 8303"/>
    </justification>
  </clause>

  <clause id="8464">
    <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(4931(a,1),8303(a,1))].">
      <j1 rule="para" parents="4931 8303"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6448(a,1),8312(a,1,2))].">
      <j1 rule="para" parents="6448 8312"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),8357(a,1,2,2))].">
      <j1 rule="para" parents="5 8357"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(5540(a,1),8397(a,1,2))].">
      <j1 rule="para" parents="5540 8397"/>
    </justification>
  </clause>

  <clause id="8473">
    <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(204(a,1),8453(a,1,2))].">
      <j1 rule="para" parents="204 8453"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = w
    ]]></literal>
    <justification jstring="[para(4835(a,1),8453(a,1,1))].">
      <j1 rule="para" parents="4835 8453"/>
    </justification>
  </clause>

  <clause id="8476">
    <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(7222(a,1),8461(a,1,2))].">
      <j1 rule="para" parents="7222 8461"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7273,a,b,7854,a),flip(a)].">
      <j1 rule="hyper" parents="370 7273 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      (x / y) * (K(y \ x,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(5674(a,1),7867(a,1,2,1))].">
      <j1 rule="para" parents="5674 7867"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      K(x \ y,x) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(7881(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7881 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5971,a,b,7889,a)].">
      <j1 rule="hyper" parents="60 5971 7889"/>
    </justification>
  </clause>

  <clause id="8485">
    <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(7891(a,1),7875(a,1,2))].">
      <j1 rule="para" parents="7891 7875"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5674(a,1),7897(a,2,1))].">
      <j1 rule="para" parents="5674 7897"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6342,a,7911,a)].">
      <j1 rule="hyper" parents="6342 7911"/>
    </justification>
  </clause>

  <clause id="8489">
    <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(20(a,2),8487(a,2,2,2))].">
      <j1 rule="para" parents="20 8487"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      T(L(x,y,z) * u,K(u,w)) = u * L(T(x,T(u,w)),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),8487(a,2,2))].">
      <j1 rule="para" parents="20 8487"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      L(x,y * T(z * y,K(y,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(T(z,T(y,u)),y,y),w) = v5
    ]]></literal>
    <justification jstring="[para(8487(a,2),3544(a,1,2,2))].">
      <j1 rule="para" parents="8487 3544"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      K(x,y) * ((x * x) * z) = (x * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(278(a,1),7914(a,2,1))].">
      <j1 rule="para" parents="278 7914"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,z) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(6547,a,7926,a)].">
      <j1 rule="hyper" parents="6547 7926"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      K(x,y) * (z * K(x,z)) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,5335,a(flip),b,7926,a)].">
      <j1 rule="hyper" parents="60 5335 7926"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(x,y) * ((x * z) / x) = x * ((T(x,y) * z) / x)
    ]]></literal>
    <justification jstring="[hyper(129,a,7926,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 7926 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) \ z) = x \ (T(T(x,y),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,7948,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="125 7948 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5338,a,7955,a)].">
      <j1 rule="hyper" parents="5338 7955"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * (T(z,u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(7955(a,1),3484(a,2,3))].">
      <j1 rule="para" parents="7955 3484"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(7501(a,1),8010(a,1,2,1))].">
      <j1 rule="para" parents="7501 8010"/>
    </justification>
  </clause>

  <clause id="8502">
    <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(8041(a,2),1151(a,1))].">
      <j1 rule="para" parents="8041 1151"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      T(L(K(x,y),z,u),x * w) = L(K(x,T(y,w)),z,u)
    ]]></literal>
    <justification jstring="[para(8159(a,1),8041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8159 8041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8504">
    <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(204(a,1),8068(a,2,2))].">
      <j1 rule="para" parents="204 8068"/>
    </justification>
  </clause>

  <clause id="8505">
    <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(2628(a,1),8068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2628 8068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(4745(a,1),8068(a,2,2))].">
      <j1 rule="para" parents="4745 8068"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(8074(a,1),7769(a,1,1,2))].">
      <j1 rule="para" parents="8074 7769"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      (x * y) \ ((T(x,z) * y) * x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5859(a,1),8085(a,1,1))].">
      <j1 rule="para" parents="5859 8085"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8020,a(flip),b,8126,a),flip(a)].">
      <j1 rule="hyper" parents="60 8020 8126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8509(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8510(a,1),7355(a,1))].">
      <j1 rule="para" parents="8510 7355"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z \ x) * (x / y) = T(T(T(x,y \ x) / y,x),x / z)
    ]]></literal>
    <justification jstring="[para(5473(a,1),8132(a,1,2))].">
      <j1 rule="para" parents="5473 8132"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      T(1 / x,T(y,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(5380,a,8135,a),flip(a)].">
      <j1 rule="hyper" parents="5380 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      ((x \ ((1 / x) \ y)) / y) * K(a(x,x,x \ (x \ y)),z) = T((x \ ((1 / x) \ y)) / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(2117(a,2),8135(a,1,2,1))].">
      <j1 rule="para" parents="2117 8135"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      T(1 / x,y / x) = T(1 / x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8513(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 8513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      T(x,y) * T(1 / y,x) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(8513(a,1),1277(a,1,2))].">
      <j1 rule="para" parents="8513 1277"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      T(1 / x,y / x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7751,a(flip),b,8515,a),flip(a)].">
      <j1 rule="hyper" parents="370 7751 8515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      (x / y) * T(y \ 1,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (x / y) = z
    ]]></literal>
    <justification jstring="[para(8517(a,1),328(a,1,2))].">
      <j1 rule="para" parents="8517 328"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6372,a,8139,a),flip(a)].">
      <j1 rule="hyper" parents="6372 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),8519(a,2,2,2))].">
      <j1 rule="para" parents="200 8519"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,u) * x) = K(y,u) * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6231(a,1),8519(a,2,2,2))].">
      <j1 rule="para" parents="6231 8519"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(5256(a,2),8178(a,1,1))].">
      <j1 rule="para" parents="5256 8178"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,8523,a(flip))].">
      <j1 rule="hyper" parents="215 8523"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      (T(x / y,y) / (y \ 1)) \ (x / y) = y \ K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5692(a,1),8524(a,2,2))].">
      <j1 rule="para" parents="5692 8524"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(4754(a,1),8191(a,1))].">
      <j1 rule="para" parents="4754 8191"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),8203(a,1,2))].">
      <j1 rule="para" parents="7864 8203"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(5918,a,8204,a),flip(a)].">
      <j1 rule="hyper" parents="5918 8204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      T(x,x \ y) * ((y / x) \ z) = x * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8210,a(flip),b,7935,a)].">
      <j1 rule="hyper" parents="129 8210 7935"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      ((x \ y) \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,8210,a(flip),b,7978,a),flip(a)].">
      <j1 rule="hyper" parents="125 8210 7978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(125,a,8210,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="125 8210 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(17(a,2),8210(a,1,2))].">
      <j1 rule="para" parents="17 8210"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      K(T(x,y),T(y,x) / x) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(5784(a,1),8210(a,1,1,1))].">
      <j1 rule="para" parents="5784 8210"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,4364,a(flip),b,8211,a)].">
      <j1 rule="hyper" parents="370 4364 8211"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(32,a,5850,a,b,8220,a)].">
      <j1 rule="hyper" parents="32 5850 8220"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(5943,a,8220,a(flip))].">
      <j1 rule="hyper" parents="5943 8220"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x,x \ 1) = (x \ (L(x,y,z) \ x)) * x
    ]]></literal>
    <justification jstring="[para(4616(a,1),8220(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4616 8220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(33,a,308,a,b,8537,a)].">
      <j1 rule="hyper" parents="33 308 8537"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(4441(a,1),8537(a,1,2))].">
      <j1 rule="para" parents="4441 8537"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),8540(a,1,2,2))].">
      <j1 rule="para" parents="4 8540"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(77(a,1),8540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 8540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6487(a,1),8540(a,1,2,2))].">
      <j1 rule="para" parents="6487 8540"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(8540(a,1),6153(a,1,1))].">
      <j1 rule="para" parents="8540 6153"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ y)) = u
    ]]></literal>
    <justification jstring="[para(8540(a,1),7336(a,1,2))].">
      <j1 rule="para" parents="8540 7336"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      T(K(x,y),z \ x) = K(T(x,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(8540(a,1),7973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8540 7973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(8543(a,1),6154(a,1,2))].">
      <j1 rule="para" parents="8543 6154"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(77(a,1),8538(a,1,2,2))].">
      <j1 rule="para" parents="77 8538"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * T(x,y) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4441(a,1),8538(a,1,2))].">
      <j1 rule="para" parents="4441 8538"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      T(x,y * (((((z \ (u \ z)) \ 1) \ 1) * T(z,u \ 1)) \ w)) = T(x,y * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(8538(a,1),4693(a,2,2,2,1))].">
      <j1 rule="para" parents="8538 4693"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      T(K(x,y),z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8547(a,2),8181(a,1))].">
      <j1 rule="para" parents="8547 8181"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),8548(a,2,2))].">
      <j1 rule="para" parents="6 8548"/>
    </justification>
  </clause>

  <clause id="8554">
    <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(8548(a,1),1883(a,1,1,2,1))].">
      <j1 rule="para" parents="8548 1883"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(5631(a,1),8326(a,1,1))].">
      <j1 rule="para" parents="5631 8326"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(74(a,1),8334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 8334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,1 / ((y * (1 / z)) / y)) = K(x,z * K(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5340(a,1),8351(a,1,2,2))].">
      <j1 rule="para" parents="5340 8351"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(31,a,8011,a,b,8356,a)].">
      <j1 rule="hyper" parents="31 8011 8356"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8289,a(flip),b,8558,a)].">
      <j1 rule="hyper" parents="60 8289 8558"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(77(a,1),8558(a,2,2,2))].">
      <j1 rule="para" parents="77 8558"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      x * K(x,y \ (z \ y)) = T(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8559,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8559 5230"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(275,a,8361,a,b,1672,a)].">
      <j1 rule="hyper" parents="275 8361 1672"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,8115,a,b,8364,a)].">
      <j1 rule="hyper" parents="60 8115 8364"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      T((x / y) * z,K(y,y \ x)) = ((y \ x) * z) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(8364(a,1),7464(a,1,1))].">
      <j1 rule="para" parents="8364 7464"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ z = u
    ]]></literal>
    <justification jstring="[para(8383(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8383 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(8383(a,1),8323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8383 8323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(5479,a,8386,a),flip(a)].">
      <j1 rule="hyper" parents="5479 8386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(8387(a,1),742(a,1))].">
      <j1 rule="para" parents="8387 742"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      (x / (x / y)) * ((x / y) * z) = y * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8364,a(flip),b,8390,a)].">
      <j1 rule="hyper" parents="129 8364 8390"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K(x,T(y / z,u)) * y = y * K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8408(a,1),8011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8408 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(5443(a,1),8416(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5443 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      (x * (y / (y / (x \ z)))) / x = y / (y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(316,a,8427,a)].">
      <j1 rule="hyper" parents="316 8427"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(5747(a,2),8429(a,2,2))].">
      <j1 rule="para" parents="5747 8429"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,8471,a)].">
      <j1 rule="hyper" parents="215 8471"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6333,a,8480,a)].">
      <j1 rule="hyper" parents="6333 8480"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(263(a,1),8586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 8586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8586(a,1),315(a,1,1))].">
      <j1 rule="para" parents="8586 315"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      T(x,K(y,z)) * y = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8586(a,1),537(a,1,1))].">
      <j1 rule="para" parents="8586 537"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8039,a,b,8587,a),flip(a)].">
      <j1 rule="hyper" parents="370 8039 8587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8294,a,b,8587,a)].">
      <j1 rule="hyper" parents="60 8294 8587"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(T(y,z),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),8587(a,2,2))].">
      <j1 rule="para" parents="18 8587"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(8587(a,1),46(a,1))].">
      <j1 rule="para" parents="8587 46"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8587(a,1),8008(a,1,2))].">
      <j1 rule="para" parents="8587 8008"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      K(x,T(y,T(z,L(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8587(a,1),8075(a,1,2))].">
      <j1 rule="para" parents="8587 8075"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      T(x \ 1,T(y,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3214(a,1),8588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3214 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6232(a,1),8588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6232 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(8588(a,1),6632(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8588 6632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(7464(a,1),8588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7464 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      T(x \ 1,y / x) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 8596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,8487,a,b,8589,a)].">
      <j1 rule="hyper" parents="370 8487 8589"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(6091(a,2),8590(a,2,2))].">
      <j1 rule="para" parents="6091 8590"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8590(a,2),8051(a,1))].">
      <j1 rule="para" parents="8590 8051"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4920,a,8591,a)].">
      <j1 rule="hyper" parents="4920 8591"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(31,a,8128,a,b,8591,a)].">
      <j1 rule="hyper" parents="31 8128 8591"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6243,a,8605,a)].">
      <j1 rule="hyper" parents="6243 8605"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      K(K(L(x \ 1,y,z) \ 1,u),w) = L(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6591,a(flip),b,8605,a),flip(a)].">
      <j1 rule="hyper" parents="370 6591 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6584,a(flip),b,8605,a),flip(a)].">
      <j1 rule="hyper" parents="370 6584 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(129,a,8605,a(flip),b,6325,a)].">
      <j1 rule="hyper" parents="129 8605 6325"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8605,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8605 5230"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8605(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8605 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8605(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="8605 5265"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      K(x,K(y,z)) \ z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8605(a,1),5703(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8605 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8605(a,1),5865(a,1,1))].">
      <j1 rule="para" parents="8605 5865"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(8605(a,1),6219(a,1,2))].">
      <j1 rule="para" parents="8605 6219"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(8605(a,1),6243(a,1))].">
      <j1 rule="para" parents="8605 6243"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(8605(a,1),6972(a,1,2))].">
      <j1 rule="para" parents="8605 6972"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[para(8605(a,1),7864(a,1,1))].">
      <j1 rule="para" parents="8605 7864"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8605(a,1),8032(a,1,2))].">
      <j1 rule="para" parents="8605 8032"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(8605(a,1),7883(a,1,1))].">
      <j1 rule="para" parents="8605 7883"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8509,a,b,8606,a)].">
      <j1 rule="hyper" parents="370 8509 8606"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8510,a(flip),b,8606,a),flip(a)].">
      <j1 rule="hyper" parents="370 8510 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8606(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8606 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(8606(a,1),5703(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8606 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(8606(a,1),5735(a,1,1))].">
      <j1 rule="para" parents="8606 5735"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8606(a,1),8027(a,1,1))].">
      <j1 rule="para" parents="8606 8027"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6222,a,8615,a)].">
      <j1 rule="hyper" parents="6222 8615"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5871,a,8615,a)].">
      <j1 rule="hyper" parents="5871 8615"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8615,a(flip),b,5875,a(flip))].">
      <j1 rule="hyper" parents="129 8615 5875"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8615(a,1),6222(a,1))].">
      <j1 rule="para" parents="8615 6222"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8511,a,8630,a),flip(a)].">
      <j1 rule="hyper" parents="8511 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,8630,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8605,a,b,8630,a)].">
      <j1 rule="hyper" parents="370 8605 8630"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8630,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8630 5230"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8630(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8630 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      x * K(y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8630(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="8630 5265"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8630(a,1),5276(a,1,1))].">
      <j1 rule="para" parents="8630 5276"/>
    </justification>
  </clause>

  <clause id="8642">
    <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(8630(a,1),5965(a,1,2))].">
      <j1 rule="para" parents="8630 5965"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8630(a,1),7864(a,1,1))].">
      <j1 rule="para" parents="8630 7864"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(x,T(u,z)))
    ]]></literal>
    <justification jstring="[para(8024(a,2),8630(a,1,2))].">
      <j1 rule="para" parents="8024 8630"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,8631,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8631,a,b,8636,a)].">
      <j1 rule="hyper" parents="370 8631 8636"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,8636,a)].">
      <j1 rule="hyper" parents="370 8630 8636"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8020,a,b,8636,a)].">
      <j1 rule="hyper" parents="370 8020 8636"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      K((x \ y) \ 1,K(z,u)) = K(z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,6410,a,b,8636,a)].">
      <j1 rule="hyper" parents="370 6410 8636"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8510,a(flip),b,8636,a),flip(a)].">
      <j1 rule="hyper" parents="370 8510 8636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,8636,a,b,8615,a)].">
      <j1 rule="hyper" parents="129 8636 8615"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8636,a,b,6404,a),flip(a)].">
      <j1 rule="hyper" parents="129 8636 6404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      (x * y) * K(z,K(u,y)) = x * T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,8636,a,b,6325,a)].">
      <j1 rule="hyper" parents="129 8636 6325"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8636,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8636 5230"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8636(a,2),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8636 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x,K(y,z)) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8636(a,2),5276(a,1,1))].">
      <j1 rule="para" parents="8636 5276"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8636(a,2),5912(a,1,1,2))].">
      <j1 rule="para" parents="8636 5912"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8636(a,2),6220(a,1,2))].">
      <j1 rule="para" parents="8636 6220"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(8636(a,1),6221(a,1,1))].">
      <j1 rule="para" parents="8636 6221"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      (x * y) * K(z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x * T(y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8636(a,2),6372(a,1,2))].">
      <j1 rule="para" parents="8636 6372"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(8636(a,2),6127(a,1,1))].">
      <j1 rule="para" parents="8636 6127"/>
    </justification>
  </clause>

  <clause id="8663">
    <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(8636(a,1),6642(a,1,2,2))].">
      <j1 rule="para" parents="8636 6642"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(8636(a,2),7864(a,1,1))].">
      <j1 rule="para" parents="8636 7864"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(8024(a,1),8636(a,1,2))].">
      <j1 rule="para" parents="8024 8636"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8636(a,2),8027(a,1,1))].">
      <j1 rule="para" parents="8636 8027"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8636(a,1),8028(a,1,2))].">
      <j1 rule="para" parents="8636 8028"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8637(a,1),6243(a,1))].">
      <j1 rule="para" parents="8637 6243"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(6584(a,1),8637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6584 8637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      K(x,K(L(y \ 1,z,u) \ 1,w)) = K(L(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(6591(a,1),8637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6591 8637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(8637(a,1),7481(a,1,1))].">
      <j1 rule="para" parents="8637 7481"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(x,K(y,z)) \ y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8645(a,1),5703(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8645 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      (x / y) * K(z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8645(a,1),5917(a,1,2))].">
      <j1 rule="para" parents="8645 5917"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8645(a,1),6243(a,1))].">
      <j1 rule="para" parents="8645 6243"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8647,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8647 5230"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8647(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8647 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      x * K(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(8647(a,1),6219(a,1,2))].">
      <j1 rule="para" parents="8647 6219"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8647(a,1),6243(a,1))].">
      <j1 rule="para" parents="8647 6243"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8647(a,1),7506(a,1,1))].">
      <j1 rule="para" parents="8647 7506"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(8647(a,1),7518(a,1,1))].">
      <j1 rule="para" parents="8647 7518"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      w = u
    ]]></literal>
    <justification jstring="[para(8647(a,1),7537(a,1,1))].">
      <j1 rule="para" parents="8647 7537"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8647(a,1),7556(a,1,1))].">
      <j1 rule="para" parents="8647 7556"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8647(a,1),7873(a,1,1))].">
      <j1 rule="para" parents="8647 7873"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8647(a,1),8032(a,1,2))].">
      <j1 rule="para" parents="8647 8032"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8647(a,1),7883(a,1,1))].">
      <j1 rule="para" parents="8647 7883"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8647(a,1),7970(a,1,1))].">
      <j1 rule="para" parents="8647 7970"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x,K(y,z)) * x = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(8648(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8648 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6116(a,1),8648(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6116 8648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8606,a,b,8623,a)].">
      <j1 rule="hyper" parents="60 8606 8623"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,8624,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5690(a,1),8624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5690 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,8635,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 8635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      x * K(y,K(x,x * z)) = T(x,K(y,z * x))
    ]]></literal>
    <justification jstring="[para(5512(a,1),8638(a,1,2,2))].">
      <j1 rule="para" parents="5512 8638"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,8651,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 8651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,x / y)) / y
    ]]></literal>
    <justification jstring="[hyper(5405,a,8655,a),flip(a)].">
      <j1 rule="hyper" parents="5405 8655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,8616,a(flip),b,8655,a)].">
      <j1 rule="hyper" parents="60 8616 8655"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(7595,a,8700,a),flip(a)].">
      <j1 rule="hyper" parents="7595 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7571,a,8700,a),flip(a)].">
      <j1 rule="hyper" parents="7571 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7523,a,8700,a)].">
      <j1 rule="hyper" parents="7523 8700"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(7504,a,8700,a),flip(a)].">
      <j1 rule="hyper" parents="7504 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6376,a,8700,a)].">
      <j1 rule="hyper" parents="6376 8700"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6233,a,8700,a)].">
      <j1 rule="hyper" parents="6233 8700"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6228,a,8700,a)].">
      <j1 rule="hyper" parents="6228 8700"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8590,a(flip),b,8700,a),flip(a)].">
      <j1 rule="hyper" parents="370 8590 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8587,a(flip),b,8700,a),flip(a)].">
      <j1 rule="hyper" parents="370 8587 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8487,a(flip),b,8700,a),flip(a)].">
      <j1 rule="hyper" parents="370 8487 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8700,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 8700 17"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      K(x,y) * R(T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8700(a,1),274(a,1,2,1))].">
      <j1 rule="para" parents="8700 274"/>
    </justification>
  </clause>

  <clause id="8713">
    <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(8700(a,1),1146(a,1,1))].">
      <j1 rule="para" parents="8700 1146"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(u,z)),y) = w
    ]]></literal>
    <justification jstring="[para(8700(a,1),1146(a,1))].">
      <j1 rule="para" parents="8700 1146"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(8700(a,1),5906(a,1,2))].">
      <j1 rule="para" parents="8700 5906"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8700(a,1),6233(a,1))].">
      <j1 rule="para" parents="8700 6233"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8700(a,1),6226(a,1,1))].">
      <j1 rule="para" parents="8700 6226"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(8700(a,1),7504(a,1))].">
      <j1 rule="para" parents="8700 7504"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8700(a,1),7571(a,1))].">
      <j1 rule="para" parents="8700 7571"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8700(a,1),8588(a,1,1))].">
      <j1 rule="para" parents="8700 8588"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8700(a,1),8589(a,1,1))].">
      <j1 rule="para" parents="8700 8589"/>
    </justification>
  </clause>

  <clause id="8723">
    <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(1162,a,8706,a)].">
      <j1 rule="hyper" parents="1162 8706"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,8587,a,b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="37 8587 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8706,a(flip),b,6182,a)].">
      <j1 rule="hyper" parents="129 8706 6182"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8706(a,1),328(a,1,2))].">
      <j1 rule="para" parents="8706 328"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8706(a,1),6181(a,1,2))].">
      <j1 rule="para" parents="8706 6181"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8706(a,1),6227(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8706 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      K(x,K(y,z)) * z = (1 / K(x,y)) * (z / (K(x,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,7591,a,b,8656,a),flip(a)].">
      <j1 rule="hyper" parents="370 7591 8656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      T(x,K(y,z)) != u \ x
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8672(a,1),45(a,1))].">
      <j1 rule="para" parents="8672 45"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8675(a,1),6998(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8675 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,8692,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5512(a,2),8692(a,1,2))].">
      <j1 rule="para" parents="5512 8692"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(5560(a,1),8692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5560 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8692(a,1),8027(a,1,1))].">
      <j1 rule="para" parents="8692 8027"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      K(x * y,x) * K(z,K(x,y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8692(a,1),8028(a,1,2))].">
      <j1 rule="para" parents="8692 8028"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,8693,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8693 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,8694,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 8694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      K(x,K(y * z,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,8636,a(flip),b,8694,a)].">
      <j1 rule="hyper" parents="60 8636 8694"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      K(x \ y,z) * K(x,K(y,z)) = T(K(x \ y,z),x)
    ]]></literal>
    <justification jstring="[para(8697(a,1),6220(a,1,2))].">
      <j1 rule="para" parents="8697 6220"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8709(a,1),6226(a,1,1))].">
      <j1 rule="para" parents="8709 6226"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      T(T(x,(y \ z) \ 1),K(u,z \ y)) = T(x,T((y \ z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6463(a,1),8709(a,1,2))].">
      <j1 rule="para" parents="6463 8709"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8709(a,2),7333(a,1))].">
      <j1 rule="para" parents="8709 7333"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(109(a,1),8724(a,1,1))].">
      <j1 rule="para" parents="109 8724"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8724(a,1),161(a,1)),flip(a)].">
      <j1 rule="para" parents="8724 161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8724(a,1),6227(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8724 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8077(a,1),8724(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8077 8724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(535,a,8725,a)].">
      <j1 rule="hyper" parents="535 8725"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(32,a,8112,a,b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 8112 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,8015,a,b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 8015 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,8004,a,b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 8004 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      T(K(x,y \ 1),z) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,6894,a,b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 6894 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,8011,a(flip),b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 8011 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      T(K(T(x,y),z),y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(32,a,7997,a(flip),b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="32 7997 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7990(a,1),8725(a,1,1))].">
      <j1 rule="para" parents="7990 8725"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(8019(a,2),8725(a,1,1))].">
      <j1 rule="para" parents="8019 8725"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8161(a,1),8725(a,1,1))].">
      <j1 rule="para" parents="8161 8725"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8125,a,8750,a),flip(a)].">
      <j1 rule="hyper" parents="8125 8750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(6115,a,8750,a),flip(a)].">
      <j1 rule="hyper" parents="6115 8750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      T(K(x,1 / T(y,z)),z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(6093,a,8750,a),flip(a)].">
      <j1 rule="hyper" parents="6093 8750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8291,a,b,8750,a)].">
      <j1 rule="hyper" parents="60 8291 8750"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8750(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8750 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(8283,a,8755,a)].">
      <j1 rule="hyper" parents="8283 8755"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8183,a,8755,a)].">
      <j1 rule="hyper" parents="8183 8755"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8125,a,8755,a),flip(a)].">
      <j1 rule="hyper" parents="8125 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,8755,a)].">
      <j1 rule="hyper" parents="316 8755"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(37,a,8124,a,b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="37 8124 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(37,a,8042,a(flip),b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="37 8042 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,8040,a(flip),b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="37 8040 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(8755(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8755 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8755(a,1),277(a,1,2))].">
      <j1 rule="para" parents="8755 277"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8755(a,1),274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8755 274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8755(a,1),7999(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8755 7999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(T(x,y),z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8303,a,8756,a)].">
      <j1 rule="hyper" parents="8303 8756"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      T(K(T(x,y),z),y) = K((u / (x * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8224,a,b,8756,a),flip(a)].">
      <j1 rule="hyper" parents="370 8224 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,8042,a,b,8756,a)].">
      <j1 rule="hyper" parents="60 8042 8756"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8756(a,1),8039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8756 8039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(8453,a,8763,a)].">
      <j1 rule="hyper" parents="8453 8763"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(8145,a,8763,a),flip(a)].">
      <j1 rule="hyper" parents="8145 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,8068,a,b,8763,a)].">
      <j1 rule="hyper" parents="60 8068 8763"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,8162,a(flip),b,8763,a),flip(a)].">
      <j1 rule="hyper" parents="60 8162 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8763(a,1,2,1))].">
      <j1 rule="para" parents="109 8763"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(262(a,1),8763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5280(a,1),8763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8763(a,1),8145(a,1))].">
      <j1 rule="para" parents="8763 8145"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8766,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 8766 5230"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,z)) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7575,a(flip),b,8766,a)].">
      <j1 rule="hyper" parents="60 7575 8766"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(20(a,2),8766(a,1,1))].">
      <j1 rule="para" parents="20 8766"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8766(a,1,2))].">
      <j1 rule="para" parents="109 8766"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(262(a,1),8766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1641(a,1),8766(a,1,2))].">
      <j1 rule="para" parents="1641 8766"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5280(a,1),8766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(8766(a,2),5265(a,1,2))].">
      <j1 rule="para" parents="8766 5265"/>
    </justification>
  </clause>

  <clause id="8799">
    <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(8766(a,1),6765(a,1,1))].">
      <j1 rule="para" parents="8766 6765"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      R(x,T(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8766(a,1),6808(a,1,3))].">
      <j1 rule="para" parents="8766 6808"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(8766(a,1),8105(a,1,2,2))].">
      <j1 rule="para" parents="8766 8105"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8766(a,1),7938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8766 7938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      R(x,T(y,z),T(K(y,u),w)) = x
    ]]></literal>
    <justification jstring="[para(6087(a,1),8800(a,1,3))].">
      <j1 rule="para" parents="6087 8800"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      x * ((x * K(y,z)) / x) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,8727,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 8727 17"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5512(a,2),8733(a,1,2))].">
      <j1 rule="para" parents="5512 8733"/>
    </justification>
  </clause>

  <clause id="8806">
    <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(82(a,1),8734(a,1,2,2))].">
      <j1 rule="para" parents="82 8734"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,8751,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8751 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8215,a,b,8752,a),flip(a)].">
      <j1 rule="hyper" parents="370 8215 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,8040,a,b,8752,a)].">
      <j1 rule="hyper" parents="60 8040 8752"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(8753(a,1),399(a,1,2,2))].">
      <j1 rule="para" parents="8753 399"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      K(x / y,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(8753(a,1),8303(a,1))].">
      <j1 rule="para" parents="8753 8303"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      T(x,T(y,z)) * (x \ z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7878,a,8758,a)].">
      <j1 rule="hyper" parents="7878 8758"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[hyper(32,a,8392,a,b,8758,a),flip(a)].">
      <j1 rule="hyper" parents="32 8392 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(32,a,6683,a,b,8758,a),flip(a)].">
      <j1 rule="hyper" parents="32 6683 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,8758,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="128 8758 7860"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      (K(x,T(y,z \ 1)) * z) * (1 / z) = ((z \ 1) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8758(a,1),1288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8758 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8758(a,1),880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8758 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8758(a,1),7644(a,1,3))].">
      <j1 rule="para" parents="8758 7644"/>
    </justification>
  </clause>

  <clause id="8826">
    <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(8758(a,1),7517(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8758 7517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(8195,a,8760,a)].">
      <j1 rule="hyper" parents="8195 8760"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ (y * x),y)) = u
    ]]></literal>
    <justification jstring="[para(8760(a,1),8195(a,1))].">
      <j1 rule="para" parents="8760 8195"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(7336,a,8765,a)].">
      <j1 rule="hyper" parents="7336 8765"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,y * z)) = K((y * T(z,u)) / x,z)
    ]]></literal>
    <justification jstring="[para(7372(a,1),8765(a,1,2))].">
      <j1 rule="para" parents="7372 8765"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8159,a(flip),b,8767,a)].">
      <j1 rule="hyper" parents="60 8159 8767"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),8767(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 8767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y * ((y \ 1) \ u))) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[para(1512(a,1),8767(a,1,2,1))].">
      <j1 rule="para" parents="1512 8767"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8768(a,1),390(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8768 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) / x = L(K(y,T(z,x)),u,w)
    ]]></literal>
    <justification jstring="[para(8768(a,1),1233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8768 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(8768(a,1),1234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8768 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(8768(a,1),2443(a,1,1,1))].">
      <j1 rule="para" parents="8768 2443"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,y)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8768(a,1),8202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8768 8202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6431,a,8783,a)].">
      <j1 rule="hyper" parents="6431 8783"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(9(a,2),8783(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8783(a,1),6279(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8783 6279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K((x * y) / x,T(z \ 1,u)) = K(y,T(T(z,u) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,8030,a,b,8784,a)].">
      <j1 rule="hyper" parents="60 8030 8784"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[para(1244(a,2),8784(a,1,1))].">
      <j1 rule="para" parents="1244 8784"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(5484(a,1),8784(a,1,1))].">
      <j1 rule="para" parents="5484 8784"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8784(a,1),8145(a,1))].">
      <j1 rule="para" parents="8784 8145"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(8784(a,1),8217(a,1,1))].">
      <j1 rule="para" parents="8784 8217"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) = K(x,T(L(u,z,y),y * z))
    ]]></literal>
    <justification jstring="[para(13(a,2),8787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13 8787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(8787(a,1),8021(a,1))].">
      <j1 rule="para" parents="8787 8021"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8078,a,8791,a)].">
      <j1 rule="hyper" parents="8078 8791"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      T(T(x,y) \ 1,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4832,a,8851,a),flip(a)].">
      <j1 rule="hyper" parents="4832 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,8851,a(flip),b,8293,a),flip(a)].">
      <j1 rule="hyper" parents="129 8851 8293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8851(a,1,2,1))].">
      <j1 rule="para" parents="109 8851"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(262(a,1),8851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(284(a,1),8851(a,1,2,1))].">
      <j1 rule="para" parents="284 8851"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5280(a,1),8851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,5234,a,b,8795,a)].">
      <j1 rule="hyper" parents="60 5234 8795"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,R((y * z) / y,u,w)) = K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1236(a,2),8795(a,1,2))].">
      <j1 rule="para" parents="1236 8795"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x,(y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8795(a,2),8181(a,1))].">
      <j1 rule="para" parents="8795 8181"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(8797(a,1),5265(a,1,2))].">
      <j1 rule="para" parents="8797 5265"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(6744(a,2),8797(a,1,1))].">
      <j1 rule="para" parents="6744 8797"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8630,a,b,8805,a)].">
      <j1 rule="hyper" parents="60 8630 8805"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(8833(a,1),6580(a,1,1,2))].">
      <j1 rule="para" parents="8833 6580"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      (T(x,y) \ 1) * x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,8852,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8852 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      T(x,y / (y / z)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7320,a(flip),b,8855,a)].">
      <j1 rule="hyper" parents="60 7320 8855"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) = T(x,T(z * (y * y),1 / y))
    ]]></literal>
    <justification jstring="[para(889(a,1),8855(a,1,2,1))].">
      <j1 rule="para" parents="889 8855"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(1236(a,2),8855(a,1,2))].">
      <j1 rule="para" parents="1236 8855"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5340(a,2),8855(a,1,2))].">
      <j1 rule="para" parents="5340 8855"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(6891(a,1),8855(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6891 8855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4783,a,b,8857,a)].">
      <j1 rule="hyper" parents="60 4783 8857"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      ((x * y) / x) \ (z * (y * K(x,y))) = R(T(z,T(y,x)),y,K(x,y))
    ]]></literal>
    <justification jstring="[para(8857(a,1),7129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8857 7129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(74(a,1),8867(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8631(a,2),8617(a,1))].">
      <j1 rule="para" parents="8631 8617"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8637(a,2),8617(a,1))].">
      <j1 rule="para" parents="8637 8617"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8624(a,2),8617(a,1))].">
      <j1 rule="para" parents="8624 8617"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8020(a,2),8674(a,1))].">
      <j1 rule="para" parents="8020 8674"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      K(x,K(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8733(a,2),8674(a,1))].">
      <j1 rule="para" parents="8733 8674"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8805(a,2),8674(a,1))].">
      <j1 rule="para" parents="8805 8674"/>
    </justification>
  </clause>

  <clause id="8890">
    <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(8024(a,1),8678(a,1,2))].">
      <j1 rule="para" parents="8024 8678"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      K(x,K(y / z,T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z \ y)) = w
    ]]></literal>
    <justification jstring="[para(8069(a,2),8678(a,1,2))].">
      <j1 rule="para" parents="8069 8678"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      K(x,K(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8740(a,2),8678(a,1))].">
      <j1 rule="para" parents="8740 8678"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8835(a,1,1,2))].">
      <j1 rule="para" parents="109 8835"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7989(a,2),8835(a,1))].">
      <j1 rule="para" parents="7989 8835"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7990(a,1),8835(a,1))].">
      <j1 rule="para" parents="7990 8835"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      T(K(T(x,y),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8024(a,2),8835(a,1,1))].">
      <j1 rule="para" parents="8024 8835"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8069(a,1),8835(a,1,1))].">
      <j1 rule="para" parents="8069 8835"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = w
    ]]></literal>
    <justification jstring="[para(8755(a,1),8835(a,1,1,2))].">
      <j1 rule="para" parents="8755 8835"/>
    </justification>
  </clause>

  <clause id="8902">
    <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(18(a,1),8847(a,1,2,1))].">
      <j1 rule="para" parents="18 8847"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      K(x,T(L(T(y,z),u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),8847(a,1,2,1))].">
      <j1 rule="para" parents="20 8847"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8847(a,1,2,1))].">
      <j1 rule="para" parents="109 8847"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8069(a,1),8847(a,1))].">
      <j1 rule="para" parents="8069 8847"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8093(a,1),8847(a,1))].">
      <j1 rule="para" parents="8093 8847"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(8072(a,1),8847(a,1))].">
      <j1 rule="para" parents="8072 8847"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(8068(a,2),8847(a,1))].">
      <j1 rule="para" parents="8068 8847"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8408(a,1),8847(a,1))].">
      <j1 rule="para" parents="8408 8847"/>
    </justification>
  </clause>

  <clause id="8912">
    <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(18(a,1),8896(a,1,2))].">
      <j1 rule="para" parents="18 8896"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),8896(a,1,1))].">
      <j1 rule="para" parents="20 8896"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),8896(a,1,2))].">
      <j1 rule="para" parents="20 8896"/>
    </justification>
  </clause>

  <clause id="8915">
    <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(22(a,2),8896(a,1,2))].">
      <j1 rule="para" parents="22 8896"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),8896(a,1,2))].">
      <j1 rule="para" parents="109 8896"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8606(a,1),8604(a,1,1))].">
      <j1 rule="para" parents="8606 8604"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8610(a,2),8122(a,1))].">
      <j1 rule="para" parents="8610 8122"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8009(a,1),8611(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8009 8611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,8072,a(flip),b,8621,a),flip(a)].">
      <j1 rule="hyper" parents="124 8072 8621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(31,a,7516,a,b,8621,a)].">
      <j1 rule="hyper" parents="31 7516 8621"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8621(a,1),40(a,1))].">
      <j1 rule="para" parents="8621 40"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(8120(a,1),8627(a,1,1,2))].">
      <j1 rule="para" parents="8120 8627"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8629(a,1),6236(a,1))].">
      <j1 rule="para" parents="8629 6236"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(8024(a,1),8632(a,1,2,2))].">
      <j1 rule="para" parents="8024 8632"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,z)))
    ]]></literal>
    <justification jstring="[hyper(8617,a,8644,a)].">
      <j1 rule="hyper" parents="8617 8644"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2902,a,8649,a)].">
      <j1 rule="hyper" parents="2902 8649"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8038,a(flip),b,8659,a),flip(a)].">
      <j1 rule="hyper" parents="370 8038 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(8693(a,1),8660(a,1,1))].">
      <j1 rule="para" parents="8693 8660"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(8163(a,1),8665(a,2,2))].">
      <j1 rule="para" parents="8163 8665"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,u) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[para(8684(a,1),6350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8684 6350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8702(a,1),272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8702 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(7506(a,2),8702(a,1,1))].">
      <j1 rule="para" parents="7506 8702"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,x)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7864(a,1),8702(a,1,1))].">
      <j1 rule="para" parents="7864 8702"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = (x \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7873(a,1),8702(a,1,1))].">
      <j1 rule="para" parents="7873 8702"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      K(x,y) * (z / K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6291(a,2),8703(a,1,2))].">
      <j1 rule="para" parents="6291 8703"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * (w * K(y,x))) = T(L(y,z,u) * w,K(x,y))
    ]]></literal>
    <justification jstring="[para(7282(a,1),8703(a,1,2))].">
      <j1 rule="para" parents="7282 8703"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x) * (z * K(x,y))) = L(z * K(x,y),K(y,x),z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8704(a,1),6230(a,1,1))].">
      <j1 rule="para" parents="8704 6230"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = x * T(K(x,1 / (y / z)),u)
    ]]></literal>
    <justification jstring="[para(8345(a,1),8708(a,1,2))].">
      <j1 rule="para" parents="8345 8708"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      ((1 / K(x,y)) * (z / (K(x,y) \ 1))) * K(x,y) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(7591(a,2),8718(a,1,1))].">
      <j1 rule="para" parents="7591 8718"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,8710,a,b,8722,a)].">
      <j1 rule="hyper" parents="370 8710 8722"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,8738,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 8738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8738(a,2),5265(a,1))].">
      <j1 rule="para" parents="8738 5265"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8945(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5690(a,1),8945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5690 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8700,a,b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="370 8700 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      T(x,K(y,y * T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4751,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="370 4751 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,8709,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="60 8709 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      T(K(x * y,x) * z,K(x,y)) = z * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8702,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="60 8702 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      T(K(x,x * T(y,z)),y) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(51,a,8950,a)].">
      <j1 rule="hyper" parents="51 8950"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8700,a,b,8948,a),flip(a)].">
      <j1 rule="hyper" parents="370 8700 8948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8949(a,1),8721(a,1,1))].">
      <j1 rule="para" parents="8949 8721"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      T(x,K(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8949(a,2),8728(a,1))].">
      <j1 rule="para" parents="8949 8728"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      (x * y) \ T(z * (x * y),K(x,y)) = T(z,T(x * y,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,8954,a(flip),b,8710,a(flip))].">
      <j1 rule="hyper" parents="125 8954 8710"/>
    </justification>
  </clause>

  <clause id="8958">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5456,a,8749,a)].">
      <j1 rule="hyper" parents="5456 8749"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,x * z))
    ]]></literal>
    <justification jstring="[para(7325(a,1),8749(a,1,1,2))].">
      <j1 rule="para" parents="7325 8749"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6084,a,b,8754,a)].">
      <j1 rule="hyper" parents="60 6084 8754"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = x \ T(x * K(x / y,z),x)
    ]]></literal>
    <justification jstring="[para(8757(a,2),6637(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8757 6637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(6115,a,8761,a),flip(a)].">
      <j1 rule="hyper" parents="6115 8761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(6093,a,8762,a),flip(a)].">
      <j1 rule="hyper" parents="6093 8762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(545(a,1),8772(a,1,2))].">
      <j1 rule="para" parents="545 8772"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8587(a,1),8772(a,1,2))].">
      <j1 rule="para" parents="8587 8772"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      T(K(x,T(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(8772(a,1),8835(a,1,1))].">
      <j1 rule="para" parents="8772 8835"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),T(y,z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,8776,a,b,6337,a(flip))].">
      <j1 rule="hyper" parents="125 8776 6337"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(8776(a,1),5720(a,2,2))].">
      <j1 rule="para" parents="8776 5720"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(8782(a,2),4920(a,1))].">
      <j1 rule="para" parents="8782 4920"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(8804(a,1),4840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8804 4840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      T(x,T(y,K(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,7889,a,b,8819,a),flip(a)].">
      <j1 rule="hyper" parents="32 7889 8819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8819(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8819 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      T(x,T(y,T(z,x))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8709(a,1),8972(a,1,2))].">
      <j1 rule="para" parents="8709 8972"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8974(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8289,a(flip),b,8820,a),flip(a)].">
      <j1 rule="hyper" parents="60 8289 8820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      (x * K(y,z \ (u \ z))) / (y \ x) = T(y,T((u * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(8559(a,1),8822(a,1,1,2))].">
      <j1 rule="para" parents="8559 8822"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8841(a,1),6675(a,1,3))].">
      <j1 rule="para" parents="8841 6675"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8979(a,1),675(a,1,1))].">
      <j1 rule="para" parents="8979 675"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(147,a,8848,a)].">
      <j1 rule="hyper" parents="147 8848"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,8848,a(flip),b,7861,a(flip))].">
      <j1 rule="hyper" parents="128 8848 7861"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8848(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8848 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * y) * x) = (z * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7340(a,1),8848(a,1,1))].">
      <j1 rule="para" parents="7340 8848"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8063(a,1),8848(a,1,1))].">
      <j1 rule="para" parents="8063 8848"/>
    </justification>
  </clause>

  <clause id="8986">
    <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(8853(a,2),271(a,1,1,1))].">
      <j1 rule="para" parents="8853 271"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      (x / y) * (1 / T(x / y,y)) = ((y \ x) \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8866(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="109 8866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,8697,a(flip),b,8929,a),flip(a)].">
      <j1 rule="hyper" parents="60 8697 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,8094,a,b,8930,a)].">
      <j1 rule="hyper" parents="31 8094 8930"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8930(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8930 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(4849,a,8944,a),flip(a)].">
      <j1 rule="hyper" parents="4849 8944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = x * K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,8960,a,b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8960 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8962(a,1),5698(a,2,2))].">
      <j1 rule="para" parents="8962 5698"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(262(a,1),8963(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="262 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(282(a,1),8963(a,1,2,2,1))].">
      <j1 rule="para" parents="282 8963"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8308,a(flip),b,8975,a),flip(a)].">
      <j1 rule="hyper" parents="370 8308 8975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(74(a,1),8998(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / T(x,y) = T(y,T(y \ z,x))
    ]]></literal>
    <justification jstring="[para(108(a,1),8982(a,1,1,2))].">
      <j1 rule="para" parents="108 8982"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      (x * T(y,z \ y)) / T(x,y) = T(y,T(y * (z \ 1),x))
    ]]></literal>
    <justification jstring="[para(2686(a,1),8982(a,1,1,2))].">
      <j1 rule="para" parents="2686 8982"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(2893(a,1),8993(a,2,2))].">
      <j1 rule="para" parents="2893 8993"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      T((x * y) \ z,K(x,x * y)) = (x * y) \ T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8947(a,1),8993(a,2,2))].">
      <j1 rule="para" parents="8947 8993"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8999(a,1),8594(a,1,2))].">
      <j1 rule="para" parents="8999 8594"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9003(a,1),8721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9003 8721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,L(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),8595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      T(T(x,y) * K(z,y),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(z,y),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8393(a,1),8603(a,1,1))].">
      <j1 rule="para" parents="8393 8603"/>
    </justification>
  </clause>

  <clause id="9009">
    <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(1244(a,2),8790(a,1,1))].">
      <j1 rule="para" parents="1244 8790"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(K(x,y) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(5228(a,1),8790(a,1,1))].">
      <j1 rule="para" parents="5228 8790"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(8059(a,1),8798(a,1))].">
      <j1 rule="para" parents="8059 8798"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),9012(a,1,2,1))].">
      <j1 rule="para" parents="109 9012"/>
    </justification>
  </clause>

  <clause id="9014">
    <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(284(a,1),9012(a,1,2,1))].">
      <j1 rule="para" parents="284 9012"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8597(a,1),9012(a,1))].">
      <j1 rule="para" parents="8597 9012"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x,T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4917(a,1),8895(a,1))].">
      <j1 rule="para" parents="4917 8895"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      K(x \ y,L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y / x,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),8897(a,1,2))].">
      <j1 rule="para" parents="20 8897"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8025(a,2),8897(a,1))].">
      <j1 rule="para" parents="8025 8897"/>
    </justification>
  </clause>

  <clause id="9019">
    <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(4791(a,1),8900(a,1))].">
      <j1 rule="para" parents="4791 8900"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7989(a,2),8900(a,1))].">
      <j1 rule="para" parents="7989 8900"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8812(a,1),8900(a,1))].">
      <j1 rule="para" parents="8812 8900"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      K(x,T(a(y,z,u),y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = w
    ]]></literal>
    <justification jstring="[para(9(a,2),8904(a,1,2,1))].">
      <j1 rule="para" parents="9 8904"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x,L(T(y \ z,u * y),y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * y)) = w
    ]]></literal>
    <justification jstring="[para(661(a,1),8904(a,1,2))].">
      <j1 rule="para" parents="661 8904"/>
    </justification>
  </clause>

  <clause id="9024">
    <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(4867(a,1),8904(a,1,2))].">
      <j1 rule="para" parents="4867 8904"/>
    </justification>
  </clause>

  <clause id="9025">
    <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(8072(a,1),8904(a,1))].">
      <j1 rule="para" parents="8072 8904"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * K(y \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(7501(a,1),8907(a,1,2))].">
      <j1 rule="para" parents="7501 8907"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * z) / y) = u
    ]]></literal>
    <justification jstring="[para(8159(a,1),8911(a,1))].">
      <j1 rule="para" parents="8159 8911"/>
    </justification>
  </clause>

  <clause id="9028">
    <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(8072(a,1),8911(a,1))].">
      <j1 rule="para" parents="8072 8911"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      T(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5692(a,2),8946(a,1,2))].">
      <j1 rule="para" parents="5692 8946"/>
    </justification>
  </clause>

  <clause id="9030">
    <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(7319(a,1),9015(a,1))].">
      <j1 rule="para" parents="7319 9015"/>
    </justification>
  </clause>

  <clause id="9031">
    <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(6939(a,2),9021(a,1))].">
      <j1 rule="para" parents="6939 9021"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      (x \ y) \ (y / (y / x)) = (y / x) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,5837,a,b,8486,a)].">
      <j1 rule="hyper" parents="125 5837 8486"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      (x / (x / y)) \ (x / y) = y \ (x / (x / (x / y)))
    ]]></literal>
    <justification jstring="[hyper(433,a,9032,a),flip(a)].">
      <j1 rule="hyper" parents="433 9032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      (x \ 1) \ ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(1313(a,1),9032(a,1,2))].">
      <j1 rule="para" parents="1313 9032"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(32,a,6275,a,b,8493,a)].">
      <j1 rule="hyper" parents="32 6275 8493"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(9035(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9035 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      K(x \ 1,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(549(a,1),8494(a,2,1,1))].">
      <j1 rule="para" parents="549 8494"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      ((x * y) / x) \ (T(y,z) * ((K(x,y) * K(z,y)) * u)) = L(u,T(y,z) \ ((x * y) / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(8498(a,1),93(a,1,2,2,1))].">
      <j1 rule="para" parents="8498 93"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(7464(a,1),8506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7464 8506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * x) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,7861,a,b,8516,a)].">
      <j1 rule="hyper" parents="60 7861 8516"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(8536(a,1),5958(a,1,1))].">
      <j1 rule="para" parents="8536 5958"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(8542(a,1),308(a,1,2))].">
      <j1 rule="para" parents="8542 308"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(8542(a,1),7336(a,1,2))].">
      <j1 rule="para" parents="8542 7336"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7014(a,1),9044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7014 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),8553(a,1,2,2))].">
      <j1 rule="para" parents="17 8553"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(5741(a,1),9047(a,1,2))].">
      <j1 rule="para" parents="5741 9047"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(406,a,9048,a)].">
      <j1 rule="hyper" parents="406 9048"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(221,a,9048,a)].">
      <j1 rule="hyper" parents="221 9048"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(253(a,2),9048(a,1,1))].">
      <j1 rule="para" parents="253 9048"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y * K(x,y)) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5278(a,1),9048(a,1,1,2))].">
      <j1 rule="para" parents="5278 9048"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,253,a,b,9050,a),flip(a)].">
      <j1 rule="hyper" parents="370 253 9050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(931,a,9053,a)].">
      <j1 rule="hyper" parents="931 9053"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(8540(a,1),9049(a,1,1))].">
      <j1 rule="para" parents="8540 9049"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),9054(a,1,3)),flip(a)].">
      <j1 rule="para" parents="109 9054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(5265,a,8561,a),flip(a)].">
      <j1 rule="hyper" parents="5265 8561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6531,a,9057,a)].">
      <j1 rule="hyper" parents="6531 9057"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      (x * K(y,x)) / (x / y) = x / (T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6525,a(flip),b,8584,a)].">
      <j1 rule="hyper" parents="60 6525 8584"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5362,a(flip),b,8584,a)].">
      <j1 rule="hyper" parents="60 5362 8584"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      T(x * K(x \ (x \ y),x),x \ y) = (x \ y) / ((((x \ y) \ y) \ y) / x)
    ]]></literal>
    <justification jstring="[para(5745(a,1),8584(a,2,2,1))].">
      <j1 rule="para" parents="5745 8584"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(8362(a,1),8585(a,1,1))].">
      <j1 rule="para" parents="8362 8585"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      L((K(x,K(y,z)) \ u) \ (y * w),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(8643(a,1),656(a,2,2))].">
      <j1 rule="para" parents="8643 656"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8650(a,1),6124(a,1,1,2))].">
      <j1 rule="para" parents="8650 6124"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(5688(a,1),8664(a,1,1,2))].">
      <j1 rule="para" parents="5688 8664"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6291(a,2),8671(a,1,2))].">
      <j1 rule="para" parents="6291 8671"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,x * z))
    ]]></literal>
    <justification jstring="[hyper(8640,a,8696,a),flip(a)].">
      <j1 rule="hyper" parents="8640 8696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      T(x,K(y,x * z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(9068(a,1),8718(a,1,1))].">
      <j1 rule="para" parents="9068 8718"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8701(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8701 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,K(x,y))) = w
    ]]></literal>
    <justification jstring="[para(8701(a,1),8181(a,1,1))].">
      <j1 rule="para" parents="8701 8181"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8854(a,1),8743(a,1,1))].">
      <j1 rule="para" parents="8854 8743"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5855,a(flip),b,8759,a),flip(a)].">
      <j1 rule="hyper" parents="370 5855 8759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(6232(a,1),9073(a,1,1))].">
      <j1 rule="para" parents="6232 9073"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[para(8019(a,2),9073(a,1,1))].">
      <j1 rule="para" parents="8019 9073"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      (x / T(y,z)) / (x / y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(147,a,9075,a)].">
      <j1 rule="hyper" parents="147 9075"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      K(x,L(T(T(y,z),z),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),8771(a,1,2))].">
      <j1 rule="para" parents="20 8771"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,w),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(8771(a,1),8835(a,1,1))].">
      <j1 rule="para" parents="8771 8835"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(8779(a,1),8898(a,1))].">
      <j1 rule="para" parents="8779 8898"/>
    </justification>
  </clause>

  <clause id="9080">
    <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(2453(a,1),8780(a,1,2))].">
      <j1 rule="para" parents="2453 8780"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,8560,a(flip),b,8792,a),flip(a)].">
      <j1 rule="hyper" parents="60 8560 8792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <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(2453(a,1),8793(a,1,1))].">
      <j1 rule="para" parents="2453 8793"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8853(a,1),8802(a,1,1))].">
      <j1 rule="para" parents="8853 8802"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7434,a(flip),b,8813,a),flip(a)].">
      <j1 rule="hyper" parents="60 7434 8813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(6949,a,8825,a)].">
      <j1 rule="hyper" parents="6949 8825"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9086(a,1),3199(a,1,1,2))].">
      <j1 rule="para" parents="9086 3199"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(8829(a,1),8011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8829 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8906,a,8846,a)].">
      <j1 rule="hyper" parents="8906 8846"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5444(a,1),8870(a,1,2,1))].">
      <j1 rule="para" parents="5444 8870"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,8009,a(flip),b,8931,a),flip(a)].">
      <j1 rule="hyper" parents="124 8009 8931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <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(8933(a,2),8634(a,1))].">
      <j1 rule="para" parents="8933 8634"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,x)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7273,a(flip),b,8937,a),flip(a)].">
      <j1 rule="hyper" parents="370 7273 8937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8746,a(flip),b,8938,a)].">
      <j1 rule="hyper" parents="60 8746 8938"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(5959,a,9096,a)].">
      <j1 rule="hyper" parents="5959 9096"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      (x \ y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(9097(a,1),5915(a,1))].">
      <j1 rule="para" parents="9097 5915"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(8953(a,1),8291(a,2,1))].">
      <j1 rule="para" parents="8953 8291"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      T(x * K(y,x),K(z,y)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8728,a,8958,a)].">
      <j1 rule="hyper" parents="8728 8958"/>
    </justification>
  </clause>

  <clause id="9101">
    <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(8958(a,2),40(a,1))].">
      <j1 rule="para" parents="8958 40"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8958(a,1),5355(a,1,1))].">
      <j1 rule="para" parents="8958 5355"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8749,a(flip),b,8959,a),flip(a)].">
      <j1 rule="hyper" parents="60 8749 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8700,a,b,9103,a),flip(a)].">
      <j1 rule="hyper" parents="370 8700 9103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),9103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      x * K(K(x * y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6238,a,9104,a)].">
      <j1 rule="hyper" parents="6238 9104"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(9104(a,1),8721(a,1,1))].">
      <j1 rule="para" parents="9104 8721"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      K(x,T((y * z) / y,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8964(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u \ 1)),T((u \ z) * u,u \ 1))) = K(x,T(y,(u \ z) * u))
    ]]></literal>
    <justification jstring="[para(8380(a,1),8965(a,1,2,1,2))].">
      <j1 rule="para" parents="8380 8965"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,8994,a)].">
      <j1 rule="hyper" parents="370 5256 8994"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9058,a(flip),b,9110,a),flip(a)].">
      <j1 rule="hyper" parents="60 9058 9110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5698,a,b,8995,a),flip(a)].">
      <j1 rule="hyper" parents="370 5698 8995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(109(a,1),9112(a,1,2,2,1))].">
      <j1 rule="para" parents="109 9112"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),9005(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 9005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ K(x,z)) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(9006(a,1),328(a,1,2))].">
      <j1 rule="para" parents="9006 328"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,468,a(flip),b,9056,a),flip(a)].">
      <j1 rule="hyper" parents="370 468 9056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(714,a,9116,a)].">
      <j1 rule="hyper" parents="714 9116"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(155,a,9117,a)].">
      <j1 rule="hyper" parents="155 9117"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(5233(a,2),9059(a,1,1))].">
      <j1 rule="para" parents="5233 9059"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,2),9062(a,1,1,2))].">
      <j1 rule="para" parents="5233 9062"/>
    </justification>
  </clause>

  <clause id="9121">
    <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(6873(a,1),9067(a,1,1,2))].">
      <j1 rule="para" parents="6873 9067"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7985,a,9074,a)].">
      <j1 rule="hyper" parents="7985 9074"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) = K(x,L(z / y,u,w))
    ]]></literal>
    <justification jstring="[para(109(a,1),9077(a,1,2,1,1))].">
      <j1 rule="para" parents="109 9077"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      K(x,L((y * z) / y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(262(a,1),9077(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="262 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      K(x,L(y * K(z,y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5280(a,1),9077(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5280 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8605(a,1),9084(a,2,1))].">
      <j1 rule="para" parents="8605 9084"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8783,a(flip),b,9085,a),flip(a)].">
      <j1 rule="hyper" parents="370 8783 9085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(6233,a,9095,a)].">
      <j1 rule="hyper" parents="6233 9095"/>
    </justification>
  </clause>

  <clause id="9129">
    <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(9100(a,2),40(a,1))].">
      <j1 rule="para" parents="9100 40"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(5610,a,9107,a)].">
      <j1 rule="hyper" parents="5610 9107"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      K(x,T(y * K(z,y),u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(5233(a,1),9108(a,1,2,1))].">
      <j1 rule="para" parents="5233 9108"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(5745(a,1),9113(a,1,2,2))].">
      <j1 rule="para" parents="5745 9113"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = ((x * (x \ y)) / x) / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[para(5745(a,1),9119(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5745 9119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9130(a,1),272(a,1,2))].">
      <j1 rule="para" parents="9130 272"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      K(x,T(T(y,z) * K(u,T(y,z)),w)) = K(x,T(T(T(y,u),z),w))
    ]]></literal>
    <justification jstring="[para(18(a,1),9131(a,2,2,1))].">
      <j1 rule="para" parents="18 9131"/>
    </justification>
  </clause>

  <clause id="9136">
    <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(20(a,2),7919(a,1,2))].">
      <j1 rule="para" parents="20 7919"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6291(a,1),8090(a,1))].">
      <j1 rule="para" parents="6291 8090"/>
    </justification>
  </clause>

  <clause id="9139">
    <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(4906(a,1),8189(a,1,2))].">
      <j1 rule="para" parents="4906 8189"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7558(a,1),8219(a,1))].">
      <j1 rule="para" parents="7558 8219"/>
    </justification>
  </clause>

  <clause id="9141">
    <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(104(a,2),9140(a,1,2,1))].">
      <j1 rule="para" parents="104 9140"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / z) = w
    ]]></literal>
    <justification jstring="[para(6468(a,2),9140(a,1))].">
      <j1 rule="para" parents="6468 9140"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(7065(a,2),9140(a,1))].">
      <j1 rule="para" parents="7065 9140"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8821(a,2),9140(a,1))].">
      <j1 rule="para" parents="8821 9140"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      x \ T(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8359(a,2),8238(a,1,2))].">
      <j1 rule="para" parents="8359 8238"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5817,a,8263,a)].">
      <j1 rule="hyper" parents="5817 8263"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a(flip),b,9146,a)].">
      <j1 rule="hyper" parents="370 13 9146"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),9146(a,1,2))].">
      <j1 rule="para" parents="109 9146"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(5753(a,1),9148(a,1,3))].">
      <j1 rule="para" parents="5753 9148"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7989(a,1),8297(a,1,1))].">
      <j1 rule="para" parents="7989 8297"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6420,a(flip),b,8368,a)].">
      <j1 rule="hyper" parents="60 6420 8368"/>
    </justification>
  </clause>

  <clause id="9152">
    <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(8665(a,2),8612(a,1,2))].">
      <j1 rule="para" parents="8665 8612"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(z,y)),y * z) = u
    ]]></literal>
    <justification jstring="[para(8951(a,1),8714(a,1))].">
      <j1 rule="para" parents="8951 8714"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      T(x / T(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x / y) = u
    ]]></literal>
    <justification jstring="[para(5855(a,1),8719(a,1,1))].">
      <j1 rule="para" parents="5855 8719"/>
    </justification>
  </clause>

  <clause id="9156">
    <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(8989(a,2),8890(a,1))].">
      <j1 rule="para" parents="8989 8890"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(545(a,1),8902(a,1,2))].">
      <j1 rule="para" parents="545 8902"/>
    </justification>
  </clause>

  <clause id="9158">
    <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(8739(a,1),8920(a,1,2))].">
      <j1 rule="para" parents="8739 8920"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7989(a,1),9137(a,1,2))].">
      <j1 rule="para" parents="7989 9137"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),9144(a,1,2,1,1))].">
      <j1 rule="para" parents="4 9144"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8289(a,1),9144(a,1))].">
      <j1 rule="para" parents="8289 9144"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(9147(a,1),629(a,1))].">
      <j1 rule="para" parents="9147 629"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(5437(a,2),9163(a,1))].">
      <j1 rule="para" parents="5437 9163"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      K(x,y) * ((1 / x) \ z) = (1 / T(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(5855(a,1),7850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5855 7850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(9036,a,7856,a),flip(a)].">
      <j1 rule="hyper" parents="9036 7856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4790,a(flip),b,9168,a),flip(a)].">
      <j1 rule="hyper" parents="370 4790 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,9168,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 9168 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      K(K(x,y) * z,x) = x / T(x,z)
    ]]></literal>
    <justification jstring="[para(9168(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="9168 5701"/>
    </justification>
  </clause>

  <clause id="9172">
    <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(9168(a,1),5454(a,1,1))].">
      <j1 rule="para" parents="9168 5454"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7500(a,1),9168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      T(x,T(x,y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[para(7858(a,1),9168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      T(x,T(x,y) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="7864 9168"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      T(x,T(y,x) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7873(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="7873 9168"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(9168(a,1),8024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9168 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      T(x \ y,(y / x) \ z) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(8210(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="8210 9168"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(8383(a,1),9168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8383 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8758(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="8758 9168"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8801(a,1),9168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8801 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9183">
    <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(9168(a,1),8897(a,1,2))].">
      <j1 rule="para" parents="9168 8897"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      T(x,y / T(z,x)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9075(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="9075 9168"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,9181,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 9181 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(9181(a,1),273(a,1,2,1))].">
      <j1 rule="para" parents="9181 273"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x * K(y,z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9181(a,1),5752(a,1,2,1))].">
      <j1 rule="para" parents="9181 5752"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6483(a,1),9181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6483 9181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6776(a,1),9181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6776 9181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(9181(a,1),8783(a,1,2))].">
      <j1 rule="para" parents="9181 8783"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = (u * T(x,y)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(9181(a,1),8982(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9181 8982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8654(a,1),9181(a,1,2))].">
      <j1 rule="para" parents="8654 9181"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(9182(a,1),8794(a,1,1))].">
      <j1 rule="para" parents="9182 8794"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,9170,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 9170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7500(a,1),9195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7506(a,2),9195(a,1,2))].">
      <j1 rule="para" parents="7506 9195"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(7858(a,1),9195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),9195(a,1,2))].">
      <j1 rule="para" parents="7864 9195"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(8256(a,1),9195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8256 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(9195(a,1),8630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9195 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8758(a,1),9195(a,1,2))].">
      <j1 rule="para" parents="8758 9195"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8801(a,1),9195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8801 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6584(a,1),9196(a,1,2,1))].">
      <j1 rule="para" parents="6584 9196"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9197(a,1),8610(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9197 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x,y * (z / x)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(5631(a,1),9202(a,1,2))].">
      <j1 rule="para" parents="5631 9202"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6291(a,2),9202(a,1,2))].">
      <j1 rule="para" parents="6291 9202"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6483(a,1),9202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6483 9202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(9202(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9202 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(430(a,1),9203(a,1,2))].">
      <j1 rule="para" parents="430 9203"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(9203(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9203 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(9203(a,1),8363(a,1,1))].">
      <j1 rule="para" parents="9203 8363"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8468,a,9207,a),flip(a)].">
      <j1 rule="hyper" parents="8468 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,9171,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 9171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(9171(a,2),5734(a,1))].">
      <j1 rule="para" parents="9171 5734"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),9215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(9215(a,1),6340(a,1,1))].">
      <j1 rule="para" parents="9215 6340"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7500(a,1),9215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(7864(a,1),9215(a,1,1))].">
      <j1 rule="para" parents="7864 9215"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      K(T(x,y) * z,y) = K(x * z,y)
    ]]></literal>
    <justification jstring="[para(7908(a,1),9215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7908 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(9215(a,1),8605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9215 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8758(a,1),9215(a,1,1))].">
      <j1 rule="para" parents="8758 9215"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(8801(a,1),9215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8801 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(8848(a,1),9215(a,1,1))].">
      <j1 rule="para" parents="8848 9215"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(8098(a,1),9218(a,1,1))].">
      <j1 rule="para" parents="8098 9218"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6130(a,1),9220(a,1,1))].">
      <j1 rule="para" parents="6130 9220"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6128(a,1),9220(a,1,1))].">
      <j1 rule="para" parents="6128 9220"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(8071(a,1),9220(a,1,1,1))].">
      <j1 rule="para" parents="8071 9220"/>
    </justification>
  </clause>

  <clause id="9235">
    <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(9227(a,1),6109(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9227 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6591(a,1),9228(a,1,1,2))].">
      <j1 rule="para" parents="6591 9228"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      K(x * K(y,z \ u),u / z) = K(x,u / z)
    ]]></literal>
    <justification jstring="[para(8058(a,1),9228(a,1,1,2))].">
      <j1 rule="para" parents="8058 9228"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      (x * (T(x,y) / y)) / x = T(x,y \ x) / T(y,x)
    ]]></literal>
    <justification jstring="[para(9176(a,1),5791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9176 5791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9185(a,2),5290(a,1))].">
      <j1 rule="para" parents="9185 5290"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(9016,a,9198,a)].">
      <j1 rule="hyper" parents="9016 9198"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(8404(a,2),9199(a,1,2))].">
      <j1 rule="para" parents="8404 9199"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(9212(a,2),5870(a,1))].">
      <j1 rule="para" parents="9212 5870"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6557,a(flip),b,9229,a),flip(a)].">
      <j1 rule="hyper" parents="370 6557 9229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6459(a,1),9232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6459 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7316(a,1),9232(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7316 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      K(x \ (y / z),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9233(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 9233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9221,a,b,9246,a)].">
      <j1 rule="hyper" parents="370 9221 9246"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),9246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(7481(a,1),9216(a,1,1))].">
      <j1 rule="para" parents="7481 9216"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6483(a,1),9241(a,1,2))].">
      <j1 rule="para" parents="6483 9241"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2218(a,1),9245(a,1,1))].">
      <j1 rule="para" parents="2218 9245"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(6042(a,2),9253(a,1))].">
      <j1 rule="para" parents="6042 9253"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8024,a(flip),b,9177,a),flip(a)].">
      <j1 rule="hyper" parents="370 8024 9177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,9201,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,9201,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      K(x * (y \ z),K(y,y \ u)) = K(u,K(y,x * (z / y)))
    ]]></literal>
    <justification jstring="[para(9206(a,2),8624(a,2,2))].">
      <j1 rule="para" parents="9206 8624"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8631,a(flip),b,9226,a),flip(a)].">
      <j1 rule="hyper" parents="370 8631 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8605,a(flip),b,9226,a),flip(a)].">
      <j1 rule="hyper" parents="370 8605 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <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(9230(a,1),5597(a,1,1,2))].">
      <j1 rule="para" parents="9230 5597"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(7908(a,1),9234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7908 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <literal><![CDATA[
      L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K(y \ (z / x),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(9249(a,1),6105(a,1,1,1,2))].">
      <j1 rule="para" parents="9249 6105"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7500(a,1),9261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 9261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8625(a,1),9261(a,1,2,2))].">
      <j1 rule="para" parents="8625 9261"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8758(a,1),9261(a,1,2,2))].">
      <j1 rule="para" parents="8758 9261"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8383(a,1),9262(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8383 9262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(9266(a,1),6808(a,1,3))].">
      <j1 rule="para" parents="9266 6808"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7150,a,9274,a)].">
      <j1 rule="hyper" parents="7150 9274"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a(flip),b,9270,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 9270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8021,a,9271,a)].">
      <j1 rule="hyper" parents="8021 9271"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6776(a,1),9272(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6776 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(7081(a,1),9272(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7081 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8021,a,9276,a)].">
      <j1 rule="hyper" parents="8021 9276"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8016(a,1),9280(a,1,2))].">
      <j1 rule="para" parents="8016 9280"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      T(K(x,y),z * T(x,u)) = T(K(x,y),z * x)
    ]]></literal>
    <justification jstring="[para(5860(a,1),9281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5860 9281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),9257(a,1,1,2))].">
      <j1 rule="para" parents="17 9257"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K(x * T(y,z \ u),u / z) = K(x * y,u / z)
    ]]></literal>
    <justification jstring="[para(2219(a,1),9237(a,1,1))].">
      <j1 rule="para" parents="2219 9237"/>
    </justification>
  </clause>

  <clause id="9285">
    <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(9268(a,1),5598(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9268 5598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9286">
    <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(9275(a,2),7544(a,1,1))].">
      <j1 rule="para" parents="9275 7544"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      T(K(x,y),(x \ z) * T(x,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8006,a(flip),b,9282,a),flip(a)].">
      <j1 rule="hyper" parents="370 8006 9282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      ((x \ y) * T(x,z)) * T(K(x,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * ((x \ y) * T(x,z)) = w
    ]]></literal>
    <justification jstring="[para(9287(a,1),328(a,1,2))].">
      <j1 rule="para" parents="9287 328"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9213(a,1),449(a,1)),flip(b)].">
      <j1 rule="para" parents="9213 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2218(a,1),9289(a,1,2))].">
      <j1 rule="para" parents="2218 9289"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6765,a(flip),b,9219,a)].">
      <j1 rule="hyper" parents="60 6765 9219"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9215,a(flip),b,9293,a),flip(a)].">
      <j1 rule="hyper" parents="370 9215 9293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(344(a,1),9294(a,1,1))].">
      <j1 rule="para" parents="344 9294"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      T(x,y) * ((1 / x) \ z) = (x * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,8492,a(flip),b,7898,a),flip(a)].">
      <j1 rule="hyper" parents="370 8492 7898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      ((x \ 1) * T(x \ 1,y)) * z = T(x \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(74(a,1),9297(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 9297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6502,a,7904,a)].">
      <j1 rule="hyper" parents="6502 7904"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),9299(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 9299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(9150,a,7925,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9150 7925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9302">
    <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(7925(a,2),9150(a,1))].">
      <j1 rule="para" parents="7925 9150"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4764(a,1),8053(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4764 8053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      T(x / T(y,T(z,x)),y) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,8106,a(flip),b,8087,a),flip(a)].">
      <j1 rule="hyper" parents="370 8106 8087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8851(a,1),9304(a,1,1,2))].">
      <j1 rule="para" parents="8851 9304"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(1498(a,1),8110(a,1,2,2))].">
      <j1 rule="para" parents="1498 8110"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(8199(a,1),6889(a,1,1,1))].">
      <j1 rule="para" parents="8199 6889"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(7436(a,2),8228(a,2,2))].">
      <j1 rule="para" parents="7436 8228"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8248(a,2),6074(a,1))].">
      <j1 rule="para" parents="8248 6074"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7238(a,1),9309(a,1))].">
      <j1 rule="para" parents="7238 9309"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),y) = w
    ]]></literal>
    <justification jstring="[para(9228(a,1),9309(a,1,1))].">
      <j1 rule="para" parents="9228 9309"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2746,a,8251,a)].">
      <j1 rule="hyper" parents="2746 8251"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1824,a,8267,a),flip(a)].">
      <j1 rule="hyper" parents="1824 8267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),z) = w
    ]]></literal>
    <justification jstring="[para(8299(a,1),9012(a,1))].">
      <j1 rule="para" parents="8299 9012"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(7394(a,1),8327(a,1,2))].">
      <j1 rule="para" parents="7394 8327"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = (y \ R(y,x \ 1,y)) / (T(y * (x \ 1),y) / y)
    ]]></literal>
    <justification jstring="[para(9316(a,1),249(a,2,2))].">
      <j1 rule="para" parents="9316 249"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[para(4896(a,1),8342(a,1,2))].">
      <j1 rule="para" parents="4896 8342"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4951(a,1),8343(a,1,2))].">
      <j1 rule="para" parents="4951 8343"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(8346(a,1),708(a,1,1))].">
      <j1 rule="para" parents="8346 708"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,((z * u) \ u) * K(z * u,1 / z))
    ]]></literal>
    <justification jstring="[para(8358(a,2),8352(a,2,2))].">
      <j1 rule="para" parents="8358 8352"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      L(x,L(y,T(z,y),T(z,y)),u) = L(x,z * (z * ((T(z,y) * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(8495(a,1),7134(a,2,2,2))].">
      <j1 rule="para" parents="8495 7134"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      (x \ 1) \ (T(T(x \ 1,x),x) \ y) = (1 / x) \ (T(x \ 1,x) \ y)
    ]]></literal>
    <justification jstring="[para(955(a,1),8496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="955 8496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),8520(a,1,2))].">
      <j1 rule="para" parents="103 8520"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = K(x,y) * ((1 / x) * (x * z))
    ]]></literal>
    <justification jstring="[para(8527(a,1),8250(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8527 8250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * T(x,x \ 1) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(8531(a,1),4532(a,1,1))].">
      <j1 rule="para" parents="8531 4532"/>
    </justification>
  </clause>

  <clause id="9329">
    <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(1500(a,1),8545(a,2,2))].">
      <j1 rule="para" parents="1500 8545"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(8555(a,2),6853(a,2,2))].">
      <j1 rule="para" parents="8555 6853"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8562(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / u) = K(x,(y * ((y \ 1) * z)) / u)
    ]]></literal>
    <justification jstring="[para(8577(a,1),5584(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8577 5584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      (x * (y / (y / z))) / x = y / (y / ((x * z) / x))
    ]]></literal>
    <justification jstring="[para(4(a,1),8582(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 8582"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6281(a,1),8609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 8609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(9150,a,8620,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9150 8620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ R(x,y,x)) = T(K(x,y),z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(7394(a,1),8620(a,1,2))].">
      <j1 rule="para" parents="7394 8620"/>
    </justification>
  </clause>

  <clause id="9337">
    <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(8620(a,2),9150(a,1))].">
      <j1 rule="para" parents="8620 9150"/>
    </justification>
  </clause>

  <clause id="9338">
    <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(8716(a,1),7636(a,1,2))].">
      <j1 rule="para" parents="8716 7636"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,9275,a(flip),b,8731,a),flip(a)].">
      <j1 rule="hyper" parents="370 9275 8731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8636(a,2),8737(a,1,2))].">
      <j1 rule="para" parents="8636 8737"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      K(x \ y,z) * K(x,K(y,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8752,a(flip),b,8742,a),flip(a)].">
      <j1 rule="hyper" parents="370 8752 8742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      K(x \ y,z) * K(y,K(x,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8630(a,1),9342(a,1,2))].">
      <j1 rule="para" parents="8630 9342"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      K(x \ y,z) * K(y,K(x,z)) = K(x \ y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8765,a,b,9343,a),flip(a)].">
      <j1 rule="hyper" parents="370 8765 9343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <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(8764(a,1),386(a,1,2))].">
      <j1 rule="para" parents="8764 386"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1498(a,1),8764(a,1,1))].">
      <j1 rule="para" parents="1498 8764"/>
    </justification>
  </clause>

  <clause id="9347">
    <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(9181(a,1),8775(a,1,1,1,2))].">
      <j1 rule="para" parents="9181 8775"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8636(a,2),8840(a,1,2,1))].">
      <j1 rule="para" parents="8636 8840"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,8859,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 8859 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),8869(a,2,2))].">
      <j1 rule="para" parents="22 8869"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8611,a(flip),b,8921,a),flip(a)].">
      <j1 rule="hyper" parents="370 8611 8921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(6223(a,1),9352(a,1,2))].">
      <j1 rule="para" parents="6223 9352"/>
    </justification>
  </clause>

  <clause id="9354">
    <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(5485(a,1),8928(a,1,2,2,2))].">
      <j1 rule="para" parents="5485 8928"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8751,a(flip),b,8932,a),flip(a)].">
      <j1 rule="hyper" parents="370 8751 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8932(a,2),8895(a,1))].">
      <j1 rule="para" parents="8932 8895"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8680,a,9355,a)].">
      <j1 rule="hyper" parents="8680 9355"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      K(x,K(y,z)) * u != K(x,z / y)
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(9355(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="9355 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ z) = K(y,z / x)
    ]]></literal>
    <justification jstring="[para(8630(a,1),9355(a,1,1))].">
      <j1 rule="para" parents="8630 9355"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8636(a,1),9355(a,1,1))].">
      <j1 rule="para" parents="8636 9355"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      K(x,K(y * z,(y * u) * z)) * K(x,R(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(5349(a,2),9357(a,1,2,2))].">
      <j1 rule="para" parents="5349 9357"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) = K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(8630(a,1),9357(a,1,1))].">
      <j1 rule="para" parents="8630 9357"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x / z) = K(y,z \ x)
    ]]></literal>
    <justification jstring="[para(8636(a,1),9357(a,1,1))].">
      <j1 rule="para" parents="8636 9357"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8648(a,1),9357(a,1,1))].">
      <j1 rule="para" parents="8648 9357"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      K(x,K(y,z * (u * (z \ x)))) * K(y,L(T(u,z \ x),z \ x,z)) = K(y,(z * (u * (z \ x))) / x)
    ]]></literal>
    <justification jstring="[para(1032(a,2),9359(a,1,2,2))].">
      <j1 rule="para" parents="1032 9359"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(9359(a,1),8681(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9359 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y * z)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(8358(a,2),9360(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8358 9360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      K(x,K(y,x / (1 / (1 / z)))) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(3693(a,2),9362(a,2,2))].">
      <j1 rule="para" parents="3693 9362"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(y,z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6236,a,9364,a)].">
      <j1 rule="hyper" parents="6236 9364"/>
    </justification>
  </clause>

  <clause id="9370">
    <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(8025(a,1),9364(a,1,1,2))].">
      <j1 rule="para" parents="8025 9364"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) * K(x,K(y * (z * u),y * z)) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),9369(a,2,2))].">
      <j1 rule="para" parents="13 9369"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,2401,a(flip),b,8980,a),flip(a)].">
      <j1 rule="hyper" parents="60 2401 8980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9373">
    <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(370,a,5031,a,b,8984,a),flip(a)].">
      <j1 rule="hyper" parents="370 5031 8984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(60,a,6090,a(flip),b,8997,a)].">
      <j1 rule="hyper" parents="60 6090 8997"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      (T(x,T(x \ y,z)) * z) \ (z * ((x \ y) \ y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(9001(a,1),6324(a,1,1,1))].">
      <j1 rule="para" parents="9001 6324"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(109(a,2),9043(a,1,1))].">
      <j1 rule="para" parents="109 9043"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4441(a,1),9055(a,1,1))].">
      <j1 rule="para" parents="4441 9055"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5256(a,2),9064(a,1,1))].">
      <j1 rule="para" parents="5256 9064"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) / x,y) = u
    ]]></literal>
    <justification jstring="[para(9090(a,2),40(a,1))].">
      <j1 rule="para" parents="9090 40"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8786,a,b,9091,a)].">
      <j1 rule="hyper" parents="370 8786 9091"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7354,a,9380,a),flip(a)].">
      <j1 rule="hyper" parents="7354 9380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9381(a,1,1,1,1))].">
      <j1 rule="para" parents="5 9381"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(9122(a,1),7066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9122 7066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(661(a,2),9123(a,1,2))].">
      <j1 rule="para" parents="661 9123"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      L(x \ y,x \ y,x \ y) = T(x \ y,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1321,a(flip),b,9178,a)].">
      <j1 rule="hyper" parents="370 1321 9178"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6856,a,b,9178,a)].">
      <j1 rule="hyper" parents="60 6856 9178"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      T(x \ y,(y / x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(9178(a,2),6462(a,1))].">
      <j1 rule="para" parents="9178 6462"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      T(x,T(y * K(x,z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8982,a(flip),b,9192,a),flip(a)].">
      <j1 rule="hyper" parents="370 8982 9192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(6483(a,1),9389(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6483 9389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8610,a(flip),b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="370 8610 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      x * K(y / z,(z \ y) \ x) = (y / z) * (x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(129,a,9243,a(flip),b,5765,a)].">
      <j1 rule="hyper" parents="129 9243 5765"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(87(a,1),9279(a,1,2,2,1))].">
      <j1 rule="para" parents="87 9279"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[para(6447(a,1),9284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6447 9284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9218,a(flip),b,9296,a),flip(a)].">
      <j1 rule="hyper" parents="370 9218 9296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),9396(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 9396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6776(a,1),9396(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6776 9396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[para(8011(a,1),9396(a,1,1,1))].">
      <j1 rule="para" parents="8011 9396"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8766(a,1),9396(a,1,1,1,2))].">
      <j1 rule="para" parents="8766 9396"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9398(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9398 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(x \ K(y,z),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(7550,a,9400,a)].">
      <j1 rule="hyper" parents="7550 9400"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) * (y \ K(u,z)) = T(y \ K(u,z),K(x,z))
    ]]></literal>
    <justification jstring="[para(9403(a,1),8639(a,1,1,2))].">
      <j1 rule="para" parents="9403 8639"/>
    </justification>
  </clause>

  <clause id="9405">
    <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(2610(a,1),9331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2610 9331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <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(2635(a,1),9331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2635 9331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9407">
    <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(7398(a,1),9334(a,1,1))].">
      <j1 rule="para" parents="7398 9334"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x,T(y,z)) * (T(x,y) \ u) = K(x,K(y,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(7858(a,1),9335(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 9335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(8741(a,1),9335(a,1,1))].">
      <j1 rule="para" parents="8741 9335"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(31,a,8028,a,b,9344,a)].">
      <j1 rule="hyper" parents="31 8028 9344"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8674,a,9410,a)].">
      <j1 rule="hyper" parents="8674 9410"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,9410,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = x * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,9410,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 9410 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8606,a,b,9411,a),flip(a)].">
      <j1 rule="hyper" parents="370 8606 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9411(a,2),8617(a,1))].">
      <j1 rule="para" parents="9411 8617"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      K(x \ y,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8668,a,9412,a)].">
      <j1 rule="hyper" parents="8668 9412"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),9412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 9412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ x)
    ]]></literal>
    <justification jstring="[para(9412(a,1),8610(a,1,2))].">
      <j1 rule="para" parents="9412 8610"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      K(x \ y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,9416,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 9416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8617,a,9419,a)].">
      <j1 rule="hyper" parents="8617 9419"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ y) = T(z \ y,K(x,y))
    ]]></literal>
    <justification jstring="[para(9419(a,1),8687(a,1,1))].">
      <j1 rule="para" parents="9419 8687"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8735,a,b,9420,a)].">
      <j1 rule="hyper" parents="60 8735 9420"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8678,a,9422,a)].">
      <j1 rule="hyper" parents="8678 9422"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8674,a,9422,a)].">
      <j1 rule="hyper" parents="8674 9422"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8668,a,9422,a)].">
      <j1 rule="hyper" parents="8668 9422"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,9422,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,9422,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 9422 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),9422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(8340(a,1),9422(a,1,2))].">
      <j1 rule="para" parents="8340 9422"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8347(a,2),9422(a,1,2))].">
      <j1 rule="para" parents="8347 9422"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(9422(a,1),8610(a,1,2))].">
      <j1 rule="para" parents="9422 8610"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,9423,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),9423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6410(a,1),9423(a,1,2))].">
      <j1 rule="para" parents="6410 9423"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6865(a,1),9424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6865 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7363,a,9425,a),flip(a)].">
      <j1 rule="hyper" parents="7363 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5517,a,9425,a)].">
      <j1 rule="hyper" parents="5517 9425"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8636,a(flip),b,9425,a),flip(a)].">
      <j1 rule="hyper" parents="370 8636 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      L(K(x \ 1,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,6586,a,b,9425,a)].">
      <j1 rule="hyper" parents="60 6586 9425"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9426(a,2),8678(a,1))].">
      <j1 rule="para" parents="9426 8678"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(6600(a,2),9432(a,1,2))].">
      <j1 rule="para" parents="6600 9432"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8668,a,9433,a)].">
      <j1 rule="hyper" parents="8668 9433"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      (1 / x) * K(y,K(x,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9433(a,1),8655(a,1,2))].">
      <j1 rule="para" parents="9433 8655"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9433(a,2),8678(a,1))].">
      <j1 rule="para" parents="9433 8678"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8668,a,9436,a)].">
      <j1 rule="hyper" parents="8668 9436"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,6132,a(flip),b,9437,a)].">
      <j1 rule="hyper" parents="60 6132 9437"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9437(a,2),8678(a,1))].">
      <j1 rule="para" parents="9437 8678"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(9438(a,2),8674(a,1))].">
      <j1 rule="para" parents="9438 8674"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,9413,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8677,a(flip),b,9413,a),flip(a)].">
      <j1 rule="hyper" parents="370 8677 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      (K(x \ y,z) * y) \ T(y,K(x,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,9449,a(flip),b,6296,a)].">
      <j1 rule="hyper" parents="125 9449 6296"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),9450(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 9450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(9453(a,1),6132(a,2,1,1))].">
      <j1 rule="para" parents="9453 6132"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,9427,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8677,a(flip),b,9427,a),flip(a)].">
      <j1 rule="hyper" parents="370 8677 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9427(a,2),5265(a,1))].">
      <j1 rule="para" parents="9427 5265"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8728,a,9455,a)].">
      <j1 rule="hyper" parents="8728 9455"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,9455,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 9455 17"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(9455(a,1),8603(a,1))].">
      <j1 rule="para" parents="9455 8603"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8728,a,9456,a)].">
      <j1 rule="hyper" parents="8728 9456"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6463(a,1),9456(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6463 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9459(a,2),8728(a,1))].">
      <j1 rule="para" parents="9459 8728"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      T(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9462(a,2),8728(a,1))].">
      <j1 rule="para" parents="9462 8728"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(9430(a,2),8678(a,1))].">
      <j1 rule="para" parents="9430 8678"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(9434(a,1),8678(a,1))].">
      <j1 rule="para" parents="9434 8678"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8945,a(flip),b,9463,a),flip(a)].">
      <j1 rule="hyper" parents="370 8945 9463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(9463(a,1),8728(a,1))].">
      <j1 rule="para" parents="9463 8728"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      T(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9463(a,2),8946(a,1))].">
      <j1 rule="para" parents="9463 8946"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),9468(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 9468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(8340(a,1),9440(a,1,2))].">
      <j1 rule="para" parents="8340 9440"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      T(K(x,y),z \ x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8612,a,9418,a),flip(a)].">
      <j1 rule="hyper" parents="8612 9418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8552,a,9473,a)].">
      <j1 rule="hyper" parents="8552 9473"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8122,a,9473,a)].">
      <j1 rule="hyper" parents="8122 9473"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,9474,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 9474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4791,a(flip),b,9474,a),flip(a)].">
      <j1 rule="hyper" parents="370 4791 9474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8374,a,9474,a(flip))].">
      <j1 rule="hyper" parents="8374 9474"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = T(K(x,y),u \ z)
    ]]></literal>
    <justification jstring="[para(6446(a,1),9474(a,1,2))].">
      <j1 rule="para" parents="6446 9474"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9474(a,2),8122(a,1))].">
      <j1 rule="para" parents="9474 8122"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,9475,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 9475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8546,a,9477,a)].">
      <j1 rule="hyper" parents="8546 9477"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,8160,a(flip),b,9477,a),flip(a)].">
      <j1 rule="hyper" parents="60 8160 9477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,9477,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 9477 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),9477(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 9477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),9477(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 9477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(9479(a,2),8021(a,1))].">
      <j1 rule="para" parents="9479 8021"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),9484(a,1,2,2))].">
      <j1 rule="para" parents="4 9484"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8160,a(flip),b,9478,a)].">
      <j1 rule="hyper" parents="60 8160 9478"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(9480(a,2),8122(a,1))].">
      <j1 rule="para" parents="9480 8122"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(200(a,1),9485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="200 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(201(a,1),9485(a,2,2))].">
      <j1 rule="para" parents="201 9485"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,9486,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 9486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9486(a,2),5265(a,1))].">
      <j1 rule="para" parents="9486 5265"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(9058(a,1),9481(a,1,2))].">
      <j1 rule="para" parents="9058 9481"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(9348(a,1),4868(a,1,1,2,1))].">
      <j1 rule="para" parents="9348 4868"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(5835(a,1),9351(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5835 9351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9391,a(flip),b,9353,a),flip(a)].">
      <j1 rule="hyper" parents="370 9391 9353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6291(a,1),9500(a,1,2))].">
      <j1 rule="para" parents="6291 9500"/>
    </justification>
  </clause>

  <clause id="9503">
    <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(9502(a,1),9339(a,1,2))].">
      <j1 rule="para" parents="9502 9339"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6657,a(flip),b,9399,a),flip(a)].">
      <j1 rule="hyper" parents="370 6657 9399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,9402,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 9402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = x * K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,9505,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 9505 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6281(a,1),9505(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6281 9505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6282(a,1),9505(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6282 9505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7996(a,1),9505(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7996 9505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7997(a,1),9505(a,1,2,1))].">
      <j1 rule="para" parents="7997 9505"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(8071(a,1),9505(a,1,2,1,2))].">
      <j1 rule="para" parents="8071 9505"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      K(x,((y * K(z,x)) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(7081(a,1),9507(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7081 9507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(9(a,2),9509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,9506,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 9506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6770(a,1),9514(a,1,2,1))].">
      <j1 rule="para" parents="6770 9514"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7997(a,1),9514(a,1,2,1))].">
      <j1 rule="para" parents="7997 9514"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9425(a,1),9439(a,1,1))].">
      <j1 rule="para" parents="9425 9439"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(9438(a,1),9439(a,1,1))].">
      <j1 rule="para" parents="9438 9439"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,9518,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 9518 13"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9518,a(flip),b,9519,a),flip(a)].">
      <j1 rule="hyper" parents="60 9518 9519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8634,a,9522,a)].">
      <j1 rule="hyper" parents="8634 9522"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,9522,a)].">
      <j1 rule="hyper" parents="370 8630 9522"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(w,K(x,(z * y) \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),9522(a,2,2,2))].">
      <j1 rule="para" parents="344 9522"/>
    </justification>
  </clause>

  <clause id="9526">
    <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(9522(a,2),8634(a,1))].">
      <j1 rule="para" parents="9522 8634"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(L(y,u,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(9522(a,2),8674(a,1))].">
      <j1 rule="para" parents="9522 8674"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(3388(a,1),9524(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3388 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(6561(a,1),9441(a,2,2))].">
      <j1 rule="para" parents="6561 9441"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(R(1 / y,y,x),z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(9051(a,1),9452(a,1,1,1,1))].">
      <j1 rule="para" parents="9051 9452"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9491(a,1),7131(a,1,2))].">
      <j1 rule="para" parents="9491 7131"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9493(a,1),5376(a,1,2))].">
      <j1 rule="para" parents="9493 5376"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(8129,a,9494,a)].">
      <j1 rule="hyper" parents="8129 9494"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(9508(a,1),7530(a,1,2,2))].">
      <j1 rule="para" parents="9508 7530"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(353(a,1),9512(a,1,2,1,1))].">
      <j1 rule="para" parents="353 9512"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(7500(a,1),7852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 7852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1029,a,8264,a),flip(a)].">
      <j1 rule="hyper" parents="1029 8264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(8264(a,1),1029(a,1))].">
      <j1 rule="para" parents="8264 1029"/>
    </justification>
  </clause>

  <clause id="9540">
    <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(370,a,7255,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="370 7255 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(253(a,2),8369(a,1,2))].">
      <j1 rule="para" parents="253 8369"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(8023(a,1),8419(a,1,2))].">
      <j1 rule="para" parents="8023 8419"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7420,a,9544,a),flip(a)].">
      <j1 rule="hyper" parents="7420 9544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,9545,a)].">
      <j1 rule="hyper" parents="316 9545"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9316(a,1),9546(a,1,1))].">
      <j1 rule="para" parents="9316 9546"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(8467,a,9495,a),flip(a)].">
      <j1 rule="hyper" parents="8467 9495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      T(x * L(L(y,z,u),w,v5),T(y,x)) = T(x * L(L(y,z,u),w,v5),y)
    ]]></literal>
    <justification jstring="[para(247(a,1),9548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 9548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(7873(a,1),8482(a,1))].">
      <j1 rule="para" parents="7873 8482"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ R((z \ u) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(1651(a,2),9550(a,1))].">
      <j1 rule="para" parents="1651 9550"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),8570(a,1,2))].">
      <j1 rule="para" parents="17 8570"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(x,K(z,y)) \ y
    ]]></literal>
    <justification jstring="[hyper(8622,a,9421,a),flip(a)].">
      <j1 rule="hyper" parents="8622 9421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      T((K(x,y) * z) \ y,K(x,y)) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(7464(a,1),9553(a,2,1))].">
      <j1 rule="para" parents="7464 9553"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8673,a,9443,a)].">
      <j1 rule="hyper" parents="8673 9443"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      T(1 / x,K(y,z)) \ 1 = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(215,a,9555,a)].">
      <j1 rule="hyper" parents="215 9555"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7501(a,1),9555(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7501 9555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = T(x,K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),9556(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 9556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      a(T(x \ 1,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(9558(a,2),2973(a,1,1))].">
      <j1 rule="para" parents="9558 2973"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8745,a,9471,a),flip(a)].">
      <j1 rule="hyper" parents="8745 9471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9471(a,1),8745(a,1))].">
      <j1 rule="para" parents="9471 8745"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8714,a,9560,a)].">
      <j1 rule="hyper" parents="8714 9560"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(1146,a,9560,a)].">
      <j1 rule="hyper" parents="1146 9560"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(982,a,9562,a),flip(a)].">
      <j1 rule="hyper" parents="982 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(6224(a,1),9562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6224 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(8706(a,1),9562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8706 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(((z \ 1) \ 1) \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(5580(a,1),9567(a,1,1,2))].">
      <j1 rule="para" parents="5580 9567"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,x / (y / z))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5828,a,9565,a)].">
      <j1 rule="hyper" parents="5828 9565"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(9477(a,1),9045(a,1))].">
      <j1 rule="para" parents="9477 9045"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      T(x / T(y \ z,y),K(y,z)) = K(y,y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(9155,a,8945,a),flip(a)].">
      <j1 rule="hyper" parents="9155 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <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(8648(a,1),9526(a,1))].">
      <j1 rule="para" parents="8648 9526"/>
    </justification>
  </clause>

  <clause id="9574">
    <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(9518(a,2),9526(a,1))].">
      <j1 rule="para" parents="9518 9526"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,9531,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="125 9531 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,9531,a(flip),b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="125 9531 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9531(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9531 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(x,y) * K(y * R(x,z,u),x) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,9532,a(flip),b,7839,a),flip(a)].">
      <j1 rule="hyper" parents="125 9532 7839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,9532,a(flip),b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="125 9532 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9580">
    <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(8630(a,1),9574(a,1,1))].">
      <j1 rule="para" parents="8630 9574"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,7831,a)].">
      <j1 rule="hyper" parents="625 7831"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(4914(a,1),7831(a,1,1))].">
      <j1 rule="para" parents="4914 7831"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7539,a(flip),b,9582,a)].">
      <j1 rule="hyper" parents="60 7539 9582"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      (K(x,y) * (1 / x)) * z = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,7849,a),flip(a)].">
      <j1 rule="hyper" parents="144 7849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(6369(a,1),9586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6369 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      ((K(x,x \ 1) / x) * y) / (1 / x) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(9588(a,1),4525(a,1,1))].">
      <j1 rule="para" parents="9588 4525"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7864(a,1),9588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      L(x \ (T(x,y) * z),x,x) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,586,a,b,9590,a)].">
      <j1 rule="hyper" parents="370 586 9590"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = L(K(x,y) * z,x,x)
    ]]></literal>
    <justification jstring="[para(7857(a,1),9591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7857 9591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ (K(y,z) * T(y,z))
    ]]></literal>
    <justification jstring="[para(4913(a,1),7865(a,2,2))].">
      <j1 rule="para" parents="4913 7865"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5507,a,7917,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5507 7917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5508,a,7918,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5508 7918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      x / (K(y,T(x,z)) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8789(a,1),7936(a,1,2,1))].">
      <j1 rule="para" parents="8789 7936"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(z,T(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,9596,a)].">
      <j1 rule="hyper" parents="215 9596"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8024(a,2),9597(a,2,1))].">
      <j1 rule="para" parents="8024 9597"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,2),9598(a,1,1,1))].">
      <j1 rule="para" parents="5233 9598"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2894,a,b,9599,a),flip(a)].">
      <j1 rule="hyper" parents="370 2894 9599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9601">
    <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(2451(a,1),9600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2451 9600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(77(a,1),7949(a,1,1,2,1))].">
      <j1 rule="para" parents="77 7949"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5688(a,1),7959(a,1,2,1))].">
      <j1 rule="para" parents="5688 7959"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(u,w) * z)) \ (w * (T(T(w,u),u) \ z)))) = K(x,y * ((z \ 1) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(9604(a,1),6622(a,1,2,2,2))].">
      <j1 rule="para" parents="9604 6622"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      (K(x,y) * z) \ (y * (T(T(y,x),x) \ u)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[para(9604(a,1),7564(a,1,2))].">
      <j1 rule="para" parents="9604 7564"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(4756(a,1),8207(a,1,1))].">
      <j1 rule="para" parents="4756 8207"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9184,a(flip),b,8280,a),flip(a)].">
      <j1 rule="hyper" parents="370 9184 8280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4443,a(flip),b,9610,a),flip(a)].">
      <j1 rule="hyper" parents="370 4443 9610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      x / (y * (z * (u * T(u \ (z \ (y \ x)),w)))) = K(w,x / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(1352(a,1),8341(a,1,2,2))].">
      <j1 rule="para" parents="1352 8341"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      x / (y * (((z \ ((y \ x) * u)) * z) / u)) = K(z,x / (y * (z / u)))
    ]]></literal>
    <justification jstring="[para(2395(a,1),8341(a,1,2,2))].">
      <j1 rule="para" parents="2395 8341"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,4835,a(flip),b,8388,a),flip(a)].">
      <j1 rule="hyper" parents="370 4835 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7960,a(flip),b,8395,a),flip(a)].">
      <j1 rule="hyper" parents="370 7960 8395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(8483(a,1),5108(a,1,2))].">
      <j1 rule="para" parents="8483 5108"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) * (K(x,w) * u) = K(x,w) * T(u,K(x,y))
    ]]></literal>
    <justification jstring="[para(9263(a,2),8521(a,1,1))].">
      <j1 rule="para" parents="9263 8521"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ (y / x) = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),8525(a,1,1,1))].">
      <j1 rule="para" parents="109 8525"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(108(a,2),8556(a,1,2,2,1))].">
      <j1 rule="para" parents="108 8556"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = K(x,y * K(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8996,a(flip),b,8557,a)].">
      <j1 rule="hyper" parents="60 8996 8557"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6090,a(flip),b,9620,a),flip(a)].">
      <j1 rule="hyper" parents="60 6090 9620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(6849(a,1),9621(a,1,2,2))].">
      <j1 rule="para" parents="6849 9621"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,8602,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 8602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(9623(a,1),8603(a,1))].">
      <j1 rule="para" parents="9623 8603"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6591(a,1),8607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6591 8607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9580,a,9625,a),flip(a)].">
      <j1 rule="hyper" parents="9580 9625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(w,L(x,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(9625(a,1),9580(a,1))].">
      <j1 rule="para" parents="9625 9580"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6584(a,1),8608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6584 8608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,((x / y) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8653(a,1,2,1))].">
      <j1 rule="para" parents="7 8653"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6584(a,1),8669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6584 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9628,a,b,9630,a)].">
      <j1 rule="hyper" parents="60 9628 9630"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8630(a,1),9631(a,1,1))].">
      <j1 rule="para" parents="8630 9631"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      x * R(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9632(a,2),5265(a,1,2))].">
      <j1 rule="para" parents="9632 5265"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,L(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6591(a,1),8670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6591 8670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9627,a,9634,a),flip(a)].">
      <j1 rule="hyper" parents="9627 9634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9625,a,b,9634,a)].">
      <j1 rule="hyper" parents="60 9625 9634"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6340(a,1),9635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6340 9635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) * y = T(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(9636(a,2),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9636 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * y = T(y,L(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(9518(a,1),9638(a,1,1))].">
      <j1 rule="para" parents="9518 9638"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8641,a,9639,a),flip(a)].">
      <j1 rule="hyper" parents="8641 9639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(9639(a,1),8641(a,1))].">
      <j1 rule="para" parents="9639 8641"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8793,a(flip),b,8799,a),flip(a)].">
      <j1 rule="hyper" parents="370 8793 8799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,w),y) = v5
    ]]></literal>
    <justification jstring="[para(8799(a,2),8913(a,1))].">
      <j1 rule="para" parents="8799 8913"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9642(a,1,2))].">
      <j1 rule="para" parents="107 9642"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5650,a,9645,a),flip(a)].">
      <j1 rule="hyper" parents="5650 9645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z))
    ]]></literal>
    <justification jstring="[para(8766(a,1),9645(a,1,1))].">
      <j1 rule="para" parents="8766 9645"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(106(a,1),9643(a,1,2,2))].">
      <j1 rule="para" parents="106 9643"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      L(K(x,y),x * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(107(a,1),9643(a,1,2))].">
      <j1 rule="para" parents="107 9643"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z),u)) = K(x,T(T(y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(8790,a,8844,a)].">
      <j1 rule="hyper" parents="8790 8844"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      K(x,T(T((y / z) \ 1,z),u)) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),9651(a,2,2,1,1))].">
      <j1 rule="para" parents="109 9651"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(5233(a,1),8858(a,1,1,1,2))].">
      <j1 rule="para" parents="5233 8858"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,x \ y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(104(a,1),8862(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8628,a,8925,a),flip(a)].">
      <j1 rule="hyper" parents="8628 8925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9655(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8766(a,1),8968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8766 8968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      L(x,y * ((K(z,u) * T(z,w)) \ 1),v5) = L(x,y * (K(u,z) / T(z,w)),v5)
    ]]></literal>
    <justification jstring="[para(9658(a,1),3784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9658 3784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9658(a,1),6482(a,1,1))].">
      <j1 rule="para" parents="9658 6482"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      ((x \ y) \ 1) * (y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),8987(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 8987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) * K((x \ y) \ 1,y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,1702,a,b,9662,a)].">
      <j1 rule="hyper" parents="60 1702 9662"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8982,a(flip),b,9002,a),flip(a)].">
      <j1 rule="hyper" parents="60 8982 9002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      (x * y) \ T(z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) \ z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(9004(a,1),8956(a,1))].">
      <j1 rule="para" parents="9004 8956"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5760(a,1),9052(a,1,2))].">
      <j1 rule="para" parents="5760 9052"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,5298,a(flip),b,9666,a),flip(a)].">
      <j1 rule="hyper" parents="370 5298 9666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(8709(a,1),9066(a,2,1))].">
      <j1 rule="para" parents="8709 9066"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(9103(a,1),9069(a,1,1))].">
      <j1 rule="para" parents="9103 9069"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7756,a(flip),b,9082,a),flip(a)].">
      <j1 rule="hyper" parents="60 7756 9082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * T(y,z),u)) = w
    ]]></literal>
    <justification jstring="[para(9099(a,2),8122(a,1))].">
      <j1 rule="para" parents="9099 8122"/>
    </justification>
  </clause>

  <clause id="9673">
    <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(8631(a,1),9126(a,2,2))].">
      <j1 rule="para" parents="8631 9126"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5497(a,2),9134(a,1,2))].">
      <j1 rule="para" parents="5497 9134"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9401,a(flip),b,9191,a)].">
      <j1 rule="hyper" parents="60 9401 9191"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8906,a,9675,a),flip(a)].">
      <j1 rule="hyper" parents="8906 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(7081(a,1),9676(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7081 9676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7996(a,1),9678(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7996 9678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7997(a,1),9678(a,1,1,2,1))].">
      <j1 rule="para" parents="7997 9678"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      K(R(R(x,K(y,z),u),K(y,z) * u,w),z) = K((((x * K(y,z)) * u) * w) / (u * w),z)
    ]]></literal>
    <justification jstring="[para(685(a,1),9680(a,1,1))].">
      <j1 rule="para" parents="685 9680"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9511,a(flip),b,9194,a)].">
      <j1 rule="hyper" parents="60 9511 9194"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8916,a,9682,a),flip(a)].">
      <j1 rule="hyper" parents="8916 9682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(87(a,1),9683(a,1,2,2))].">
      <j1 rule="para" parents="87 9683"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),9683(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6281 9683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(7467(a,1),9683(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7467 9683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(104(a,2),9685(a,2,2)),flip(a)].">
      <j1 rule="para" parents="104 9685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(7081(a,1),9686(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7081 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,5694,a(flip),b,9688,a)].">
      <j1 rule="hyper" parents="60 5694 9688"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(87(a,1),9689(a,1,2,2,1))].">
      <j1 rule="para" parents="87 9689"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(353(a,1),9689(a,1,2,2,1))].">
      <j1 rule="para" parents="353 9689"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7996(a,1),9689(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7996 9689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7997(a,1),9689(a,1,2,2,1))].">
      <j1 rule="para" parents="7997 9689"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      K(x,R(R(y,K(z,x),u),K(z,x) * u,w)) = K(x,(((y * K(z,x)) * u) * w) / (u * w))
    ]]></literal>
    <justification jstring="[para(685(a,1),9694(a,1,2))].">
      <j1 rule="para" parents="685 9694"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(x * (y \ z),K(y,y \ u)) = K(K(u,y),x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8605,a,b,9264,a),flip(a)].">
      <j1 rule="hyper" parents="370 8605 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      ((x \ 1) * T(x \ 1,x \ (x \ y))) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7723(a,1),9298(a,2,1))].">
      <j1 rule="para" parents="7723 9298"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(9313(a,1),5740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9313 5740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5892,a(flip),b,9698,a),flip(a)].">
      <j1 rule="hyper" parents="370 5892 9698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(5742,a,9699,a),flip(a)].">
      <j1 rule="hyper" parents="5742 9699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5742,a,9700,a),flip(a)].">
      <j1 rule="hyper" parents="5742 9700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),9701(a,1,2,1))].">
      <j1 rule="para" parents="4 9701"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(77(a,1),9701(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 9701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y \ 1)) = T(x,(((y \ 1) \ z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4974(a,1),9703(a,1,2,2))].">
      <j1 rule="para" parents="4974 9703"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      T(x,(L(y,z,y) * z) \ 1) = T(x,y / (y * (z * y)))
    ]]></literal>
    <justification jstring="[para(5524(a,1),9703(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5524 9703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      T(x,(y \ 1) \ (y / z)) = T(x,(y * y) / z)
    ]]></literal>
    <justification jstring="[hyper(6497,a,9704,a)].">
      <j1 rule="hyper" parents="6497 9704"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6647,a(flip),b,9704,a),flip(a)].">
      <j1 rule="hyper" parents="370 6647 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(5935(a,1),9704(a,1,2))].">
      <j1 rule="para" parents="5935 9704"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(9704(a,1),9481(a,1,2))].">
      <j1 rule="para" parents="9704 9481"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9111,a(flip),b,9710,a),flip(a)].">
      <j1 rule="hyper" parents="60 9111 9710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9318,a(flip),b,9319,a),flip(a)].">
      <j1 rule="hyper" parents="60 9318 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5835(a,1),9349(a,1,2,1))].">
      <j1 rule="para" parents="5835 9349"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(6979(a,1),9377(a,2,2))].">
      <j1 rule="para" parents="6979 9377"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      L((x * (K(y,x) / T(x,z))) \ u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(9384(a,1),656(a,1,1,1))].">
      <j1 rule="para" parents="9384 656"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(((x * (y * x)) / x) / y,T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(1916(a,1),9393(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1916 9393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      K(x,T(y,z)) * (T(x,y) \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,8683,a(flip),b,9408,a),flip(a)].">
      <j1 rule="hyper" parents="370 8683 9408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7289(a,1),9584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7289 9584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,9719,a(flip),b,7935,a)].">
      <j1 rule="hyper" parents="129 9719 7935"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5677(a,1),9593(a,2,2))].">
      <j1 rule="para" parents="5677 9593"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(77(a,1),9602(a,2,2,1,2))].">
      <j1 rule="para" parents="77 9602"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5916,a,9722,a)].">
      <j1 rule="hyper" parents="5916 9722"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6281(a,1),9722(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 9722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,7,a(flip),b,9725,a),flip(a)].">
      <j1 rule="hyper" parents="128 7 9725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6833,a(flip),b,9727,a),flip(a)].">
      <j1 rule="hyper" parents="60 6833 9727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      R(x / T(y,z),y,y) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2741,a,9723,a)].">
      <j1 rule="hyper" parents="2741 9723"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(214(a,1),9729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="214 9729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      R(x,(y * z) * T(y,z),u) = R(x,R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(9730(a,1),2760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9730 2760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      L(x,(y * z) * T(y,z),u) = L(x,R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(9730(a,1),3778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9730 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <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(9609(a,1),691(a,1))].">
      <j1 rule="para" parents="9609 691"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(9140,a,9614,a)].">
      <j1 rule="hyper" parents="9140 9614"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(8377(a,1),9734(a,1,2))].">
      <j1 rule="para" parents="8377 9734"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6878,a,b,9735,a)].">
      <j1 rule="hyper" parents="370 6878 9735"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(9735(a,2),7555(a,1,1))].">
      <j1 rule="para" parents="9735 7555"/>
    </justification>
  </clause>

  <clause id="9738">
    <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(128,a,9615,a,b,8848,a)].">
      <j1 rule="hyper" parents="128 9615 8848"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9621,a(flip),b,9622,a),flip(a)].">
      <j1 rule="hyper" parents="60 9621 9622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(60,a,9374,a(flip),b,9739,a),flip(a)].">
      <j1 rule="hyper" parents="60 9374 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(8182,a,9740,a),flip(a)].">
      <j1 rule="hyper" parents="8182 9740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(9647(a,2),8913(a,1))].">
      <j1 rule="para" parents="9647 8913"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) * z = z * K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(9652(a,1),8109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9652 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(155,a,9653,a)].">
      <j1 rule="hyper" parents="155 9653"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      T(x * (y / z),K(u,z)) \ (x * (y / z)) = K(x * (z \ y),K(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5699,a(flip),b,9696,a)].">
      <j1 rule="hyper" parents="370 5699 9696"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(9709(a,1),6505(a,1,2))].">
      <j1 rule="para" parents="9709 6505"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9745(a,1),7511(a,1,2))].">
      <j1 rule="para" parents="9745 7511"/>
    </justification>
  </clause>

  <clause id="9749">
    <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(9745(a,1),7520(a,1,2))].">
      <j1 rule="para" parents="9745 7520"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = ((u * x) / u) / ((u * (x * K(y,T(x,z)))) / u)
    ]]></literal>
    <justification jstring="[para(8025(a,1),9748(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8025 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <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(9679(a,1),9748(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9679 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (K(x * y,z) * ((x * y) * u)) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(7896(a,1),660(a,1,1))].">
      <j1 rule="para" parents="7896 660"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8249,a(flip),b,7912,a),flip(a)].">
      <j1 rule="hyper" parents="60 8249 7912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(9311,a,9753,a),flip(a)].">
      <j1 rule="hyper" parents="9311 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7629,a(flip),b,9753,a),flip(a)].">
      <j1 rule="hyper" parents="60 7629 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      K(R(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7628,a(flip),b,9753,a),flip(a)].">
      <j1 rule="hyper" parents="60 7628 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9753(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      R(R(K(x,y),z,u),x * w,v5) = R(K(R(x,w,v5),y),z,u)
    ]]></literal>
    <justification jstring="[para(9753(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9753 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(8120(a,1),9753(a,1,1))].">
      <j1 rule="para" parents="8120 9753"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      K(R(x,K(x,y) * (x \ z),u),w) = R(K(x,w),K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(7892(a,1),9753(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7892 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      K(x,y) * R(x,z,R(x,u,w)) = T(R(x,z,R(x,u,w)),y)
    ]]></literal>
    <justification jstring="[para(9755(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9755 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * K(w,R(x,y,R(x,z,u))) = (K(x,w) / R(x,y,R(x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(9755(a,1),5968(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9755 5968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(R(x,u,L(T(x,y),w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(8910,a,9756,a),flip(a)].">
      <j1 rule="hyper" parents="8910 9756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,700,a(flip),b,9757,a),flip(a)].">
      <j1 rule="hyper" parents="370 700 9757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(9757(a,2),103(a,1,1))].">
      <j1 rule="para" parents="9757 103"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),9757(a,1,1))].">
      <j1 rule="para" parents="100 9757"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(9757(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9757 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7754,a(flip),b,9764,a),flip(a)].">
      <j1 rule="hyper" parents="370 7754 9764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9228,a(flip),b,9754,a),flip(a)].">
      <j1 rule="hyper" parents="370 9228 9754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      K(R(R(x,K(y,z),u),w,v5),z) = K(R(x,w,v5),z)
    ]]></literal>
    <justification jstring="[para(26(a,1),9769(a,1,1))].">
      <j1 rule="para" parents="26 9769"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(77(a,1),9766(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 9766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9772(a,2,1,2))].">
      <j1 rule="para" parents="7 9772"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(8031(a,1),9772(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8031 9772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8363,a(flip),b,9773,a),flip(a)].">
      <j1 rule="hyper" parents="60 8363 9773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6690,a(flip),b,9775,a),flip(a)].">
      <j1 rule="hyper" parents="370 6690 9775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(9775(a,2),8459(a,1))].">
      <j1 rule="para" parents="9775 8459"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      K(R(x,y,L(T(x,z),u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(8896,a,9763,a),flip(a)].">
      <j1 rule="hyper" parents="8896 9763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(9778(a,1),5770(a,2,1,1))].">
      <j1 rule="para" parents="9778 5770"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      T(x,R(y,z,L(T(y,u),w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5770,a,b,9780,a),flip(a)].">
      <j1 rule="hyper" parents="370 5770 9780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9753,a(flip),b,9759,a),flip(a)].">
      <j1 rule="hyper" parents="60 9753 9759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,9782,a,b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="126 9782 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      K(x,y) * R(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,22,a,b,9761,a),flip(a)].">
      <j1 rule="hyper" parents="370 22 9761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5869,a,9783,a),flip(a)].">
      <j1 rule="hyper" parents="5869 9783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9786">
    <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="[hyper(125,a,9784,a(flip),b,7892,a),flip(a)].">
      <j1 rule="hyper" parents="125 9784 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (y * R(T(x,y),z,R(x,u,w))) * x
    ]]></literal>
    <justification jstring="[para(9784(a,1),8275(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9784 8275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7294(a,1),7913(a,1,1))].">
      <j1 rule="para" parents="7294 7913"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(150,a,9788,a)].">
      <j1 rule="hyper" parents="150 9788"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,9789,a(flip),b,7892,a),flip(a)].">
      <j1 rule="hyper" parents="125 9789 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,9789,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="125 9789 7860"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      T(x,K(y,z)) \ R(x,u,x) = x \ R(T(x,K(y,z)),u,x)
    ]]></literal>
    <justification jstring="[hyper(8685,a,9790,a)].">
      <j1 rule="hyper" parents="8685 9790"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8030,a,b,8054,a),flip(a)].">
      <j1 rule="hyper" parents="370 8030 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9193(a,1),8190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9193 8190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8170,a(flip),b,9794,a),flip(a)].">
      <j1 rule="hyper" parents="370 8170 9794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8598,a(flip),b,9795,a)].">
      <j1 rule="hyper" parents="60 8598 9795"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8261,a(flip),b,9797,a)].">
      <j1 rule="hyper" parents="60 8261 9797"/>
    </justification>
  </clause>

  <clause id="9800">
    <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(8270(a,1),5796(a,1,1))].">
      <j1 rule="para" parents="8270 5796"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      T(x,x \ 1) * ((x * x) \ y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(8439,a,8364,a)].">
      <j1 rule="hyper" parents="8439 8364"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      T(x,y) * ((x * x) \ z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(8439,a,8250,a)].">
      <j1 rule="hyper" parents="8439 8250"/>
    </justification>
  </clause>

  <clause id="9803">
    <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(8505(a,2),8181(a,1))].">
      <j1 rule="para" parents="8505 8181"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6457,a(flip),b,8544,a),flip(a)].">
      <j1 rule="hyper" parents="370 6457 8544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),9804(a,1,2,2,1))].">
      <j1 rule="para" parents="7 9804"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,9806,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 9806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9807(a,1),308(a,1,2))].">
      <j1 rule="para" parents="9807 308"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4441(a,1),9808(a,2,2))].">
      <j1 rule="para" parents="4441 9808"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(8011(a,1),8838(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8011 8838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      x * (K(y,x) * K(x,T(z,y))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(8861,a,7845,a),flip(a)].">
      <j1 rule="hyper" parents="8861 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(7404,a,9811,a)].">
      <j1 rule="hyper" parents="7404 9811"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7518,a,9812,a)].">
      <j1 rule="hyper" parents="7518 9812"/>
    </justification>
  </clause>

  <clause id="9814">
    <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(9812(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9812 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      K(x \ y,x) * T(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5279(a,1),9813(a,1,2,1))].">
      <j1 rule="para" parents="5279 9813"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      (x / y) * T(y \ x,T(z,y)) = (y \ x) * T(x / y,z)
    ]]></literal>
    <justification jstring="[para(9815(a,1),8481(a,1,2))].">
      <j1 rule="para" parents="9815 8481"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      (x / y) * T(y \ x,z \ y) = (y \ x) * T(x / y,y / z)
    ]]></literal>
    <justification jstring="[para(7314(a,1),9816(a,1,2))].">
      <j1 rule="para" parents="7314 9816"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(8912,a,9083,a),flip(a)].">
      <j1 rule="hyper" parents="8912 9083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = K(x,x \ 1) * (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(9145,a,7064,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9145 7064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(9229(a,1),9210(a,2,2))].">
      <j1 rule="para" parents="9229 9210"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9822(a,2),7601(a,1))].">
      <j1 rule="para" parents="9822 7601"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5572(a,1),9306(a,1,2))].">
      <j1 rule="para" parents="5572 9306"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(9345,a,6184,a),flip(a)].">
      <j1 rule="hyper" parents="9345 6184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(5355,a,9826,a),flip(a)].">
      <j1 rule="hyper" parents="5355 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9828">
    <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(982,a,9826,a)].">
      <j1 rule="hyper" parents="982 9826"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,9827,a),flip(a)].">
      <j1 rule="hyper" parents="31 5256 9827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9830">
    <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(880(a,1),9513(a,1,2))].">
      <j1 rule="para" parents="880 9513"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6092,a(flip),b,9830,a),flip(a)].">
      <j1 rule="hyper" parents="60 6092 9830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,9831,a)].">
      <j1 rule="hyper" parents="53 9831"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(51,a,9833,a)].">
      <j1 rule="hyper" parents="51 9833"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,9833,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 9833 17"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9833(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9833 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9833(a,1),7997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9833 7997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9836(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="9836 5311"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9834(a,1),7997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9834 7997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(7518,a,9575,a)].">
      <j1 rule="hyper" parents="7518 9575"/>
    </justification>
  </clause>

  <clause id="9841">
    <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(9575(a,1),2896(a,1))].">
      <j1 rule="para" parents="9575 2896"/>
    </justification>
  </clause>

  <clause id="9842">
    <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(9578(a,1),2896(a,1))].">
      <j1 rule="para" parents="9578 2896"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(77(a,1),9747(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 9747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(8254,a,9793,a),flip(a)].">
      <j1 rule="hyper" parents="8254 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9793(a,1),645(a,1)),flip(b)].">
      <j1 rule="para" parents="9793 645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <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(60,a,6883,a,b,9844,a)].">
      <j1 rule="hyper" parents="60 6883 9844"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      x * K(y,T((x \ z) \ 1,u)) = K(y,T(x / z,u)) * x
    ]]></literal>
    <justification jstring="[para(9844(a,2),8580(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9844 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,7622,a(flip),b,9818,a)].">
      <j1 rule="hyper" parents="60 7622 9818"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9849(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      K(x,T(y,z / L(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9007,a,b,9851,a)].">
      <j1 rule="hyper" parents="60 9007 9851"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(213(a,1),9852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="213 9852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(727(a,1),9852(a,1,2,2))].">
      <j1 rule="para" parents="727 9852"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9278,a(flip),b,9854,a)].">
      <j1 rule="hyper" parents="60 9278 9854"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),9856(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9858">
    <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(9857(a,1),8904(a,1))].">
      <j1 rule="para" parents="9857 8904"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8774,a,9825,a)].">
      <j1 rule="hyper" parents="8774 9825"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7075,a(flip),b,7943,a)].">
      <j1 rule="hyper" parents="60 7075 7943"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,9861,a)].">
      <j1 rule="hyper" parents="51 9861"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      x / ((y \ z) * (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      ((y \ z) * (z \ y)) \ x = u
    ]]></literal>
    <justification jstring="[para(9861(a,1),369(a,1,2))].">
      <j1 rule="para" parents="9861 369"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),9864(a,1,2,1))].">
      <j1 rule="para" parents="4 9864"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,9868,a),flip(a)].">
      <j1 rule="hyper" parents="4977 9868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,9868,a)].">
      <j1 rule="hyper" parents="52 9868"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(51,a,9868,a)].">
      <j1 rule="hyper" parents="51 9868"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(251(a,2),9871(a,1,1,2))].">
      <j1 rule="para" parents="251 9871"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9088,a(flip),b,9873,a)].">
      <j1 rule="hyper" parents="60 9088 9873"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9874(a,1),2944(a,1,1))].">
      <j1 rule="para" parents="9874 2944"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(9242(a,1),7981(a,2,1))].">
      <j1 rule="para" parents="9242 7981"/>
    </justification>
  </clause>

  <clause id="9878">
    <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(6638(a,1),9877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6638 9877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8024,a(flip),b,8062,a),flip(a)].">
      <j1 rule="hyper" parents="370 8024 8062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      K(L(x,y,z),u) \ K(L(x,y,z),T(u,z * y)) = K(z * (y * x),K(L(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(125,a,8164,a(flip),b,8684,a)].">
      <j1 rule="hyper" parents="125 8164 8684"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(7836(a,1),8196(a,2,2))].">
      <j1 rule="para" parents="7836 8196"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x \ 1) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(202(a,1),8304(a,1,2))].">
      <j1 rule="para" parents="202 8304"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) \ z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9884(a,1),7953(a,1,1))].">
      <j1 rule="para" parents="9884 7953"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) \ z) = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(8448,a,9886,a)].">
      <j1 rule="hyper" parents="8448 9886"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      (x / y) * ((T(x / y,y) \ 1) \ z) = (y \ x) * (((x / y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 9887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ (z * (K(y,z) * x)) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8784,a(flip),b,8332,a),flip(a)].">
      <j1 rule="hyper" parents="370 8784 8332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),K(x * (y \ 1),x)) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(3494(a,1),8339(a,1,1))].">
      <j1 rule="para" parents="3494 8339"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(8406(a,1),5942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8406 5942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6037,a(flip),b,9891,a),flip(a)].">
      <j1 rule="hyper" parents="370 6037 9891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5580,a(flip),b,9892,a),flip(a)].">
      <j1 rule="hyper" parents="370 5580 9892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      L(K(x,T(y,z)),x,u) = (x * z) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(8446,a,8503,a),flip(a)].">
      <j1 rule="hyper" parents="8446 8503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6463(a,1),8507(a,2,2))].">
      <j1 rule="para" parents="6463 8507"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5575(a,1),9895(a,2,2))].">
      <j1 rule="para" parents="5575 9895"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(155,a,9896,a)].">
      <j1 rule="hyper" parents="155 9896"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(32,a,6573,a(flip),b,9897,a),flip(a)].">
      <j1 rule="hyper" parents="32 6573 9897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(135,a,9898,a)].">
      <j1 rule="hyper" parents="135 9898"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(8684(a,1),9899(a,1,2,2))].">
      <j1 rule="para" parents="8684 9899"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      L(x,y,z) \ T(x,x \ 1) = (x \ (L(x,y,z) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(4579,a,8539,a)].">
      <j1 rule="hyper" parents="4579 8539"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      L(x,y,z) \ T(x,x \ 1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2169(a,1),9901(a,2,1))].">
      <j1 rule="para" parents="2169 9901"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      T(T(x,y \ z),K(u,y \ z)) = T(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(6446(a,1),8744(a,1,1))].">
      <j1 rule="para" parents="6446 8744"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(8748,a,9903,a),flip(a)].">
      <j1 rule="hyper" parents="8748 9903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,y)) = K((y * T(z,u)) / x,z)
    ]]></literal>
    <justification jstring="[hyper(8456,a,8831,a)].">
      <j1 rule="hyper" parents="8456 8831"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8783(a,1),8843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8783 8843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(9906(a,1),401(a,1))].">
      <j1 rule="para" parents="9906 401"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(9907,a,6858,a),flip(a)].">
      <j1 rule="hyper" parents="9907 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(5426(a,1),9908(a,1,2))].">
      <j1 rule="para" parents="5426 9908"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(8221(a,1),9909(a,2,2))].">
      <j1 rule="para" parents="8221 9909"/>
    </justification>
  </clause>

  <clause id="9911">
    <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(8935(a,1),8519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8935 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      T(x,T((y * z) \ z,u)) = T(x,T(z \ (y \ z),u))
    ]]></literal>
    <justification jstring="[hyper(8973,a,8977,a),flip(a)].">
      <j1 rule="hyper" parents="8973 8977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,7789,a(flip),b,9046,a),flip(a)].">
      <j1 rule="hyper" parents="370 7789 9046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1771(a,1),9913(a,1,1))].">
      <j1 rule="para" parents="1771 9913"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3921,a,b,9914,a),flip(a)].">
      <j1 rule="hyper" parents="370 3921 9914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3287,a,9915,a)].">
      <j1 rule="hyper" parents="3287 9915"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = (1 / L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,3954,a,b,9916,a),flip(a)].">
      <j1 rule="hyper" parents="370 3954 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(221,a,9916,a)].">
      <j1 rule="hyper" parents="221 9916"/>
    </justification>
  </clause>

  <clause id="9919">
    <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(9916(a,1),311(a,1,1))].">
      <j1 rule="para" parents="9916 311"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (x \ 1) = ((x \ 1) \ ((y * x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(251(a,1),9916(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="251 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ (u * w)) = ((L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u)) * w
    ]]></literal>
    <justification jstring="[para(9916(a,1),1565(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9916 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),x \ L(x,y,z),x) = R(L(x,y,z) \ (x * 1),u,w)
    ]]></literal>
    <justification jstring="[para(9916(a,1),1077(a,1,1,1))].">
      <j1 rule="para" parents="9916 1077"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ ((1 / (x \ L(x,y,z))) \ u)) = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(9916(a,1),2071(a,1,1))].">
      <j1 rule="para" parents="9916 2071"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = R(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9916(a,1),2759(a,1,2))].">
      <j1 rule="para" parents="9916 2759"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ L(x,y,z),u) = ((x \ L(x,y,z)) \ u) / u
    ]]></literal>
    <justification jstring="[para(9916(a,1),2786(a,1,1))].">
      <j1 rule="para" parents="9916 2786"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ 1 = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(3823(a,1),9916(a,1,1))].">
      <j1 rule="para" parents="3823 9916"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L((x \ L(x,y,z)) \ 1,u,w) \ v5) = (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(9916(a,1),4017(a,1,1))].">
      <j1 rule="para" parents="9916 4017"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      L((x \ 1) \ y,z,u) \ ((x \ 1) \ y) = ((x \ y) \ L(x \ y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(3970(a,1),9916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3970 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(9918(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9918 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,2783,a(flip),b,9924,a),flip(a)].">
      <j1 rule="hyper" parents="60 2783 9924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      L(x,x,y) \ x = ((x \ 1) \ ((y * x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(4081,a,9920,a)].">
      <j1 rule="hyper" parents="4081 9920"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      L(x,x,y) \ x = (x * ((y * x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(3992(a,1),9932(a,2,1))].">
      <j1 rule="para" parents="3992 9932"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8532,a(flip),b,9072,a),flip(a)].">
      <j1 rule="hyper" parents="370 8532 9072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,9934,a(flip),b,7839,a)].">
      <j1 rule="hyper" parents="125 9934 7839"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),w)) = K(x,T(T(T(z,y),u),w))
    ]]></literal>
    <justification jstring="[para(5314(a,2),9135(a,1,2,1))].">
      <j1 rule="para" parents="5314 9135"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5955,a,9186,a)].">
      <j1 rule="hyper" parents="5955 9186"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(7018,a,9247,a)].">
      <j1 rule="hyper" parents="7018 9247"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,8528,a(flip),b,9303,a),flip(a)].">
      <j1 rule="hyper" parents="60 8528 9303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      R(K(x,y),x * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7912(a,1),9310(a,1))].">
      <j1 rule="para" parents="7912 9310"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9759(a,1),9941(a,1))].">
      <j1 rule="para" parents="9759 9941"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      x \ T(x * ((1 / x) \ y),x) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(7243,a,9328,a)].">
      <j1 rule="hyper" parents="7243 9328"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = ((1 / x) \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(553(a,1),9943(a,1,2,1))].">
      <j1 rule="para" parents="553 9943"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[para(945(a,1),9944(a,2,1))].">
      <j1 rule="para" parents="945 9944"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      x \ T((x * x) * y,x) = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2874,a(flip),b,9945,a),flip(a)].">
      <j1 rule="hyper" parents="370 2874 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / u) = K(x,L(z,y,y) / u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),9332(a,2,2,1))].">
      <j1 rule="para" parents="2074 9332"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(9152,a,9354,a),flip(a)].">
      <j1 rule="hyper" parents="9152 9354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(9030,a,9948,a),flip(a)].">
      <j1 rule="hyper" parents="9030 9948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ K(u,y)) = T(z \ K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(9423(a,1),9404(a,1,1))].">
      <j1 rule="para" parents="9423 9404"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,z)) = T(x,K(u,z)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8622,a,9950,a),flip(a)].">
      <j1 rule="hyper" parents="8622 9950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8234,a(flip),b,9409,a),flip(a)].">
      <j1 rule="hyper" parents="60 8234 9409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9953">
    <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(8019(a,2),9503(a,1,2))].">
      <j1 rule="para" parents="8019 9503"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9414,a(flip),b,9529,a),flip(a)].">
      <j1 rule="hyper" parents="370 9414 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(77(a,1),9954(a,1,2,2,1,2))].">
      <j1 rule="para" parents="77 9954"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6059,a,9955,a)].">
      <j1 rule="hyper" parents="6059 9955"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      T(T(x / T(y \ 1,y),K(y,1)),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(9571(a,2),6993(a,1,1))].">
      <j1 rule="para" parents="9571 6993"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      ((1 / x) * y) / (x \ 1) = ((x \ 1) * y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1725(a,1),9589(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1725 9589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9959">
    <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(5537(a,1),9594(a,1,2))].">
      <j1 rule="para" parents="5537 9594"/>
    </justification>
  </clause>

  <clause id="9960">
    <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(5537(a,1),9595(a,1,2))].">
      <j1 rule="para" parents="5537 9595"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(9616(a,1),3637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9616 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      L(x,(y \ K(y,z)) * T(y,u),w) = L(x,K(y,z) * K(y,u),w)
    ]]></literal>
    <justification jstring="[para(9616(a,1),5163(a,1,2))].">
      <j1 rule="para" parents="9616 5163"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(6291(a,1),9687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6291 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9785(a,1),9714(a,2,2))].">
      <j1 rule="para" parents="9785 9714"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9349,a,b,9964,a)].">
      <j1 rule="hyper" parents="370 9349 9964"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9351,a(flip),b,9965,a),flip(a)].">
      <j1 rule="hyper" parents="60 9351 9965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9499,a,b,9966,a)].">
      <j1 rule="hyper" parents="60 9499 9966"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      T(x,R((y \ z) \ z,u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(108(a,1),9967(a,1,2,1))].">
      <j1 rule="para" parents="108 9967"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      T(x,R(((y / T(1 / z,u)) \ 1) \ K(z,z \ 1),w,v5)) = T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(6899(a,1),9968(a,1,2,1,1))].">
      <j1 rule="para" parents="6899 9968"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(788,a,9737,a)].">
      <j1 rule="hyper" parents="788 9737"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(32,a,9847,a(flip),b,9744,a),flip(a)].">
      <j1 rule="hyper" parents="32 9847 9744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4441(a,1),9809(a,1,1))].">
      <j1 rule="para" parents="4441 9809"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(109(a,1),9972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="109 9972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      T(x \ T(y,x \ 1),x * x) = ((x \ 1) \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3631,a(flip),b,9820,a),flip(a)].">
      <j1 rule="hyper" parents="370 3631 9820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      T(x \ T(x * y,x \ 1),x * x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,4994,a(flip),b,9974,a),flip(a)].">
      <j1 rule="hyper" parents="370 4994 9974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = T(T(x * K(z * T(x,v5),x),w),u) \ T(T(x,w),u)
    ]]></literal>
    <justification jstring="[para(9251(a,1),9880(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9251 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),K(y \ x,x)) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(5993(a,1),9890(a,1,2))].">
      <j1 rule="para" parents="5993 9890"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),K(x,y)) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(9470,a,9977,a)].">
      <j1 rule="hyper" parents="9470 9977"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      L(x \ (y \ x),z,u) \ (x \ (y \ x)) = (x \ (L(y,z,u) * (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(876(a,1),9926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="876 9926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,9940,a(flip),b,9935,a),flip(a)].">
      <j1 rule="hyper" parents="370 9940 9935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y))
    ]]></literal>
    <justification jstring="[para(9938(a,1),608(a,1,2))].">
      <j1 rule="para" parents="9938 608"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5996,a(flip),b,9939,a),flip(a)].">
      <j1 rule="hyper" parents="370 5996 9939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9656,a(flip),b,9949,a)].">
      <j1 rule="hyper" parents="60 9656 9949"/>
    </justification>
  </clause>

  <clause id="9984">
    <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(9983(a,1),8122(a,1))].">
      <j1 rule="para" parents="9983 8122"/>
    </justification>
  </clause>

  <clause id="9985">
    <literal><![CDATA[
      T(T(x / (1 / y),K(y,1)),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(955(a,1),9957(a,1,1,1,2))].">
      <j1 rule="para" parents="955 9957"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      T(T(x / (1 / y),1),y) = T((1 / y) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(223(a,1),9985(a,1,1,2))].">
      <j1 rule="para" parents="223 9985"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[para(222(a,1),9986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="222 9986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      (x \ 1) \ T(y,x * x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4319,a(flip),b,9987,a)].">
      <j1 rule="hyper" parents="60 4319 9987"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y / (z * (K(u,x) / ((z \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[hyper(60,a,6172,a(flip),b,9963,a),flip(a)].">
      <j1 rule="hyper" parents="60 6172 9963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5381,a,8310,a),flip(a)].">
      <j1 rule="hyper" parents="5381 8310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      K(L((x \ y) \ y,z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,8073,a,b,9991,a)].">
      <j1 rule="hyper" parents="60 8073 9991"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9991(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9991 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = (v5 * K(L(y,u,w),T(x,z))) \ (v5 * x)
    ]]></literal>
    <justification jstring="[para(9992(a,1),5853(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9992 5853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(123,a,8088,a(flip),b,9993,a),flip(a)].">
      <j1 rule="hyper" parents="123 8088 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),9995(a,2,2))].">
      <j1 rule="para" parents="20 9995"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(8181,a,9996,a)].">
      <j1 rule="hyper" parents="8181 9996"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),9997(a,1,2))].">
      <j1 rule="para" parents="20 9997"/>
    </justification>
  </clause>

  <clause id="9999">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9998(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10000">
    <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(5323(a,1),9999(a,1,2,1))].">
      <j1 rule="para" parents="5323 9999"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      (x * y) \ ((T(x,z) * y) * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8375(a,1),8316(a,1))].">
      <j1 rule="para" parents="8375 8316"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      (x / y) / T(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) \ (x / y) = u
    ]]></literal>
    <justification jstring="[para(6857(a,1),8437(a,1))].">
      <j1 rule="para" parents="6857 8437"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(8796(a,1),8922(a,1,2))].">
      <j1 rule="para" parents="8796 8922"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),8824(a,1,1))].">
      <j1 rule="para" parents="8019 8824"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      ((x * y) / x) \ (z * (y * K(x,y))) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5632,a(flip),b,8873,a),flip(a)].">
      <j1 rule="hyper" parents="370 5632 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6109,a(flip),b,9235,a),flip(a)].">
      <j1 rule="hyper" parents="370 6109 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6281(a,1),10007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6281 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      T(K(x,y),z) * K(x * y,x) = T(x,K(y,z)) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8685,a,9336,a),flip(a)].">
      <j1 rule="hyper" parents="8685 9336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(8359(a,2),9552(a,1))].">
      <j1 rule="para" parents="8359 9552"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(9533(a,1),9601(a,1,2))].">
      <j1 rule="para" parents="9533 9601"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2896,a,10011,a)].">
      <j1 rule="hyper" parents="2896 10011"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(9942,a,9654,a)].">
      <j1 rule="hyper" parents="9942 9654"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8847,a,10013,a)].">
      <j1 rule="hyper" parents="8847 10013"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9774,a(flip),b,10014,a)].">
      <j1 rule="hyper" parents="370 9774 10014"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),10015(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 10015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),10016(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 10016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * x),w) = K(R(K(u,y) * x,z,w),y)
    ]]></literal>
    <justification jstring="[para(9220(a,1),10017(a,1,1))].">
      <j1 rule="para" parents="9220 10017"/>
    </justification>
  </clause>

  <clause id="10020">
    <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(9641,a,9828,a)].">
      <j1 rule="hyper" parents="9641 9828"/>
    </justification>
  </clause>

  <clause id="10021">
    <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(7494(a,1),8165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7494 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(8690(a,1),8662(a,1,1))].">
      <j1 rule="para" parents="8690 8662"/>
    </justification>
  </clause>

  <clause id="10023">
    <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(10022(a,1),105(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10022 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10024">
    <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(10022(a,1),7519(a,1,2))].">
      <j1 rule="para" parents="10022 7519"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) = T(x,T(z * (y * y),y \ 1))
    ]]></literal>
    <justification jstring="[para(4443(a,1),8868(a,2,2))].">
      <j1 rule="para" parents="4443 8868"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(9014,a,8871,a)].">
      <j1 rule="hyper" parents="9014 8871"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,9701,a(flip),b,10026,a),flip(a)].">
      <j1 rule="hyper" parents="370 9701 10026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4656,a(flip),b,10027,a),flip(a)].">
      <j1 rule="hyper" parents="370 4656 10027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = x * K(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(6091(a,2),8942(a,2,2))].">
      <j1 rule="para" parents="6091 8942"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y * z)) / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(17(a,2),9023(a,1,2,1,1))].">
      <j1 rule="para" parents="17 9023"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(9168(a,1),9172(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9168 9172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5454,a(flip),b,10032,a),flip(a)].">
      <j1 rule="hyper" parents="370 5454 10032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10035">
    <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(60,a,5597,a(flip),b,10033,a),flip(a)].">
      <j1 rule="hyper" parents="60 5597 10033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,9547,a(flip),b,9307,a(flip))].">
      <j1 rule="hyper" parents="128 9547 9307"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      (x \ 1) \ (T(T(x \ 1,x),x) \ y) = (1 / x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(955(a,1),9323(a,2,2,1))].">
      <j1 rule="para" parents="955 9323"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      (x \ 1) \ (T(1 / x,x) \ y) = (1 / x) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(955(a,1),10037(a,1,2,1,1))].">
      <j1 rule="para" parents="955 10037"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      (1 / x) \ ((1 / x) \ y) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),10038(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 10038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      x \ ((x * x) * ((1 / x) \ y)) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(1442,a,10039,a)].">
      <j1 rule="hyper" parents="1442 10039"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[para(579(a,1),9325(a,2,2))].">
      <j1 rule="para" parents="579 9325"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5797,a(flip),b,9405,a),flip(a)].">
      <j1 rule="hyper" parents="370 5797 9405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10043">
    <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(4(a,1),10042(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10044">
    <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(370,a,5798,a(flip),b,9406,a),flip(a)].">
      <j1 rule="hyper" parents="370 5798 9406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(9534(a,1),7560(a,1))].">
      <j1 rule="para" parents="9534 7560"/>
    </justification>
  </clause>

  <clause id="10046">
    <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(5741(a,1),9540(a,1,1))].">
      <j1 rule="para" parents="5741 9540"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      x / (y * (z * ((u \ (z \ (y \ x))) * u))) = K(u,x / (y * (u / (z \ 1))))
    ]]></literal>
    <justification jstring="[para(4951(a,1),9613(a,1,2,2))].">
      <j1 rule="para" parents="4951 9613"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8657,a,9617,a)].">
      <j1 rule="hyper" parents="8657 9617"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6992,a,10048,a),flip(a)].">
      <j1 rule="hyper" parents="6992 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10051">
    <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(8639(a,1),10048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8639 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) * K(u,y) = T(x * K(u,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9008,a,10049,a),flip(a)].">
      <j1 rule="hyper" parents="9008 10049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10053">
    <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(6591(a,1),10049(a,2,2))].">
      <j1 rule="para" parents="6591 10049"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1058,a,10050,a),flip(a)].">
      <j1 rule="hyper" parents="1058 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,9670,a(flip),b,10054,a),flip(a)].">
      <j1 rule="hyper" parents="370 9670 10054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      T((K(x,y) * z) * K(x,u),K(x,y)) = (z * K(x,y)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(7464(a,1),10054(a,2,1))].">
      <j1 rule="para" parents="7464 10054"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = (z * K(y,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10054(a,1),8711(a,1,2))].">
      <j1 rule="para" parents="10054 8711"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / T(K(y,z),x * K(y,z * x))
    ]]></literal>
    <justification jstring="[para(10055(a,1),5781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10055 5781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      T(x * K(y,z),T(z,u)) = T(x,T(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8587(a,1),10052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8587 10052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,u)) = K(x,y) * T(z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(6996,a,10059,a),flip(a)].">
      <j1 rule="hyper" parents="6996 10059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      K(x,y) * T(z / T(x,u),T(x,u)) = T(x,u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(7605,a,10060,a),flip(a)].">
      <j1 rule="hyper" parents="7605 10060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      T(K(x,y) * (z * K(x,u)),K(x,y)) = (z * K(x,y)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(7463(a,1),10056(a,1,1))].">
      <j1 rule="para" parents="7463 10056"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),10061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      K(x,y) * (T(x,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10063(a,1),391(a,1))].">
      <j1 rule="para" parents="10063 391"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,u) = (x * K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7571,a,10062,a)].">
      <j1 rule="hyper" parents="7571 10062"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(6302,a,10065,a)].">
      <j1 rule="hyper" parents="6302 10065"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(10066(a,2),721(a,1))].">
      <j1 rule="para" parents="10066 721"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),10066(a,1,1,1))].">
      <j1 rule="para" parents="6281 10066"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(9137,a,10068,a),flip(a)].">
      <j1 rule="hyper" parents="9137 10068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8024(a,1),10069(a,1,1,2))].">
      <j1 rule="para" parents="8024 10069"/>
    </justification>
  </clause>

  <clause id="10071">
    <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(8636(a,1),9673(a,1,1,1))].">
      <j1 rule="para" parents="8636 9673"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      ((x \ 1) * T(1 / x,y)) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7723(a,1),9697(a,1,1,2))].">
      <j1 rule="para" parents="7723 9697"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      (x \ T(x \ 1,y)) * z = T(1 / x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2088(a,1),10072(a,1,1))].">
      <j1 rule="para" parents="2088 10072"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,9972,a(flip),b,9715,a)].">
      <j1 rule="hyper" parents="60 9972 9715"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9803,a,9755,a),flip(a)].">
      <j1 rule="hyper" parents="9803 9755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      (x / y) * (((y \ x) \ 1) \ z) = (y \ x) * (((x / y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),9888(a,1,2,1,1))].">
      <j1 rule="para" parents="109 9888"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      (x \ y) * (((y / x) \ 1) \ 1) = (1 / (y / x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4420,a(flip),b,10077,a),flip(a)].">
      <j1 rule="hyper" parents="60 4420 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),9973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 9973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8085,a(flip),b,9994,a),flip(a)].">
      <j1 rule="hyper" parents="370 8085 9994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),10080(a,2,2))].">
      <j1 rule="para" parents="20 10080"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5821(a,2),10081(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5821 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      T(x,T(y * z,y * y) / (1 / y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * (y * y),y)) = u
    ]]></literal>
    <justification jstring="[para(10025(a,2),9496(a,1))].">
      <j1 rule="para" parents="10025 9496"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,10030,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 10030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10085">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(9029,a,10084,a)].">
      <j1 rule="hyper" parents="9029 10084"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),10084(a,2,2,2))].">
      <j1 rule="para" parents="109 10084"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9471,a(flip),b,10086,a)].">
      <j1 rule="hyper" parents="60 9471 10086"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10085,a(flip),b,10087,a)].">
      <j1 rule="hyper" parents="60 10085 10087"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9624,a,10088,a)].">
      <j1 rule="hyper" parents="9624 10088"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(74(a,1),10089(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="74 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9132,a(flip),b,10090,a),flip(a)].">
      <j1 rule="hyper" parents="60 9132 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9092,a,b,10091,a)].">
      <j1 rule="hyper" parents="60 9092 10091"/>
    </justification>
  </clause>

  <clause id="10093">
    <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(10051(a,1),10071(a,1,1))].">
      <j1 rule="para" parents="10051 10071"/>
    </justification>
  </clause>

  <clause id="10094">
    <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(8636(a,1),10093(a,2,1))].">
      <j1 rule="para" parents="8636 10093"/>
    </justification>
  </clause>

  <clause id="10095">
    <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(8630(a,1),10094(a,2,2))].">
      <j1 rule="para" parents="8630 10094"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,10079,a(flip),b,10074,a),flip(a)].">
      <j1 rule="hyper" parents="370 10079 10074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6264,a,10096,a),flip(a)].">
      <j1 rule="hyper" parents="6264 10096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(221,a,10097,a)].">
      <j1 rule="hyper" parents="221 10097"/>
    </justification>
  </clause>

  <clause id="10099">
    <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(7454(a,1),7866(a,1,1,2))].">
      <j1 rule="para" parents="7454 7866"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(9220(a,1),8169(a,1,1))].">
      <j1 rule="para" parents="9220 8169"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(9173(a,1),10100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9173 10100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7862,a(flip),b,10101,a),flip(a)].">
      <j1 rule="hyper" parents="370 7862 10101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(7873(a,1),10103(a,1,2))].">
      <j1 rule="para" parents="7873 10103"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9799,a,b,10105,a)].">
      <j1 rule="hyper" parents="60 9799 10105"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7192,a,b,10106,a)].">
      <j1 rule="hyper" parents="60 7192 10106"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(10108(a,1),6552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10108 6552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7997(a,1),10110(a,1,2,2))].">
      <j1 rule="para" parents="7997 10110"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,10111,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 10111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(7890(a,1),10113(a,1,2))].">
      <j1 rule="para" parents="7890 10113"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(9305(a,2),10114(a,1,2))].">
      <j1 rule="para" parents="9305 10114"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(7845(a,1),8200(a,1,2))].">
      <j1 rule="para" parents="7845 8200"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      T(K(T(x,y),z * (u / (x * u))),y) = K(x,R(x \ 1,x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8779,a,b,8230,a)].">
      <j1 rule="hyper" parents="60 8779 8230"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (y / (x * y))) = u
    ]]></literal>
    <justification jstring="[para(8230(a,1),9079(a,1))].">
      <j1 rule="para" parents="8230 9079"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(3535,a,8281,a)].">
      <j1 rule="hyper" parents="3535 8281"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9883,a(flip),b,8373,a)].">
      <j1 rule="hyper" parents="60 9883 8373"/>
    </justification>
  </clause>

  <clause id="10123">
    <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(2022(a,2),8842(a,1,1))].">
      <j1 rule="para" parents="2022 8842"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(6147(a,1),9843(a,2,2))].">
      <j1 rule="para" parents="6147 9843"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,6151,a(flip),b,10124,a),flip(a)].">
      <j1 rule="hyper" parents="60 6151 10124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(4441(a,1),10125(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4441 10125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(4441(a,1),10126(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4441 10126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,10127,a)].">
      <j1 rule="hyper" parents="215 10127"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ T(y / x,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),10128(a,1,1,1,1))].">
      <j1 rule="para" parents="109 10128"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      (((x \ y) / (x \ 1)) \ (y / x)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),10129(a,2,2))].">
      <j1 rule="para" parents="109 10129"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      (x \ K(x,x \ y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(9618(a,1),10130(a,1,1))].">
      <j1 rule="para" parents="9618 10130"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      (x \ K(x,(x \ 1) * y)) \ (y / x) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(7744(a,2),10131(a,1,1,2))].">
      <j1 rule="para" parents="7744 10131"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      (R(x,y,z) \ K(R(x,y,z),R(x,y,z) \ 1)) \ (K(x,u) / R(x,y,z)) = (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u))
    ]]></literal>
    <justification jstring="[para(10007(a,1),10132(a,1,1,2))].">
      <j1 rule="para" parents="10007 10132"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5280(a,1),10000(a,2,2,1))].">
      <j1 rule="para" parents="5280 10000"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      K(x,L(L(y,z,y),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5526(a,1),10134(a,1,2,1))].">
      <j1 rule="para" parents="5526 10134"/>
    </justification>
  </clause>

  <clause id="10136">
    <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(5099(a,1),10135(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5099 10135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,6780,a(flip),b,10136,a),flip(a)].">
      <j1 rule="hyper" parents="370 6780 10136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(7969(a,1),10122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7969 10122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y) = u
    ]]></literal>
    <justification jstring="[para(10138(a,2),2079(a,1))].">
      <j1 rule="para" parents="10138 2079"/>
    </justification>
  </clause>

  <clause id="10141">
    <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(7543(a,1),10123(a,2,2))].">
      <j1 rule="para" parents="7543 10123"/>
    </justification>
  </clause>

  <clause id="10142">
    <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(10123(a,1),9426(a,2,2))].">
      <j1 rule="para" parents="10123 9426"/>
    </justification>
  </clause>

  <clause id="10143">
    <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(7864(a,1),7921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 7921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10144">
    <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(10143(a,2),629(a,1))].">
      <j1 rule="para" parents="10143 629"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(10144,a,5880,a),flip(a)].">
      <j1 rule="hyper" parents="10144 5880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      L(x,y,T(y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(10144,a,614,a)].">
      <j1 rule="hyper" parents="10144 614"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5880(a,1),10144(a,1))].">
      <j1 rule="para" parents="5880 10144"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      L(x,y \ z,z / y) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6033,a(flip),b,10146,a)].">
      <j1 rule="hyper" parents="60 6033 10146"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,(y \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),10148(a,1,3)),flip(a)].">
      <j1 rule="para" parents="74 10148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,z * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5923,a,b,10145,a),flip(a)].">
      <j1 rule="hyper" parents="370 5923 10145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7457,a(flip),b,10145,a),flip(a)].">
      <j1 rule="hyper" parents="60 7457 10145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      L(x,y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y) = u
    ]]></literal>
    <justification jstring="[para(10145(a,1),635(a,1))].">
      <j1 rule="para" parents="10145 635"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10145(a,2),5924(a,1))].">
      <j1 rule="para" parents="10145 5924"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6033,a(flip),b,10151,a)].">
      <j1 rule="hyper" parents="60 6033 10151"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(10151(a,1),20(a,2,1))].">
      <j1 rule="para" parents="10151 20"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      L(x,T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6032(a,1),10152(a,1))].">
      <j1 rule="para" parents="6032 10152"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      L(x,y \ z,z / y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6033(a,1),10152(a,1))].">
      <j1 rule="para" parents="6033 10152"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,10157,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 10157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      L(T(x,y),T(z,x),x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(9165,a,10162,a),flip(a)].">
      <j1 rule="hyper" parents="9165 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10115,a(flip),b,10163,a),flip(a)].">
      <j1 rule="hyper" parents="60 10115 10163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,10151,a,b,10156,a)].">
      <j1 rule="hyper" parents="370 10151 10156"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      L(x \ y,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(10156(a,1),1081(a,1))].">
      <j1 rule="para" parents="10156 1081"/>
    </justification>
  </clause>

  <clause id="10168">
    <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="[hyper(370,a,10116,a,b,10150,a)].">
      <j1 rule="hyper" parents="370 10116 10150"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),10161(a,1,3))].">
      <j1 rule="para" parents="74 10161"/>
    </justification>
  </clause>

  <clause id="10171">
    <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(8019(a,2),8055(a,1,2,1))].">
      <j1 rule="para" parents="8019 8055"/>
    </justification>
  </clause>

  <clause id="10172">
    <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(1836(a,1),8166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1836 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(5843(a,1),8372(a,1,1))].">
      <j1 rule="para" parents="5843 8372"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(8833(a,1),10173(a,1,2))].">
      <j1 rule="para" parents="8833 10173"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(9376(a,1),8381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9376 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5997,a,b,10175,a),flip(a)].">
      <j1 rule="hyper" parents="370 5997 10175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5997,a,b,10176,a)].">
      <j1 rule="hyper" parents="60 5997 10176"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(129,a,10177,a(flip),b,5332,a),flip(a)].">
      <j1 rule="hyper" parents="129 10177 5332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      L(x,y,z * (T(1 / (1 / z),u) \ K(w,z))) = L(x,y,K(w,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(4970(a,1),8499(a,1,3))].">
      <j1 rule="para" parents="4970 8499"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(7806(a,1),8581(a,2,1))].">
      <j1 rule="para" parents="7806 8581"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(T(x / (x / y),x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6878,a,b,8961,a),flip(a)].">
      <j1 rule="hyper" parents="370 6878 8961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = (y / x) / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),9133(a,2,1,1))].">
      <j1 rule="para" parents="5 9133"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2396(a,1),9151(a,1,1))].">
      <j1 rule="para" parents="2396 9151"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(9447,a,9454,a)].">
      <j1 rule="hyper" parents="9447 9454"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9446,a(flip),b,10186,a),flip(a)].">
      <j1 rule="hyper" parents="370 9446 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <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(707(a,2),10187(a,1,2,2))].">
      <j1 rule="para" parents="707 10187"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      x / (y * (z * ((u \ (z \ (y \ x))) * u))) = K(u,x / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),9612(a,1,2,2,2))].">
      <j1 rule="para" parents="107 9612"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      K(x,x \ y) * K((x \ y) \ 1,y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(5331(a,1),9663(a,1,1))].">
      <j1 rule="para" parents="5331 9663"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      T(x * (y / z),K(u,z)) \ ((x * (z \ y)) * K(z,z \ y)) = K(x * (z \ y),K(z,z \ u))
    ]]></literal>
    <justification jstring="[para(5631(a,2),9746(a,1,2))].">
      <j1 rule="para" parents="5631 9746"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,T(y,u)))) / x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(T(z,x),u)) = w
    ]]></literal>
    <justification jstring="[para(9750(a,1),8424(a,1))].">
      <j1 rule="para" parents="9750 8424"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      x \ (y \ L(y,z,u)) != (y \ L(y,z,u)) * (y \ L(y,z,u))
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ y = x
    ]]></literal>
    <justification jstring="[para(9919(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="9919 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      L((x \ 1) \ y,z,u) \ ((x \ 1) \ y) = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9916,a(flip),b,9928,a),flip(a)].">
      <j1 rule="hyper" parents="370 9916 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ R(y,x,x),z,u) \ (((x \ 1) \ 1) \ R(y,x,x)) = L(T(y * x,x \ 1),z,u) \ ((x \ 1) \ R(y,x,x))
    ]]></literal>
    <justification jstring="[para(1120(a,1),10194(a,2,1,1))].">
      <j1 rule="para" parents="1120 10194"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10043(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10044(a,1,1,2,1))].">
      <j1 rule="para" parents="4 10044"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      K(x,y / (z * (x / (u \ 1)))) = K(x,y / (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10189,a(flip),b,10047,a),flip(a)].">
      <j1 rule="hyper" parents="60 10189 10047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      x / L((y \ ((z \ 1) \ (z \ x))) * y,z \ 1,z) = K(y,x / (z * (y / ((z \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[para(300(a,1),10047(a,1,2))].">
      <j1 rule="para" parents="300 10047"/>
    </justification>
  </clause>

  <clause id="10200">
    <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(60,a,8395,a,b,10172,a)].">
      <j1 rule="hyper" parents="60 8395 10172"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6846(a,1),10178(a,2,2))].">
      <j1 rule="para" parents="6846 10178"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(7749(a,1),10201(a,2,2))].">
      <j1 rule="para" parents="7749 10201"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,3302,a(flip),b,10202,a),flip(a)].">
      <j1 rule="hyper" parents="370 3302 10202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),10203(a,1,1))].">
      <j1 rule="para" parents="74 10203"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(74(a,1),10204(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5444(a,1),10205(a,1,1))].">
      <j1 rule="para" parents="5444 10205"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,K(y,x / y) / (x \ y)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10207(a,2),2007(a,1,2))].">
      <j1 rule="para" parents="10207 2007"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) / T(z,w))) = L(x,y,K(u,z) * K(w,z))
    ]]></literal>
    <justification jstring="[para(8414(a,1),10179(a,1,3,2))].">
      <j1 rule="para" parents="8414 10179"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(8400(a,1),10181(a,2,1))].">
      <j1 rule="para" parents="8400 10181"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,10210,a(flip),b,8961,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 10210 8961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(5747(a,2),10211(a,2,2,1))].">
      <j1 rule="para" parents="5747 10211"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(31,a,10211,a(flip),b,10213,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="31 10211 10213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,(y * x) / y),u)
    ]]></literal>
    <justification jstring="[para(5455(a,1),10214(a,1,1,1))].">
      <j1 rule="para" parents="5455 10214"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6117,a(flip),b,10185,a)].">
      <j1 rule="hyper" parents="60 6117 10185"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(10010,a,10200,a)].">
      <j1 rule="hyper" parents="10010 10200"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(((y * x) / y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[para(8855(a,1),10215(a,2,1,2))].">
      <j1 rule="para" parents="8855 10215"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      T(T(x,y),z) \ (K(x,y) * u) = T(x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(8255,a,8307,a)].">
      <j1 rule="hyper" parents="8255 8307"/>
    </justification>
  </clause>

  <clause id="10221">
    <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(9315,a,9267,a)].">
      <j1 rule="hyper" parents="9315 9267"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,5597,a(flip),b,10221,a),flip(a)].">
      <j1 rule="hyper" parents="60 5597 10221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10224">
    <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(8851(a,1),10223(a,1,2))].">
      <j1 rule="para" parents="8851 10223"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      K(x \ (y / z),L(z,u,w)) = K(x \ (z \ y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(6106,a,9269,a),flip(a)].">
      <j1 rule="hyper" parents="6106 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8702(a,1),9286(a,1,1,3))].">
      <j1 rule="para" parents="8702 9286"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7506(a,1),10226(a,2,2))].">
      <j1 rule="para" parents="7506 10226"/>
    </justification>
  </clause>

  <clause id="10228">
    <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(370,a,9277,a(flip),b,9338,a),flip(a)].">
      <j1 rule="hyper" parents="370 9277 9338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,174,a(flip),b,10023,a),flip(a)].">
      <j1 rule="hyper" parents="370 174 10023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5249,a,b,10230,a),flip(a)].">
      <j1 rule="hyper" parents="370 5249 10230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,10231,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 10231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = K(y \ x,z \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(9383(a,1),8512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9383 8512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      T(T(T(x,y \ x) / y,x),x / z) = T(x / y,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8143,a(flip),b,10234,a),flip(a)].">
      <j1 rule="hyper" parents="370 8143 10234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[para(5473(a,1),10235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5473 10235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u \ 1)),T((u \ z) * u,u))) = K(x,T(y,(u \ z) * u))
    ]]></literal>
    <justification jstring="[para(9495(a,1),9109(a,1,2))].">
      <j1 rule="para" parents="9495 9109"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),T((u \ z) * u,u))) = K(x,T(y,(u \ z) * u))
    ]]></literal>
    <justification jstring="[para(9455(a,1),10237(a,1,2,1))].">
      <j1 rule="para" parents="9455 10237"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,4675,a(flip),b,9568,a)].">
      <j1 rule="hyper" parents="60 4675 9568"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9567,a(flip),b,10239,a),flip(a)].">
      <j1 rule="hyper" parents="60 9567 10239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8153,a(flip),b,9577,a),flip(a)].">
      <j1 rule="hyper" parents="370 8153 9577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,2859,a(flip),b,9619,a),flip(a)].">
      <j1 rule="hyper" parents="370 2859 9619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6206,a(flip),b,10243,a),flip(a)].">
      <j1 rule="hyper" parents="370 6206 10243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(8410(a,1),10244(a,1,2))].">
      <j1 rule="para" parents="8410 10244"/>
    </justification>
  </clause>

  <clause id="10246">
    <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(10245(a,1),896(a,1,2))].">
      <j1 rule="para" parents="10245 896"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (R(x,z,R(x,u,w)) * y) * x
    ]]></literal>
    <justification jstring="[para(274(a,1),9787(a,2,1))].">
      <j1 rule="para" parents="274 9787"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,7634,a(flip),b,10247,a),flip(a)].">
      <j1 rule="hyper" parents="60 7634 10247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * ((x \ y) \ 1),T(y \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(9846(a,1),9845(a,1))].">
      <j1 rule="para" parents="9846 9845"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),x * L(x,y,z),x) = R(L(x,y,z) \ (x * 1),u,w)
    ]]></literal>
    <justification jstring="[hyper(4133,a,9922,a)].">
      <j1 rule="hyper" parents="4133 9922"/>
    </justification>
  </clause>

  <clause id="10251">
    <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(6591(a,1),10053(a,1,1,2))].">
      <j1 rule="para" parents="6591 10053"/>
    </justification>
  </clause>

  <clause id="10252">
    <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(4849,a,10251,a),flip(a)].">
      <j1 rule="hyper" parents="4849 10251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5303(a,1),10168(a,1,1))].">
      <j1 rule="para" parents="5303 10168"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(7864(a,1),10253(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7864 10253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,269,a(flip),b,10254,a),flip(a)].">
      <j1 rule="hyper" parents="370 269 10254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),z) = u
    ]]></literal>
    <justification jstring="[para(10254(a,2),1197(a,1))].">
      <j1 rule="para" parents="10254 1197"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(10147,a,10255,a),flip(a)].">
      <j1 rule="hyper" parents="10147 10255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      L(x,y * K(z,y),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7944,a,b,10257,a)].">
      <j1 rule="hyper" parents="60 7944 10257"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x,T(y,x)) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8213,a(flip),b,10258,a),flip(a)].">
      <j1 rule="hyper" parents="60 8213 10258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),x,x * L(x,y,z)) = R(L(x,y,z) \ (x * 1),u,w)
    ]]></literal>
    <justification jstring="[hyper(4173,a,10250,a)].">
      <j1 rule="hyper" parents="4173 10250"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),x,x * L(x,y,z)) = R(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(3(a,1),10260(a,2,1,2))].">
      <j1 rule="para" parents="3 10260"/>
    </justification>
  </clause>

  <clause id="10262">
    <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(8024(a,1),8826(a,2,1,2))].">
      <j1 rule="para" parents="8024 8826"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) = T(K(y,z) * x,T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7505(a,1),8941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7505 8941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) = T(K(y,z) * x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5906,a(flip),b,10263,a),flip(a)].">
      <j1 rule="hyper" parents="370 5906 10263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10265">
    <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(5(a,1),9738(a,1,2))].">
      <j1 rule="para" parents="5 9738"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = K(x \ L(x,y,z),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(4874,a,10265,a)].">
      <j1 rule="hyper" parents="4874 10265"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = K(L(x,y,z),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(8431,a,10266,a),flip(a)].">
      <j1 rule="hyper" parents="8431 10266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,K(x,y),y \ x) = (x / y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(8575,a,9878,a),flip(a)].">
      <j1 rule="hyper" parents="8575 9878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * (y * z)) = K(L(z,y,x),T(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,6931,a,b,9882,a)].">
      <j1 rule="hyper" parents="35 6931 9882"/>
    </justification>
  </clause>

  <clause id="10271">
    <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(9953(a,1),10262(a,2,1))].">
      <j1 rule="para" parents="9953 10262"/>
    </justification>
  </clause>

  <clause id="10272">
    <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(370,a,10227,a(flip),b,10271,a),flip(a)].">
      <j1 rule="hyper" parents="370 10227 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10273">
    <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(8024(a,1),10272(a,1,1,2))].">
      <j1 rule="para" parents="8024 10272"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8758(a,1),10273(a,1,2))].">
      <j1 rule="para" parents="8758 10273"/>
    </justification>
  </clause>

  <clause id="10275">
    <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(9837(a,2),10274(a,1,1))].">
      <j1 rule="para" parents="9837 10274"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4898(a,1),7821(a,2,1))].">
      <j1 rule="para" parents="4898 7821"/>
    </justification>
  </clause>

  <clause id="10277">
    <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(7908(a,1),7971(a,2,2))].">
      <j1 rule="para" parents="7908 7971"/>
    </justification>
  </clause>

  <clause id="10278">
    <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(10277(a,2),629(a,1))].">
      <j1 rule="para" parents="10277 629"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      T(x,y * (((z \ (((u \ 1) \ 1) \ z)) * T(z,u \ 1)) \ w)) = T(x,y * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(4534(a,1),8551(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4534 8551"/>
    </justification>
  </clause>

  <clause id="10281">
    <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(223(a,1),9121(a,1,1))].">
      <j1 rule="para" parents="223 9121"/>
    </justification>
  </clause>

  <clause id="10283">
    <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(6291(a,1),10281(a,1,2))].">
      <j1 rule="para" parents="6291 10281"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,5598,a(flip),b,9285,a),flip(a)].">
      <j1 rule="hyper" parents="370 5598 9285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[para(108(a,1),10284(a,1,1,1))].">
      <j1 rule="para" parents="108 10284"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(8863(a,1),9367(a,2,1))].">
      <j1 rule="para" parents="8863 9367"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(8976(a,2),10286(a,2,2))].">
      <j1 rule="para" parents="8976 10286"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9321,a,b,10287,a)].">
      <j1 rule="hyper" parents="60 9321 10287"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      K(x,1 / (1 / (y \ (y / z)))) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(6053,a,10288,a)].">
      <j1 rule="hyper" parents="6053 10288"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      K((((x * K(y,z)) * u) * w) / (u * w),z) = K(R(x,K(y,z) * u,w),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9771,a(flip),b,9681,a),flip(a)].">
      <j1 rule="hyper" parents="60 9771 9681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      K(R(x * K(y,z),u,w),z) = K(R(x,K(y,z) * u,w),z)
    ]]></literal>
    <justification jstring="[para(15(a,2),10292(a,1,1))].">
      <j1 rule="para" parents="15 10292"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z,K(x,y) * u,w),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9039,a,b,10294,a)].">
      <j1 rule="hyper" parents="60 9039 10294"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * x),w) = K(R(x,K(u,y) * z,w),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10019,a,b,10295,a)].">
      <j1 rule="hyper" parents="60 10019 10295"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(z * T(x,v5),u),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9880,a(flip),b,9976,a),flip(a)].">
      <j1 rule="hyper" parents="370 9880 9976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),w)) = K(x,T(T(x * y,u),w))
    ]]></literal>
    <justification jstring="[para(106(a,1),10297(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="106 10297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(77(a,1),10276(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 10276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) \ u) \ w)) = T(x,y * ((z \ u) \ w))
    ]]></literal>
    <justification jstring="[para(8550(a,1),10280(a,1,2,2,1))].">
      <j1 rule="para" parents="8550 10280"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(1 / y,z,u)) * v5)) = K(x,L(T(1 / y,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),7963(a,2,2,1))].">
      <j1 rule="para" parents="20 7963"/>
    </justification>
  </clause>

  <clause id="10302">
    <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(8357,a,8371,a),flip(a)].">
      <j1 rule="hyper" parents="8357 8371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,8215,a(flip),b,10302,a),flip(a)].">
      <j1 rule="hyper" parents="370 8215 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8357,a,10304,a)].">
      <j1 rule="hyper" parents="8357 10304"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(9021,a,10305,a)].">
      <j1 rule="hyper" parents="9021 10305"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8476,a,10306,a)].">
      <j1 rule="hyper" parents="8476 10306"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6199,a(flip),b,10308,a)].">
      <j1 rule="hyper" parents="60 6199 10308"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(253(a,1),10308(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="253 10308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10311">
    <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(10310(a,2),6052(a,1))].">
      <j1 rule="para" parents="10310 6052"/>
    </justification>
  </clause>

  <clause id="10312">
    <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(4917(a,1),8986(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4917 8986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <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(4917(a,1),10312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4917 10312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <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(10313(a,1),883(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10313 883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,10036,a(flip),b,9317,a),flip(a)].">
      <j1 rule="hyper" parents="370 10036 9317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(9551,a,7964,a)].">
      <j1 rule="hyper" parents="9551 7964"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      K(x,y / (z * (x / ((z \ 1) \ 1)))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7495,a(flip),b,10199,a),flip(a)].">
      <j1 rule="hyper" parents="60 7495 10199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      K(x,y / (z * ((z \ 1) * x))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10198,a(flip),b,10320,a)].">
      <j1 rule="hyper" parents="60 10198 10320"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      K(x,y / L(x,z \ 1,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(300(a,1),10322(a,1,2,2))].">
      <j1 rule="para" parents="300 10322"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      K(x,L(x,y \ 1,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8146,a(flip),b,10323,a)].">
      <j1 rule="hyper" parents="60 8146 10323"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(655(a,1),10324(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="655 10324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <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(10325(a,1),6402(a,1,2))].">
      <j1 rule="para" parents="10325 6402"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ (K(w,L(y \ 1,z,u)) * v5)) = K(x,L(T(1 / y,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(5440(a,1),10301(a,1,2,2,1))].">
      <j1 rule="para" parents="5440 10301"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,w) \ v5) = K(x,T(L(y \ 1,u,w),z) \ v5)
    ]]></literal>
    <justification jstring="[para(7890(a,1),10327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7890 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,w) \ v5) = K(x,L(T(y \ 1,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),10328(a,2,2,1))].">
      <j1 rule="para" parents="20 10328"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,9748,a(flip),b,9751,a),flip(a)].">
      <j1 rule="hyper" parents="370 9748 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(8848(a,1),10330(a,1,2,1,2,1))].">
      <j1 rule="para" parents="8848 10330"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      K(x,x \ y) * (z * (x \ y)) = T(z * (y / x),K(y,x))
    ]]></literal>
    <justification jstring="[hyper(160,a,10191,a)].">
      <j1 rule="hyper" parents="160 10191"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      K(x,x \ y) * (z * (x \ y)) = T(z * (y / x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8700,a,b,10332,a),flip(a)].">
      <j1 rule="hyper" parents="370 8700 10332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) * (L(x,y,z) \ x) = T(x * (1 / L(x,y,z)),K(L(x,y,z),1))
    ]]></literal>
    <justification jstring="[para(2162(a,1),10333(a,1,2))].">
      <j1 rule="para" parents="2162 10333"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = K(x,x \ 1) * (((x \ 1) \ y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(5009(a,2),10333(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5009 10333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,10092,a(flip),b,10208,a)].">
      <j1 rule="hyper" parents="60 10092 10208"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(4609(a,2),10336(a,2,1))].">
      <j1 rule="para" parents="4609 10336"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = z
    ]]></literal>
    <justification jstring="[para(10337(a,2),388(a,1)),flip(b)].">
      <j1 rule="para" parents="10337 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),y \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10326(a,1,2,2,1))].">
      <j1 rule="para" parents="5 10326"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6419,a,10339,a),flip(a)].">
      <j1 rule="hyper" parents="6419 10339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = (T(x \ 1,x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,7950,a(flip),b,10335,a),flip(a)].">
      <j1 rule="hyper" parents="370 7950 10335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ T(x * y,x \ 1),K(x,1)) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(955(a,1),10342(a,2,1,1))].">
      <j1 rule="para" parents="955 10342"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),K(x,1)) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(5009(a,1),10343(a,1,1))].">
      <j1 rule="para" parents="5009 10343"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (1 / x),1) = ((1 / x) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,1),10344(a,1,2))].">
      <j1 rule="para" parents="223 10344"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      ((1 / x) \ y) * (x \ 1) = ((x \ 1) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(226,a,10345,a),flip(a)].">
      <j1 rule="hyper" parents="226 10345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      ((x \ 1) \ (y * x)) * (1 / x) = T(y,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,7038,a(flip),b,10346,a),flip(a)].">
      <j1 rule="hyper" parents="60 7038 10346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7473,a(flip),b,7905,a),flip(a)].">
      <j1 rule="hyper" parents="370 7473 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9149,a(flip),b,10349,a)].">
      <j1 rule="hyper" parents="60 9149 10349"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z
    ]]></literal>
    <justification jstring="[para(531(a,1),8258(a,1,2))].">
      <j1 rule="para" parents="531 8258"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z
    ]]></literal>
    <justification jstring="[para(272(a,1),10352(a,1,2,2))].">
      <j1 rule="para" parents="272 10352"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(7860(a,1),10353(a,1,2,2))].">
      <j1 rule="para" parents="7860 10353"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      (x * y) / (x * (K(z,u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) / (x * (z \ y))) = w
    ]]></literal>
    <justification jstring="[para(10354(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10354 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1950(a,1),10354(a,1,1,2))].">
      <j1 rule="para" parents="1950 10354"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      K(x,y * (K(z,x \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(10354(a,1),8013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 8013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(10354(a,1),9168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 9168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      K(x,T(y,z * (K(u,x) * w))) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(10354(a,1),9261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10354 9261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(10354(a,1),9509(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10354 9509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(10354(a,1),9693(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10354 9693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      K(x,y * (K(x \ 1,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(7500(a,1),10357(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 10357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      K(x,y * (z / T(u,x \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(9075(a,1),10362(a,1,2,2))].">
      <j1 rule="para" parents="9075 10362"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      K(T(x,y),z * (y / (x * y))) = K(T(x,y),z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(6486(a,1),10363(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6486 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      R(x,y,z) * (K(x,u) * w) = K(x,u) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(7518,a,10356,a),flip(a)].">
      <j1 rule="hyper" parents="7518 10356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(7500(a,1),10356(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 10356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10367">
    <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(8766(a,1),10356(a,1,1))].">
      <j1 rule="para" parents="8766 10356"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,67,a(flip),b,10365,a),flip(a)].">
      <j1 rule="hyper" parents="125 67 10365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      (1 / (K(x,y) \ R(x,z,u))) \ (K(x,y) * (R(x,z,u) \ 1)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,10368,a,b,2438,a)].">
      <j1 rule="hyper" parents="125 10368 2438"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9733,a,10366,a)].">
      <j1 rule="hyper" parents="9733 10366"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      T(K(T(x,y),z * ((x * y) \ y)),y) = K(x,R(x \ 1,x,y) * z)
    ]]></literal>
    <justification jstring="[para(10364(a,1),10118(a,1,1))].">
      <j1 rule="para" parents="10364 10118"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,z * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(8898,a,10372,a),flip(a)].">
      <j1 rule="hyper" parents="8898 10372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10375">
    <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(8766(a,1),10367(a,1,2,2,1))].">
      <j1 rule="para" parents="8766 10367"/>
    </justification>
  </clause>

  <clause id="10377">
    <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(8000(a,1),8663(a,2,1))].">
      <j1 rule="para" parents="8000 8663"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      L((K(x,K(y,z)) * u) \ (y * w),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(8679(a,1),9063(a,1,1,1))].">
      <j1 rule="para" parents="8679 9063"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = K(x,x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(6790(a,1),10334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6790 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = L(x,y,z) \ T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4575,a(flip),b,10379,a),flip(a)].">
      <j1 rule="hyper" parents="370 4575 10379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),K(L(x,y,z),1)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,9902,a(flip),b,10380,a),flip(a)].">
      <j1 rule="hyper" parents="370 9902 10380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      T(x * (1 / L(x,y,z)),1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(223(a,1),10382(a,1,2))].">
      <j1 rule="para" parents="223 10382"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * x = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(226,a,10383,a),flip(a)].">
      <j1 rule="hyper" parents="226 10383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      L(x,y,z) \ (x * (1 / L(x,y,z))) = (L(x,y,z) * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,10384,a(flip),b,944,a)].">
      <j1 rule="hyper" parents="125 10384 944"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      T(x,((L(y,z,u) \ 1) * y) * w) = T(x,(y * (L(y,z,u) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(10384(a,2),4698(a,1,2,1))].">
      <j1 rule="para" parents="10384 4698"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      x * (L(x,y,z) \ (1 / L(x,y,z))) = (L(x,y,z) * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2194,a,10386,a)].">
      <j1 rule="hyper" parents="2194 10386"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      (L(x,y,z) \ x) / L(x,y,z) = (L(x,y,z) * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,2172,a(flip),b,10389,a)].">
      <j1 rule="hyper" parents="60 2172 10389"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      (x \ (L(x,y,z) * L(x,y,z))) \ L(x \ (L(x,y,z) * L(x,y,z)),u,w) = x \ ((L(x,y,z) * L(x,y,z)) * L((L(x,y,z) \ x) / L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10390(a,2),3823(a,2,2,2,1))].">
      <j1 rule="para" parents="10390 3823"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      K(x * K(x \ y,T(x,z)),u) * (x * T(x \ y,z)) = (x * T(x \ y,z)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(8376(a,1),8285(a,1,1,1))].">
      <j1 rule="para" parents="8376 8285"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(5569(a,1),9368(a,1,1,2))].">
      <j1 rule="para" parents="5569 9368"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(9417(a,1),10393(a,1,1))].">
      <j1 rule="para" parents="9417 10393"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(31,a,10289,a(flip),b,10394,a),flip(a)].">
      <j1 rule="hyper" parents="31 10289 10394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6662,a(flip),b,10395,a)].">
      <j1 rule="hyper" parents="60 6662 10395"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(R(y \ 1,y,x),z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(6011(a,1),9530(a,1,2,2))].">
      <j1 rule="para" parents="6011 9530"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y / K((z * ((u \ 1) / z)) \ 1,x))
    ]]></literal>
    <justification jstring="[para(7176(a,2),9990(a,2,2,2))].">
      <j1 rule="para" parents="7176 9990"/>
    </justification>
  </clause>

  <clause id="10400">
    <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(7839(a,1),10099(a,1,1))].">
      <j1 rule="para" parents="7839 10099"/>
    </justification>
  </clause>

  <clause id="10401">
    <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(1029,a,10400,a),flip(a)].">
      <j1 rule="hyper" parents="1029 10400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10402">
    <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(10400(a,1),1029(a,1))].">
      <j1 rule="para" parents="10400 1029"/>
    </justification>
  </clause>

  <clause id="10403">
    <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(7858(a,1),10401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 10401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(77(a,1),10299(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="77 10299"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(789,a,10404,a)].">
      <j1 rule="hyper" parents="789 10404"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(z,R(y \ 1,y,x))) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(8700(a,1),10398(a,1,2))].">
      <j1 rule="para" parents="8700 10398"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9207,a(flip),b,10399,a),flip(a)].">
      <j1 rule="hyper" parents="370 9207 10399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4701(a,1),10407(a,1,2,2))].">
      <j1 rule="para" parents="4701 10407"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6298(a,1),10409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6298 10409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(8936(a,1),9498(a,1))].">
      <j1 rule="para" parents="8936 9498"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(7864(a,1),9752(a,1,2))].">
      <j1 rule="para" parents="7864 9752"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      T(T(x,x * y) * K(z,T(x,(x * K(z,x)) * y)),u) = T(T(x * K(z,x),u),y * (x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(10358(a,1),8206(a,1,1,1))].">
      <j1 rule="para" parents="10358 8206"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      T(T(x,x * y) * K(z,T(x,x * (K(z,x) * y))),u) = T(T(x * K(z,x),u),y * (x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7845(a,1),10414(a,1,1,2,2,2))].">
      <j1 rule="para" parents="7845 10414"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x,x * u) * K(y,T(x,x * u)),z)
    ]]></literal>
    <justification jstring="[para(10358(a,1),10415(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10358 10415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u * (x * K(y,x))) = T(T(x,x * u) * K(y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[para(7325(a,1),10417(a,2,1,2))].">
      <j1 rule="para" parents="7325 10417"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      T(x,x * y) * K(z,T(x,y)) = T(x * K(z,x),y * x)
    ]]></literal>
    <justification jstring="[hyper(7653,a,10418,a),flip(a)].">
      <j1 rule="hyper" parents="7653 10418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10421">
    <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(8605(a,1),9911(a,2,1))].">
      <j1 rule="para" parents="8605 9911"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(L(x,y,z) \ x,u,w) \ v5) = (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(9916(a,1),9927(a,1,2,1,1))].">
      <j1 rule="para" parents="9916 9927"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ 1) = L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(2175,a,10422,a),flip(a)].">
      <j1 rule="hyper" parents="2175 10422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x) = L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2175,a,10423,a),flip(a)].">
      <j1 rule="hyper" parents="2175 10423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(((y / T(1 / z,u)) \ 1) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,5054,a(flip),b,9969,a),flip(a)].">
      <j1 rule="hyper" parents="60 5054 9969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      T(x,R(T(y / T(z \ 1,u),K(z,z \ 1)),w,v5)) = T(x,R(y / T(1 / z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,4680,a(flip),b,10425,a),flip(a)].">
      <j1 rule="hyper" parents="370 4680 10425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      T(x,R(y / T(1 / z,u),w,v5)) = T(x,R(y / T(z \ 1,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4353(a,1),10427(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4353 10427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      (1 / (K(x,y) * R(y,z,u))) \ (K(y,x) * (R(y,z,u) \ 1)) = (R(y,z,u) \ K(y,x)) * (K(y,x) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(7506(a,1),10369(a,1,1,2))].">
      <j1 rule="para" parents="7506 10369"/>
    </justification>
  </clause>

  <clause id="10431">
    <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(370,a,9335,a(flip),b,10421,a),flip(a)].">
      <j1 rule="hyper" parents="370 9335 10421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * K(x,u)) \ (K(x,u) * (R(x,y,z) \ 1)) = (R(x,y,z) \ K(x,u)) * (K(x,u) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(6805(a,1),10430(a,1,1))].">
      <j1 rule="para" parents="6805 10430"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),4043(a,2,2,1))].">
      <j1 rule="para" parents="13 4043"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ (x \ (x * y)),u,w))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(1598(a,1),10433(a,1,2))].">
      <j1 rule="para" parents="1598 10433"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),10434(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="4 10434"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) \ L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(1346(a,1),10435(a,1,2,2))].">
      <j1 rule="para" parents="1346 10435"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3816,a,b,10436,a),flip(a)].">
      <j1 rule="hyper" parents="370 3816 10436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10438">
    <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(3816(a,1),10436(a,1,2,2,2))].">
      <j1 rule="para" parents="3816 10436"/>
    </justification>
  </clause>

  <clause id="10439">
    <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(843,a,10438,a)].">
      <j1 rule="hyper" parents="843 10438"/>
    </justification>
  </clause>

  <clause id="10440">
    <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(629,a,10438,a),flip(a)].">
      <j1 rule="hyper" parents="629 10438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10441">
    <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(10438(a,1),629(a,1))].">
      <j1 rule="para" parents="10438 629"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x \ L(x,u,w),y,z)) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,10439,a(flip),b,2157,a),flip(a)].">
      <j1 rule="hyper" parents="125 10439 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      L(L(x,y,y),z,u) * a(y,y,x) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(10440(a,1),2933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10440 2933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = L(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(10440(a,1),3862(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10440 3862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      L(x,L(y,z,u) * L(L(y,z,u),w,v5),v6) = L(x,L(y \ L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(10440(a,1),3863(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10440 3863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10447">
    <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(10440(a,1),9916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10440 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10448">
    <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(10440(a,1),9929(a,1,1))].">
      <j1 rule="para" parents="10440 9929"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ 1 = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1364,a,10447,a),flip(a)].">
      <j1 rule="hyper" parents="1364 10447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,u,w) = L(x \ L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(25(a,1),10447(a,1,1))].">
      <j1 rule="para" parents="25 10447"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = L(x,y,L(z * L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3981,a(flip),b,10445,a),flip(a)].">
      <j1 rule="hyper" parents="370 3981 10445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      L(x,L(y,z,u) * L(L(y,z,u),w,v5),v6) = L(x,L(y * L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,3984,a(flip),b,10446,a),flip(a)].">
      <j1 rule="hyper" parents="370 3984 10446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <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(629,a,10437,a),flip(a)].">
      <j1 rule="hyper" parents="629 10437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10455">
    <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(1069(a,1),10453(a,2,1,2))].">
      <j1 rule="para" parents="1069 10453"/>
    </justification>
  </clause>

  <clause id="10456">
    <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(9086(a,1),10453(a,1,1))].">
      <j1 rule="para" parents="9086 10453"/>
    </justification>
  </clause>

  <clause id="10457">
    <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(2171(a,1),10455(a,1,2))].">
      <j1 rule="para" parents="2171 10455"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),10457(a,2,1,2))].">
      <j1 rule="para" parents="222 10457"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1709(a,2),10458(a,2,1))].">
      <j1 rule="para" parents="1709 10458"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4585,a(flip),b,10459,a),flip(a)].">
      <j1 rule="hyper" parents="370 4585 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10462">
    <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(9086(a,1),10456(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9086 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10463">
    <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(370,a,10453,a(flip),b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="370 10453 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10465">
    <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(1769(a,1),10463(a,2,1))].">
      <j1 rule="para" parents="1769 10463"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1769(a,1),10465(a,1,1))].">
      <j1 rule="para" parents="1769 10465"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      T((x * K(y,x)) * (R(K(y,x),x,(x * K(y,x)) \ 1) \ 1),z) = (x * K(y,x)) * (T(x,z) * (x \ K(x,y)))
    ]]></literal>
    <justification jstring="[para(5964(a,1),5006(a,2,2,2))].">
      <j1 rule="para" parents="5964 5006"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * (K(y,x) \ 1),z)
    ]]></literal>
    <justification jstring="[para(8363(a,1),10467(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8363 10467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T((x * K(y,x)) * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5865(a,1),10468(a,2,1,2))].">
      <j1 rule="para" parents="5865 10468"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),10469(a,2,1))].">
      <j1 rule="para" parents="6281 10469"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(147,a,10471,a)].">
      <j1 rule="hyper" parents="147 10471"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = T(x * K(z,x),x \ K(x,z)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10472(a,1),4574(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10472 4574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ K(x,z)) \ 1) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(7061(a,1),10473(a,2,1))].">
      <j1 rule="para" parents="7061 10473"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),(x \ 1) \ K(z,x)) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(7062(a,1),10474(a,1,2,2))].">
      <j1 rule="para" parents="7062 10474"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),T(x,z)) = ((x \ 1) \ K(z,x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8872(a,1),10475(a,1,2))].">
      <j1 rule="para" parents="8872 10475"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9006(a,1),10476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9006 10476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(9115,a,10477,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9115 10477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      K((x \ y) \ 1,((z \ K(z,u)) * T(z,w)) \ 1) = K(y \ x,T(z,w) \ ((z \ 1) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(10478(a,1),6467(a,1,2,1))].">
      <j1 rule="para" parents="10478 6467"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      (((x \ K(x,y)) \ 1) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(10478(a,2),6902(a,1,2,1))].">
      <j1 rule="para" parents="10478 6902"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      K((x * (K(y,x) / T(x,z))) \ 1,((u \ K(u,w)) * T(u,v5)) \ 1) = K(((x \ 1) \ K(y,x)) \ T(x,z),T(u,v5) \ ((u \ 1) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(9384(a,1),10480(a,1,1,1))].">
      <j1 rule="para" parents="9384 10480"/>
    </justification>
  </clause>

  <clause id="10483">
    <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(2798(a,1),5106(a,1,1))].">
      <j1 rule="para" parents="2798 5106"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(4215(a,1),10483(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4215 10483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),10484(a,2,1,1,2))].">
      <j1 rule="para" parents="2 10484"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(77(a,1),10485(a,2,2))].">
      <j1 rule="para" parents="77 10485"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(4963(a,1),10486(a,1,1))].">
      <j1 rule="para" parents="4963 10486"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7478,a(flip),b,10487,a),flip(a)].">
      <j1 rule="hyper" parents="370 7478 10487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(10487(a,1),40(a,1))].">
      <j1 rule="para" parents="10487 40"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4995,a(flip),b,10488,a)].">
      <j1 rule="hyper" parents="60 4995 10488"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),10488(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 10488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(10490(a,1),6167(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10490 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(7355,a,10491,a)].">
      <j1 rule="hyper" parents="7355 10491"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,9432,a(flip),b,10493,a(flip))].">
      <j1 rule="hyper" parents="125 9432 10493"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(8019(a,2),10492(a,2,2))].">
      <j1 rule="para" parents="8019 10492"/>
    </justification>
  </clause>

  <clause id="10497">
    <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(10496(a,2),9156(a,1))].">
      <j1 rule="para" parents="10496 9156"/>
    </justification>
  </clause>

  <clause id="10498">
    <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(5801(a,1),8554(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5801 8554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(370,a,1876,a(flip),b,10498,a),flip(a)].">
      <j1 rule="hyper" parents="370 1876 10498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(8548(a,1),10499(a,1,3))].">
      <j1 rule="para" parents="8548 10499"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * R(1 / (y / x),y / x,y * (x / y)) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(10500(a,1),4213(a,1,1,1))].">
      <j1 rule="para" parents="10500 4213"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(10500(a,1),10501(a,1,2))].">
      <j1 rule="para" parents="10500 10501"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      T(x / y,(x / y) \ (1 / (y / x))) = x / y
    ]]></literal>
    <justification jstring="[hyper(413,a,10502,a)].">
      <j1 rule="hyper" parents="413 10502"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      T(x / y,(x / y) \ ((y / x) \ 1)) = x / y
    ]]></literal>
    <justification jstring="[hyper(60,a,4658,a(flip),b,10503,a)].">
      <j1 rule="hyper" parents="60 4658 10503"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(129,a,10504,a(flip),b,108,a(flip))].">
      <j1 rule="hyper" parents="129 10504 108"/>
    </justification>
  </clause>

  <clause id="10506">
    <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(77(a,1),9329(a,1,1,2))].">
      <j1 rule="para" parents="77 9329"/>
    </justification>
  </clause>

  <clause id="10507">
    <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(20(a,2),10506(a,1,1))].">
      <j1 rule="para" parents="20 10506"/>
    </justification>
  </clause>

  <clause id="10508">
    <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(1498(a,1),10507(a,1,1))].">
      <j1 rule="para" parents="1498 10507"/>
    </justification>
  </clause>

  <clause id="10509">
    <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(77(a,1),10508(a,1,2,2,2))].">
      <j1 rule="para" parents="77 10508"/>
    </justification>
  </clause>

  <clause id="10510">
    <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(20(a,2),10509(a,1,2,2))].">
      <j1 rule="para" parents="20 10509"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1498(a,1),10510(a,1,2,2))].">
      <j1 rule="para" parents="1498 10510"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10511(a,1,2))].">
      <j1 rule="para" parents="4 10511"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(10512(a,1),7714(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10512 7714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(215,a,10514,a)].">
      <j1 rule="hyper" parents="215 10514"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,4632,a(flip),b,10515,a)].">
      <j1 rule="hyper" parents="60 4632 10515"/>
    </justification>
  </clause>

  <clause id="10517">
    <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(5954(a,1),9981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5954 9981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10518">
    <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(370,a,7983,a(flip),b,10517,a),flip(a)].">
      <j1 rule="hyper" parents="370 7983 10517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10520">
    <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(370,a,7864,a(flip),b,10518,a),flip(a)].">
      <j1 rule="hyper" parents="370 7864 10518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10521">
    <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(5954(a,1),10520(a,1,2))].">
      <j1 rule="para" parents="5954 10520"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9187,a(flip),b,10521,a)].">
      <j1 rule="hyper" parents="60 9187 10521"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      (x \ (L(x,y,z) \ u)) * L((x \ (L(x,y,z) \ u)) \ (x \ u),w,v5) = L(L(x,y,z),w,v5) * (L(x,y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[para(2178(a,1),2206(a,1,2,1,1))].">
      <j1 rule="para" parents="2178 2206"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      (x \ (1 / x)) * (y / (((x \ 1) * x) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1211(a,1),3276(a,1,1))].">
      <j1 rule="para" parents="1211 3276"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      (x \ (1 / x)) * (y / (K(x,x \ 1) * (((x \ 1) \ 1) \ z))) = T(y / ((1 / x) \ z),(x \ 1) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1724(a,2),10525(a,1,2,2,1))].">
      <j1 rule="para" parents="1724 10525"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(y \ 1) \ ((y \ 1) \ 1)) = (y \ (1 / y)) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(3558(a,1),10526(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3558 10526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(y \ 1) \ ((y \ 1) \ 1)) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,10527,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),(1 / y) \ y) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[para(9034(a,1),10528(a,1,2))].">
      <j1 rule="para" parents="9034 10528"/>
    </justification>
  </clause>

  <clause id="10531">
    <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(1332(a,1),3332(a,1,1,2,1))].">
      <j1 rule="para" parents="1332 3332"/>
    </justification>
  </clause>

  <clause id="10532">
    <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(2039(a,1),10531(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2039 10531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <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(4436(a,1),10532(a,2,1))].">
      <j1 rule="para" parents="4436 10532"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(257(a,1),10534(a,2,1))].">
      <j1 rule="para" parents="257 10534"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,444,a(flip),b,10535,a),flip(a)].">
      <j1 rule="hyper" parents="370 444 10535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1
    ]]></literal>
    <justification jstring="[hyper(129,a,10536,a(flip),b,88,a),flip(a)].">
      <j1 rule="hyper" parents="129 10536 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,3,a(flip),b,10539,a)].">
      <j1 rule="hyper" parents="128 3 10539"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (1 * R(1 \ ((x \ (x / y)) \ 1),z,u)) = ((x * y) \ x) \ R((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3501(a,1),3504(a,2,2,1))].">
      <j1 rule="para" parents="3501 3504"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (1 * R(1 \ ((x \ (x / y)) \ 1),z,u)) = (x * y) \ (x * R(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,2514,a(flip),b,10541,a),flip(a)].">
      <j1 rule="hyper" parents="370 2514 10541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (1 * R(1 \ ((x \ (x / y)) \ 1),z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),10542(a,2,2,2,1))].">
      <j1 rule="para" parents="4 10542"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      (1 / x) * T((1 / ((x \ 1) \ 1)) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1307(a,1),3689(a,1,1))].">
      <j1 rule="para" parents="1307 3689"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      (1 / x) * T((x \ 1) \ (((x \ 1) \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),10545(a,1,2,1,1))].">
      <j1 rule="para" parents="74 10545"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),(x \ 1) \ 1) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1015(a,1),10546(a,1,2,1))].">
      <j1 rule="para" parents="1015 10546"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),x) = (x \ (x \ y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4441(a,1),10548(a,1,2))].">
      <j1 rule="para" parents="4441 10548"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = (x \ (x / y)) \ L(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(3503(a,1),4045(a,2,2,1))].">
      <j1 rule="para" parents="3503 4045"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = x \ ((x / y) * L((x / y) \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3823,a(flip),b,10550,a),flip(a)].">
      <j1 rule="hyper" parents="370 3823 10550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(1 \ (((x * y) \ x) \ 1),z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),10551(a,2,2,2,1))].">
      <j1 rule="para" parents="77 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (1 * L(((x * y) \ x) \ 1,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(62(a,1),10552(a,1,2,2,1))].">
      <j1 rule="para" parents="62 10552"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ L(((x * y) \ x) \ 1,z,u) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(392,a,10553,a)].">
      <j1 rule="hyper" parents="392 10553"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      ((x * y) \ x) \ L((x * y) \ x,z,u) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3829,a,10554,a)].">
      <j1 rule="hyper" parents="3829 10554"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      (x * y) \ (x * L(x \ (x * y),z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4048,a,10555,a)].">
      <j1 rule="hyper" parents="4048 10555"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),10556(a,1,2,2,1))].">
      <j1 rule="para" parents="4 10556"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(822,a,10557,a)].">
      <j1 rule="hyper" parents="822 10557"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      ((x * (y / x)) * x) \ (y * L(T(x,x \ y),z,u)) = y \ ((y / T(x,x \ y)) * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(5804(a,2),10557(a,1,1))].">
      <j1 rule="para" parents="5804 10557"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (x * (((x \ 1) \ 1) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(74(a,1),4707(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="74 4707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (x * (x \ (z * ((x \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[para(4985(a,1),10561(a,2,2,2))].">
      <j1 rule="para" parents="4985 10561"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(x \ 1) \ ((x \ 1) \ 1)) = ((1 / x) \ y) \ (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),10563(a,2,2))].">
      <j1 rule="para" parents="5 10563"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      (x \ y) \ T(z * (x \ 1),(1 / x) \ x) = ((1 / x) \ y) \ (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(9034(a,1),10564(a,1,2,2))].">
      <j1 rule="para" parents="9034 10564"/>
    </justification>
  </clause>

  <clause id="10567">
    <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(5(a,1),7091(a,2,2,1,2))].">
      <j1 rule="para" parents="5 7091"/>
    </justification>
  </clause>

  <clause id="10568">
    <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(370,a,273,a(flip),b,10567,a),flip(a)].">
      <j1 rule="hyper" parents="370 273 10567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <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(273(a,1),10568(a,1,2))].">
      <j1 rule="para" parents="273 10568"/>
    </justification>
  </clause>

  <clause id="10570">
    <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(7506(a,1),10569(a,1,2,2))].">
      <j1 rule="para" parents="7506 10569"/>
    </justification>
  </clause>

  <clause id="10571">
    <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(370,a,10453,a(flip),b,10570,a),flip(a)].">
      <j1 rule="hyper" parents="370 10453 10570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6633(a,1),9717(a,2,2,1))].">
      <j1 rule="para" parents="6633 9717"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(L(x,T(y,x),x),T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(5485(a,1),10572(a,2,2,2,1))].">
      <j1 rule="para" parents="5485 10572"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,T(x,x * y) \ z)
    ]]></literal>
    <justification jstring="[para(7287(a,1),10573(a,2,2))].">
      <j1 rule="para" parents="7287 10573"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = z * K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9198(a,1),10574(a,2,2))].">
      <j1 rule="para" parents="9198 10574"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      (((x * (y * x)) / x) / y) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5766,a(flip),b,10576,a),flip(a)].">
      <j1 rule="hyper" parents="370 5766 10576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / (((x * (y * x)) / x) / y)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(6633(a,1),10577(a,1,1))].">
      <j1 rule="para" parents="6633 10577"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      L(x,T(y,x),x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(6633(a,1),10579(a,1,2,2))].">
      <j1 rule="para" parents="6633 10579"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,T(y,x),x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(6632(a,1),10580(a,1,1))].">
      <j1 rule="para" parents="6632 10580"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      L(x,y,x) * (z / L(x,y,x)) = x * (z / x)
    ]]></literal>
    <justification jstring="[para(6632(a,1),10581(a,1,2,2))].">
      <j1 rule="para" parents="6632 10581"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      ((x \ y) * x) / L(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,73,a(flip),b,10582,a),flip(a)].">
      <j1 rule="hyper" parents="125 73 10582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      (L(x,y,x) \ z) * L(x,y,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[hyper(155,a,10583,a)].">
      <j1 rule="hyper" parents="155 10583"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      (x \ (L(x,y,x) * z)) * x = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5002,a,10583,a(flip))].">
      <j1 rule="hyper" parents="5002 10583"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      ((x \ y) * x) / L(x,z,x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,z,x) \ y = u
    ]]></literal>
    <justification jstring="[para(10584(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10584 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      (1 / R(x,y,z)) \ (K(x,u) / R(x,y,z)) = (R(x,y,z) \ 1) \ (R(x,y,z) \ K(x,u))
    ]]></literal>
    <justification jstring="[para(1712(a,1),10133(a,1,1))].">
      <j1 rule="para" parents="1712 10133"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      (1 / R(x,y,z)) * K(x,u) = K(x,u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,7624,a(flip),b,10587,a)].">
      <j1 rule="hyper" parents="129 7624 10587"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      K(x,x * y) / T(x,y) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,7366,a,b,10588,a)].">
      <j1 rule="hyper" parents="32 7366 10588"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ (K(x,y) * (R(x,z,u) \ 1)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(10588(a,1),10432(a,1,1))].">
      <j1 rule="para" parents="10588 10432"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ (R(x,z,u) \ K(x,y)) = (R(x,z,u) \ K(x,y)) * (K(x,y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(10368(a,1),10590(a,1,2))].">
      <j1 rule="para" parents="10368 10590"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(x,y) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1802,a,10591,a)].">
      <j1 rule="hyper" parents="1802 10591"/>
    </justification>
  </clause>

  <clause id="10593">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) \ 1 = K(y,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,10592,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * K(w,R(x,y,R(x,z,u))) = K(w,x) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9762,a,b,10593,a)].">
      <j1 rule="hyper" parents="60 9762 10593"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4792,a,10594,a),flip(a)].">
      <j1 rule="hyper" parents="4792 10594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8915,a,10595,a),flip(a)].">
      <j1 rule="hyper" parents="8915 10595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8896,a,10596,a),flip(a)].">
      <j1 rule="hyper" parents="8896 10596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ u) * L((L(x,y,z) \ u) \ u,w,v5)) = L(L(x,y,z),w,v5) * (L(x,y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,2521,a(flip),b,10524,a)].">
      <j1 rule="hyper" parents="60 2521 10524"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      x \ (L(L(x,y,z),u,w) * (L(x,y,z) \ v5)) = L(L(x,y,z),u,w) * (L(x,y,z) \ (x \ v5))
    ]]></literal>
    <justification jstring="[para(876(a,1),10600(a,1,2))].">
      <j1 rule="para" parents="876 10600"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      x \ (L(L(x,y,z),u,w) * (L(x,y,z) \ v5)) = L(L(x,y,z),u,w) * (x \ (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(2178(a,1),10601(a,2,2))].">
      <j1 rule="para" parents="2178 10601"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x \ (L(x,y,z) \ (L(x,y,z) * v5))) = x \ (L(L(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),10602(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      x \ (L(L(x,y,z),u,w) * v5) = L(L(x,y,z),u,w) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),10603(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10607">
    <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(103(a,1),2502(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="103 2502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10608">
    <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(370,a,1270,a(flip),b,10607,a),flip(a)].">
      <j1 rule="hyper" parents="370 1270 10607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10609">
    <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(370,a,3228,a(flip),b,10608,a),flip(a)].">
      <j1 rule="hyper" parents="370 3228 10608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10610">
    <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(1270(a,1),10609(a,1,1))].">
      <j1 rule="para" parents="1270 10609"/>
    </justification>
  </clause>

  <clause id="10611">
    <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(2574(a,1),10610(a,2,1))].">
      <j1 rule="para" parents="2574 10610"/>
    </justification>
  </clause>

  <clause id="10612">
    <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(32,a,103,a,b,10611,a),flip(a)].">
      <j1 rule="hyper" parents="32 103 10611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5386,a,10612,a),flip(a)].">
      <j1 rule="hyper" parents="5386 10612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(2590,a,10612,a),flip(a)].">
      <j1 rule="hyper" parents="2590 10612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5245(a,1),10613(a,1,1))].">
      <j1 rule="para" parents="5245 10613"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(9309,a,10615,a),flip(a)].">
      <j1 rule="hyper" parents="9309 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5428(a,1),10615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5428 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6463(a,1),10615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6463 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(8340(a,1),10615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8340 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(10615(a,1),9632(a,2,2))].">
      <j1 rule="para" parents="10615 9632"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(26(a,1),10616(a,1,2,1))].">
      <j1 rule="para" parents="26 10616"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,10617,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 10617 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(10617(a,1),7551(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10617 7551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(10617(a,1),9215(a,1,1,1))].">
      <j1 rule="para" parents="10617 9215"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(103(a,1),10624(a,1,1))].">
      <j1 rule="para" parents="103 10624"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(9753(a,1),10624(a,1,1,1))].">
      <j1 rule="para" parents="9753 10624"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(7481(a,1),10626(a,1,1))].">
      <j1 rule="para" parents="7481 10626"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(7908(a,1),10626(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7908 10626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(8785(a,1),10626(a,1,1,1))].">
      <j1 rule="para" parents="8785 10626"/>
    </justification>
  </clause>

  <clause id="10630">
    <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(10625(a,1),10035(a,1,1,2))].">
      <j1 rule="para" parents="10625 10035"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(5016,a,10623,a)].">
      <j1 rule="hyper" parents="5016 10623"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(839,a,10623,a)].">
      <j1 rule="hyper" parents="839 10623"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(779,a,10623,a)].">
      <j1 rule="hyper" parents="779 10623"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(722,a,10623,a)].">
      <j1 rule="hyper" parents="722 10623"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,7976,a(flip),b,10623,a),flip(a)].">
      <j1 rule="hyper" parents="60 7976 10623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(127,a,10623,a(flip),b,427,a(flip))].">
      <j1 rule="hyper" parents="127 10623 427"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(10623(a,2),143(a,1)),flip(b)].">
      <j1 rule="para" parents="10623 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <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(10004(a,1),10631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10004 10631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(10627(a,2),5597(a,1,1,2))].">
      <j1 rule="para" parents="10627 5597"/>
    </justification>
  </clause>

  <clause id="10640">
    <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(9071,a,10629,a)].">
      <j1 rule="hyper" parents="9071 10629"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      R(K(x,y),z,u) != (z * u) / w
    ]]></literal>
    <literal><![CDATA[
      (K(y,x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(10632(a,1),42(a,1))].">
      <j1 rule="para" parents="10632 42"/>
    </justification>
  </clause>

  <clause id="10642">
    <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(10618(a,1),10142(a,1,2))].">
      <j1 rule="para" parents="10618 10142"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(9141,a,10619,a),flip(a)].">
      <j1 rule="hyper" parents="9141 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(706(a,1),10619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="706 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(673(a,1),10619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="673 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10643(a,2,2,1))].">
      <j1 rule="para" parents="7 10643"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),10643(a,2,2,2))].">
      <j1 rule="para" parents="7 10643"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(74(a,1),10643(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 10643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10649">
    <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(4216(a,1),10643(a,1,1,2))].">
      <j1 rule="para" parents="4216 10643"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(7446,a,10647,a),flip(a)].">
      <j1 rule="hyper" parents="7446 10647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,7629,a(flip),b,10647,a),flip(a)].">
      <j1 rule="hyper" parents="60 7629 10647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(7345(a,1),10647(a,1,1))].">
      <j1 rule="para" parents="7345 10647"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9208,a(flip),b,10650,a),flip(a)].">
      <j1 rule="hyper" parents="370 9208 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(100(a,2),10648(a,1,2))].">
      <j1 rule="para" parents="100 10648"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      K(x,R(y,T(y,x) \ z,u)) = R(K(x,T(y,x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(5983,a,10654,a)].">
      <j1 rule="hyper" parents="5983 10654"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,9767,a(flip),b,10654,a)].">
      <j1 rule="hyper" parents="60 9767 10654"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,10654,a(flip),b,9767,a(flip))].">
      <j1 rule="hyper" parents="129 10654 9767"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),10654(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(17(a,2),10654(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w))
    ]]></literal>
    <justification jstring="[para(210(a,1),10654(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="210 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(7890(a,1),10654(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7890 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(9309,a,10658,a),flip(a)].">
      <j1 rule="hyper" parents="9309 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7446,a,10658,a),flip(a)].">
      <j1 rule="hyper" parents="7446 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7440,a,10658,a),flip(a)].">
      <j1 rule="hyper" parents="7440 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6920,a,10658,a)].">
      <j1 rule="hyper" parents="6920 10658"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10017,a(flip),b,10658,a)].">
      <j1 rule="hyper" parents="60 10017 10658"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,9213,a(flip),b,10658,a),flip(a)].">
      <j1 rule="hyper" parents="60 9213 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(10658(a,1),22(a,2,1))].">
      <j1 rule="para" parents="10658 22"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10658(a,1),9204(a,1,2,1))].">
      <j1 rule="para" parents="10658 9204"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(10658(a,1),8272(a,1,1))].">
      <j1 rule="para" parents="10658 8272"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      T(x,R(y,z,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,10663,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 10663 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      K(x,K(y,R(z,u,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10658(a,1),10663(a,1,2))].">
      <j1 rule="para" parents="10658 10663"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,10664,a(flip),b,6108,a),flip(a)].">
      <j1 rule="hyper" parents="129 10664 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,10671,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(708(a,1),10674(a,1,2))].">
      <j1 rule="para" parents="708 10674"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u))
    ]]></literal>
    <justification jstring="[para(1091(a,1),10674(a,1,2))].">
      <j1 rule="para" parents="1091 10674"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),T(x,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10123,a(flip),b,10666,a),flip(a)].">
      <j1 rule="hyper" parents="60 10123 10666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(7481(a,1),10669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7481 10669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(7500(a,1),10669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 10669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8016(a,1),10669(a,1,2))].">
      <j1 rule="para" parents="8016 10669"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      K(x,K(y,T((z * x) / u,u / x))) = K(x,K(y,(u / x) \ z))
    ]]></literal>
    <justification jstring="[para(1096(a,1),10672(a,1,2,2))].">
      <j1 rule="para" parents="1096 10672"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8919(a,1),10682(a,1,2))].">
      <j1 rule="para" parents="8919 10682"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(7879(a,1),10682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7879 10682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(7913(a,1),10682(a,1,2))].">
      <j1 rule="para" parents="7913 10682"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6442(a,1),10683(a,1,2))].">
      <j1 rule="para" parents="6442 10683"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9188,a(flip),b,10677,a),flip(a)].">
      <j1 rule="hyper" parents="370 9188 10677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9203,a(flip),b,10667,a),flip(a)].">
      <j1 rule="hyper" parents="370 9203 10667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      K(x,R(R(y,K(z,x),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(26(a,1),10690(a,1,2))].">
      <j1 rule="para" parents="26 10690"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),10685(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 10685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      x / R(K(y,z),u,w) = x * R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(221,a,10656,a)].">
      <j1 rule="hyper" parents="221 10656"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7652(a,2),10656(a,1,1))].">
      <j1 rule="para" parents="7652 10656"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10371(a,1),10656(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10371 10656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      R((x * R(K(y,z),u,u \ 1)) * K(z,y),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(10694(a,1),7631(a,1,1,1))].">
      <j1 rule="para" parents="10694 7631"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,10697,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 10697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,R(x,y,z) / (w / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10647,a(flip),b,10699,a)].">
      <j1 rule="hyper" parents="60 10647 10699"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9309,a,10652,a),flip(a)].">
      <j1 rule="hyper" parents="9309 10652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(10652(a,1),9309(a,1))].">
      <j1 rule="para" parents="10652 9309"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8832,a,b,10701,a)].">
      <j1 rule="hyper" parents="60 8832 10701"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(2467(a,1),10701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2467 10701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(10704(a,2),8011(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10704 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      K(x,(((y * K(z,x)) * u) * w) / (u * w)) = K(x,R(y,K(z,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9695,a(flip),b,10692,a)].">
      <j1 rule="hyper" parents="60 9695 10692"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(8832(a,2),10702(a,1))].">
      <j1 rule="para" parents="8832 10702"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      L(x,y,x) * K(x,R(z \ 1,u,w) \ 1) = L(x * R(K(x,z),u,w),y,x)
    ]]></literal>
    <justification jstring="[para(10622(a,1),7289(a,2,1))].">
      <j1 rule="para" parents="10622 7289"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      K(x,R(y,T(y,x) \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5688(a,1),10655(a,2,1))].">
      <j1 rule="para" parents="5688 10655"/>
    </justification>
  </clause>

  <clause id="10711">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,10668,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 10668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9390,a(flip),b,10678,a),flip(a)].">
      <j1 rule="hyper" parents="370 9390 10678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(9025,a,10686,a)].">
      <j1 rule="hyper" parents="9025 10686"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),10711(a,2,2))].">
      <j1 rule="para" parents="22 10711"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8019(a,2),10714(a,1,1))].">
      <j1 rule="para" parents="8019 10714"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),10715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      R(K(x,y),(y * K(z,y)) * u,w) = K(x,R(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(5280(a,1),10715(a,1,1,2))].">
      <j1 rule="para" parents="5280 10715"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,700,a(flip),b,10716,a),flip(a)].">
      <j1 rule="hyper" parents="370 700 10716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7635,a(flip),b,10716,a)].">
      <j1 rule="hyper" parents="60 7635 10716"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a(flip),b,10718,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 10718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(717(a,1),10621(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="717 10621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),10644(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 10644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      K(x / y,(x / y) / z) = K(x / y,x / (z * y))
    ]]></literal>
    <justification jstring="[hyper(9309,a,10646,a)].">
      <j1 rule="hyper" parents="9309 10646"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9320,a(flip),b,10646,a)].">
      <j1 rule="hyper" parents="60 9320 10646"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      K(x / y,x / (z * y)) = K(x / y,z \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(8463,a,10723,a),flip(a)].">
      <j1 rule="hyper" parents="8463 10723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10726">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(z * y) \ x) = u
    ]]></literal>
    <justification jstring="[para(10725(a,1),8818(a,1))].">
      <j1 rule="para" parents="10725 8818"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,9422,a(flip),b,10620,a),flip(a)].">
      <j1 rule="hyper" parents="370 9422 10620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) * x = T(x,K(R(z,u,w) \ 1,y))
    ]]></literal>
    <justification jstring="[para(10620(a,2),8687(a,1,1))].">
      <j1 rule="para" parents="10620 8687"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9422(a,1),10727(a,1,1))].">
      <j1 rule="para" parents="9422 10727"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      x * R(K(x,K(y,z)),u,w) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,10729,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 10729 5230"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9632,a(flip),b,10729,a)].">
      <j1 rule="hyper" parents="60 9632 10729"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,1),10729(a,1,1))].">
      <j1 rule="para" parents="8636 10729"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10729,a(flip),b,10732,a),flip(a)].">
      <j1 rule="hyper" parents="60 10729 10732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9631,a(flip),b,10732,a)].">
      <j1 rule="hyper" parents="60 9631 10732"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9633,a,10730,a)].">
      <j1 rule="hyper" parents="9633 10730"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      R(K(x,y),K(x,y) * z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,10710,a(flip),b,10661,a),flip(a)].">
      <j1 rule="hyper" parents="370 10710 10661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,x),z) = R(K(x,y),y \ 1,z)
    ]]></literal>
    <justification jstring="[para(7513(a,1),10736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7513 10736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = ((((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z)) * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(10737(a,2),2530(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10737 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4756,a(flip),b,10673,a),flip(a)].">
      <j1 rule="hyper" parents="370 4756 10673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10651,a,b,10688,a)].">
      <j1 rule="hyper" parents="60 10651 10688"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10076,a(flip),b,10693,a),flip(a)].">
      <j1 rule="hyper" parents="60 10076 10693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),10741(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 10741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(210(a,1),10741(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="210 10741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8911,a,10743,a),flip(a)].">
      <j1 rule="hyper" parents="8911 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8621,a,b,10743,a),flip(a)].">
      <j1 rule="hyper" parents="370 8621 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9394,a,b,10744,a)].">
      <j1 rule="hyper" parents="60 9394 10744"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),10748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 10748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8924,a,10746,a)].">
      <j1 rule="hyper" parents="8924 10746"/>
    </justification>
  </clause>

  <clause id="10751">
    <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(10746(a,2),8920(a,1))].">
      <j1 rule="para" parents="10746 8920"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(103(a,1),10750(a,1,2,2))].">
      <j1 rule="para" parents="103 10750"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(8634,a,10752,a)].">
      <j1 rule="hyper" parents="8634 10752"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(10752(a,1),8666(a,1,1))].">
      <j1 rule="para" parents="10752 8666"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(448(a,1),10751(a,1,2,2,1))].">
      <j1 rule="para" parents="448 10751"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (x * y),y)) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),10755(a,1,2))].">
      <j1 rule="para" parents="109 10755"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3839(a,1),10705(a,1,2,1))].">
      <j1 rule="para" parents="3839 10705"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      x \ R(x * K(y,x),z,y \ 1) = K(y,x) * (x \ R(x,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(125,a,10739,a,b,7958,a)].">
      <j1 rule="hyper" parents="125 10739 7958"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8992,a,10754,a),flip(a)].">
      <j1 rule="hyper" parents="8992 10754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10760(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 10760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(10755,a,10761,a),flip(a)].">
      <j1 rule="hyper" parents="10755 10761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),10762(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 10762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10764">
    <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(10762(a,1),8839(a,1,1,1))].">
      <j1 rule="para" parents="10762 8839"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      x / (R(K(y,z),u,(K(y,z) * u) \ 1) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,10634,a,b,10636,a)].">
      <j1 rule="hyper" parents="60 10634 10636"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,9312,a(flip),b,10636,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 9312 10636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[para(6438(a,1),10766(a,1,1))].">
      <j1 rule="para" parents="6438 10766"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      L(x,y * (K(z,u) / T(u,w)),v5) = L(x,y * (T(u,z) \ K(w,u)),v5)
    ]]></literal>
    <justification jstring="[para(10767(a,1),9659(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10767 9659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(5124(a,1),10614(a,1,1))].">
      <j1 rule="para" parents="5124 10614"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5140,a(flip),b,10769,a),flip(a)].">
      <j1 rule="hyper" parents="370 5140 10769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <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(370,a,5148,a,b,10770,a)].">
      <j1 rule="hyper" parents="370 5148 10770"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      K(x,K((y * x) / z,T(u,z))) = K(x,K(u,(z / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(9094,a,10684,a)].">
      <j1 rule="hyper" parents="9094 10684"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ (u * x)))
    ]]></literal>
    <justification jstring="[hyper(8891,a,10772,a),flip(a)].">
      <j1 rule="hyper" parents="8891 10772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = R(K(x,K(y,w)),z,u) * x
    ]]></literal>
    <justification jstring="[para(9426(a,1),10728(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9426 10728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = K(x,R(K(y,w),z,u)) * x
    ]]></literal>
    <justification jstring="[para(9632(a,1),10774(a,2,1))].">
      <j1 rule="para" parents="9632 10774"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      T(x,K(R(y,z,u) \ 1,w)) = T(x,R(K(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,10775,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10777">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9465,a,10776,a),flip(a)].">
      <j1 rule="hyper" parents="9465 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10735,a(flip),b,10777,a)].">
      <j1 rule="hyper" parents="60 10735 10777"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      T(x,K(y,R(z \ 1,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(9464,a,10778,a),flip(a)].">
      <j1 rule="hyper" parents="9464 10778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      T(x,K(y \ z,R(u,y,y \ 1))) = T(x,K(u,T(z * (y \ 1),y)))
    ]]></literal>
    <justification jstring="[para(910(a,1),10778(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="910 10778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10781">
    <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(10778(a,1),10048(a,2,2))].">
      <j1 rule="para" parents="10778 10048"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,R(z,y,x))) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(10779(a,1),10406(a,1,2))].">
      <j1 rule="para" parents="10779 10406"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,5597,a(flip),b,10630,a),flip(a)].">
      <j1 rule="hyper" parents="60 5597 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10785">
    <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(10783(a,1),10319(a,2,2,2,1,1))].">
      <j1 rule="para" parents="10783 10319"/>
    </justification>
  </clause>

  <clause id="10786">
    <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(10649(a,1),10734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10649 10734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      R(K(x * y,x),(x * y) * z,u) = K(x * y,R(R(x,y,z),y * z,u))
    ]]></literal>
    <justification jstring="[para(10662(a,1),10660(a,1,1))].">
      <j1 rule="para" parents="10662 10660"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      R(K(x,y),y * (K(z,y) * u),w) = K(x,R(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(7845(a,1),10717(a,1,2))].">
      <j1 rule="para" parents="7845 10717"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(10405(a,1),10724(a,1,1))].">
      <j1 rule="para" parents="10405 10724"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1040(a,1),10759(a,2,2))].">
      <j1 rule="para" parents="1040 10759"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(5352(a,1),10790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5352 10790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(10791(a,1),9510(a,1,2,1))].">
      <j1 rule="para" parents="10791 9510"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(x,R(T(y * K(z,y),z),u,w)) = K(x,R(y,K(z,y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10658,a(flip),b,10788,a),flip(a)].">
      <j1 rule="hyper" parents="60 10658 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(x,R(y,K(z,y) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5280(a,1),10793(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 10793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1811(a,2),10794(a,1,2,2))].">
      <j1 rule="para" parents="1811 10794"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7500(a,1),10794(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10659,a,b,10795,a)].">
      <j1 rule="hyper" parents="60 10659 10795"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10797(a,1,2))].">
      <j1 rule="para" parents="5 10797"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(5850(a,1),10797(a,1,2))].">
      <j1 rule="para" parents="5850 10797"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6268(a,1),10797(a,1,2))].">
      <j1 rule="para" parents="6268 10797"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      R(K(x,y),z * (y * K(u,x)),w) = K(x,R(y * K(u,x),z,w))
    ]]></literal>
    <justification jstring="[para(9203(a,1),10797(a,1,1))].">
      <j1 rule="para" parents="9203 10797"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(10796(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10796 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(8758(a,1),10796(a,1,2,2))].">
      <j1 rule="para" parents="8758 10796"/>
    </justification>
  </clause>

  <clause id="10804">
    <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(2022(a,1),10798(a,2,2))].">
      <j1 rule="para" parents="2022 10798"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,10803,a(flip),b,10800,a),flip(a)].">
      <j1 rule="hyper" parents="370 10803 10800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),10805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,10799,a,b,10807,a)].">
      <j1 rule="hyper" parents="60 10799 10807"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(701,a,10808,a),flip(a)].">
      <j1 rule="hyper" parents="701 10808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7996(a,1),10808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7996 10808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = w / (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,7511,a,b,10809,a),flip(a)].">
      <j1 rule="hyper" parents="370 7511 10809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(10641,a,10814,a)].">
      <j1 rule="hyper" parents="10641 10814"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(701,a,10812,a),flip(a)].">
      <j1 rule="hyper" parents="701 10812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),10812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 10812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10816(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10816 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,10815,a)].">
      <j1 rule="hyper" parents="625 10815"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2894(a,1),10815(a,1,1))].">
      <j1 rule="para" parents="2894 10815"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = (x \ R(x,y,x)) * z
    ]]></literal>
    <justification jstring="[para(7394(a,1),10815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7394 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(5886,a,10819,a)].">
      <j1 rule="hyper" parents="5886 10819"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      L(T(x / (x / y),y \ x),K(z,u),K(u,w)) = y
    ]]></literal>
    <justification jstring="[hyper(370,a,5839,a(flip),b,10819,a),flip(a)].">
      <j1 rule="hyper" parents="370 5839 10819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      L(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(6591(a,1),10819(a,1,2))].">
      <j1 rule="para" parents="6591 10819"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,K(y,z),K(u,K(z,w))) = x
    ]]></literal>
    <justification jstring="[para(8630(a,1),10819(a,1,3))].">
      <j1 rule="para" parents="8630 10819"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5885,a,10822,a)].">
      <j1 rule="hyper" parents="5885 10822"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1838,a,10822,a),flip(a)].">
      <j1 rule="hyper" parents="1838 10822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7618,a(flip),b,10822,a)].">
      <j1 rule="hyper" parents="60 7618 10822"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(z,y) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7618,a(flip),b,10826,a)].">
      <j1 rule="hyper" parents="60 7618 10826"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      (K(x,K(y,z)) * K(u,y)) * w = K(x,K(y,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(1838,a,10825,a),flip(a)].">
      <j1 rule="hyper" parents="1838 10825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      (K(x,y) * L(K(z,x),u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1838,a,10824,a),flip(a)].">
      <j1 rule="hyper" parents="1838 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(10823(a,1),9781(a,1,2,3))].">
      <j1 rule="para" parents="10823 9781"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,u) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(10818(a,1),389(a,1,2))].">
      <j1 rule="para" parents="10818 389"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2894(a,2),10818(a,1,1))].">
      <j1 rule="para" parents="2894 10818"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u * K(K(x,y) * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(10818(a,1),5240(a,1,1))].">
      <j1 rule="para" parents="10818 5240"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(8186(a,1),10818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8186 10818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,10818,a(flip),b,10820,a),flip(a)].">
      <j1 rule="hyper" parents="60 10818 10820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * z = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9604,a(flip),b,10827,a),flip(a)].">
      <j1 rule="hyper" parents="370 9604 10827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,y \ 1)) = ((y \ K(y,z)) * T(y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,9961,a(flip),b,10828,a),flip(a)].">
      <j1 rule="hyper" parents="60 9961 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(788,a,10828,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="788 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = z \ ((K(y,x) * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(10828(a,1),849(a,1,1))].">
      <j1 rule="para" parents="10828 849"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(6237,a,10841,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6237 10841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = (K(z,x) * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(10843(a,1),7574(a,2,1))].">
      <j1 rule="para" parents="10843 7574"/>
    </justification>
  </clause>

  <clause id="10845">
    <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(10835(a,1),5448(a,2,2,1))].">
      <j1 rule="para" parents="10835 5448"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) * K(y,u) = K(x,y) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(8726,a,10838,a)].">
      <j1 rule="hyper" parents="8726 10838"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,7935,a,b,10838,a)].">
      <j1 rule="hyper" parents="370 7935 10838"/>
    </justification>
  </clause>

  <clause id="10848">
    <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(6763(a,1),10838(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6763 10838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(7500(a,1),10838(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 10838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(7500(a,1),10838(a,2,2))].">
      <j1 rule="para" parents="7500 10838"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(7518,a,10849,a)].">
      <j1 rule="hyper" parents="7518 10849"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,10849,a(flip),b,10818,a)].">
      <j1 rule="hyper" parents="128 10849 10818"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(7518,a,10850,a)].">
      <j1 rule="hyper" parents="7518 10850"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) != K(x,z) * w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * u = w
    ]]></literal>
    <justification jstring="[para(10851(a,1),40(a,1))].">
      <j1 rule="para" parents="10851 40"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * u = w
    ]]></literal>
    <justification jstring="[para(10851(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10851 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(8636(a,2),10851(a,1,1))].">
      <j1 rule="para" parents="8636 10851"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(7512(a,1),10852(a,1,1))].">
      <j1 rule="para" parents="7512 10852"/>
    </justification>
  </clause>

  <clause id="10858">
    <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(10853(a,1),2530(a,1,1,1,1))].">
      <j1 rule="para" parents="10853 2530"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(z,K(x,x * y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8711(a,1),10821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8711 10821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9760,a(flip),b,10860,a)].">
      <j1 rule="hyper" parents="60 9760 10860"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(7500(a,1),10860(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,9757,a(flip),b,10861,a),flip(a)].">
      <j1 rule="hyper" parents="370 9757 10861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),10864(a,1,2))].">
      <j1 rule="para" parents="5232 10864"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),10864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 10864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(10865(a,1),10635(a,1,1))].">
      <j1 rule="para" parents="10865 10635"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10296,a(flip),b,10817,a),flip(a)].">
      <j1 rule="hyper" parents="60 10296 10817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10017,a(flip),b,10869,a),flip(a)].">
      <j1 rule="hyper" parents="60 10017 10869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(10871(a,1),5767(a,2,2,2))].">
      <j1 rule="para" parents="10871 5767"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(7839(a,1),10847(a,1,2))].">
      <j1 rule="para" parents="7839 10847"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(8016(a,1),10867(a,1,2,2))].">
      <j1 rule="para" parents="8016 10867"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10872(a,2),5768(a,1))].">
      <j1 rule="para" parents="10872 5768"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      x * ((y / T(z,y)) * u) != (y / z) * u
    ]]></literal>
    <literal><![CDATA[
      R(K(z,y),z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(10868(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="10868 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10874,a(flip),b,10801,a)].">
      <j1 rule="hyper" parents="60 10874 10801"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10797,a(flip),b,10878,a),flip(a)].">
      <j1 rule="hyper" parents="60 10797 10878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6281(a,1),10880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6281 10880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10882">
    <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(10831(a,2),1368(a,1,2))].">
      <j1 rule="para" parents="10831 1368"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = z \ (K(y,x) * (K(y,x) * u))
    ]]></literal>
    <justification jstring="[para(10827(a,1),10842(a,2,2))].">
      <j1 rule="para" parents="10827 10842"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      (x * K(y * z,y)) * K(y,z) = K(y * z,y) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8952(a,1),10846(a,1,1))].">
      <j1 rule="para" parents="8952 10846"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8636(a,2),10856(a,2,2,1))].">
      <j1 rule="para" parents="8636 10856"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = z \ (K(x,y) * (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(9604(a,1),10883(a,1,1))].">
      <j1 rule="para" parents="9604 10883"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(387,a,10885,a),flip(a)].">
      <j1 rule="hyper" parents="387 10885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = z \ (y * (T(T(y,x),x) \ u))
    ]]></literal>
    <justification jstring="[para(9604(a,1),10886(a,2,2))].">
      <j1 rule="para" parents="9604 10886"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(8636(a,2),10887(a,1,2,1))].">
      <j1 rule="para" parents="8636 10887"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(9143,a,10789,a)].">
      <j1 rule="hyper" parents="9143 10789"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9685,a(flip),b,10890,a),flip(a)].">
      <j1 rule="hyper" parents="60 9685 10890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10892">
    <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(107(a,1),10890(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 10890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9691,a(flip),b,10891,a)].">
      <j1 rule="hyper" parents="60 9691 10891"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,10893,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 10893 5230"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      (K(x,y) * L(K(x,z) \ 1,u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(5865(a,2),10832(a,1,1,2,1))].">
      <j1 rule="para" parents="5865 10832"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(6208(a,1),10840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6208 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(370,a,7967,a(flip),b,10896,a),flip(a)].">
      <j1 rule="hyper" parents="370 7967 10896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(9074(a,1),10897(a,2,2))].">
      <j1 rule="para" parents="9074 10897"/>
    </justification>
  </clause>

  <clause id="10899">
    <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(249(a,2),10857(a,1,2,2,2))].">
      <j1 rule="para" parents="249 10857"/>
    </justification>
  </clause>

  <clause id="10900">
    <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(8024(a,1),10638(a,1,1))].">
      <j1 rule="para" parents="8024 10638"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,K(z,x) * u,w))
    ]]></literal>
    <justification jstring="[para(15(a,2),10707(a,1,2))].">
      <j1 rule="para" parents="15 10707"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,8501,a,b,10902,a)].">
      <j1 rule="hyper" parents="60 8501 10902"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10880,a(flip),b,10902,a),flip(a)].">
      <j1 rule="hyper" parents="60 10880 10902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7500(a,1),10904(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 10904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(682(a,1),10906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="682 10906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,((y * K(x,z)) * u) * ((K(x,z) * u) \ 1))
    ]]></literal>
    <justification jstring="[para(735(a,1),10906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="735 10906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),w,v5)) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(26(a,1),10907(a,1,2))].">
      <j1 rule="para" parents="26 10907"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      x * K(x,R(y,K(z,x) * u,w)) = T(x,R(K(z,x) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,10903,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 10903 5230"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      T(x,R(K(y,x) * z,u,w)) = T(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(5265,a,10910,a),flip(a)].">
      <j1 rule="hyper" parents="5265 10910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      T(x,R(x \ y,K(z,x) * u,w)) = T(x,R(T(x,z) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(7873(a,1),10911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7873 10911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10875,a,10912,a),flip(a)].">
      <j1 rule="hyper" parents="10875 10912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(7056,a,10913,a)].">
      <j1 rule="hyper" parents="7056 10913"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(8755(a,1),10764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8755 10764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(155,a,10916,a)].">
      <j1 rule="hyper" parents="155 10916"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(y \ (y * x),y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10917(a,1,1,1,1))].">
      <j1 rule="para" parents="4 10917"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      K(x * y,R(R(x,y,z),y * z,u)) = K(R(x * y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(9941,a,10787,a),flip(a)].">
      <j1 rule="hyper" parents="9941 10787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      K(R(R(x,y,z),y * z,u),x * y) = w / (K(R(x * y,z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(10920(a,1),7511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10920 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(z,K(x,y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8947(a,1),10859(a,1,2))].">
      <j1 rule="para" parents="8947 10859"/>
    </justification>
  </clause>

  <clause id="10923">
    <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(8067(a,1),10900(a,1,1))].">
      <j1 rule="para" parents="8067 10900"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      K(R(R(x,y,z),y * z,u),x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10921(a,2),7520(a,1))].">
      <j1 rule="para" parents="10921 7520"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10004,a(flip),b,10923,a),flip(a)].">
      <j1 rule="hyper" parents="60 10004 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(7084(a,2),10925(a,1,1))].">
      <j1 rule="para" parents="7084 10925"/>
    </justification>
  </clause>

  <clause id="10927">
    <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(10926(a,1),5871(a,1))].">
      <j1 rule="para" parents="10926 5871"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      L(x * R(K(x,y),z,u),w,x) = L(x,w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10617(a,1),10709(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10617 10709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      L(x * R(K(x,y),z,u),w,x) = R(K(x,y),z,u) * L(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4930,a,b,10928,a),flip(a)].">
      <j1 rule="hyper" parents="370 4930 10928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <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(6763(a,1),10848(a,1,1))].">
      <j1 rule="para" parents="6763 10848"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8340,a(flip),b,10721,a),flip(a)].">
      <j1 rule="hyper" parents="370 8340 10721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10619,a(flip),b,10932,a)].">
      <j1 rule="hyper" parents="60 10619 10932"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(7345(a,1),10933(a,1,1))].">
      <j1 rule="para" parents="7345 10933"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(9941,a,10934,a),flip(a)].">
      <j1 rule="hyper" parents="9941 10934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),10935(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 10935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10937">
    <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(8205(a,1),10935(a,1,2,1))].">
      <j1 rule="para" parents="8205 10935"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9757,a(flip),b,10936,a),flip(a)].">
      <j1 rule="hyper" parents="60 9757 10936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10939">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(4441(a,1),10771(a,2,1,2))].">
      <j1 rule="para" parents="4441 10771"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(9704(a,1),10939(a,1,1,2))].">
      <j1 rule="para" parents="9704 10939"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),10940(a,1,1,2,2))].">
      <j1 rule="para" parents="6 10940"/>
    </justification>
  </clause>

  <clause id="10942">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4938,a(flip),b,10941,a),flip(a)].">
      <j1 rule="hyper" parents="60 4938 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(10942(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="10942 5131"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(5133,a,10944,a)].">
      <j1 rule="hyper" parents="5133 10944"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(263(a,1),10945(a,1,3)),flip(a)].">
      <j1 rule="para" parents="263 10945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(632,a,10947,a)].">
      <j1 rule="hyper" parents="632 10947"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3430,a,10948,a)].">
      <j1 rule="hyper" parents="3430 10948"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(10949(a,1),3542(a,1))].">
      <j1 rule="para" parents="10949 3542"/>
    </justification>
  </clause>

  <clause id="10952">
    <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(8678,a,10786,a)].">
      <j1 rule="hyper" parents="8678 10786"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10919(a,2,2,1,1))].">
      <j1 rule="para" parents="4 10919"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,10953,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="128 10953 259"/>
    </justification>
  </clause>

  <clause id="10955">
    <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(10953(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10953 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10957">
    <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(10952(a,1),8678(a,1))].">
      <j1 rule="para" parents="10952 8678"/>
    </justification>
  </clause>

  <clause id="10958">
    <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(22(a,2),10640(a,1,1,2))].">
      <j1 rule="para" parents="22 10640"/>
    </justification>
  </clause>

  <clause id="10959">
    <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(60,a,10734,a(flip),b,10642,a)].">
      <j1 rule="hyper" parents="60 10734 10642"/>
    </justification>
  </clause>

  <clause id="10960">
    <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(8700(a,1),10958(a,1,2))].">
      <j1 rule="para" parents="8700 10958"/>
    </justification>
  </clause>

  <clause id="10961">
    <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(4767(a,1),10960(a,1,2))].">
      <j1 rule="para" parents="4767 10960"/>
    </justification>
  </clause>

  <clause id="10963">
    <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(10961(a,1),5597(a,1,1,2))].">
      <j1 rule="para" parents="10961 5597"/>
    </justification>
  </clause>

  <clause id="10964">
    <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(5454(a,1),10963(a,1,1))].">
      <j1 rule="para" parents="5454 10963"/>
    </justification>
  </clause>

  <clause id="10965">
    <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(60,a,7185,a(flip),b,10964,a),flip(a)].">
      <j1 rule="hyper" parents="60 7185 10964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10966">
    <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(370,a,8024,a(flip),b,10892,a),flip(a)].">
      <j1 rule="hyper" parents="370 8024 10892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10967">
    <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(6(a,1),10858(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(10809(a,1),10967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10809 10967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      ((x * y) / x) \ (T(y,z) * (K(z,y) * (K(x,y) * u))) = L(u,T(y,z) \ ((x * y) / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(10969(a,1),9038(a,1,2,2))].">
      <j1 rule="para" parents="10969 9038"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = ((u * y) / u) \ (y * (K(u,y) * x))
    ]]></literal>
    <justification jstring="[para(7871(a,1),10970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7871 10970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8336,a(flip),b,10972,a),flip(a)].">
      <j1 rule="hyper" parents="370 8336 10972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,7500,a(flip),b,10973,a),flip(a)].">
      <j1 rule="hyper" parents="370 7500 10973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(8498(a,1),10975(a,1,2))].">
      <j1 rule="para" parents="8498 10975"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(10977(a,1),47(a,2))].">
      <j1 rule="para" parents="10977 47"/>
    </justification>
  </clause>

  <clause id="10979">
    <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(60,a,10361,a(flip),b,10937,a),flip(a)].">
      <j1 rule="hyper" parents="60 10361 10937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = (K(y,x) * (x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(7609(a,1),10738(a,2,1,1))].">
      <j1 rule="para" parents="7609 10738"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,y),z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(7873(a,1),10981(a,2,1))].">
      <j1 rule="para" parents="7873 10981"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10737(a,1),10983(a,1,2,1))].">
      <j1 rule="para" parents="10737 10983"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(8367(a,1),10984(a,1,2,1))].">
      <j1 rule="para" parents="8367 10984"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(10985(a,1),9536(a,1,2))].">
      <j1 rule="para" parents="10985 9536"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10947,a(flip),b,10987,a)].">
      <j1 rule="hyper" parents="60 10947 10987"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(10951,a,10988,a)].">
      <j1 rule="hyper" parents="10951 10988"/>
    </justification>
  </clause>

  <clause id="10993">
    <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(92(a,1),2505(a,1,2,1,2,1))].">
      <j1 rule="para" parents="92 2505"/>
    </justification>
  </clause>

  <clause id="10994">
    <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(60,a,1841,a(flip),b,10993,a),flip(a)].">
      <j1 rule="hyper" parents="60 1841 10993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10995">
    <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(1635(a,1),10994(a,2,2))].">
      <j1 rule="para" parents="1635 10994"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) = L(x * ((u * (x \ 1)) / u),y,z)
    ]]></literal>
    <justification jstring="[hyper(625,a,10995,a),flip(a)].">
      <j1 rule="hyper" parents="625 10995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = K(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5386,a,10996,a),flip(a)].">
      <j1 rule="hyper" parents="5386 10996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5245(a,1),10997(a,1,1))].">
      <j1 rule="para" parents="5245 10997"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4604,a,10998,a),flip(a)].">
      <j1 rule="hyper" parents="4604 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(77(a,1),10998(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5428(a,1),10998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5428 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(6089(a,1),10998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6089 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6463(a,1),10998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6463 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,10999,a,b,10460,a)].">
      <j1 rule="hyper" parents="125 10999 10460"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10999(a,2),6791(a,1,2))].">
      <j1 rule="para" parents="10999 6791"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5075(a,1),11000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5075 11000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(11000(a,1),9181(a,1,2,2))].">
      <j1 rule="para" parents="11000 9181"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6765(a,1),11007(a,1,2,2))].">
      <j1 rule="para" parents="6765 11007"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(628(a,1),11008(a,1,2))].">
      <j1 rule="para" parents="628 11008"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6598,a(flip),b,11001,a)].">
      <j1 rule="hyper" parents="60 6598 11001"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(11001(a,1),7552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11001 7552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11012">
    <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(11001(a,1),10998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11001 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(6767,a,11010,a)].">
      <j1 rule="hyper" parents="6767 11010"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(11010(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11010 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <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(8914,a,11013,a),flip(a)].">
      <j1 rule="hyper" parents="8914 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y / u,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,11013,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 11013 13"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7327,a(flip),b,11013,a),flip(a)].">
      <j1 rule="hyper" parents="60 7327 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),11013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),11013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6272(a,1),11013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6272 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(11013(a,1),6768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11013 6768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7447(a,1),11013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7447 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7449(a,1),11013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7449 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9743,a,11017,a)].">
      <j1 rule="hyper" parents="9743 11017"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7137,a,11017,a)].">
      <j1 rule="hyper" parents="7137 11017"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,11017,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 11017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,11017,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 11017 5160"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,1),11024(a,1,1))].">
      <j1 rule="para" parents="25 11024"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1492(a,2),11024(a,1,1))].">
      <j1 rule="para" parents="1492 11024"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(11024(a,1),5280(a,1,1,2))].">
      <j1 rule="para" parents="11024 5280"/>
    </justification>
  </clause>

  <clause id="11036">
    <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(11024(a,1),6108(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11024 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(7529(a,1),11024(a,1,1))].">
      <j1 rule="para" parents="7529 11024"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(11024(a,1),8797(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11024 8797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      K((K(x,y) * z) \ (K(x,y) * u),x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6752,a(flip),b,11022,a)].">
      <j1 rule="hyper" parents="60 6752 11022"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(9743,a,11023,a)].">
      <j1 rule="hyper" parents="9743 11023"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(9009,a,11034,a)].">
      <j1 rule="hyper" parents="9009 11034"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(653(a,1),11034(a,1,1))].">
      <j1 rule="para" parents="653 11034"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(11035(a,1),5316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11035 5316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      T(x,L(y,z,x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,11043,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 11043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(344(a,1),11043(a,1,2))].">
      <j1 rule="para" parents="344 11043"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(656(a,1),11043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 11043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11040(a,1),5770(a,2,1,1))].">
      <j1 rule="para" parents="11040 5770"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5289,a,11044,a)].">
      <j1 rule="hyper" parents="5289 11044"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),11048(a,1,2))].">
      <j1 rule="para" parents="25 11048"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(344(a,1),11048(a,1,2))].">
      <j1 rule="para" parents="344 11048"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(656(a,1),11048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(1076(a,1),11048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1076 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(11048(a,1),6765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11048 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3465,a,11018,a),flip(a)].">
      <j1 rule="hyper" parents="3465 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(635,a,11018,a),flip(a)].">
      <j1 rule="hyper" parents="635 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ (x * (y * z)) = L(K(u,z),y * z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6932,a,b,11018,a)].">
      <j1 rule="hyper" parents="370 6932 11018"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7458,a(flip),b,11018,a),flip(a)].">
      <j1 rule="hyper" parents="60 7458 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7455,a(flip),b,11018,a),flip(a)].">
      <j1 rule="hyper" parents="60 7455 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7417,a(flip),b,11018,a),flip(a)].">
      <j1 rule="hyper" parents="60 7417 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      K(x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11018(a,1),7351(a,1))].">
      <j1 rule="para" parents="11018 7351"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11018(a,1),9236(a,1,1,2))].">
      <j1 rule="para" parents="11018 9236"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,1),11058(a,1,2))].">
      <j1 rule="para" parents="25 11058"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(7522(a,1),11058(a,1,2))].">
      <j1 rule="para" parents="7522 11058"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(11059(a,1),8630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11059 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(20(a,1),11060(a,1,2))].">
      <j1 rule="para" parents="20 11060"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),11060(a,1,2))].">
      <j1 rule="para" parents="344 11060"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(344(a,1),11061(a,1,2))].">
      <j1 rule="para" parents="344 11061"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1492(a,2),11061(a,1,2))].">
      <j1 rule="para" parents="1492 11061"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(7529(a,1),11061(a,1,2))].">
      <j1 rule="para" parents="7529 11061"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(87(a,1),11062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="87 11062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7025,a,b,11025,a)].">
      <j1 rule="hyper" parents="60 7025 11025"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6905,a,b,11025,a)].">
      <j1 rule="hyper" parents="60 6905 11025"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5339,a,b,11025,a)].">
      <j1 rule="hyper" parents="60 5339 11025"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),11025(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 11025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(11025(a,1),6904(a,1,2))].">
      <j1 rule="para" parents="11025 6904"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(11025(a,1),8757(a,1,1))].">
      <j1 rule="para" parents="11025 8757"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      L(x * K(y \ (x * z),x),u,w) / L(x,u,w) = K((x \ y) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(11027(a,1),6105(a,1,1,1,2))].">
      <j1 rule="para" parents="11027 6105"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,11028,a)].">
      <j1 rule="hyper" parents="2810 11028"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(163,a,11082,a(flip))].">
      <j1 rule="hyper" parents="163 11082"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      (T(x,y) * z) * K(u,x) = T(x,y) * (z * K(u,x))
    ]]></literal>
    <justification jstring="[para(11082(a,1),687(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11082 687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(2833(a,1),11082(a,1,3))].">
      <j1 rule="para" parents="2833 11082"/>
    </justification>
  </clause>

  <clause id="11088">
    <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(11084(a,1),688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11084 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(11084(a,1),9765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11084 9765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(11087(a,1),675(a,1,1))].">
      <j1 rule="para" parents="11087 675"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11045(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 11045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      T(x,T(y,x) \ (x \ z)) = T(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11045(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 11045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x * y,T(x,y \ (x \ z))) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(11045(a,1),8120(a,1,2))].">
      <j1 rule="para" parents="11045 8120"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9180,a,b,11046,a)].">
      <j1 rule="hyper" parents="60 9180 11046"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(10756,a,11050,a)].">
      <j1 rule="hyper" parents="10756 11050"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6907,a,b,11050,a)].">
      <j1 rule="hyper" parents="60 6907 11050"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11050(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 11050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(300(a,1),11050(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="300 11050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(11050(a,1),6177(a,2,2))].">
      <j1 rule="para" parents="11050 6177"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10792,a(flip),b,11051,a),flip(a)].">
      <j1 rule="hyper" parents="60 10792 11051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      T(T(x,K(y,z \ (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(11051(a,1),9566(a,1,1,2))].">
      <j1 rule="para" parents="11051 9566"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(9283,a,11076,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9283 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11104">
    <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(11076(a,1),6105(a,1,1,1,2))].">
      <j1 rule="para" parents="11076 6105"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(11076(a,2),9283(a,1))].">
      <j1 rule="para" parents="11076 9283"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(9283,a,11078,a)].">
      <j1 rule="hyper" parents="9283 11078"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(11078(a,1),9283(a,1))].">
      <j1 rule="para" parents="11078 9283"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6859,a,b,11096,a)].">
      <j1 rule="hyper" parents="60 6859 11096"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,6854,a,b,11096,a)].">
      <j1 rule="hyper" parents="60 6854 11096"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (x * z)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),11096(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 11096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(94(a,2),11096(a,1,2))].">
      <j1 rule="para" parents="94 11096"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(270(a,1),11096(a,1,2)),flip(a)].">
      <j1 rule="para" parents="270 11096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11078,a(flip),b,11106,a),flip(a)].">
      <j1 rule="hyper" parents="60 11078 11106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8797,a(flip),b,11038,a),flip(a)].">
      <j1 rule="hyper" parents="370 8797 11038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(656(a,1),11114(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="656 11114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5770,a,b,11047,a),flip(a)].">
      <j1 rule="hyper" parents="370 5770 11047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(94(a,1),11116(a,1,2))].">
      <j1 rule="para" parents="94 11116"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(11006(a,2),5427(a,1))].">
      <j1 rule="para" parents="11006 5427"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(386,a,11011,a),flip(a)].">
      <j1 rule="hyper" parents="386 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,w) = K(x,w) * L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2897,a(flip),b,11011,a),flip(a)].">
      <j1 rule="hyper" parents="370 2897 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(11011(a,2),143(a,1)),flip(b)].">
      <j1 rule="para" parents="11011 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11122">
    <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(11011(a,1),10020(a,1,1))].">
      <j1 rule="para" parents="11011 10020"/>
    </justification>
  </clause>

  <clause id="11123">
    <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(11011(a,1),10252(a,1,1))].">
      <j1 rule="para" parents="11011 10252"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8243,a,11019,a),flip(a)].">
      <j1 rule="hyper" parents="8243 11019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(94(a,1),11019(a,2,2))].">
      <j1 rule="para" parents="94 11019"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(344(a,1),11019(a,2,2))].">
      <j1 rule="para" parents="344 11019"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(656(a,1),11019(a,2,2))].">
      <j1 rule="para" parents="656 11019"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(1497(a,1),11019(a,2,2))].">
      <j1 rule="para" parents="1497 11019"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5306(a,1),11124(a,1,2))].">
      <j1 rule="para" parents="5306 11124"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(791,a,11021,a)].">
      <j1 rule="hyper" parents="791 11021"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(484,a,11021,a)].">
      <j1 rule="hyper" parents="484 11021"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(339,a,11021,a),flip(a)].">
      <j1 rule="hyper" parents="339 11021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      x / L(K(y,z),u,w) != x * v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(11021(a,2),40(a,1))].">
      <j1 rule="para" parents="11021 40"/>
    </justification>
  </clause>

  <clause id="11134">
    <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(11021(a,1),155(a,1))].">
      <j1 rule="para" parents="11021 155"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(z,y),v5) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6924(a,2),11021(a,1,2))].">
      <j1 rule="para" parents="6924 11021"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6936,a,11075,a)].">
      <j1 rule="hyper" parents="6936 11075"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(11077(a,1),5100(a,2,1))].">
      <j1 rule="para" parents="11077 5100"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      T(x,(y * x) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9176,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="60 9176 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      T(x,L(x \ y,x,z)) = T(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[para(94(a,2),11138(a,1,2))].">
      <j1 rule="para" parents="94 11138"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10966,a,b,11095,a)].">
      <j1 rule="hyper" parents="60 10966 11095"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(11109(a,1),5105(a,2,2))].">
      <j1 rule="para" parents="11109 5105"/>
    </justification>
  </clause>

  <clause id="11142">
    <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(11119(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11119 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9509,a(flip),b,11129,a)].">
      <j1 rule="hyper" parents="60 9509 11129"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8194,a,11143,a)].">
      <j1 rule="hyper" parents="8194 11143"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(109(a,1),11143(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(11143(a,1),8194(a,1))].">
      <j1 rule="para" parents="11143 8194"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8907,a,11144,a),flip(a)].">
      <j1 rule="hyper" parents="8907 11144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,u)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,11143,a,b,11144,a)].">
      <j1 rule="hyper" parents="370 11143 11144"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      (((x \ y) \ y) * L(K(z,u),w,v5)) \ T(x,x \ y) = L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(914,a,11131,a)].">
      <j1 rule="hyper" parents="914 11131"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(530(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="530 11131"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6200,a(flip),b,11136,a),flip(a)].">
      <j1 rule="hyper" parents="60 6200 11136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(7501(a,1),11147(a,1,2,1))].">
      <j1 rule="para" parents="7501 11147"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      K(x,T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ x) = u
    ]]></literal>
    <justification jstring="[para(11148(a,1),9290(a,1))].">
      <j1 rule="para" parents="11148 9290"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(9283,a,11152,a),flip(a)].">
      <j1 rule="hyper" parents="9283 11152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(11156(a,1),5767(a,2,2,2))].">
      <j1 rule="para" parents="11156 5767"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(11054(a,2),9648(a,1))].">
      <j1 rule="para" parents="11054 9648"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6907(a,2),11070(a,1))].">
      <j1 rule="para" parents="6907 11070"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),11105(a,1,1,1))].">
      <j1 rule="para" parents="7 11105"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(11113(a,1),11105(a,1))].">
      <j1 rule="para" parents="11113 11105"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ (x \ ((y * L(y \ z,u,w)) * x)))
    ]]></literal>
    <justification jstring="[para(2605(a,1),11110(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2605 11110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,11019,a,b,11111,a)].">
      <j1 rule="hyper" parents="60 11019 11111"/>
    </justification>
  </clause>

  <clause id="11165">
    <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(8549(a,1),11111(a,2,2,2,2))].">
      <j1 rule="para" parents="8549 11111"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6766(a,2),11121(a,1))].">
      <j1 rule="para" parents="6766 11121"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11019,a(flip),b,11125,a)].">
      <j1 rule="hyper" parents="60 11019 11125"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(11125(a,1),6363(a,1))].">
      <j1 rule="para" parents="11125 6363"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7343(a,1),11125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7343 11125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(9649,a,11127,a)].">
      <j1 rule="hyper" parents="9649 11127"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(6363,a,11127,a)].">
      <j1 rule="hyper" parents="6363 11127"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,11127,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 11127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11127,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 11127 13"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(11127(a,1),20(a,2,1))].">
      <j1 rule="para" parents="11127 20"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(11127(a,1),6363(a,1))].">
      <j1 rule="para" parents="11127 6363"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11127(a,1),7847(a,1))].">
      <j1 rule="para" parents="11127 7847"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10758,a(flip),b,11171,a),flip(a)].">
      <j1 rule="hyper" parents="60 10758 11171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      x * K(x,y \ (z * x)) = T(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,11171,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 11171 5230"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(6852(a,2),11171(a,1,2,1))].">
      <j1 rule="para" parents="6852 11171"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(7506(a,1),11171(a,1,2,1))].">
      <j1 rule="para" parents="7506 11171"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(5265,a,11178,a),flip(a)].">
      <j1 rule="hyper" parents="5265 11178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(11181(a,1),7387(a,1,2))].">
      <j1 rule="para" parents="11181 7387"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      (x * y) \ ((T(x,z \ (u * x)) * y) * x) = T(x,T((u \ z) \ x,y))
    ]]></literal>
    <justification jstring="[para(11181(a,1),8508(a,1,2,1,1))].">
      <j1 rule="para" parents="11181 8508"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),11182(a,1,2,2,2))].">
      <j1 rule="para" parents="5 11182"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5572,a(flip),b,11128,a),flip(a)].">
      <j1 rule="hyper" parents="370 5572 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7621,a,11130,a),flip(a)].">
      <j1 rule="hyper" parents="7621 11130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9743,a,11186,a)].">
      <j1 rule="hyper" parents="9743 11186"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11018,a(flip),b,11186,a)].">
      <j1 rule="hyper" parents="60 11018 11186"/>
    </justification>
  </clause>

  <clause id="11189">
    <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(5895(a,1),11187(a,1,1))].">
      <j1 rule="para" parents="5895 11187"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,T(y,u)),u,x) = x * u
    ]]></literal>
    <justification jstring="[para(7997(a,1),11132(a,1,1,2))].">
      <j1 rule="para" parents="7997 11132"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11132(a,1),9236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11132 9236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(5855(a,1),11191(a,1,1,2))].">
      <j1 rule="para" parents="5855 11191"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(6677(a,1),11191(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6677 11191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(7366(a,1),11191(a,1,1,2))].">
      <j1 rule="para" parents="7366 11191"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(8011(a,1),11191(a,1,1,2))].">
      <j1 rule="para" parents="8011 11191"/>
    </justification>
  </clause>

  <clause id="11196">
    <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(11195(a,1),6107(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11195 6107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <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(11195(a,1),6108(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11195 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(8541(a,1),11192(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8541 11192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(9044(a,1),11192(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9044 11192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y) = K(x * ((z * y) \ z),y)
    ]]></literal>
    <justification jstring="[para(6712(a,1),11193(a,1,1,2))].">
      <j1 rule="para" parents="6712 11193"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(6859(a,2),11159(a,1))].">
      <j1 rule="para" parents="6859 11159"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(6752(a,2),11162(a,1))].">
      <j1 rule="para" parents="6752 11162"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(6905(a,1),11162(a,1))].">
      <j1 rule="para" parents="6905 11162"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,z \ ((x \ z) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,11097,a(flip),b,11164,a),flip(a)].">
      <j1 rule="hyper" parents="370 11097 11164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = w
    ]]></literal>
    <justification jstring="[para(74(a,1),11166(a,1,2,2))].">
      <j1 rule="para" parents="74 11166"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(96(a,1),11166(a,1,2))].">
      <j1 rule="para" parents="96 11166"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      K(x,(y \ 1) * R(x,z,u)) = K(x,y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,7666,a(flip),b,11185,a),flip(a)].">
      <j1 rule="hyper" parents="60 7666 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(1497(a,1),11003(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1497 11003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(11003(a,1),6501(a,1))].">
      <j1 rule="para" parents="11003 6501"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9400,a(flip),b,11039,a)].">
      <j1 rule="hyper" parents="60 9400 11039"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5685(a,1),11211(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5685 11211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(7500(a,1),11211(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 11211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(7858(a,1),11211(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 11211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8766(a,1),11211(a,1,1,2,1))].">
      <j1 rule="para" parents="8766 11211"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8758(a,1),11211(a,1,1,2))].">
      <j1 rule="para" parents="8758 11211"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(6130(a,1),11214(a,1,1,2))].">
      <j1 rule="para" parents="6130 11214"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8354(a,1),11214(a,1,1,2))].">
      <j1 rule="para" parents="8354 11214"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6776(a,1),11218(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6776 11218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(8766(a,1),11218(a,1,1,2,2))].">
      <j1 rule="para" parents="8766 11218"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z)
    ]]></literal>
    <justification jstring="[para(265(a,1),11219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="265 11219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8911,a,11053,a),flip(a)].">
      <j1 rule="hyper" parents="8911 11053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(10708,a,11224,a),flip(a)].">
      <j1 rule="hyper" parents="10708 11224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(9027,a,11224,a)].">
      <j1 rule="hyper" parents="9027 11224"/>
    </justification>
  </clause>

  <clause id="11227">
    <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(11224(a,2),8111(a,1,1))].">
      <j1 rule="para" parents="11224 8111"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(11224(a,1),10708(a,1))].">
      <j1 rule="para" parents="11224 10708"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10653,a,b,11225,a)].">
      <j1 rule="hyper" parents="60 10653 11225"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      K(x,y / (x \ z)) * u = K(x,(z / y) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(54,a,11225,a)].">
      <j1 rule="hyper" parents="54 11225"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11225(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 11225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(11225(a,1),10646(a,1,1))].">
      <j1 rule="para" parents="11225 10646"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11226(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 11226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8850,a,11229,a)].">
      <j1 rule="hyper" parents="8850 11229"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8828,a,11229,a)].">
      <j1 rule="hyper" parents="8828 11229"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),11231(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 11231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(9255,a,11233,a)].">
      <j1 rule="hyper" parents="9255 11233"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1041(a,1),11236(a,1,2,1,2))].">
      <j1 rule="para" parents="1041 11236"/>
    </justification>
  </clause>

  <clause id="11239">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),11237(a,1,2,2))].">
      <j1 rule="para" parents="6 11237"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11239(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8773,a,11234,a)].">
      <j1 rule="hyper" parents="8773 11234"/>
    </justification>
  </clause>

  <clause id="11242">
    <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(11234(a,1),9984(a,1))].">
      <j1 rule="para" parents="11234 9984"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(74(a,1),11241(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 11241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(10653(a,2),11228(a,1))].">
      <j1 rule="para" parents="10653 11228"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(8827(a,2),11244(a,1))].">
      <j1 rule="para" parents="8827 11244"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9510,a(flip),b,11065,a),flip(a)].">
      <j1 rule="hyper" parents="60 9510 11065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(7481(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7481 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(7858(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7858 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(11246(a,1),8019(a,2,1))].">
      <j1 rule="para" parents="11246 8019"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8758(a,1),11246(a,1,2,2))].">
      <j1 rule="para" parents="8758 11246"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(8257(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8257 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(10354(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10354 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,11051,a,b,11248,a)].">
      <j1 rule="hyper" parents="370 11051 11248"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(5631(a,1),11251(a,1,2,2))].">
      <j1 rule="para" parents="5631 11251"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,x)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(7081(a,1),11251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7081 11251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11254(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(11254(a,1),8621(a,1,2,2))].">
      <j1 rule="para" parents="11254 8621"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      K(x,(y * x) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6907,a,b,11257,a)].">
      <j1 rule="hyper" parents="60 6907 11257"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11260(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,11243,a(flip),b,11261,a),flip(a)].">
      <j1 rule="hyper" parents="370 11243 11261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(77(a,1),11252(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 11252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(74(a,1),11262(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 11262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6686,a(flip),b,11263,a),flip(a)].">
      <j1 rule="hyper" parents="60 6686 11263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11249,a(flip),b,11068,a),flip(a)].">
      <j1 rule="hyper" parents="370 11249 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(54,a,11079,a)].">
      <j1 rule="hyper" parents="54 11079"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(9379,a,11080,a)].">
      <j1 rule="hyper" parents="9379 11080"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3747,a,11086,a)].">
      <j1 rule="hyper" parents="3747 11086"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(7137,a,11270,a)].">
      <j1 rule="hyper" parents="7137 11270"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6032,a(flip),b,11270,a)].">
      <j1 rule="hyper" parents="60 6032 11270"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(7017,a,11272,a)].">
      <j1 rule="hyper" parents="7017 11272"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,11272,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 11272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),11090(a,1,2,2))].">
      <j1 rule="para" parents="8019 11090"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,4898,a(flip),b,11099,a),flip(a)].">
      <j1 rule="hyper" parents="60 4898 11099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,7159,a(flip),b,11108,a)].">
      <j1 rule="hyper" parents="60 7159 11108"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9516,a(flip),b,11117,a)].">
      <j1 rule="hyper" parents="60 9516 11117"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5700(a,1),11278(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5700 11278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(5857(a,1),11278(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5857 11278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(7481(a,1),11278(a,1,2,2))].">
      <j1 rule="para" parents="7481 11278"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7479(a,1),11278(a,1,2,2))].">
      <j1 rule="para" parents="7479 11278"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8210(a,1),11278(a,1,2,2))].">
      <j1 rule="para" parents="8210 11278"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7335,a,11280,a)].">
      <j1 rule="hyper" parents="7335 11280"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      T(x,T(y \ x,z)) = T(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8156,a(flip),b,11280,a)].">
      <j1 rule="hyper" parents="60 8156 11280"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(11281(a,1),8527(a,1,2,1))].">
      <j1 rule="para" parents="11281 8527"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,11094,a,b,11282,a)].">
      <j1 rule="hyper" parents="370 11094 11282"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(11283(a,2),5313(a,1))].">
      <j1 rule="para" parents="11283 5313"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = L(T(y,x \ z),u,w) \ L(y,u,w)
    ]]></literal>
    <justification jstring="[para(11283(a,1),5724(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11283 5724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      K(x,T(y,z \ (y \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(11283(a,1),11182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11283 11182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11293">
    <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(11286(a,2),9139(a,1,1))].">
      <j1 rule="para" parents="11286 9139"/>
    </justification>
  </clause>

  <clause id="11294">
    <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(11288(a,1),5724(a,1,1,1))].">
      <j1 rule="para" parents="11288 5724"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11093,a(flip),b,11291,a),flip(a)].">
      <j1 rule="hyper" parents="60 11093 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(11091(a,1),11291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11091 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,6883,a,b,11295,a),flip(a)].">
      <j1 rule="hyper" parents="370 6883 11295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8621,a,b,11296,a)].">
      <j1 rule="hyper" parents="370 8621 11296"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6883,a,b,11297,a)].">
      <j1 rule="hyper" parents="60 6883 11297"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11301(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 11301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(10726,a,11145,a),flip(a)].">
      <j1 rule="hyper" parents="10726 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9482,a(flip),b,11184,a),flip(a)].">
      <j1 rule="hyper" parents="370 9482 11184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10681,a,b,11208,a)].">
      <j1 rule="hyper" parents="60 10681 11208"/>
    </justification>
  </clause>

  <clause id="11308">
    <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(11213(a,1),6109(a,1,1,1,2))].">
      <j1 rule="para" parents="11213 6109"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(9183,a,11217,a),flip(a)].">
      <j1 rule="hyper" parents="9183 11217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7481(a,1),11217(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7481 11217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8897,a,11309,a),flip(a)].">
      <j1 rule="hyper" parents="8897 11309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(11311(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11311 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11313">
    <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(621(a,1),11221(a,2,1))].">
      <j1 rule="para" parents="621 11221"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(6439,a,11230,a)].">
      <j1 rule="hyper" parents="6439 11230"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10689,a,b,11314,a)].">
      <j1 rule="hyper" parents="60 10689 11314"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,11250,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 11250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <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(621(a,1),11253(a,1,2))].">
      <j1 rule="para" parents="621 11253"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(60,a,8559,a(flip),b,11255,a),flip(a)].">
      <j1 rule="hyper" parents="60 8559 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      K(x,y \ ((z * K(x,u)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6281(a,1),11256(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6281 11256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11215,a(flip),b,11271,a),flip(a)].">
      <j1 rule="hyper" parents="370 11215 11271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(11320(a,1),8636(a,2,2))].">
      <j1 rule="para" parents="11320 8636"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8897,a,11274,a),flip(a)].">
      <j1 rule="hyper" parents="8897 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (y \ x),y) = u
    ]]></literal>
    <justification jstring="[para(11274(a,1),8897(a,1))].">
      <j1 rule="para" parents="11274 8897"/>
    </justification>
  </clause>

  <clause id="11325">
    <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(1976,a,11275,a),flip(a)].">
      <j1 rule="hyper" parents="1976 11275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(11276(a,1),40(a,1))].">
      <j1 rule="para" parents="11276 40"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),11277(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 11277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(11277(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="11277 6294"/>
    </justification>
  </clause>

  <clause id="11329">
    <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(11284(a,1),5724(a,1,1,1))].">
      <j1 rule="para" parents="11284 5724"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (z * x),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,8176,a,b,11310,a)].">
      <j1 rule="hyper" parents="60 8176 11310"/>
    </justification>
  </clause>

  <clause id="11331">
    <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(6268(a,1),11310(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6268 11310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,11312,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 11312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      K(x,(y * K(z,x)) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(8801(a,1),11332(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8801 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,1 / (z / w)))
    ]]></literal>
    <justification jstring="[para(11333(a,2),9428(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11333 9428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(5275(a,2),11316(a,1,2,1,2))].">
      <j1 rule="para" parents="5275 11316"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(8079(a,1),11316(a,1,2,1,2))].">
      <j1 rule="para" parents="8079 11316"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      K(x,y \ (((z / x) * u) * w)) = K(x,y \ (((x \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(8564(a,1),11319(a,1,2,2,1))].">
      <j1 rule="para" parents="8564 11319"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9508,a(flip),b,11327,a)].">
      <j1 rule="hyper" parents="60 9508 11327"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3(a,1),11338(a,2,2,1))].">
      <j1 rule="para" parents="3 11338"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      (x * y) * K(z,u * u) = x * (y * K(z,u * u))
    ]]></literal>
    <justification jstring="[para(613(a,1),11016(a,1,2,2))].">
      <j1 rule="para" parents="613 11016"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11016(a,1),9202(a,1,2))].">
      <j1 rule="para" parents="11016 9202"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),11341(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6281 11341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(8011(a,1),11341(a,1,2,2))].">
      <j1 rule="para" parents="8011 11341"/>
    </justification>
  </clause>

  <clause id="11344">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11000(a,1),11341(a,1,2,2,2))].">
      <j1 rule="para" parents="11000 11341"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(354(a,1),11342(a,1,2,2))].">
      <j1 rule="para" parents="354 11342"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      K(x,y * (T(z,x) / u)) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(2217(a,1),11342(a,1,2,2))].">
      <j1 rule="para" parents="2217 11342"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(10354(a,1),11343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10354 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      K(x \ y,z * (x / ((x \ y) * x))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(9049(a,1),11346(a,1,2,2))].">
      <j1 rule="para" parents="9049 11346"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(11132(a,1),11344(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11132 11344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      x * (T(T(y,x),z) * K(u,w * w)) = (T(y,z) * x) * K(u,w * w)
    ]]></literal>
    <justification jstring="[para(272(a,1),11340(a,1,1)),flip(a)].">
      <j1 rule="para" parents="272 11340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5691,a(flip),b,11112,a),flip(a)].">
      <j1 rule="hyper" parents="370 5691 11112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(5423(a,1),11118(a,1,1))].">
      <j1 rule="para" parents="5423 11118"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6363,a,11126,a),flip(a)].">
      <j1 rule="hyper" parents="6363 11126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11355">
    <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(5537(a,1),11126(a,2,2,1))].">
      <j1 rule="para" parents="5537 11126"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(7506(a,1),11126(a,1,1,2))].">
      <j1 rule="para" parents="7506 11126"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(8118(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="8118 11126"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      L(K(x,(y * (x \ z)) \ (u \ w)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(9508(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="9508 11126"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      L(K(x,x \ (y \ z)),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(11126(a,2),11159(a,1))].">
      <j1 rule="para" parents="11126 11159"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(11254(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="11254 11126"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(11261(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="11261 11126"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(11354(a,1),8143(a,1,1))].">
      <j1 rule="para" parents="11354 8143"/>
    </justification>
  </clause>

  <clause id="11363">
    <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(11151(a,1),6973(a,1))].">
      <j1 rule="para" parents="11151 6973"/>
    </justification>
  </clause>

  <clause id="11364">
    <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(2189(a,1),11169(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2189 11169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(z,T(y,u)),u,x) = w
    ]]></literal>
    <justification jstring="[para(11190(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11190 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * (K(y,x) * z))),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(11190(a,1),8837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11190 8837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9248,a(flip),b,11194,a)].">
      <j1 rule="hyper" parents="60 9248 11194"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5591,a(flip),b,11209,a),flip(a)].">
      <j1 rule="hyper" parents="370 5591 11209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9252,a(flip),b,11367,a),flip(a)].">
      <j1 rule="hyper" parents="370 9252 11367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),11369(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10627,a(flip),b,11370,a)].">
      <j1 rule="hyper" parents="60 10627 11370"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(11371(a,1),5767(a,2,2,2))].">
      <j1 rule="para" parents="11371 5767"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5767,a,b,11372,a),flip(a)].">
      <j1 rule="hyper" parents="370 5767 11372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,11373,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 11373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5289,a,11374,a)].">
      <j1 rule="hyper" parents="5289 11374"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10681,a,b,11375,a)].">
      <j1 rule="hyper" parents="60 10681 11375"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7356,a,11376,a)].">
      <j1 rule="hyper" parents="7356 11376"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(77(a,1),11368(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 11368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(11002(a,1),7554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11002 7554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(8766(a,1),11015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8766 11015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),11380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(214(a,1),11380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="214 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11383">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(308(a,1),11380(a,1,2,2))].">
      <j1 rule="para" parents="308 11380"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(9035(a,1),11380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9035 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,11382,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 11382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11382,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 11382 13"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11382(a,1,2))].">
      <j1 rule="para" parents="7 11382"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6269(a,1),11381(a,1,2))].">
      <j1 rule="para" parents="6269 11381"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(11388(a,1),9635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11388 9635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,11013,a(flip),b,11389,a),flip(a)].">
      <j1 rule="hyper" parents="370 11013 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(635,a,11391,a),flip(a)].">
      <j1 rule="hyper" parents="635 11391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5886,a,11392,a)].">
      <j1 rule="hyper" parents="5886 11392"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11392,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 11392 13"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(11392(a,1),336(a,1,2))].">
      <j1 rule="para" parents="11392 336"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      (x * K(y,z)) * L(K(u,y),w,v5) = x * (K(y,z) * L(K(u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(11392(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="11392 528"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8766(a,1),11392(a,1,2))].">
      <j1 rule="para" parents="8766 11392"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,11393,a(flip),b,11130,a)].">
      <j1 rule="hyper" parents="129 11393 11130"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10377,a,b,11399,a)].">
      <j1 rule="hyper" parents="60 10377 11399"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,T(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,T(y,w))) = v5
    ]]></literal>
    <justification jstring="[para(11399(a,1),336(a,1,2))].">
      <j1 rule="para" parents="11399 336"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * K(y,u)) = K(y,u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(10067,a,11395,a)].">
      <j1 rule="hyper" parents="10067 11395"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = z * (K(y,u) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10057,a,b,11395,a)].">
      <j1 rule="hyper" parents="60 10057 11395"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10068,a(flip),b,11395,a)].">
      <j1 rule="hyper" parents="60 10068 11395"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      ((K(x,y) \ z) * ((K(x,y) \ 1) \ 1)) * K(u,x) = ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[para(4463(a,1),11395(a,1,1))].">
      <j1 rule="para" parents="4463 11395"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z,K(x,y)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(8705(a,1),11395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8705 11395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6302,a,11400,a)].">
      <j1 rule="hyper" parents="6302 11400"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2894(a,2),11400(a,1,1,2))].">
      <j1 rule="para" parents="2894 11400"/>
    </justification>
  </clause>

  <clause id="11412">
    <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(11400(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11400 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11413">
    <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(275,a,11406,a,b,869,a)].">
      <j1 rule="hyper" parents="275 11406 869"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * (K(x,y) * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,10884,a(flip),b,11406,a)].">
      <j1 rule="hyper" parents="60 10884 11406"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5855(a,1),11406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5855 11406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(691,a,11409,a)].">
      <j1 rule="hyper" parents="691 11409"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(625,a,11409,a)].">
      <j1 rule="hyper" parents="625 11409"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,7617,a(flip),b,11409,a),flip(a)].">
      <j1 rule="hyper" parents="60 7617 11409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(2833(a,1),11418(a,1,2))].">
      <j1 rule="para" parents="2833 11418"/>
    </justification>
  </clause>

  <clause id="11422">
    <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(11418(a,1),4287(a,1,1,1))].">
      <j1 rule="para" parents="11418 4287"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(6591(a,1),11418(a,1,2))].">
      <j1 rule="para" parents="6591 11418"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(11418(a,1),6347(a,1,1))].">
      <j1 rule="para" parents="11418 6347"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(10617(a,1),11418(a,1,3))].">
      <j1 rule="para" parents="10617 11418"/>
    </justification>
  </clause>

  <clause id="11427">
    <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(11419(a,1),529(a,1,2,1))].">
      <j1 rule="para" parents="11419 529"/>
    </justification>
  </clause>

  <clause id="11428">
    <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="[para(11423(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11423 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11429">
    <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(11423(a,1),726(a,1,1))].">
      <j1 rule="para" parents="11423 726"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(11425(a,1),48(a,2))].">
      <j1 rule="para" parents="11425 48"/>
    </justification>
  </clause>

  <clause id="11431">
    <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(370,a,9579,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="370 9579 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11432">
    <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(370,a,9576,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="370 9576 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5805,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="60 5805 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(11424(a,2),2902(a,1))].">
      <j1 rule="para" parents="11424 2902"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(7419,a,11433,a)].">
      <j1 rule="hyper" parents="7419 11433"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(11433(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="11433 6294"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(11433(a,1),6300(a,1,1))].">
      <j1 rule="para" parents="11433 6300"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),11436(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 11436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(263(a,1),11439(a,1,2)),flip(a)].">
      <j1 rule="para" parents="263 11439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(6923(a,1),11440(a,1,2))].">
      <j1 rule="para" parents="6923 11440"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9823,a,11441,a),flip(a)].">
      <j1 rule="hyper" parents="9823 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7402,a,11441,a)].">
      <j1 rule="hyper" parents="7402 11441"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7399,a,11441,a)].">
      <j1 rule="hyper" parents="7399 11441"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7396,a,11441,a)].">
      <j1 rule="hyper" parents="7396 11441"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(156,a,11441,a)].">
      <j1 rule="hyper" parents="156 11441"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9791,a,b,11441,a)].">
      <j1 rule="hyper" parents="60 9791 11441"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7651,a,b,11441,a)].">
      <j1 rule="hyper" parents="60 7651 11441"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7395,a(flip),b,11441,a)].">
      <j1 rule="hyper" parents="60 7395 11441"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      a(x,y,x) != x \ z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11441(a,1),44(a,1))].">
      <j1 rule="para" parents="11441 44"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),2017(a,1,1))].">
      <j1 rule="para" parents="11441 2017"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      a(x,y,x) \ R(x,y,x) = x
    ]]></literal>
    <justification jstring="[para(11441(a,1),2019(a,1,1))].">
      <j1 rule="para" parents="11441 2019"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      a(x,y,x) * (x \ 1) = R(x \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),2035(a,1,1))].">
      <j1 rule="para" parents="11441 2035"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),7397(a,1,1))].">
      <j1 rule="para" parents="11441 7397"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(11441(a,1),7399(a,1))].">
      <j1 rule="para" parents="11441 7399"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(11441(a,1),7659(a,1,1))].">
      <j1 rule="para" parents="11441 7659"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),8097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11441 8097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),9316(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11441 9316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(11441(a,1),10317(a,1,3))].">
      <j1 rule="para" parents="11441 10317"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11446(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11446 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      a(x,y,x) * x != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11452(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11452 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11459(a,1),502(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11459 502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(7518,a,11443,a)].">
      <j1 rule="hyper" parents="7518 11443"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11443(a,1),7601(a,1))].">
      <j1 rule="para" parents="11443 7601"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(11443(a,1),10835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11443 10835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7518,a,11444,a)].">
      <j1 rule="hyper" parents="7518 11444"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6302,a,11444,a)].">
      <j1 rule="hyper" parents="6302 11444"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(11444(a,1),7514(a,1,2))].">
      <j1 rule="para" parents="11444 7514"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(11444(a,1),10818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11444 10818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(11444(a,1),10829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11444 10829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,11445,a(flip),b,7642,a)].">
      <j1 rule="hyper" parents="129 11445 7642"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(11445(a,1),7641(a,1,1))].">
      <j1 rule="para" parents="11445 7641"/>
    </justification>
  </clause>

  <clause id="11475">
    <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(129,a,8138,a(flip),b,11454,a)].">
      <j1 rule="hyper" parents="129 8138 11454"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5993(a,1),11454(a,1,2))].">
      <j1 rule="para" parents="5993 11454"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(5(a,1),11458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 11458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(11458(a,1),109(a,1,1))].">
      <j1 rule="para" parents="11458 109"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = y * R(y \ T(y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11458(a,1),883(a,1,1,1))].">
      <j1 rule="para" parents="11458 883"/>
    </justification>
  </clause>

  <clause id="11480">
    <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(11458(a,2),269(a,1,2,2))].">
      <j1 rule="para" parents="11458 269"/>
    </justification>
  </clause>

  <clause id="11481">
    <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(11458(a,2),620(a,1,2,2))].">
      <j1 rule="para" parents="11458 620"/>
    </justification>
  </clause>

  <clause id="11482">
    <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(11458(a,2),1199(a,1,2,2,2))].">
      <j1 rule="para" parents="11458 1199"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(7391(a,2),11460(a,1))].">
      <j1 rule="para" parents="7391 11460"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(7394(a,2),11460(a,1))].">
      <j1 rule="para" parents="7394 11460"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      a(x,y,x) * 1 != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(3(a,2),11465(a,1))].">
      <j1 rule="para" parents="3 11465"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),11467(a,1,1,2))].">
      <j1 rule="para" parents="5 11467"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      (x * K(y,y * z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,y),K(y,y * z),x) = u
    ]]></literal>
    <justification jstring="[para(11467(a,1),629(a,1,2,2))].">
      <j1 rule="para" parents="11467 629"/>
    </justification>
  </clause>

  <clause id="11488">
    <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(6459(a,1),11468(a,2,1))].">
      <j1 rule="para" parents="6459 11468"/>
    </justification>
  </clause>

  <clause id="11490">
    <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(11473(a,1),1391(a,1,1,2))].">
      <j1 rule="para" parents="11473 1391"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      a(x,y,T(x,z)) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7643,a,11442,a)].">
      <j1 rule="hyper" parents="7643 11442"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11492(a,2),11460(a,1))].">
      <j1 rule="para" parents="11492 11460"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(11447(a,1),2017(a,1,1))].">
      <j1 rule="para" parents="11447 2017"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(8278(a,1),11494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8278 11494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      K(x,x \ y) * (K(y,x) * z) = a(x,x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(11449(a,1),10820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11449 10820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(7967(a,1),11466(a,1,2))].">
      <j1 rule="para" parents="7967 11466"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(10855,a,11471,a),flip(a)].">
      <j1 rule="hyper" parents="10855 11471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = a(y,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(788,a,11472,a)].">
      <j1 rule="hyper" parents="788 11472"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5512(a,2),11472(a,1,2,1))].">
      <j1 rule="para" parents="5512 11472"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8187,a(flip),b,11502,a),flip(a)].">
      <j1 rule="hyper" parents="60 8187 11502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),11500(a,1,2,1,2))].">
      <j1 rule="para" parents="5 11500"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,10837,a(flip),b,11503,a)].">
      <j1 rule="hyper" parents="60 10837 11503"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3847,a,11506,a),flip(a)].">
      <j1 rule="hyper" parents="3847 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      x / R(x,y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,11452,a(flip),b,11506,a)].">
      <j1 rule="hyper" parents="128 11452 11506"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,4,a(flip),b,11506,a)].">
      <j1 rule="hyper" parents="125 4 11506"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10193,a,11506,a(flip))].">
      <j1 rule="hyper" parents="10193 11506"/>
    </justification>
  </clause>

  <clause id="11512">
    <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(11507(a,1),3823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11507 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4217,a,11508,a)].">
      <j1 rule="hyper" parents="4217 11508"/>
    </justification>
  </clause>

  <clause id="11515">
    <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(11508(a,1),2745(a,1,1,2,1))].">
      <j1 rule="para" parents="11508 2745"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,11514,a(flip),b,1957,a)].">
      <j1 rule="hyper" parents="125 11514 1957"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ 1 = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11485,a,11509,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11485 11509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(11516(a,1),4050(a,2,2))].">
      <j1 rule="para" parents="11516 4050"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,11400,a,b,11411,a(flip))].">
      <j1 rule="hyper" parents="32 11400 11411"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(11463(a,1),11478(a,1,1))].">
      <j1 rule="para" parents="11463 11478"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(147,a,11520,a)].">
      <j1 rule="hyper" parents="147 11520"/>
    </justification>
  </clause>

  <clause id="11523">
    <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(11520(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="11520 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2894(a,1),11522(a,2,2))].">
      <j1 rule="para" parents="2894 11522"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2894(a,2),11522(a,1,2))].">
      <j1 rule="para" parents="2894 11522"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      u * K(K(x,y) * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(11522(a,1),10836(a,1))].">
      <j1 rule="para" parents="11522 10836"/>
    </justification>
  </clause>

  <clause id="11527">
    <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(11525(a,1),10845(a,2,2))].">
      <j1 rule="para" parents="11525 10845"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(8187(a,1),11420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8187 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / x) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,11498,a(flip),b,8382,a)].">
      <j1 rule="hyper" parents="129 11498 8382"/>
    </justification>
  </clause>

  <clause id="11530">
    <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(11521(a,1),2945(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11521 2945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11381,a(flip),b,11020,a),flip(a)].">
      <j1 rule="hyper" parents="60 11381 11020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(8011(a,1),11531(a,1,2,2))].">
      <j1 rule="para" parents="8011 11531"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7020,a(flip),b,11037,a)].">
      <j1 rule="hyper" parents="60 7020 11037"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(7355,a,11534,a),flip(a)].">
      <j1 rule="hyper" parents="7355 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,11535,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 11535 5230"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5767,a,b,11157,a),flip(a)].">
      <j1 rule="hyper" parents="370 5767 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(11289,a,11539,a),flip(a)].">
      <j1 rule="hyper" parents="11289 11539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5289,a,11540,a)].">
      <j1 rule="hyper" parents="5289 11540"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11541(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 11541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(x,(y \ x) \ (z * x)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11248,a,b,11542,a)].">
      <j1 rule="hyper" parents="60 11248 11542"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(2160(a,1),11177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2160 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(11019(a,1),11210(a,1))].">
      <j1 rule="para" parents="11019 11210"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8897,a,11264,a)].">
      <j1 rule="hyper" parents="8897 11264"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11303,a(flip),b,11546,a)].">
      <j1 rule="hyper" parents="60 11303 11546"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,(x * ((x \ y) / z)) \ y) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),11547(a,2,2))].">
      <j1 rule="para" parents="77 11547"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9844,a(flip),b,11273,a),flip(a)].">
      <j1 rule="hyper" parents="370 9844 11273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8636,a(flip),b,11322,a),flip(a)].">
      <j1 rule="hyper" parents="370 8636 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9428,a(flip),b,11334,a),flip(a)].">
      <j1 rule="hyper" parents="370 9428 11334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2(a,1),11552(a,1,2,2,1))].">
      <j1 rule="para" parents="2 11552"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(11553(a,1),8655(a,1,2))].">
      <j1 rule="para" parents="11553 8655"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(T(x,w),y \ T(x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8024,a,b,11336,a),flip(a)].">
      <j1 rule="hyper" parents="370 8024 11336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,11335,a(flip),b,11336,a),flip(a)].">
      <j1 rule="hyper" parents="370 11335 11336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(1498(a,1),11379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1498 11379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,11533,a(flip),b,11385,a),flip(a)].">
      <j1 rule="hyper" parents="370 11533 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11561">
    <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(665(a,1),11390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="665 11390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8172,a(flip),b,11416,a),flip(a)].">
      <j1 rule="hyper" parents="370 8172 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(11445(a,1),11562(a,1,2))].">
      <j1 rule="para" parents="11445 11562"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),11563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(10586,a,11564,a),flip(a)].">
      <j1 rule="hyper" parents="10586 11564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(2486,a,11564,a)].">
      <j1 rule="hyper" parents="2486 11564"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,11564,a)].">
      <j1 rule="hyper" parents="215 11564"/>
    </justification>
  </clause>

  <clause id="11569">
    <literal><![CDATA[
      x * (y / a(x,z,x)) = L(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,78,a(flip),b,11565,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 78 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      L(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11565(a,1),229(a,1))].">
      <j1 rule="para" parents="11565 229"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7381,a(flip),b,11566,a)].">
      <j1 rule="hyper" parents="60 7381 11566"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),11566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 11566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <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(1173(a,1),11567(a,1,2))].">
      <j1 rule="para" parents="1173 11567"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(11458(a,2),11567(a,1,1))].">
      <j1 rule="para" parents="11458 11567"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,2157,a,b,11569,a)].">
      <j1 rule="hyper" parents="31 2157 11569"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9720,a,b,11571,a)].">
      <j1 rule="hyper" parents="60 9720 11571"/>
    </justification>
  </clause>

  <clause id="11577">
    <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(10162(a,1),11571(a,1,2,1))].">
      <j1 rule="para" parents="10162 11571"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,11575,a(flip),b,7383,a(flip))].">
      <j1 rule="hyper" parents="125 11575 7383"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      (T(x * K(y \ x,z),x) / x) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8757(a,1),11574(a,1,2))].">
      <j1 rule="para" parents="8757 11574"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) != u * w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,x) = w
    ]]></literal>
    <justification jstring="[para(11576(a,2),40(a,1))].">
      <j1 rule="para" parents="11576 40"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8279,a,b,11456,a)].">
      <j1 rule="hyper" parents="370 8279 11456"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6372,a,11538,a),flip(a)].">
      <j1 rule="hyper" parents="6372 11538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(5673(a,1),11583(a,2,1))].">
      <j1 rule="para" parents="5673 11583"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      L(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11057(a,1),6933(a,1))].">
      <j1 rule="para" parents="11057 6933"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,y),u,w))) * K(y,z) = x * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(1190,a,11135,a)].">
      <j1 rule="hyper" parents="1190 11135"/>
    </justification>
  </clause>

  <clause id="11588">
    <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(621(a,1),11170(a,2,2))].">
      <j1 rule="para" parents="621 11170"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,11174,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 11174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(7159(a,1),11202(a,1))].">
      <j1 rule="para" parents="7159 11202"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(K(a(x,z,T(y,z)),z),u)
    ]]></literal>
    <justification jstring="[para(11223(a,1),8605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11223 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(11028(a,1),11387(a,2,2))].">
      <j1 rule="para" parents="11028 11387"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,y) * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(10068(a,2),11412(a,1))].">
      <j1 rule="para" parents="10068 11412"/>
    </justification>
  </clause>

  <clause id="11594">
    <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(370,a,10269,a,b,11529,a),flip(a)].">
      <j1 rule="hyper" parents="370 10269 11529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(8019(a,2),11589(a,1,1))].">
      <j1 rule="para" parents="8019 11589"/>
    </justification>
  </clause>

  <clause id="11596">
    <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(4896(a,2),11592(a,2,2))].">
      <j1 rule="para" parents="4896 11592"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6363,a,11595,a)].">
      <j1 rule="hyper" parents="6363 11595"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11235,a(flip),b,11597,a),flip(a)].">
      <j1 rule="hyper" parents="370 11235 11597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(11597(a,2),11245(a,1))].">
      <j1 rule="para" parents="11597 11245"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),11598(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(5835(a,1),11600(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5835 11600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(6030(a,2),11600(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6030 11600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,6108,a(flip),b,11036,a),flip(a)].">
      <j1 rule="hyper" parents="370 6108 11036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(655(a,1),11603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="655 11603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(6725,a,11604,a),flip(a)].">
      <j1 rule="hyper" parents="6725 11604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(11137(a,1),9319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11137 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(11326,a,11141,a)].">
      <j1 rule="hyper" parents="11326 11141"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(11607(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11607 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,11608,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 11608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11609(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 11609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(5647,a,11610,a)].">
      <j1 rule="hyper" parents="5647 11610"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,11611,a)].">
      <j1 rule="hyper" parents="60 6754 11611"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11042,a(flip),b,11612,a),flip(a)].">
      <j1 rule="hyper" parents="60 11042 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8322,a(flip),b,11613,a),flip(a)].">
      <j1 rule="hyper" parents="370 8322 11613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(9283,a,11614,a)].">
      <j1 rule="hyper" parents="9283 11614"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9504,a(flip),b,11615,a)].">
      <j1 rule="hyper" parents="60 9504 11615"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      K(T(x,y \ 1) \ (z * y),y) = K((x * (y \ 1)) \ z,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),11615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 11615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11103,a(flip),b,11616,a),flip(a)].">
      <j1 rule="hyper" parents="370 11103 11616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11619">
    <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(11618(a,1),5598(a,1,2,1,2))].">
      <j1 rule="para" parents="11618 5598"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8324,a(flip),b,11617,a),flip(a)].">
      <j1 rule="hyper" parents="60 8324 11617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6798,a,b,11620,a)].">
      <j1 rule="hyper" parents="60 6798 11620"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6758,a,b,11620,a)].">
      <j1 rule="hyper" parents="60 6758 11620"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7190,a(flip),b,11153,a),flip(a)].">
      <j1 rule="hyper" parents="370 7190 11153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11180,a(flip),b,11623,a)].">
      <j1 rule="hyper" parents="60 11180 11623"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(7467(a,1),11625(a,1,2,2))].">
      <j1 rule="para" parents="7467 11625"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),11626(a,1,2,2,2))].">
      <j1 rule="para" parents="74 11626"/>
    </justification>
  </clause>

  <clause id="11628">
    <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(11627(a,1),11207(a,1))].">
      <j1 rule="para" parents="11627 11207"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(62(a,1),11172(a,2,1))].">
      <j1 rule="para" parents="62 11172"/>
    </justification>
  </clause>

  <clause id="11630">
    <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(1975(a,1),11172(a,2,1))].">
      <j1 rule="para" parents="1975 11172"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(11629(a,1),9434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11629 9434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      x * (y * K(z,(x \ 1) \ y)) = (x * y) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(62(a,1),11173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="62 11173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11633">
    <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(921(a,1),11198(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="921 11198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,10310,a,b,11220,a)].">
      <j1 rule="hyper" parents="60 10310 11220"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(31,a,11299,a,b,11259,a),flip(a)].">
      <j1 rule="hyper" parents="31 11299 11259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,11635,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 11635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <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(1951(a,1),11635(a,1,2,2))].">
      <j1 rule="para" parents="1951 11635"/>
    </justification>
  </clause>

  <clause id="11638">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8634,a,11636,a)].">
      <j1 rule="hyper" parents="8634 11636"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10773,a,b,11638,a)].">
      <j1 rule="hyper" parents="60 10773 11638"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(11638(a,1),9431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11638 9431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9273,a(flip),b,11639,a)].">
      <j1 rule="hyper" parents="60 9273 11639"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(9467,a,11641,a)].">
      <j1 rule="hyper" parents="9467 11641"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(11641(a,1),8621(a,1,2))].">
      <j1 rule="para" parents="11641 8621"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11551,a,b,11642,a)].">
      <j1 rule="hyper" parents="60 11551 11642"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(8674,a,11644,a)].">
      <j1 rule="hyper" parents="8674 11644"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x * y,K(z,L(a(x,y,u),x * (y * u),K(x * y,w)))) = K(x * y,K(z,(T(x * y,w) * u) \ L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(10413(a,1),11645(a,1,2,2))].">
      <j1 rule="para" parents="10413 11645"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8920,a,11643,a),flip(a)].">
      <j1 rule="hyper" parents="8920 11643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,11115,a(flip),b,11647,a)].">
      <j1 rule="hyper" parents="60 11115 11647"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),11647(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      K(x,T(y,z \ (x \ u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11648(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ ((x * z) * u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(9(a,2),11649(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z * u),z,u))) = K(x,T(y,a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(880(a,1),11651(a,1,2,2))].">
      <j1 rule="para" parents="880 11651"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8908,a,11652,a),flip(a)].">
      <j1 rule="hyper" parents="8908 11652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8904,a,11653,a)].">
      <j1 rule="hyper" parents="8904 11653"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,11653,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 11653 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      T(x,T(y,a(x,z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,11656,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 11656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      (T(x,x \ y) * a(x,z,u)) \ (a(x,z,u) * ((x \ y) \ y)) = K(a(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(11657(a,1),9375(a,1,1,1))].">
      <j1 rule="para" parents="11657 9375"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ (z \ R(x,y,y \ 1))) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11238,a(flip),b,11654,a),flip(a)].">
      <j1 rule="hyper" parents="60 11238 11654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(4098(a,1),11268(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4098 11268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10041,a(flip),b,11287,a),flip(a)].">
      <j1 rule="hyper" parents="60 10041 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      (((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(11287(a,1),6560(a,1,2,1))].">
      <j1 rule="para" parents="11287 6560"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      L(K(x,y) * z,x,x) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9592,a(flip),b,11661,a)].">
      <j1 rule="hyper" parents="60 9592 11661"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      L(x * K(y,z),y,y) = L(x,y,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(3963,a,11663,a),flip(a)].">
      <j1 rule="hyper" parents="3963 11663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(6305,a,11328,a),flip(a)].">
      <j1 rule="hyper" parents="6305 11328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(11328(a,1),6305(a,1))].">
      <j1 rule="para" parents="11328 6305"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9399,a(flip),b,11665,a)].">
      <j1 rule="hyper" parents="60 9399 11665"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      L(x * K((y * z) \ (x \ u),x),w,v5) / L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(11665(a,1),6105(a,1,1,1,2))].">
      <j1 rule="para" parents="11665 6105"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      K((x * y) \ ((1 / y) \ z),1 / y) = K(x \ z,1 / y)
    ]]></literal>
    <justification jstring="[para(76(a,1),11667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 11667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      1 / (x \ K((y * z) \ (x \ u),x)) = T(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(11667(a,1),5767(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11667 5767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      K((x * (y \ z)) \ ((1 / (y \ z)) \ u),1 / (y \ z)) = K(x \ u,z \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6465,a(flip),b,11669,a),flip(a)].">
      <j1 rule="hyper" parents="370 6465 11669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(9399(a,1),11666(a,1))].">
      <j1 rule="para" parents="9399 11666"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      L(K(x,y),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z \ u) / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(77(a,1),11363(a,1,1,2))].">
      <j1 rule="para" parents="77 11363"/>
    </justification>
  </clause>

  <clause id="11674">
    <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(7506(a,1),11363(a,1,1,2))].">
      <j1 rule="para" parents="7506 11363"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (x \ y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11254(a,1),11363(a,1,1))].">
      <j1 rule="para" parents="11254 11363"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11261(a,1),11363(a,1,1))].">
      <j1 rule="para" parents="11261 11363"/>
    </justification>
  </clause>

  <clause id="11677">
    <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(11365,a,7082,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11365 7082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(11445(a,1),11414(a,2,2))].">
      <j1 rule="para" parents="11445 11414"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(7518,a,11678,a)].">
      <j1 rule="hyper" parents="7518 11678"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11471,a(flip),b,11678,a)].">
      <j1 rule="hyper" parents="60 11471 11678"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(275,a,11471,a(flip),b,11678,a(flip))].">
      <j1 rule="hyper" parents="275 11471 11678"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(275,a,11678,a(flip),b,11471,a(flip))].">
      <j1 rule="hyper" parents="275 11678 11471"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      (a(x,y,x) * z) / a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(128,a,11471,a(flip),b,11678,a(flip))].">
      <j1 rule="hyper" parents="128 11471 11678"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6524,a,11682,a)].">
      <j1 rule="hyper" parents="6524 11682"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,11682,a),flip(a)].">
      <j1 rule="hyper" parents="4977 11682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(3282,a,11682,a)].">
      <j1 rule="hyper" parents="3282 11682"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11682(a,1),328(a,1,2))].">
      <j1 rule="para" parents="11682 328"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(11682(a,1),494(a,1))].">
      <j1 rule="para" parents="11682 494"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      T(x,y \ R(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(11439(a,1),11682(a,1,2))].">
      <j1 rule="para" parents="11439 11682"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(11685(a,1),324(a,1)),flip(a)].">
      <j1 rule="para" parents="11685 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(11685(a,1),5364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11685 5364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      x / (y \ R(y,z,y)) = (y \ R(y,z,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,11691,a),flip(a)].">
      <j1 rule="hyper" parents="4977 11691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11441,a,b,11681,a),flip(a)].">
      <j1 rule="hyper" parents="370 11441 11681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ u = x
    ]]></literal>
    <justification jstring="[para(11681(a,1),368(a,1,2))].">
      <j1 rule="para" parents="11681 368"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) / L(a(y,z,y),u,x) = x * u
    ]]></literal>
    <justification jstring="[para(11681(a,1),609(a,1,2,1))].">
      <j1 rule="para" parents="11681 609"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,11571,a,b,11680,a)].">
      <j1 rule="hyper" parents="370 11571 11680"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(370,a,11565,a(flip),b,11680,a),flip(a)].">
      <j1 rule="hyper" parents="370 11565 11680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,11572,a(flip),b,11680,a)].">
      <j1 rule="hyper" parents="125 11572 11680"/>
    </justification>
  </clause>

  <clause id="11705">
    <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(125,a,11680,a,b,879,a)].">
      <j1 rule="hyper" parents="125 11680 879"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11509,a,b,11680,a)].">
      <j1 rule="hyper" parents="60 11509 11680"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11680(a,2),40(a,1))].">
      <j1 rule="para" parents="11680 40"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(11680(a,1),880(a,1,2,1))].">
      <j1 rule="para" parents="11680 880"/>
    </justification>
  </clause>

  <clause id="11709">
    <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(11680(a,1),1068(a,1,1))].">
      <j1 rule="para" parents="11680 1068"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      x * (y \ R(y,z,y)) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[para(11441(a,2),11680(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11441 11680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * u = x
    ]]></literal>
    <justification jstring="[para(11683(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="11683 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(11686(a,1),11569(a,1,2))].">
      <j1 rule="para" parents="11686 11569"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(11686(a,1),11579(a,1,2))].">
      <j1 rule="para" parents="11686 11579"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      T(a(1 / x,y,1 / x),z) = (1 / x) \ R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(2721(a,1),11698(a,2,2))].">
      <j1 rule="para" parents="2721 11698"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(742,a,11702,a),flip(a)].">
      <j1 rule="hyper" parents="742 11702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      R(x \ 1,y,x) = L(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,11453,a(flip),b,11703,a)].">
      <j1 rule="hyper" parents="60 11453 11703"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      R(1 / x,y,x) \ 1 = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7104,a,11717,a)].">
      <j1 rule="hyper" parents="7104 11717"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      R(1 / x,y,x) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(221,a,11718,a),flip(a)].">
      <j1 rule="hyper" parents="221 11718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      1 / L(x \ 1,y,x \ 1) = R(x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),11719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 11719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      a(x,x,x) \ y = y * a(x,x,x)
    ]]></literal>
    <justification jstring="[para(3953(a,1),11706(a,1,1))].">
      <j1 rule="para" parents="3953 11706"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) / (K(y,z) * x) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,11710,a,b,11471,a)].">
      <j1 rule="hyper" parents="128 11710 11471"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      L(1 / x,y,x) \ 1 = R(x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,5078,a(flip),b,11720,a)].">
      <j1 rule="hyper" parents="60 5078 11720"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      L(1 / x,y,x) \ 1 = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a(flip),b,11726,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 11726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      L(1 / x,y,x) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(221,a,11727,a),flip(a)].">
      <j1 rule="hyper" parents="221 11727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(11572(a,1),11679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11572 11679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      T(K(x * y,x),K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (x \ R(x,y,x))) = u
    ]]></literal>
    <justification jstring="[para(11722(a,1),494(a,1,1))].">
      <j1 rule="para" parents="11722 494"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      ((K(x,y) * z) \ (z * (x \ R(x,y,x)))) / ((z * (x \ R(x,y,x))) / K(x * y,x)) = ((z * (x \ R(x,y,x))) / (K(x,y) * z)) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11722(a,1),6578(a,1,2,2))].">
      <j1 rule="para" parents="11722 6578"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3178,a(flip),b,11519,a),flip(a)].">
      <j1 rule="hyper" parents="370 3178 11519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(7893(a,1),11733(a,1,2))].">
      <j1 rule="para" parents="7893 11733"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7292(a,1),11734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7292 11734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7321,a,b,11735,a)].">
      <j1 rule="hyper" parents="60 7321 11735"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(11735(a,1),7626(a,1,1))].">
      <j1 rule="para" parents="11735 7626"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      T(x / ((y \ L(T(y,z),u,y)) \ y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(11736(a,1),7348(a,1,1,2,1))].">
      <j1 rule="para" parents="11736 7348"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,8619,a(flip),b,11554,a),flip(a)].">
      <j1 rule="hyper" parents="60 8619 11554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(8019(a,2),11739(a,2,1))].">
      <j1 rule="para" parents="8019 11739"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(9487(a,1),11740(a,2,1))].">
      <j1 rule="para" parents="9487 11740"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) != u / z
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(11741(a,2),43(a,1))].">
      <j1 rule="para" parents="11741 43"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[para(11741(a,2),5855(a,1,1))].">
      <j1 rule="para" parents="11741 5855"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(11581,a,11577,a),flip(a)].">
      <j1 rule="hyper" parents="11581 11577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(T(x,u),y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11681,a,b,11744,a)].">
      <j1 rule="hyper" parents="370 11681 11744"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      a(T(T(x,y),x \ z),u,T((x \ z) \ z,y)) = a(T(x,y),u,T(x,y))
    ]]></literal>
    <justification jstring="[para(364(a,1),11744(a,1,3))].">
      <j1 rule="para" parents="364 11744"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      a(T(T(x,y),x \ z),u,T((x \ z) \ z,y)) = a((x \ z) \ z,u,(x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(364(a,2),11744(a,1,1))].">
      <j1 rule="para" parents="364 11744"/>
    </justification>
  </clause>

  <clause id="11749">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z,x) = u
    ]]></literal>
    <justification jstring="[para(11745(a,1),225(a,1)),flip(b)].">
      <j1 rule="para" parents="11745 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(5673(a,1),11584(a,1,1,1))].">
      <j1 rule="para" parents="5673 11584"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6992,a,11750,a),flip(a)].">
      <j1 rule="hyper" parents="6992 11750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      (x * (y * z)) * L(K(z,y),T(x,y * z),y * z) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(11751(a,2),611(a,2,2))].">
      <j1 rule="para" parents="11751 611"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      T(x * K(y,x),x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(11751(a,2),8191(a,1))].">
      <j1 rule="para" parents="11751 8191"/>
    </justification>
  </clause>

  <clause id="11755">
    <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(909(a,1),11605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="909 11605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,7511,a(flip),b,11606,a),flip(a)].">
      <j1 rule="hyper" parents="370 7511 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,9713,a(flip),b,11756,a)].">
      <j1 rule="hyper" parents="60 9713 11756"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,9685,a,b,11758,a)].">
      <j1 rule="hyper" parents="60 9685 11758"/>
    </justification>
  </clause>

  <clause id="11760">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11759(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(9118(a,1),11759(a,1,2,2,1))].">
      <j1 rule="para" parents="9118 11759"/>
    </justification>
  </clause>

  <clause id="11762">
    <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(11637(a,2),9467(a,1))].">
      <j1 rule="para" parents="11637 9467"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8610,a(flip),b,11640,a),flip(a)].">
      <j1 rule="hyper" parents="370 8610 11640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(9489,a,11763,a)].">
      <j1 rule="hyper" parents="9489 11763"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),11764(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      L(K(x,y),z,u) \ L(T(K(x,y),w \ v5),z,u) = K(L(K(x,y),z,u),w \ (v5 / x))
    ]]></literal>
    <justification jstring="[para(11765(a,1),5262(a,1,2,1))].">
      <j1 rule="para" parents="11765 5262"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      T(x,(y * (x * z)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(5768,a,11670,a),flip(a)].">
      <j1 rule="hyper" parents="5768 11670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9515,a,b,11767,a)].">
      <j1 rule="hyper" parents="60 9515 11767"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11005,a(flip),b,11004,a),flip(a)].">
      <j1 rule="hyper" parents="60 11005 11004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      (1 / x) * a(y,y,x) = 1 / L(x,y,y)
    ]]></literal>
    <justification jstring="[para(1362(a,1),11769(a,1,2))].">
      <j1 rule="para" parents="1362 11769"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(11073,a,7187,a),flip(a)].">
      <j1 rule="hyper" parents="11073 7187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9026,a,11772,a)].">
      <j1 rule="hyper" parents="9026 11772"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11772(a,1,2,1,1))].">
      <j1 rule="para" parents="4 11772"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(8401(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8401 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      K(x,y * (x / z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[para(6298(a,1),11773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6298 11773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6677(a,1),11773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6677 11773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(11774(a,1),5280(a,1,1,2))].">
      <j1 rule="para" parents="11774 5280"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      x * K(x,y * (z \ x)) = T(x,y * (x / z))
    ]]></literal>
    <justification jstring="[hyper(129,a,11777,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 11777 5230"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      (x * K(y,z * (u \ y))) \ x = K(z * (y / u),y)
    ]]></literal>
    <justification jstring="[para(11777(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="11777 6294"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      T(x,y * (x / z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(5265,a,11780,a),flip(a)].">
      <j1 rule="hyper" parents="5265 11780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(6305,a,11781,a),flip(a)].">
      <j1 rule="hyper" parents="6305 11781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10340(a,1),11778(a,1,2))].">
      <j1 rule="para" parents="10340 11778"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),11784(a,1,2,2))].">
      <j1 rule="para" parents="108 11784"/>
    </justification>
  </clause>

  <clause id="11786">
    <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(60,a,6472,a(flip),b,11785,a),flip(a)].">
      <j1 rule="hyper" parents="60 6472 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,11779,a(flip),b,6278,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 11779 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      T(x * y,K(y,x) * z) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(276,a,11787,a)].">
      <j1 rule="hyper" parents="276 11787"/>
    </justification>
  </clause>

  <clause id="11789">
    <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(11787(a,2),10954(a,1,1))].">
      <j1 rule="para" parents="11787 10954"/>
    </justification>
  </clause>

  <clause id="11790">
    <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(11788(a,1),328(a,1,2))].">
      <j1 rule="para" parents="11788 328"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      T(x * y,T(x,y) \ z) = T(x * y,x \ z)
    ]]></literal>
    <justification jstring="[para(7873(a,1),11788(a,1,2))].">
      <j1 rule="para" parents="7873 11788"/>
    </justification>
  </clause>

  <clause id="11792">
    <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(370,a,11021,a(flip),b,11122,a),flip(a)].">
      <j1 rule="hyper" parents="370 11021 11122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      L(K(x,K(y \ 1,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(6894(a,2),11356(a,2,2,1))].">
      <j1 rule="para" parents="6894 11356"/>
    </justification>
  </clause>

  <clause id="11794">
    <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(7633(a,2),11356(a,2,2,1))].">
      <j1 rule="para" parents="7633 11356"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(11363,a,11357,a),flip(a)].">
      <j1 rule="hyper" parents="11363 11357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11795(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,11339,a(flip),b,11796,a),flip(a)].">
      <j1 rule="hyper" parents="370 11339 11796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11098,a(flip),b,11797,a)].">
      <j1 rule="hyper" parents="60 11098 11797"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,4905,a,b,11361,a),flip(a)].">
      <j1 rule="hyper" parents="370 4905 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11800">
    <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(2578(a,2),11361(a,2,2,1,2))].">
      <j1 rule="para" parents="2578 11361"/>
    </justification>
  </clause>

  <clause id="11801">
    <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(370,a,7338,a(flip),b,11364,a),flip(a)].">
      <j1 rule="hyper" parents="370 7338 11364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      T(x * R(x \ (x * y),z,u),x) = R(y * a(x,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,2634,a,b,11479,a)].">
      <j1 rule="hyper" parents="370 2634 11479"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(1498(a,1),11558(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1498 11558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(u,w) * z)) * (u * (T(T(u,w),w) \ z)))) = K(x,y * ((z \ 1) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(11804(a,1),9605(a,1,2,2))].">
      <j1 rule="para" parents="11804 9605"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(11681(a,1),11708(a,2,1))].">
      <j1 rule="para" parents="11681 11708"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(11458(a,2),11806(a,1,2,1))].">
      <j1 rule="para" parents="11458 11806"/>
    </justification>
  </clause>

  <clause id="11809">
    <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(8717,a,11792,a)].">
      <j1 rule="hyper" parents="8717 11792"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = T(y * R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11803(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3747,a,11088,a)].">
      <j1 rule="hyper" parents="3747 11088"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11801,a(flip),b,11811,a)].">
      <j1 rule="hyper" parents="60 11801 11811"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),11812(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) * (L(y,u,w) * z) = L(y,u,w) * (z * K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(11812(a,1),8049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11812 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11009(a,1),11812(a,1,2))].">
      <j1 rule="para" parents="11009 11812"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),11816(a,1,2,2,2))].">
      <j1 rule="para" parents="5 11816"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(9189(a,1),11816(a,1,2))].">
      <j1 rule="para" parents="9189 11816"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8454,a,11818,a),flip(a)].">
      <j1 rule="hyper" parents="8454 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9268,a,b,11819,a)].">
      <j1 rule="hyper" parents="60 9268 11819"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(8454,a,11817,a),flip(a)].">
      <j1 rule="hyper" parents="8454 11817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),11822(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9114,a(flip),b,11823,a)].">
      <j1 rule="hyper" parents="60 9114 11823"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11601,a(flip),b,11824,a)].">
      <j1 rule="hyper" parents="60 11601 11824"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11231,a(flip),b,11825,a),flip(a)].">
      <j1 rule="hyper" parents="60 11231 11825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(10755,a,11826,a),flip(a)].">
      <j1 rule="hyper" parents="10755 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11828">
    <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(60,a,10713,a(flip),b,11827,a)].">
      <j1 rule="hyper" parents="60 10713 11827"/>
    </justification>
  </clause>

  <clause id="11829">
    <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(370,a,11011,a(flip),b,11123,a),flip(a)].">
      <j1 rule="hyper" parents="370 11011 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(11146,a,11179,a)].">
      <j1 rule="hyper" parents="11146 11179"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      T(x,T((y \ z) \ x,u)) = T(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(10001,a,11183,a),flip(a)].">
      <j1 rule="hyper" parents="10001 11183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11832">
    <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(370,a,8295,a(flip),b,11325,a),flip(a)].">
      <j1 rule="hyper" parents="370 8295 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9407,a(flip),b,11832,a)].">
      <j1 rule="hyper" parents="60 9407 11832"/>
    </justification>
  </clause>

  <clause id="11834">
    <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(11833(a,1),9158(a,1))].">
      <j1 rule="para" parents="11833 9158"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11834,a,11457,a),flip(a)].">
      <j1 rule="hyper" parents="11834 11457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(11835(a,1),11567(a,1,1))].">
      <j1 rule="para" parents="11835 11567"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4763(a,1),11836(a,1,2))].">
      <j1 rule="para" parents="4763 11836"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8441,a,11837,a)].">
      <j1 rule="hyper" parents="8441 11837"/>
    </justification>
  </clause>

  <clause id="11839">
    <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(7273(a,2),11331(a,1,1,2))].">
      <j1 rule="para" parents="7273 11331"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      x * (T(T(y,x),z) * K(u,w * w)) = T(y,z) * (x * K(u,w * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,11340,a(flip),b,11350,a),flip(a)].">
      <j1 rule="hyper" parents="370 11340 11350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = u
    ]]></literal>
    <justification jstring="[para(11362(a,1),8144(a,1))].">
      <j1 rule="para" parents="11362 8144"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * L(K(u,z),w,v5)) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[para(6281(a,1),11398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 11398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11845">
    <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(9735(a,2),11402(a,1,1))].">
      <j1 rule="para" parents="9735 11402"/>
    </justification>
  </clause>

  <clause id="11846">
    <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(2903(a,2),11427(a,2,2))].">
      <j1 rule="para" parents="2903 11427"/>
    </justification>
  </clause>

  <clause id="11847">
    <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(6281(a,1),11427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11848">
    <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(2897(a,1),11428(a,2,2))].">
      <j1 rule="para" parents="2897 11428"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(32,a,11496,a(flip),b,11582,a(flip))].">
      <j1 rule="hyper" parents="32 11496 11582"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(5003,a,11660,a),flip(a)].">
      <j1 rule="hyper" parents="5003 11660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(11152(a,1),11851(a,1,1,2))].">
      <j1 rule="para" parents="11152 11851"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      a(T(T(x,y),x \ z),u,T((x \ z) \ z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,u,x) = w
    ]]></literal>
    <justification jstring="[para(11746(a,2),11749(a,1))].">
      <j1 rule="para" parents="11746 11749"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,11760,a(flip),b,11761,a),flip(a)].">
      <j1 rule="hyper" parents="370 11760 11761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,9690,a,b,11854,a)].">
      <j1 rule="hyper" parents="60 9690 11854"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(77(a,1),11855(a,2,2,2,1))].">
      <j1 rule="para" parents="77 11855"/>
    </justification>
  </clause>

  <clause id="11857">
    <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(370,a,272,a(flip),b,11829,a),flip(a)].">
      <j1 rule="hyper" parents="370 272 11829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,11597,a(flip),b,11830,a)].">
      <j1 rule="hyper" parents="60 11597 11830"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11222,a(flip),b,11839,a),flip(a)].">
      <j1 rule="hyper" parents="60 11222 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((z * T(y,u)) / x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9905,a(flip),b,11859,a),flip(a)].">
      <j1 rule="hyper" parents="60 9905 11859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      K((x * T(y,z)) / u,y) = K(x / (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(11324,a,11861,a),flip(a)].">
      <j1 rule="hyper" parents="11324 11861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),11862(a,1,1,1))].">
      <j1 rule="para" parents="107 11862"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      K(x / (y \ z),y) = K((z / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(9777,a,11864,a),flip(a)].">
      <j1 rule="hyper" parents="9777 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11323,a,b,11865,a)].">
      <j1 rule="hyper" parents="60 11323 11865"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,x)) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11330,a,b,11866,a)].">
      <j1 rule="hyper" parents="60 11330 11866"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),11867(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,5994,a(flip),b,11868,a)].">
      <j1 rule="hyper" parents="60 5994 11868"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(9253,a,11869,a)].">
      <j1 rule="hyper" parents="9253 11869"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      (T(x,L(K(y,z),u,w)) * K(v5,z)) * (K(z,v5) * L(K(y,z),u,w)) = x * ((x * L(K(y,z),u,w)) / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5448,a(flip),b,11842,a),flip(a)].">
      <j1 rule="hyper" parents="370 5448 11842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11872">
    <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(60,a,9347,a,b,11846,a)].">
      <j1 rule="hyper" parents="60 9347 11846"/>
    </justification>
  </clause>

  <clause id="11873">
    <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(128,a,10657,a(flip),b,11847,a)].">
      <j1 rule="hyper" parents="128 10657 11847"/>
    </justification>
  </clause>

  <clause id="11874">
    <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(6302,a,11848,a)].">
      <j1 rule="hyper" parents="6302 11848"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(62(a,1),11858(a,1,2,1))].">
      <j1 rule="para" parents="62 11858"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,11243,a(flip),b,11875,a)].">
      <j1 rule="hyper" parents="370 11243 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11597,a(flip),b,11876,a)].">
      <j1 rule="hyper" parents="60 11597 11876"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),11877(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="62 11877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(11227,a,10706,a)].">
      <j1 rule="hyper" parents="11227 10706"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(129,a,11879,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 11879 5230"/>
    </justification>
  </clause>

  <clause id="11881">
    <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(11880(a,1),5265(a,1))].">
      <j1 rule="para" parents="11880 5265"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,5724,a(flip),b,11290,a),flip(a)].">
      <j1 rule="hyper" parents="370 5724 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K(x \ (z * y),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),11882(a,1,1,2,1))].">
      <j1 rule="para" parents="4 11882"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5830,a,11294,a),flip(a)].">
      <j1 rule="hyper" parents="5830 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,w) * K(y,T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(10070(a,2),11403(a,1))].">
      <j1 rule="para" parents="10070 11403"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(6307,a,11429,a)].">
      <j1 rule="hyper" parents="6307 11429"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2897,a(flip),b,11887,a),flip(a)].">
      <j1 rule="hyper" parents="370 2897 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6281(a,1),11888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6281 11888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(11889(a,1),9169(a,1,2))].">
      <j1 rule="para" parents="11889 9169"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11391(a,1),11889(a,1,2))].">
      <j1 rule="para" parents="11391 11889"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11890(a,1),8011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11890 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(11134,a,11891,a)].">
      <j1 rule="hyper" parents="11134 11891"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(7518,a,11891,a)].">
      <j1 rule="hyper" parents="7518 11891"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2899,a,11891,a)].">
      <j1 rule="hyper" parents="2899 11891"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(1035,a,11891,a)].">
      <j1 rule="hyper" parents="1035 11891"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11120,a,b,11891,a)].">
      <j1 rule="hyper" parents="60 11120 11891"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,11891,a(flip),b,11120,a)].">
      <j1 rule="hyper" parents="129 11891 11120"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      T(x,y) * L(K(y,x),z,u) = x * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,11891,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 11891 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6765(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="6765 11891"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(11891(a,1),7655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11891 7655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(10998(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="10998 11891"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      K(1 / x,y) * K(y,1 / L(x,z,u)) = a(u,z,K(1 / x,y))
    ]]></literal>
    <justification jstring="[para(11006(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="11006 11891"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(11622(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="11622 11891"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(11891(a,1),11587(a,1,1,2))].">
      <j1 rule="para" parents="11891 11587"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,K(z,y)) = x * L(K(y,z),w,u)
    ]]></literal>
    <justification jstring="[para(11891(a,1),11842(a,1,2))].">
      <j1 rule="para" parents="11891 11842"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(11891(a,1),11874(a,1,1,2))].">
      <j1 rule="para" parents="11891 11874"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11429,a,b,11896,a)].">
      <j1 rule="hyper" parents="60 11429 11896"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(z,y * x,K(u,x))
    ]]></literal>
    <justification jstring="[para(6765(a,1),11896(a,1,1))].">
      <j1 rule="para" parents="6765 11896"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(11018(a,1),11896(a,1,1))].">
      <j1 rule="para" parents="11018 11896"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w) \ (K(L(K(x,y),z,u),w) * K(x,y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8449,a,11898,a)].">
      <j1 rule="hyper" parents="8449 11898"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != K(u,w)
    ]]></literal>
    <literal><![CDATA[
      L(K(u,w),z,y) = x
    ]]></literal>
    <justification jstring="[para(11898(a,1),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11898 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      L(K(x,y),z,u) * w != K(x,y)
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(11899(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="11899 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11918">
    <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(6760(a,1),11899(a,1,1))].">
      <j1 rule="para" parents="6760 11899"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11902(a,1),8204(a,2,2))].">
      <j1 rule="para" parents="11902 8204"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(11119(a,1),11903(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11119 11903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      (x * T(y,z)) * L(K(z,y),u,w) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(5860(a,1),11909(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5860 11909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(32,a,11908,a,b,11910,a)].">
      <j1 rule="hyper" parents="32 11908 11910"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,5287,a(flip),b,11923,a),flip(a)].">
      <j1 rule="hyper" parents="60 5287 11923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(z,u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(11923(a,1),515(a,1,1))].">
      <j1 rule="para" parents="11923 515"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(125,a,7500,a(flip),b,11920,a),flip(a)].">
      <j1 rule="hyper" parents="125 7500 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(y,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(60,a,10930,a(flip),b,11926,a)].">
      <j1 rule="hyper" parents="60 10930 11926"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(60,a,11903,a(flip),b,11927,a),flip(a)].">
      <j1 rule="hyper" parents="60 11903 11927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(722,a,11928,a)].">
      <j1 rule="hyper" parents="722 11928"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,11892,a,b,11928,a),flip(a)].">
      <j1 rule="hyper" parents="370 11892 11928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) * v5 = w
    ]]></literal>
    <justification jstring="[para(11928(a,1),156(a,1))].">
      <j1 rule="para" parents="11928 156"/>
    </justification>
  </clause>

  <clause id="11933">
    <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(11930(a,2),40(a,1))].">
      <j1 rule="para" parents="11930 40"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11897(a,1),7128(a,1,1))].">
      <j1 rule="para" parents="11897 7128"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = ((x / y) * y) \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5359,a,b,11912,a)].">
      <j1 rule="hyper" parents="370 5359 11912"/>
    </justification>
  </clause>

  <clause id="11936">
    <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(6591(a,1),11904(a,1,1))].">
      <j1 rule="para" parents="6591 11904"/>
    </justification>
  </clause>

  <clause id="11937">
    <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(8605(a,1),11905(a,1,2))].">
      <j1 rule="para" parents="8605 11905"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      x * (T(y,z) * L(K(z,y),u,w)) = (x * y) * a(w,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8155,a,11922,a)].">
      <j1 rule="hyper" parents="8155 11922"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * (y * a(z,u,K(y,w)))
    ]]></literal>
    <justification jstring="[para(11900(a,1),11938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11900 11938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,11939,a(flip),b,82,a),flip(a)].">
      <j1 rule="hyper" parents="124 11939 82"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(8766(a,1),11940(a,1,3,3))].">
      <j1 rule="para" parents="8766 11940"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(11907(a,1),7516(a,1,2))].">
      <j1 rule="para" parents="11907 7516"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(y,x)) * (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(11931,a,11934,a)].">
      <j1 rule="hyper" parents="11931 11934"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(11916,a,11942,a)].">
      <j1 rule="hyper" parents="11916 11942"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),11944(a,2,2,2,1))].">
      <j1 rule="para" parents="5 11944"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5512(a,2),11944(a,1,1))].">
      <j1 rule="para" parents="5512 11944"/>
    </justification>
  </clause>

  <clause id="11947">
    <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(341(a,1),11946(a,2,2))].">
      <j1 rule="para" parents="341 11946"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6771,a(flip),b,11947,a),flip(a)].">
      <j1 rule="hyper" parents="370 6771 11947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),K(z,u)) = K(z,K(u,a(x,z,T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(370,a,8631,a(flip),b,11591,a),flip(a)].">
      <j1 rule="hyper" parents="370 8631 11591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6137,a,11619,a),flip(a)].">
      <j1 rule="hyper" parents="6137 11619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(1497(a,1),11951(a,1,1,1))].">
      <j1 rule="para" parents="1497 11951"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(6731,a,11952,a)].">
      <j1 rule="hyper" parents="6731 11952"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11274,a(flip),b,11953,a),flip(a)].">
      <j1 rule="hyper" parents="370 11274 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11041,a(flip),b,11954,a),flip(a)].">
      <j1 rule="hyper" parents="60 11041 11954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8906,a,11955,a),flip(a)].">
      <j1 rule="hyper" parents="8906 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9776,a(flip),b,11956,a),flip(a)].">
      <j1 rule="hyper" parents="370 9776 11956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11957(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),11958(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 11958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(5518,a,11959,a)].">
      <j1 rule="hyper" parents="5518 11959"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(10311,a,11960,a)].">
      <j1 rule="hyper" parents="10311 11960"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(2770(a,2),11961(a,1,1,2))].">
      <j1 rule="para" parents="2770 11961"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,10309,a(flip),b,11962,a)].">
      <j1 rule="hyper" parents="60 10309 11962"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,11634,a(flip),b,11963,a)].">
      <j1 rule="hyper" parents="60 11634 11963"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(11841,a,10236,a)].">
      <j1 rule="hyper" parents="11841 10236"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      x * (K(y,y \ z) * K(u,T(y,z))) = (x / T(z / (z / y),u)) * y
    ]]></literal>
    <justification jstring="[hyper(11886,a,8865,a)].">
      <j1 rule="hyper" parents="11886 8865"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(10174(a,1),11968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10174 11968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(7079(a,1),11969(a,2,2))].">
      <j1 rule="para" parents="7079 11969"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ ((z * x) * u))) = K(x,K(y,a(z,x,T(u,x))))
    ]]></literal>
    <justification jstring="[hyper(8674,a,11950,a)].">
      <j1 rule="hyper" parents="8674 11950"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8181,a,11140,a)].">
      <j1 rule="hyper" parents="8181 11140"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11032,a(flip),b,11313,a),flip(a)].">
      <j1 rule="hyper" parents="370 11032 11313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(11672,a,11973,a)].">
      <j1 rule="hyper" parents="11672 11973"/>
    </justification>
  </clause>

  <clause id="11976">
    <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(2404(a,1),11480(a,1,2,2))].">
      <j1 rule="para" parents="2404 11480"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9845,a,11550,a)].">
      <j1 rule="hyper" parents="9845 11550"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(10249,a,11977,a)].">
      <j1 rule="hyper" parents="10249 11977"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8787,a(flip),b,11978,a),flip(a)].">
      <j1 rule="hyper" parents="370 8787 11978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8904,a,11979,a)].">
      <j1 rule="hyper" parents="8904 11979"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9395,a,b,11980,a)].">
      <j1 rule="hyper" parents="60 9395 11980"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11744(a,1),11573(a,1,1,2))].">
      <j1 rule="para" parents="11744 11573"/>
    </justification>
  </clause>

  <clause id="11984">
    <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(125,a,11594,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 11594 92"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),1 / ((y * z) \ y)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11671(a,2,2))].">
      <j1 rule="para" parents="4 11671"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11361(a,1),11675(a,1))].">
      <j1 rule="para" parents="11361 11675"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11360(a,1),11676(a,1))].">
      <j1 rule="para" parents="11360 11676"/>
    </justification>
  </clause>

  <clause id="11989">
    <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(8148,a,11919,a)].">
      <j1 rule="hyper" parents="8148 11919"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(204(a,1),11989(a,1,2,2))].">
      <j1 rule="para" parents="204 11989"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10331,a(flip),b,11972,a)].">
      <j1 rule="hyper" parents="60 10331 11972"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10749,a(flip),b,11991,a)].">
      <j1 rule="hyper" parents="60 10749 11991"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9535,a(flip),b,11993,a),flip(a)].">
      <j1 rule="hyper" parents="60 9535 11993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(188(a,1),11993(a,2,2))].">
      <j1 rule="para" parents="188 11993"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11100,a(flip),b,11995,a)].">
      <j1 rule="hyper" parents="60 11100 11995"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11996(a,2,2))].">
      <j1 rule="para" parents="4 11996"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11659,a(flip),b,11998,a),flip(a)].">
      <j1 rule="hyper" parents="60 11659 11998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(63(a,1),11994(a,1,2,2))].">
      <j1 rule="para" parents="63 11994"/>
    </justification>
  </clause>

  <clause id="12002">
    <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(60,a,258,a(flip),b,11976,a),flip(a)].">
      <j1 rule="hyper" parents="60 258 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,11807,a(flip),b,12002,a),flip(a)].">
      <j1 rule="hyper" parents="370 11807 12002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12004">
    <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(5280(a,1),12003(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5280 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6106,a,11081,a),flip(a)].">
      <j1 rule="hyper" parents="6106 11081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6106,a,11104,a),flip(a)].">
      <j1 rule="hyper" parents="6106 11104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,6107,a(flip),b,11196,a),flip(a)].">
      <j1 rule="hyper" parents="370 6107 11196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,6108,a(flip),b,11197,a),flip(a)].">
      <j1 rule="hyper" parents="370 6108 11197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5303(a,1),12009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5303 12009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(10359(a,1),11366(a,1,1))].">
      <j1 rule="para" parents="10359 11366"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9810,a(flip),b,12011,a)].">
      <j1 rule="hyper" parents="60 9810 12011"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * (y \ z))) = w
    ]]></literal>
    <justification jstring="[para(12011(a,2),10355(a,1))].">
      <j1 rule="para" parents="12011 10355"/>
    </justification>
  </clause>

  <clause id="12015">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(10355,a,12012,a(flip))].">
      <j1 rule="hyper" parents="10355 12012"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * z) = y * (K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(155,a,12015,a(flip))].">
      <j1 rule="hyper" parents="155 12015"/>
    </justification>
  </clause>

  <clause id="12017">
    <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(12015(a,2),10955(a,1))].">
      <j1 rule="para" parents="12015 10955"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(12017,a,10891,a),flip(a)].">
      <j1 rule="hyper" parents="12017 10891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12018(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 12018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,2),12019(a,2,2))].">
      <j1 rule="para" parents="15 12019"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(11487,a,11404,a)].">
      <j1 rule="hyper" parents="11487 11404"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11445,a(flip),b,12022,a),flip(a)].">
      <j1 rule="hyper" parents="370 11445 12022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(12023(a,1),432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12023 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,11686,a(flip),b,12024,a),flip(a)].">
      <j1 rule="hyper" parents="370 11686 12024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      (x / K(y,z)) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(11467(a,1),12025(a,1,1,2))].">
      <j1 rule="para" parents="11467 12025"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[para(6291(a,1),12026(a,1,1))].">
      <j1 rule="para" parents="6291 12026"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,7617,a(flip),b,12027,a)].">
      <j1 rule="hyper" parents="60 7617 12027"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,11528,a(flip),b,12028,a)].">
      <j1 rule="hyper" parents="60 11528 12028"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      (a(x,y,x) * (z * x)) / R(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(32,a,4,a(flip),b,12028,a),flip(a)].">
      <j1 rule="hyper" parents="32 4 12028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      x \ (a(x,y,x) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,12028,a(flip),b,7385,a(flip))].">
      <j1 rule="hyper" parents="125 12028 7385"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11686,a,b,12029,a),flip(a)].">
      <j1 rule="hyper" parents="370 11686 12029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      a(x,y,x) \ K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(T(x,z),y,x) = u
    ]]></literal>
    <justification jstring="[para(12029(a,1),8485(a,1))].">
      <j1 rule="para" parents="12029 8485"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(155,a,12030,a),flip(a)].">
      <j1 rule="hyper" parents="155 12030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[para(12030(a,1),80(a,1,1,1))].">
      <j1 rule="para" parents="12030 80"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(842,a,12031,a),flip(a)].">
      <j1 rule="hyper" parents="842 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      x / (y \ L(y,z,y)) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,6,a(flip),b,12033,a)].">
      <j1 rule="hyper" parents="128 6 12033"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ x = u
    ]]></literal>
    <justification jstring="[para(12033(a,2),11690(a,1))].">
      <j1 rule="para" parents="12033 11690"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(11689,a,12036,a)].">
      <j1 rule="hyper" parents="11689 12036"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,12036,a(flip),b,172,a(flip))].">
      <j1 rule="hyper" parents="128 12036 172"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(12036(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12036 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12037(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12037 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <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(92(a,1),12037(a,1,2))].">
      <j1 rule="para" parents="92 12037"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(11689,a,12038,a)].">
      <j1 rule="hyper" parents="11689 12038"/>
    </justification>
  </clause>

  <clause id="12049">
    <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(12038(a,1),693(a,1,1,1))].">
      <j1 rule="para" parents="12038 693"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      x / (a(y,z,y) \ 1) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11504(a,2),12040(a,1,2))].">
      <j1 rule="para" parents="11504 12040"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(378,a,12042,a),flip(a)].">
      <j1 rule="hyper" parents="378 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(12042(a,1),11694(a,1,1,2))].">
      <j1 rule="para" parents="12042 11694"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(12042(a,1),11982(a,1,1))].">
      <j1 rule="para" parents="12042 11982"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(755,a,12048,a),flip(a)].">
      <j1 rule="hyper" parents="755 12048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      R(x,a(y,z,y),a(y,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(821,a,12050,a)].">
      <j1 rule="hyper" parents="821 12050"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      R(x,a(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(11504(a,1),12055(a,1,3))].">
      <j1 rule="para" parents="11504 12055"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(11441(a,2),12056(a,1,2))].">
      <j1 rule="para" parents="11441 12056"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(5540(a,1),12051(a,1,2))].">
      <j1 rule="para" parents="5540 12051"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(1984,a,12054,a),flip(a)].">
      <j1 rule="hyper" parents="1984 12054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,10162,a(flip),b,12053,a),flip(a)].">
      <j1 rule="hyper" parents="370 10162 12053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      (x \ T(K(y \ x,z) * x,x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8970(a,1),11580(a,1,1))].">
      <j1 rule="para" parents="8970 11580"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      K(a(x,y,z),T(x,u)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(7389,a,11658,a)].">
      <j1 rule="hyper" parents="7389 11658"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      K(x \ R(x,y,z),R(x,x \ R(x,y,z),y * z)) = K(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10680,a,b,12065,a)].">
      <j1 rule="hyper" parents="60 10680 12065"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      K(a(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(6882,a,12066,a),flip(a)].">
      <j1 rule="hyper" parents="6882 12066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,12067,a)].">
      <j1 rule="hyper" parents="53 12067"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12069,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 12069 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2963(a,2),12069(a,1,1))].">
      <j1 rule="para" parents="2963 12069"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) / z,z,K(y,x)) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,11943,a(flip),b,12070,a),flip(a)].">
      <j1 rule="hyper" parents="60 11943 12070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = u
    ]]></literal>
    <justification jstring="[para(11789(a,1),693(a,1))].">
      <j1 rule="para" parents="11789 693"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(12073,a,12020,a)].">
      <j1 rule="hyper" parents="12073 12020"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(12074(a,1),679(a,1,1))].">
      <j1 rule="para" parents="12074 679"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,10670,a(flip),b,12075,a),flip(a)].">
      <j1 rule="hyper" parents="60 10670 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5303(a,1),12076(a,2,1))].">
      <j1 rule="para" parents="5303 12076"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(11790,a,12077,a)].">
      <j1 rule="hyper" parents="11790 12077"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,12077,a(flip),b,11787,a(flip))].">
      <j1 rule="hyper" parents="125 12077 11787"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(755,a,12078,a)].">
      <j1 rule="hyper" parents="755 12078"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      K(x / y,y) * (x \ z) = (y * (x / y)) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,351,a(flip),b,12078,a),flip(a)].">
      <j1 rule="hyper" parents="125 351 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,12078,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(7977(a,1),12078(a,1,2))].">
      <j1 rule="para" parents="7977 12078"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(12079(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12079 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12083,a(flip),b,7935,a)].">
      <j1 rule="hyper" parents="129 12083 7935"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),12083(a,1,2,1))].">
      <j1 rule="para" parents="5 12083"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      (K(x,y) * (((x * y) \ z) * (u * u))) * w = ((y * x) \ z) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(12083(a,1),122(a,2,1))].">
      <j1 rule="para" parents="12083 122"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ z) * y) = ((y * x) \ z) * y
    ]]></literal>
    <justification jstring="[para(12083(a,1),7456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12083 7456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ z = u
    ]]></literal>
    <justification jstring="[para(12083(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12083 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      x * ((y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(12083(a,1),7877(a,1,2))].">
      <j1 rule="para" parents="12083 7877"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(8605(a,1),12083(a,1,1))].">
      <j1 rule="para" parents="8605 12083"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      x * (K(y \ x,y) * R(((y \ x) * y) \ z,u,w)) = (y \ x) * (y * R(y \ ((y \ x) \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,1602,a(flip),b,12081,a),flip(a)].">
      <j1 rule="hyper" parents="370 1602 12081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(5674(a,1),12082(a,1,1))].">
      <j1 rule="para" parents="5674 12082"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      (x * (x \ (y / (1 / x)))) * (1 / T(x,x \ (y / (1 / x)))) = (T(y,x) / (1 / x)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2546(a,1),12085(a,2,1))].">
      <j1 rule="para" parents="2546 12085"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      T(x,y) * (((x * y) \ z) * y) = x * (((y * x) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12090,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 12090 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(12094(a,1),11343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12094 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      (K(x,y * y) * (((y * y) \ (x \ z)) * (u * u))) * w = (((y * y) * x) \ z) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(517(a,1),12089(a,1,1,2,1))].">
      <j1 rule="para" parents="517 12089"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K((x \ 1) \ 1,(z * (L(y,x \ 1,x) / x)) \ u)
    ]]></literal>
    <justification jstring="[para(11798(a,1),11799(a,1,1))].">
      <j1 rule="para" parents="11798 11799"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (K(L(K(x,y),u,w),z) * K(x,y)) = a(w,u,K(x,y))
    ]]></literal>
    <justification jstring="[para(20(a,2),11915(a,1,1))].">
      <j1 rule="para" parents="20 11915"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      (x \ T(x * K(x / y,z),x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8757(a,1),12064(a,1,1,2,1))].">
      <j1 rule="para" parents="8757 12064"/>
    </justification>
  </clause>

  <clause id="12107">
    <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(2630(a,1),11431(a,1,2))].">
      <j1 rule="para" parents="2630 11431"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1030,a,12107,a)].">
      <j1 rule="hyper" parents="1030 12107"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1029,a,12107,a),flip(a)].">
      <j1 rule="hyper" parents="1029 12107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12110">
    <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(12107(a,1),1029(a,1))].">
      <j1 rule="para" parents="12107 1029"/>
    </justification>
  </clause>

  <clause id="12111">
    <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(125,a,10224,a,b,12108,a)].">
      <j1 rule="hyper" parents="125 10224 12108"/>
    </justification>
  </clause>

  <clause id="12112">
    <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(12108(a,1),40(a,1))].">
      <j1 rule="para" parents="12108 40"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9842,a,12109,a)].">
      <j1 rule="hyper" parents="9842 12109"/>
    </justification>
  </clause>

  <clause id="12114">
    <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(12109(a,1),9786(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12109 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12116">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12113(a,1),6300(a,1,1))].">
      <j1 rule="para" parents="12113 6300"/>
    </justification>
  </clause>

  <clause id="12117">
    <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(10628(a,1),12113(a,1,1))].">
      <j1 rule="para" parents="10628 12113"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,z,u)) * K(x,y) = K(x,y / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),12116(a,1,2,2))].">
      <j1 rule="para" parents="7 12116"/>
    </justification>
  </clause>

  <clause id="12119">
    <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(7880,a,12114,a)].">
      <j1 rule="hyper" parents="7880 12114"/>
    </justification>
  </clause>

  <clause id="12120">
    <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(9551,a,12119,a)].">
      <j1 rule="hyper" parents="9551 12119"/>
    </justification>
  </clause>

  <clause id="12121">
    <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(60,a,10785,a(flip),b,12120,a),flip(a)].">
      <j1 rule="hyper" parents="60 10785 12120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z,x) = u
    ]]></literal>
    <justification jstring="[para(11747(a,1),11853(a,1))].">
      <j1 rule="para" parents="11747 11853"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) * (L(y,u,w) * z) = L(y,u,w) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8045,a(flip),b,11815,a),flip(a)].">
      <j1 rule="hyper" parents="370 8045 11815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * w) = K(u,x) * (L(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(11186(a,1),12123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11186 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * (w * K(y,x))) = L(y,z,u) * T(w,K(y,x))
    ]]></literal>
    <justification jstring="[para(7505(a,1),12124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7505 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      T(L(x,y,z) * u,K(w,x)) = L(x,y,z) * T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,8940,a(flip),b,12125,a)].">
      <j1 rule="hyper" parents="60 8940 12125"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      T(L(x,y,z) * u,K(x,w)) = L(x,y,z) * T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(8728,a,12127,a)].">
      <j1 rule="hyper" parents="8728 12127"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,K(w,u)) = T(L(x,y,z) * u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8654,a,b,12128,a)].">
      <j1 rule="hyper" parents="370 8654 12128"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      K(x,K(y,L(y,z,u) * w)) = K(y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,8616,a,b,12129,a)].">
      <j1 rule="hyper" parents="31 8616 12129"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      K(x,K(y,L(y,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(12130(a,2),8634(a,1))].">
      <j1 rule="para" parents="12130 8634"/>
    </justification>
  </clause>

  <clause id="12133">
    <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(9445(a,1),11937(a,1,1))].">
      <j1 rule="para" parents="9445 11937"/>
    </justification>
  </clause>

  <clause id="12134">
    <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(9428(a,1),12133(a,1,2))].">
      <j1 rule="para" parents="9428 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <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(8630(a,1),12134(a,1,1))].">
      <j1 rule="para" parents="8630 12134"/>
    </justification>
  </clause>

  <clause id="12136">
    <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(9442(a,1),12135(a,2,3))].">
      <j1 rule="para" parents="9442 12135"/>
    </justification>
  </clause>

  <clause id="12137">
    <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(12136(a,1),6236(a,1))].">
      <j1 rule="para" parents="12136 6236"/>
    </justification>
  </clause>

  <clause id="12138">
    <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(5280(a,1),12004(a,2,2))].">
      <j1 rule="para" parents="5280 12004"/>
    </justification>
  </clause>

  <clause id="12139">
    <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(12110,a,12111,a)].">
      <j1 rule="hyper" parents="12110 12111"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(60,a,10046,a(flip),b,12139,a),flip(a)].">
      <j1 rule="hyper" parents="60 10046 12139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(9539,a,12140,a)].">
      <j1 rule="hyper" parents="9539 12140"/>
    </justification>
  </clause>

  <clause id="12142">
    <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(10402,a,12121,a)].">
      <j1 rule="hyper" parents="10402 12121"/>
    </justification>
  </clause>

  <clause id="12145">
    <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(10248(a,1),12142(a,2,2,2))].">
      <j1 rule="para" parents="10248 12142"/>
    </justification>
  </clause>

  <clause id="12146">
    <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(5(a,1),12145(a,2,2,2,1))].">
      <j1 rule="para" parents="5 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),12146(a,2,2))].">
      <j1 rule="para" parents="4 12146"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12109,a(flip),b,12147,a),flip(a)].">
      <j1 rule="hyper" parents="370 12109 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9539,a,12149,a),flip(a)].">
      <j1 rule="hyper" parents="9539 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10403,a(flip),b,12149,a),flip(a)].">
      <j1 rule="hyper" parents="60 10403 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12153">
    <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(4976(a,1),11293(a,1,1))].">
      <j1 rule="para" parents="4976 11293"/>
    </justification>
  </clause>

  <clause id="12154">
    <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(11329(a,1),5830(a,1))].">
      <j1 rule="para" parents="11329 5830"/>
    </justification>
  </clause>

  <clause id="12155">
    <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(10819(a,1),11413(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10819 11413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12156">
    <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(2894(a,1),12155(a,1,2,2))].">
      <j1 rule="para" parents="2894 12155"/>
    </justification>
  </clause>

  <clause id="12157">
    <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(12156(a,1),5942(a,1,1))].">
      <j1 rule="para" parents="12156 5942"/>
    </justification>
  </clause>

  <clause id="12158">
    <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(7502(a,1),12157(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7502 12157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12159">
    <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(5741(a,1),11490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5741 11490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <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(11705(a,1),11709(a,1))].">
      <j1 rule="para" parents="11705 11709"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w \ (v5 / x)) = K(L(K(x,y),z,u),w \ v5)
    ]]></literal>
    <justification jstring="[hyper(5381,a,11766,a),flip(a)].">
      <j1 rule="hyper" parents="5381 11766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w \ (v5 / x)) = K(y,K(w \ v5,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,9626,a(flip),b,12161,a),flip(a)].">
      <j1 rule="hyper" parents="370 9626 12161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(x,K(y \ (z / u),L(u,w,v5))) = K(x,K(y \ z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(9627,a,12162,a)].">
      <j1 rule="hyper" parents="9627 12162"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(z,w,v5))) = K(x,K(y \ u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(10225(a,1),12163(a,1,2))].">
      <j1 rule="para" parents="10225 12163"/>
    </justification>
  </clause>

  <clause id="12165">
    <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(11828(a,2),8908(a,1))].">
      <j1 rule="para" parents="11828 8908"/>
    </justification>
  </clause>

  <clause id="12166">
    <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(8033(a,1),12117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8033 12117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12167">
    <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(370,a,12113,a(flip),b,12166,a),flip(a)].">
      <j1 rule="hyper" parents="370 12113 12166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,w,v5)) = a(x,R(x,z,u) \ y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(109(a,1),12167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 12167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(12169(a,1),12118(a,1,1))].">
      <j1 rule="para" parents="12169 12118"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8100,a(flip),b,12170,a),flip(a)].">
      <j1 rule="hyper" parents="370 8100 12170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12172">
    <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(11831(a,1),12153(a,1,1))].">
      <j1 rule="para" parents="11831 12153"/>
    </justification>
  </clause>

  <clause id="12173">
    <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(62(a,1),12172(a,1,1,2,1))].">
      <j1 rule="para" parents="62 12172"/>
    </justification>
  </clause>

  <clause id="12174">
    <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(8029(a,1),12173(a,1,2))].">
      <j1 rule="para" parents="8029 12173"/>
    </justification>
  </clause>

  <clause id="12175">
    <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(4905(a,1),12174(a,1,2))].">
      <j1 rule="para" parents="4905 12174"/>
    </justification>
  </clause>

  <clause id="12176">
    <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(370,a,5164,a(flip),b,12175,a),flip(a)].">
      <j1 rule="hyper" parents="370 5164 12175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      L(x,T(y \ 1,z) \ 1,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11838,a(flip),b,12176,a),flip(a)].">
      <j1 rule="hyper" parents="60 11838 12176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5165,a(flip),b,12177,a)].">
      <j1 rule="hyper" parents="60 5165 12177"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(109(a,1),12179(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 12179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12181">
    <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(60,a,11064,a(flip),b,11317,a),flip(a)].">
      <j1 rule="hyper" parents="60 11064 11317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10360,a(flip),b,12181,a),flip(a)].">
      <j1 rule="hyper" parents="60 10360 12181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),12183(a,2,2))].">
      <j1 rule="para" parents="13 12183"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7500(a,1),12185(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 12185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7506(a,2),12185(a,1,2,2))].">
      <j1 rule="para" parents="7506 12185"/>
    </justification>
  </clause>

  <clause id="12188">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(12186(a,1),7530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12186 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7530,a(flip),b,12188,a),flip(a)].">
      <j1 rule="hyper" parents="370 7530 12188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(5700(a,1),12189(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5700 12189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <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(11507(a,1),11512(a,2,2,1))].">
      <j1 rule="para" parents="11507 11512"/>
    </justification>
  </clause>

  <clause id="12192">
    <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(12191(a,2),10441(a,1))].">
      <j1 rule="para" parents="12191 10441"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),y \ (y * z)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(6503,a,11986,a)].">
      <j1 rule="hyper" parents="6503 11986"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12193(a,1,2))].">
      <j1 rule="para" parents="4 12193"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ ((1 / ((x * y) \ x)) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(11204,a,12194,a)].">
      <j1 rule="hyper" parents="11204 12194"/>
    </justification>
  </clause>

  <clause id="12196">
    <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(529(a,1),12046(a,1,1))].">
      <j1 rule="para" parents="529 12046"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ T(y * L(y \ z,u,w),x))
    ]]></literal>
    <justification jstring="[para(17(a,2),11163(a,2,2,2))].">
      <j1 rule="para" parents="17 11163"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9200,a(flip),b,12197,a),flip(a)].">
      <j1 rule="hyper" parents="370 9200 12197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      K(x,L((y * x) \ (z * x),u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(746(a,1),12198(a,1,2))].">
      <j1 rule="para" parents="746 12198"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      K(x,L((y / x) \ z,u,w)) = K(x,L(y \ (z * x),u,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),12200(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      K(x,L(y \ (((y / x) * z) * x),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),12201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      L(K(x,y \ (((y / x) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(11206,a,12202,a)].">
      <j1 rule="hyper" parents="11206 12202"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      L(K(x,y \ (((x \ y) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(11337(a,1),12203(a,1,1))].">
      <j1 rule="para" parents="11337 12203"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      L(K(x,y),((z / x) * y) * x,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11258(a,1),12204(a,1,1))].">
      <j1 rule="para" parents="11258 12204"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      K(L(x,(y / x) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(9648,a,12205,a)].">
      <j1 rule="hyper" parents="9648 12205"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,9870,a(flip),b,12206,a),flip(a)].">
      <j1 rule="hyper" parents="60 9870 12206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(12206(a,1),9214(a,1,2,2))].">
      <j1 rule="para" parents="12206 9214"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6879,a(flip),b,12208,a)].">
      <j1 rule="hyper" parents="60 6879 12208"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9300,a(flip),b,12209,a),flip(a)].">
      <j1 rule="hyper" parents="60 9300 12209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(12206(a,1),12209(a,1,2,2))].">
      <j1 rule="para" parents="12206 12209"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      K(x,(L(T(x,y),z,u) \ w) \ 1) = K(x,w \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),12212(a,1,2,1,1))].">
      <j1 rule="para" parents="20 12212"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6464,a,12214,a)].">
      <j1 rule="hyper" parents="6464 12214"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K((x \ y) \ T(y,x),z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(2276(a,1),12215(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2276 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L(L(T(x,x \ y),y,x),u,w)) = K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(2277(a,1),12215(a,1,2,2,1))].">
      <j1 rule="para" parents="2277 12215"/>
    </justification>
  </clause>

  <clause id="12218">
    <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(8181,a,11189,a),flip(a)].">
      <j1 rule="hyper" parents="8181 11189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <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(11744(a,1),11475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11744 11475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11821,a(flip),b,12219,a),flip(a)].">
      <j1 rule="hyper" parents="60 11821 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8089,a,12220,a)].">
      <j1 rule="hyper" parents="8089 12220"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      a(x,y,x) != z * K(x,T(y,u))
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(x,u)) = z
    ]]></literal>
    <justification jstring="[para(12222(a,1),41(a,1))].">
      <j1 rule="para" parents="12222 41"/>
    </justification>
  </clause>

  <clause id="12225">
    <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(7393(a,1),12222(a,1,1))].">
      <j1 rule="para" parents="7393 12222"/>
    </justification>
  </clause>

  <clause id="12226">
    <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(9971(a,1),12222(a,1,1))].">
      <j1 rule="para" parents="9971 12222"/>
    </justification>
  </clause>

  <clause id="12227">
    <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(18(a,1),12224(a,2,2,2))].">
      <j1 rule="para" parents="18 12224"/>
    </justification>
  </clause>

  <clause id="12228">
    <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(4(a,1),11588(a,1,2,1))].">
      <j1 rule="para" parents="4 11588"/>
    </justification>
  </clause>

  <clause id="12230">
    <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(13(a,2),12228(a,1,2))].">
      <j1 rule="para" parents="13 12228"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(11158,a,12230,a)].">
      <j1 rule="hyper" parents="11158 12230"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11049,a(flip),b,12231,a),flip(a)].">
      <j1 rule="hyper" parents="370 11049 12231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),12232(a,2,2,2))].">
      <j1 rule="para" parents="5 12232"/>
    </justification>
  </clause>

  <clause id="12235">
    <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(5537(a,1),12234(a,1,1,2))].">
      <j1 rule="para" parents="5537 12234"/>
    </justification>
  </clause>

  <clause id="12236">
    <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(7323,a,12235,a)].">
      <j1 rule="hyper" parents="7323 12235"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12190,a(flip),b,12236,a),flip(a)].">
      <j1 rule="hyper" parents="60 12190 12236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      K((x * (y * z)) \ u,L(z,w,v5)) = K((x * y) \ (z \ u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(6106,a,11668,a),flip(a)].">
      <j1 rule="hyper" parents="6106 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      L(K(L(x,y,z) \ u,L(x,w,v5)),u,z * y) = K((z * y) \ (x \ ((z * y) * u)),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(6802,a,12239,a)].">
      <j1 rule="hyper" parents="6802 12239"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(201(a,1),11677(a,2,1,2))].">
      <j1 rule="para" parents="201 11677"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2477(a,1),12241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2477 12241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(7017,a,12242,a)].">
      <j1 rule="hyper" parents="7017 12242"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,12242,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 12242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = (((v5 \ v6) \ v6) * K(y,x)) \ T(v5,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(12242(a,1),11149(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12242 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6295,a(flip),b,12245,a),flip(a)].">
      <j1 rule="hyper" parents="370 6295 12245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,11127,a(flip),b,12246,a),flip(a)].">
      <j1 rule="hyper" parents="60 11127 12246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <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(125,a,107,a(flip),b,11752,a)].">
      <j1 rule="hyper" parents="125 107 11752"/>
    </justification>
  </clause>

  <clause id="12249">
    <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(10927,a,12248,a)].">
      <j1 rule="hyper" parents="10927 12248"/>
    </justification>
  </clause>

  <clause id="12250">
    <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(11590,a,12249,a)].">
      <j1 rule="hyper" parents="11590 12249"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,z \ (x \ (z * (y * x))))
    ]]></literal>
    <justification jstring="[para(7(a,1),12250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,11351,a(flip),b,12251,a),flip(a)].">
      <j1 rule="hyper" parents="370 11351 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(262(a,1),12252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 12252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(12252(a,1),11752(a,1,2))].">
      <j1 rule="para" parents="12252 11752"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(6778,a,12254,a),flip(a)].">
      <j1 rule="hyper" parents="6778 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,12255,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="128 12255 107"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      (x * y) \ (z * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,x),x * y) = u
    ]]></literal>
    <justification jstring="[para(12255(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12255 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(491,a,12256,a),flip(a)].">
      <j1 rule="hyper" parents="491 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x,y,z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(103(a,1),12256(a,1,1))].">
      <j1 rule="para" parents="103 12256"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),12258(a,1,1,2))].">
      <j1 rule="para" parents="7 12258"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(12258(a,1),9241(a,1,2))].">
      <j1 rule="para" parents="12258 9241"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,9910,a,b,12261,a)].">
      <j1 rule="hyper" parents="60 9910 12261"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,12264,a),flip(a)].">
      <j1 rule="hyper" parents="215 12264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(12265(a,2),4539(a,2,1))].">
      <j1 rule="para" parents="12265 4539"/>
    </justification>
  </clause>

  <clause id="12267">
    <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(10207(a,2),12266(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10207 12266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5435,a(flip),b,11755,a),flip(a)].">
      <j1 rule="hyper" parents="370 5435 11755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(909(a,1),12268(a,1,2))].">
      <j1 rule="para" parents="909 12268"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(6065,a,12269,a),flip(a)].">
      <j1 rule="hyper" parents="6065 12269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8572,a(flip),b,12270,a),flip(a)].">
      <j1 rule="hyper" parents="370 8572 12270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(10989(a,1),11786(a,1,2,1))].">
      <j1 rule="para" parents="10989 11786"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6472,a(flip),b,12272,a),flip(a)].">
      <j1 rule="hyper" parents="60 6472 12272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12275">
    <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(107(a,1),11857(a,1,1))].">
      <j1 rule="para" parents="107 11857"/>
    </justification>
  </clause>

  <clause id="12276">
    <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(370,a,11814,a(flip),b,12218,a),flip(a)].">
      <j1 rule="hyper" parents="370 11814 12218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8783,a(flip),b,12276,a),flip(a)].">
      <j1 rule="hyper" parents="370 8783 12276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12279">
    <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(9093(a,1),11845(a,1,2,2))].">
      <j1 rule="para" parents="9093 11845"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(391,a,12279,a)].">
      <j1 rule="hyper" parents="391 12279"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(7521,a,12280,a)].">
      <j1 rule="hyper" parents="7521 12280"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(9736(a,1),12281(a,1,1))].">
      <j1 rule="para" parents="9736 12281"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,9244,a(flip),b,12282,a),flip(a)].">
      <j1 rule="hyper" parents="370 9244 12282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9970,a(flip),b,12283,a)].">
      <j1 rule="hyper" parents="60 9970 12283"/>
    </justification>
  </clause>

  <clause id="12285">
    <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(12284(a,1),6546(a,1,1,1,2))].">
      <j1 rule="para" parents="12284 6546"/>
    </justification>
  </clause>

  <clause id="12286">
    <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(5256(a,2),12285(a,1,1,1))].">
      <j1 rule="para" parents="5256 12285"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6229,a,12286,a),flip(a)].">
      <j1 rule="hyper" parents="6229 12286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(12287(a,1),10228(a,1,1))].">
      <j1 rule="para" parents="12287 10228"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(755,a,12098,a)].">
      <j1 rule="hyper" parents="755 12098"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(5753(a,2),12289(a,1,2,2))].">
      <j1 rule="para" parents="5753 12289"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6839(a,1),12291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6839 12291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(480,a,12292,a)].">
      <j1 rule="hyper" parents="480 12292"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(109(a,1),12293(a,1,2,2))].">
      <j1 rule="para" parents="109 12293"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(12294(a,1),6256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12294 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(12295(a,2),3666(a,1,1))].">
      <j1 rule="para" parents="12295 3666"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(10338,a,12296,a)].">
      <j1 rule="hyper" parents="10338 12296"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,12297,a,b,xx)].">
      <j1 rule="hyper" parents="129 12297"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      (K(x,y * y) * T(x \ z,y * y)) * u = (((y * y) * x) \ z) * ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(847(a,1),12103(a,1,1,2))].">
      <j1 rule="para" parents="847 12103"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) * u = (((y * y) * x) \ z) * ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(8405(a,2),12300(a,1,1))].">
      <j1 rule="para" parents="8405 12300"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      K((x \ 1) \ 1,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(11675,a,12104,a),flip(a)].">
      <j1 rule="hyper" parents="11675 12104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      K(x,(y * (L(z,x \ 1,x) / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(5390,a,12302,a)].">
      <j1 rule="hyper" parents="5390 12302"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      K(x,(y * (x \ L(z,x \ 1,x))) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(11987,a,12303,a)].">
      <j1 rule="hyper" parents="11987 12303"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(511(a,1),12304(a,1,2,1,2))].">
      <j1 rule="para" parents="511 12304"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,11338,a(flip),b,12305,a),flip(a)].">
      <j1 rule="hyper" parents="370 11338 12305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ T(u,x)) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(17(a,2),12306(a,1,2,2))].">
      <j1 rule="para" parents="17 12306"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      K(x,(y * ((x \ 1) * z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(9290,a,12307,a)].">
      <j1 rule="hyper" parents="9290 12307"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,12305,a(flip),b,12308,a)].">
      <j1 rule="hyper" parents="60 12305 12308"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(11988,a,12309,a)].">
      <j1 rule="hyper" parents="11988 12309"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,11360,a,b,12309,a)].">
      <j1 rule="hyper" parents="60 11360 12309"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5278(a,1),12309(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5278 12309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(12309(a,1),9534(a,1,2,2))].">
      <j1 rule="para" parents="12309 9534"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(12309(a,1),11358(a,1,1))].">
      <j1 rule="para" parents="12309 11358"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5968(a,2),12312(a,1,2,1,1))].">
      <j1 rule="para" parents="5968 12312"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(7560,a,12313,a),flip(a)].">
      <j1 rule="hyper" parents="7560 12313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(10045,a,12316,a)].">
      <j1 rule="hyper" parents="10045 12316"/>
    </justification>
  </clause>

  <clause id="12318">
    <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(12317(a,1),12288(a,1,1,2,2))].">
      <j1 rule="para" parents="12317 12288"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,5591,a,b,12315,a)].">
      <j1 rule="hyper" parents="60 5591 12315"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,12311,a(flip),b,12314,a),flip(a)].">
      <j1 rule="hyper" parents="60 12311 12314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,11318,a(flip),b,12320,a)].">
      <j1 rule="hyper" parents="60 11318 12320"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,8558,a,b,12321,a),flip(a)].">
      <j1 rule="hyper" parents="60 8558 12321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9855,a(flip),b,12322,a),flip(a)].">
      <j1 rule="hyper" parents="370 9855 12322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12323(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,((z * u) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,8107,a(flip),b,12324,a),flip(a)].">
      <j1 rule="hyper" parents="60 8107 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,6463,a(flip),b,12325,a),flip(a)].">
      <j1 rule="hyper" parents="370 6463 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5981,a,12326,a),flip(a)].">
      <j1 rule="hyper" parents="5981 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11258,a(flip),b,12326,a),flip(a)].">
      <j1 rule="hyper" parents="60 11258 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(12327(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="12327 6294"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      T(x,K(y,z * (y \ u))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12327(a,1),8945(a,1,2))].">
      <j1 rule="para" parents="12327 8945"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      L(K(x,x \ y),y,x \ z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11205,a,b,12328,a)].">
      <j1 rule="hyper" parents="60 11205 12328"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12331(a,1,3))].">
      <j1 rule="para" parents="4 12331"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(11363,a,12333,a)].">
      <j1 rule="hyper" parents="11363 12333"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(11359,a,12333,a)].">
      <j1 rule="hyper" parents="11359 12333"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,12333,a,b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="126 12333 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      a(x,y,K(z \ y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,12333,a(flip),b,11895,a),flip(a)].">
      <j1 rule="hyper" parents="124 12333 11895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      a(x,y * z,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),12337(a,1,3,2))].">
      <j1 rule="para" parents="4 12337"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,12338,a)].">
      <j1 rule="hyper" parents="49 12338"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      L(K(x,y),x * y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,12339,a)].">
      <j1 rule="hyper" parents="49 12339"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11585,a,12341,a)].">
      <j1 rule="hyper" parents="11585 12341"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9649,a,12341,a)].">
      <j1 rule="hyper" parents="9649 12341"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12253,a(flip),b,12342,a)].">
      <j1 rule="hyper" parents="60 12253 12342"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12342,a(flip),b,6777,a)].">
      <j1 rule="hyper" parents="129 12342 6777"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12342,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 12342 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(656(a,1),12343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="656 12343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      K(x,y) * L(x,y,z) = L(T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(12343(a,1),5302(a,1,1))].">
      <j1 rule="para" parents="12343 5302"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(12343(a,1),11559(a,1,1))].">
      <j1 rule="para" parents="12343 11559"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,12342,a,b,12346,a),flip(a)].">
      <j1 rule="hyper" parents="370 12342 12346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12020,a(flip),b,12346,a)].">
      <j1 rule="hyper" parents="60 12020 12346"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(12346(a,1),10953(a,1,1))].">
      <j1 rule="para" parents="12346 10953"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11856,a(flip),b,12354,a)].">
      <j1 rule="hyper" parents="60 11856 12354"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10654,a(flip),b,12354,a)].">
      <j1 rule="hyper" parents="60 10654 12354"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      T(x,R(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12354,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 12354 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(26(a,1),12354(a,1,2))].">
      <j1 rule="para" parents="26 12354"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,z)) = K(z,R(1 / y,y,x) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(12354(a,1),10782(a,1,2,2))].">
      <j1 rule="para" parents="12354 10782"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,12348,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 12348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11139,a(flip),b,12362,a)].">
      <j1 rule="hyper" parents="60 11139 12362"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12362,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 12362 17"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      T(x \ y,(x \ y) \ z) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(656(a,1),12362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 12362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      T(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = T(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(669(a,1),12362(a,1,2))].">
      <j1 rule="para" parents="669 12362"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(12362(a,1),7161(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12362 7161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,12359,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 12359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12377">
    <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(716(a,1),12371(a,1,2))].">
      <j1 rule="para" parents="716 12371"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(11203,a,12340,a)].">
      <j1 rule="hyper" parents="11203 12340"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12340,a(flip),b,563,a)].">
      <j1 rule="hyper" parents="129 12340 563"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(9031,a,12358,a)].">
      <j1 rule="hyper" parents="9031 12358"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12335(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 12335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(12335(a,2),8883(a,1,2))].">
      <j1 rule="para" parents="12335 8883"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1203,a,12347,a)].">
      <j1 rule="hyper" parents="1203 12347"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      (x * K(y,z)) / (y * z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(809,a,12347,a)].">
      <j1 rule="hyper" parents="809 12347"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (x * (z * y)) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,12347,a(flip),b,6269,a)].">
      <j1 rule="hyper" parents="125 12347 6269"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      (x * y) * K(z,y / z) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),12347(a,1,1,2))].">
      <j1 rule="para" parents="7 12347"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      ((x * y) * z) * K(z,y) = R(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[para(103(a,1),12347(a,1,1))].">
      <j1 rule="para" parents="103 12347"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (K(u,z) \ 1),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(12347(a,1),3778(a,2,2))].">
      <j1 rule="para" parents="12347 3778"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      (x * (K(y,z) * (K(y,u) * w))) * K(K(y,u) * w,K(y,z)) = x * (K(y,u) * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[para(7463(a,1),12347(a,2,2))].">
      <j1 rule="para" parents="7463 12347"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[para(12347(a,1),8703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12347 8703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7150,a,12384,a)].">
      <j1 rule="hyper" parents="7150 12384"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),12384(a,1,2))].">
      <j1 rule="para" parents="5 12384"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7237,a(flip),b,12396,a),flip(a)].">
      <j1 rule="hyper" parents="60 7237 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,710,a(flip),b,12395,a)].">
      <j1 rule="hyper" parents="60 710 12395"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      R(x,y,R(T(z,y),u,w)) = R(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),12395(a,1,3))].">
      <j1 rule="para" parents="22 12395"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(12395(a,1),679(a,1,1))].">
      <j1 rule="para" parents="12395 679"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      R(x,y,T(z,y * z)) = R(x,y,L(z,y,z))
    ]]></literal>
    <justification jstring="[para(5486(a,1),12395(a,1,3))].">
      <j1 rule="para" parents="5486 12395"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8019(a,2),12395(a,1,3))].">
      <j1 rule="para" parents="8019 12395"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,11232,a(flip),b,12397,a),flip(a)].">
      <j1 rule="hyper" parents="60 11232 12397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10646,a(flip),b,12397,a),flip(a)].">
      <j1 rule="hyper" parents="60 10646 12397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(12397(a,1),438(a,1,1))].">
      <j1 rule="para" parents="12397 438"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12353(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="12353 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(11383(a,1),12413(a,1))].">
      <j1 rule="para" parents="11383 12413"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(12262,a,12357,a)].">
      <j1 rule="hyper" parents="12262 12357"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11240,a(flip),b,12357,a),flip(a)].">
      <j1 rule="hyper" parents="60 11240 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10890,a(flip),b,12357,a)].">
      <j1 rule="hyper" parents="60 10890 12357"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) = (w * (u * T(y,y \ z))) \ (w * (u * y))
    ]]></literal>
    <justification jstring="[para(12364(a,1),6932(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12364 6932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      ((x * T(y,x)) * L(x,y,z)) \ (x * (y * L(x,y,z))) = K(L(x,y,z),x * T(y,x))
    ]]></literal>
    <justification jstring="[para(12366(a,1),2164(a,1,2,2))].">
      <j1 rule="para" parents="12366 2164"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12378(a,1,1,2,2))].">
      <j1 rule="para" parents="5 12378"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11269,a,b,12381,a)].">
      <j1 rule="hyper" parents="60 11269 12381"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      R(x,y \ x,L(1 / (y \ x),y \ x,x)) = x / ((x \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4296,a(flip),b,12385,a)].">
      <j1 rule="hyper" parents="60 4296 12385"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(12418(a,1),10894(a,1,2))].">
      <j1 rule="para" parents="12418 10894"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(7583(a,1),12420(a,1,2,2))].">
      <j1 rule="para" parents="7583 12420"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11078,a(flip),b,12427,a),flip(a)].">
      <j1 rule="hyper" parents="60 11078 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(12428(a,1),8015(a,1,1))].">
      <j1 rule="para" parents="12428 8015"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      K(L(x,y,z) \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2178(a,1),12432(a,1,1,2,1))].">
      <j1 rule="para" parents="2178 12432"/>
    </justification>
  </clause>

  <clause id="12435">
    <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(6792(a,1),12432(a,1,1,2,1))].">
      <j1 rule="para" parents="6792 12432"/>
    </justification>
  </clause>

  <clause id="12436">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10660,a,b,12360,a)].">
      <j1 rule="hyper" parents="60 10660 12360"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7317(a,1),12399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7317 12399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (x * T(y,z)) * T(T(K(y,u),w),T(y,z)) = x * (T(K(y,u),w) * T(y,z))
    ]]></literal>
    <justification jstring="[para(8803(a,1),12402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8803 12402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      R(x,y,L(z,y,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7151,a(flip),b,12403,a),flip(a)].">
      <j1 rule="hyper" parents="60 7151 12403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      R(L(x,y,x),y,L(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,5532,a(flip),b,12439,a),flip(a)].">
      <j1 rule="hyper" parents="370 5532 12439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(5692(a,1),12387(a,1,2))].">
      <j1 rule="para" parents="5692 12387"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,10639,a,b,12400,a)].">
      <j1 rule="hyper" parents="370 10639 12400"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      (x * (y * z)) * K(y,y \ (y * z)) = x * (T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(5448(a,2),12441(a,2,2))].">
      <j1 rule="para" parents="5448 12441"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a,b,12370,a)].">
      <j1 rule="hyper" parents="370 13 12370"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8261,a(flip),b,12444,a)].">
      <j1 rule="hyper" parents="60 8261 12444"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      L(x,x \ y,y / x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(996,a,12446,a),flip(a)].">
      <j1 rule="hyper" parents="996 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,748,a(flip),b,12446,a),flip(a)].">
      <j1 rule="hyper" parents="60 748 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,96,a(flip),b,12446,a),flip(a)].">
      <j1 rule="hyper" parents="60 96 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      (x * y) / L(z,z \ y,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12446(a,1),727(a,1,2))].">
      <j1 rule="para" parents="12446 727"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12446(a,1),6800(a,1,1))].">
      <j1 rule="para" parents="12446 6800"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      L(x,x \ y,x \ y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(10161,a,12449,a)].">
      <j1 rule="hyper" parents="10161 12449"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      L(x,y,z) = (z * ((x * y) / x)) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),12451(a,1,2))].">
      <j1 rule="para" parents="4 12451"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      (x * x) \ (x * (x / y)) = 1 / L(y,y \ x,x)
    ]]></literal>
    <justification jstring="[para(12451(a,2),575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12451 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * (x * y) = L(x,y,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),12454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 12454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      L(R(x,y,z),x \ u,x \ u) = R((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(12454(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12454 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      L(L(x,y,z),x \ u,x \ u) = L((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(12454(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12454 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = ((1 / (y / x)) * y) \ x
    ]]></literal>
    <justification jstring="[para(12454(a,1),1362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12454 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      1 / L(x,x \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y / x) = z
    ]]></literal>
    <justification jstring="[para(12456(a,1),555(a,1))].">
      <j1 rule="para" parents="12456 555"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6305,a,12329,a),flip(a)].">
      <j1 rule="hyper" parents="6305 12329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12463(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      K((x \ y) \ T(z,x),x \ y) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),12350(a,2,1,2))].">
      <j1 rule="para" parents="107 12350"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,12078,a(flip),b,12355,a),flip(a)].">
      <j1 rule="hyper" parents="370 12078 12355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(12355(a,2),12086(a,1))].">
      <j1 rule="para" parents="12355 12086"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(7489,a,12466,a)].">
      <j1 rule="hyper" parents="7489 12466"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(787,a,12466,a)].">
      <j1 rule="hyper" parents="787 12466"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(764,a,12466,a)].">
      <j1 rule="hyper" parents="764 12466"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(387,a,12466,a),flip(a)].">
      <j1 rule="hyper" parents="387 12466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,304,a(flip),b,12466,a),flip(a)].">
      <j1 rule="hyper" parents="370 304 12466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      T(x,y) * ((y * x) * z) = x * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12466,a(flip),b,7935,a)].">
      <j1 rule="hyper" parents="129 12466 7935"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10256,a,12469,a)].">
      <j1 rule="hyper" parents="10256 12469"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      L(x,y,z * K(y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10153,a,12469,a)].">
      <j1 rule="hyper" parents="10153 12469"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10147,a,12469,a)].">
      <j1 rule="hyper" parents="10147 12469"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,10254,a(flip),b,12469,a),flip(a)].">
      <j1 rule="hyper" parents="60 10254 12469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,12469,a(flip),b,10254,a(flip))].">
      <j1 rule="hyper" parents="129 12469 10254"/>
    </justification>
  </clause>

  <clause id="12482">
    <literal><![CDATA[
      L(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),12469(a,1,2))].">
      <j1 rule="para" parents="5 12469"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5688(a,1),12469(a,1,3))].">
      <j1 rule="para" parents="5688 12469"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      L(x,y,K(z \ 1,y * z)) = x
    ]]></literal>
    <justification jstring="[para(5400(a,1),12482(a,1,3))].">
      <j1 rule="para" parents="5400 12482"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,12469,a,b,12477,a)].">
      <j1 rule="hyper" parents="370 12469 12477"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      (T(x,y) * (1 / y)) \ (x * z) = L((1 / T(y,x)) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10121,a(flip),b,12477,a)].">
      <j1 rule="hyper" parents="60 10121 12477"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8261,a(flip),b,12477,a)].">
      <j1 rule="hyper" parents="60 8261 12477"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      L(1 / T(x,y),x,y) = y \ (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5787,a(flip),b,12477,a),flip(a)].">
      <j1 rule="hyper" parents="60 5787 12477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,663,a(flip),b,12477,a),flip(a)].">
      <j1 rule="hyper" parents="60 663 12477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(108(a,1),12477(a,1,2))].">
      <j1 rule="para" parents="108 12477"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(12477(a,1),1360(a,2,1))].">
      <j1 rule="para" parents="12477 1360"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(3173,a,12479,a)].">
      <j1 rule="hyper" parents="3173 12479"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      L(K(x,y) * (x \ z),x,y) = (T(y,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10259,a(flip),b,12479,a),flip(a)].">
      <j1 rule="hyper" parents="60 10259 12479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6033,a(flip),b,12479,a)].">
      <j1 rule="hyper" parents="60 6033 12479"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(12483(a,1),10278(a,1))].">
      <j1 rule="para" parents="12483 10278"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      T(L(L(x * K(y,x),y,x),z,u) * y,x * K(y,x)) = L(x * K(y,x),z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(12478(a,1),6795(a,1,1,1,1))].">
      <j1 rule="para" parents="12478 6795"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,658,a(flip),b,12496,a),flip(a)].">
      <j1 rule="hyper" parents="60 658 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12496,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="129 12496 95"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ (z / (z / y))) = L(x,y \ z,y / (z / y))
    ]]></literal>
    <justification jstring="[para(1943(a,1),12496(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1943 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      L(x \ y,z,y / x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(10166(a,1),12498(a,1))].">
      <j1 rule="para" parents="10166 12498"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10257(a,2),12498(a,1))].">
      <j1 rule="para" parents="10257 12498"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(404,a,12471,a)].">
      <j1 rule="hyper" parents="404 12471"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      (x * y) \ T(z,K(x,y)) = (y * x) \ (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(8939(a,1),12471(a,1,2))].">
      <j1 rule="para" parents="8939 12471"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ z = u
    ]]></literal>
    <justification jstring="[para(12472(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12472 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (T(K(x,y),z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,5883,a,b,12480,a(flip))].">
      <j1 rule="hyper" parents="129 5883 12480"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,y) = (y \ (T(y,x) / x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12488(a,1),874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12488 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      (1 / T(x,y)) \ L(1 / T(x,y),x,y) = (y \ (T(y,x) / x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12488(a,1),1526(a,2,1))].">
      <j1 rule="para" parents="12488 1526"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      L(1 / T(1 / x,y),1 / x,y) = y \ (T(y,x \ 1) / (1 / x))
    ]]></literal>
    <justification jstring="[para(4443(a,1),12488(a,2,2,1))].">
      <j1 rule="para" parents="4443 12488"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,x,y) = ((1 / x) * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(3535,a,12489,a)].">
      <j1 rule="hyper" parents="3535 12489"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      L(T(x * x,y) \ z,x * x,y) = y \ (((x * x) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,974,a(flip),b,12489,a),flip(a)].">
      <j1 rule="hyper" parents="370 974 12489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      L(T(x,y / x) \ z,x,x \ y) = (x * (y / x)) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12496,a(flip),b,12489,a)].">
      <j1 rule="hyper" parents="60 12496 12489"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),x,u) = (x * u) \ (u * L(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(4205(a,1),12489(a,1,1))].">
      <j1 rule="para" parents="4205 12489"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      K(x,L(T(y,1 / z) \ u,y,1 / z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(12489(a,2),5587(a,1,2))].">
      <j1 rule="para" parents="12489 5587"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x \ u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,10558,a,b,12500,a),flip(a)].">
      <j1 rule="hyper" parents="370 10558 12500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12521">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(12501(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12501 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      L(((x \ y) \ y) \ z,x,x \ y) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(798,a,12490,a),flip(a)].">
      <j1 rule="hyper" parents="798 12490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(5232(a,1),12507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5232 12507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      x \ (((y \ x) * (K(y,y \ x) * z)) * y) = ((y \ x) * y) \ (((y \ x) * z) * y)
    ]]></literal>
    <justification jstring="[para(8275(a,2),12507(a,1,2))].">
      <j1 rule="para" parents="8275 12507"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3417,a,b,12523,a),flip(a)].">
      <j1 rule="hyper" parents="370 3417 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      T(x \ (x / y),y) = L(1 / y,y,y \ x)
    ]]></literal>
    <justification jstring="[para(12523(a,1),1054(a,1,1))].">
      <j1 rule="para" parents="12523 1054"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      L(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,y) = z
    ]]></literal>
    <justification jstring="[para(12526(a,1),3425(a,1))].">
      <j1 rule="para" parents="12526 3425"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),12467(a,1,2))].">
      <j1 rule="para" parents="82 12467"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(12473(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12473 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12485(a,1),11058(a,1,2))].">
      <j1 rule="para" parents="12485 11058"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(109(a,1),12532(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 12532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(663(a,1),12532(a,1,2)),flip(a)].">
      <j1 rule="para" parents="663 12532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((y \ x) * y) \ z = u
    ]]></literal>
    <justification jstring="[para(5(a,1),12509(a,1,1))].">
      <j1 rule="para" parents="5 12509"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9387,a,b,12368,a)].">
      <j1 rule="hyper" parents="60 9387 12368"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9692,a(flip),b,12421,a),flip(a)].">
      <j1 rule="hyper" parents="60 9692 12421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(8111,a,12433,a)].">
      <j1 rule="hyper" parents="8111 12433"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10763,a(flip),b,12538,a)].">
      <j1 rule="hyper" parents="60 10763 12538"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(12539(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12539 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      (x * y) \ T(z * (x * y),K(x,y)) = T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,12392,a,b,12470,a(flip))].">
      <j1 rule="hyper" parents="125 12392 12470"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      T((x * y) \ z,K(x,y)) = (y * x) \ (z / K(x,y))
    ]]></literal>
    <justification jstring="[hyper(9665,a,12508,a)].">
      <j1 rule="hyper" parents="9665 12508"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,y \ (z * x))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12536(a,1),9569(a,1,2))].">
      <j1 rule="para" parents="12536 9569"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12420,a(flip),b,12537,a),flip(a)].">
      <j1 rule="hyper" parents="60 12420 12537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,8957,a(flip),b,12541,a)].">
      <j1 rule="hyper" parents="60 8957 12541"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      K(x,y * z) * T(x,z) = T(T(x,z),z * y)
    ]]></literal>
    <justification jstring="[hyper(8969,a,12545,a)].">
      <j1 rule="hyper" parents="8969 12545"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12545(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) = T(x,T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(848(a,1),12545(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="848 12545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),u * (u \ z))) = K(x,T(y,(u \ z) * u))
    ]]></literal>
    <justification jstring="[para(12545(a,1),10238(a,1,2))].">
      <j1 rule="para" parents="12545 10238"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(32,a,8076,a,b,12546,a)].">
      <j1 rule="hyper" parents="32 8076 12546"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(9570,a,12551,a)].">
      <j1 rule="hyper" parents="9570 12551"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8906,a,12551,a)].">
      <j1 rule="hyper" parents="8906 12551"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8896,a,12551,a),flip(a)].">
      <j1 rule="hyper" parents="8896 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      K(x / y,z * y) = K(y \ x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8453,a,12551,a),flip(a)].">
      <j1 rule="hyper" parents="8453 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12551,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 12551 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x,T(y * (z * u),y * z)) = K(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(92(a,1),12551(a,1,2,1))].">
      <j1 rule="para" parents="92 12551"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      K(x,y * z) * ((z * y) \ u) = T(z * y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(12551(a,1),8097(a,1,1))].">
      <j1 rule="para" parents="12551 8097"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      K(x,y * z) * z = z * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(12551(a,1),8758(a,1,1))].">
      <j1 rule="para" parents="12551 8758"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ 1) * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12551(a,1),9481(a,1))].">
      <j1 rule="para" parents="12551 9481"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12552(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      K(x,T((y * z) * u,z * u)) = K(x,(z * u) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(103(a,1),12552(a,1,2,1))].">
      <j1 rule="para" parents="103 12552"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(z,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(12552(a,1),8056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12552 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4845(a,1),12557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4845 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(9728(a,2),12562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9728 12562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,12556,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 12556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12556(a,2),5265(a,1))].">
      <j1 rule="para" parents="12556 5265"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(9154,a,12567,a)].">
      <j1 rule="hyper" parents="9154 12567"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12567(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      K(T(x * y,x) / z,T(u,y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ T(x * y,x),u) = w
    ]]></literal>
    <justification jstring="[para(12567(a,1),8461(a,1,2))].">
      <j1 rule="para" parents="12567 8461"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      T(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = u
    ]]></literal>
    <justification jstring="[para(12567(a,1),9154(a,1))].">
      <j1 rule="para" parents="12567 9154"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      T(x,(x \ y) * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(12570(a,2),5742(a,1))].">
      <j1 rule="para" parents="12570 5742"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      T(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(4845(a,1),12575(a,1,2))].">
      <j1 rule="para" parents="4845 12575"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5865,a(flip),b,12564,a),flip(a)].">
      <j1 rule="hyper" parents="370 5865 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12564(a,2),5871(a,1))].">
      <j1 rule="para" parents="12564 5871"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(8847,a,12578,a),flip(a)].">
      <j1 rule="hyper" parents="8847 12578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      K(x * T(x \ y,z),T(u,x)) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[para(536(a,1),12578(a,1,1))].">
      <j1 rule="para" parents="536 12578"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      K(x * ((x \ 1) \ (y * z)),T(u,z)) = K(z * (x * ((x \ 1) \ y)),u)
    ]]></literal>
    <justification jstring="[para(1657(a,1),12578(a,1,1))].">
      <j1 rule="para" parents="1657 12578"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = T(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[para(12578(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12578 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12578(a,1),8011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12578 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12578(a,1),8758(a,1,1))].">
      <j1 rule="para" parents="12578 8758"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12578(a,1),8847(a,1))].">
      <j1 rule="para" parents="12578 8847"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      x / ((y * z) * K(u,T(y * z,z))) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(12578(a,1),8092(a,2,2))].">
      <j1 rule="para" parents="12578 8092"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,z * y)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12402(a,1),12578(a,1,1))].">
      <j1 rule="para" parents="12402 12578"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(9481,a,12580,a)].">
      <j1 rule="hyper" parents="9481 12580"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5448(a,2),12582(a,1,1))].">
      <j1 rule="para" parents="5448 12582"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6124(a,1),12582(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6124 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(8700(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="8700 12569"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      T(T(x,K(y,z)),(z \ 1) * y) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(9455(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="9455 12569"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z \ 1)) = T(x,(z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9459(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="9459 12569"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,12580,a(flip),b,12593,a),flip(a)].">
      <j1 rule="hyper" parents="370 12580 12593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      K(T(x,y) * y,z) = z / T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a(flip),b,12598,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 12598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5733,a,12599,a)].">
      <j1 rule="hyper" parents="5733 12599"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      K(T(x,y) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12599(a,2),5734(a,1))].">
      <j1 rule="para" parents="12599 5734"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,12600,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 12600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      (T(x,y) * y) * T(z,y * x) = z * (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,12600,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 12600 17"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u * z)) = T(x,(u * z) * T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(12569(a,1),12600(a,1,2,1))].">
      <j1 rule="para" parents="12569 12600"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5289,a,12602,a)].">
      <j1 rule="hyper" parents="5289 12602"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12602(a,2),5265(a,1))].">
      <j1 rule="para" parents="12602 5265"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      K(x,T(y,(1 / z) \ u) * ((z \ 1) \ u)) = K(x,((1 / z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5588,a(flip),b,12605,a)].">
      <j1 rule="hyper" parents="60 5588 12605"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8951(a,2),12568(a,1))].">
      <j1 rule="para" parents="8951 12568"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8955(a,2),12568(a,1))].">
      <j1 rule="para" parents="8955 12568"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      K((x * x) * (y * z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * ((x * x) * y),u) = w
    ]]></literal>
    <justification jstring="[para(28(a,1),12579(a,1,1))].">
      <j1 rule="para" parents="28 12579"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * (x * y),u) = w
    ]]></literal>
    <justification jstring="[para(6270(a,1),12579(a,1,1))].">
      <j1 rule="para" parents="6270 12579"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * y) * R(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12402(a,1),12579(a,1,1))].">
      <j1 rule="para" parents="12402 12579"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      K(x * K(y,(x \ z) \ 1),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((y * (z \ x)) / y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(5557(a,2),12588(a,1,1))].">
      <j1 rule="para" parents="5557 12588"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      K(L(T(x,y),z,u) * y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y * L(x,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),12601(a,1,1,1))].">
      <j1 rule="para" parents="20 12601"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      T(x,T(y,z * u) * (T(u,z) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(T(u,z) * z) * y) = w
    ]]></literal>
    <justification jstring="[para(12600(a,1),12606(a,1,2,1))].">
      <j1 rule="para" parents="12600 12606"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      K(x,T(T(y * z,y),u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(8292,a,12565,a)].">
      <j1 rule="hyper" parents="8292 12565"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12565(a,1),5980(a,1))].">
      <j1 rule="para" parents="12565 5980"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12565(a,1),8847(a,1))].">
      <j1 rule="para" parents="12565 8847"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ x) * y) = u
    ]]></literal>
    <justification jstring="[para(9482(a,1),12623(a,1))].">
      <j1 rule="para" parents="9482 12623"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(9490(a,1),12623(a,1))].">
      <j1 rule="para" parents="9490 12623"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      K(x,T(y * (z * u),y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(92(a,1),12626(a,1,2,1))].">
      <j1 rule="para" parents="92 12626"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      K(x,(y \ 1) \ (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(1658(a,1),12626(a,1,2))].">
      <j1 rule="para" parents="1658 12626"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      K(x,y * ((y * z) / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12562(a,2),12626(a,1))].">
      <j1 rule="para" parents="12562 12626"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * (1 \ z)) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(2913(a,1),12591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2913 12591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),12610(a,1))].">
      <j1 rule="para" parents="18 12610"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(8648(a,1),12611(a,1,1,2))].">
      <j1 rule="para" parents="8648 12611"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(z,z * u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(8692(a,1),12611(a,1,1,2))].">
      <j1 rule="para" parents="8692 12611"/>
    </justification>
  </clause>

  <clause id="12635">
    <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(8763(a,1),12611(a,1,1,2))].">
      <j1 rule="para" parents="8763 12611"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(5448(a,2),12629(a,1,2))].">
      <j1 rule="para" parents="5448 12629"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      T((x * y) \ z,K(x,y)) = (y * x) \ (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6291(a,1),12542(a,2,2))].">
      <j1 rule="para" parents="6291 12542"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(12544(a,1),10702(a,1))].">
      <j1 rule="para" parents="12544 10702"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9488,a(flip),b,12566,a),flip(a)].">
      <j1 rule="hyper" parents="60 9488 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10098(a,1),12640(a,1,2))].">
      <j1 rule="para" parents="10098 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      T(T(x,K((y \ 1) \ z,y)),z) = T(x,((y \ 1) \ z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),12596(a,1,2))].">
      <j1 rule="para" parents="5 12596"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z) * (z \ 1)) = T(x,(z \ 1) * T(y,z))
    ]]></literal>
    <justification jstring="[para(5667(a,1),12597(a,1,1,2))].">
      <j1 rule="para" parents="5667 12597"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      (x * ((x * y) / x)) * T(z,y * x) = z * (T(x,y) * y)
    ]]></literal>
    <justification jstring="[para(5448(a,1),12603(a,1,1))].">
      <j1 rule="para" parents="5448 12603"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = (y * x) \ (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8728,a,12638,a)].">
      <j1 rule="hyper" parents="8728 12638"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      T((x * (y \ 1)) \ x,K(x,y \ 1)) = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6916,a,b,12638,a),flip(a)].">
      <j1 rule="hyper" parents="370 6916 12638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11559,a(flip),b,12352,a),flip(a)].">
      <j1 rule="hyper" parents="60 11559 12352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(1409(a,1),12647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1409 12647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      R(x \ R(x,y,x),x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(2014(a,1),12437(a,1,1))].">
      <j1 rule="para" parents="2014 12437"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * (x * y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12457(a,2,3))].">
      <j1 rule="para" parents="4 12457"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      a(x,y,(((z * u) / z) * (z * u)) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(12651(a,1),3127(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12651 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      L(T(x \ 1,x * y) \ z,x,x \ y) = ((1 / x) * (x \ y)) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(7751(a,1),12515(a,1,1,1))].">
      <j1 rule="para" parents="7751 12515"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      L(((x \ K(x,y)) \ K(x,y)) \ z,x,x \ K(x,y)) = K(x,y) \ ((((y * x) / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(5935(a,2),12522(a,2,2,1))].">
      <j1 rule="para" parents="5935 12522"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      T((x * (y \ 1)) \ x,K(x,y)) = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(9457,a,12646,a)].">
      <j1 rule="hyper" parents="9457 12646"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),K(x,y)) = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[para(3494(a,1),12655(a,1,1))].">
      <j1 rule="para" parents="3494 12655"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      L(x,x,x * y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,9978,a(flip),b,12656,a),flip(a)].">
      <j1 rule="hyper" parents="60 9978 12656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(11441(a,1),12650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11441 12650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12044,a,12659,a),flip(a)].">
      <j1 rule="hyper" parents="12044 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <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(60,a,686,a,b,12660,a)].">
      <j1 rule="hyper" parents="60 686 12660"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,12430,a),flip(a)].">
      <j1 rule="hyper" parents="5265 12430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      (x * (y * z)) * K(y,z) = x * (T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12443(a,1,2,2))].">
      <j1 rule="para" parents="4 12443"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      (L(x,y,z) \ (x * L(x \ L(x,y,z),x,u))) * (L(x,y,z) \ x) = L(L(x,y,z) \ x,x,x \ u)
    ]]></literal>
    <justification jstring="[para(12520(a,1),4046(a,1,1,2,2))].">
      <j1 rule="para" parents="12520 4046"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,12540,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8181,a,12667,a)].">
      <j1 rule="hyper" parents="8181 12667"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(74(a,1),12668(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="74 12668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      K((x \ 1) * T((x \ 1) \ y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[hyper(9481,a,12583,a)].">
      <j1 rule="hyper" parents="9481 12583"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(12354(a,1),12436(a,1,1))].">
      <j1 rule="para" parents="12354 12436"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = (R(x,z,u) * (x * y)) / (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(12442(a,1),5366(a,1,1))].">
      <j1 rule="para" parents="12442 5366"/>
    </justification>
  </clause>

  <clause id="12674">
    <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(389,a,12486,a),flip(a)].">
      <j1 rule="hyper" parents="389 12486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),12511(a,2,2,1))].">
      <j1 rule="para" parents="8019 12511"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      x \ (((y * y) \ x) * z) = T(y * y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(635,a,12516,a),flip(a)].">
      <j1 rule="hyper" parents="635 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11999,a(flip),b,12531,a),flip(a)].">
      <j1 rule="hyper" parents="370 11999 12531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      R(K(x,T(y,(z * x) * (z \ 1))),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10719,a(flip),b,12678,a)].">
      <j1 rule="hyper" parents="60 10719 12678"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),z * (u / T(y * z,u)))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(5789(a,2),12563(a,1,2,1))].">
      <j1 rule="para" parents="5789 12563"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      L(x,(y * (z * u)) * K(z,u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(5865(a,1),12390(a,1,2,2))].">
      <j1 rule="para" parents="5865 12390"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      L(x,y * (T(z,u) * u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(12665(a,1),12682(a,1,2))].">
      <j1 rule="para" parents="12665 12682"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      L(x,y * ((z \ u) * z),w) = L(x,y * (z * (u / z)),w)
    ]]></literal>
    <justification jstring="[para(109(a,1),12683(a,1,2,2,1))].">
      <j1 rule="para" parents="109 12683"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),z)) = K(x,T(y,(u \ z) * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),12550(a,1,2,2))].">
      <j1 rule="para" parents="5 12550"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(8588(a,1),12685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8588 12685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) = T(x,((z \ 1) \ y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(8713,a,12642,a)].">
      <j1 rule="hyper" parents="8713 12642"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      T(T(x,K((y \ 1) \ (y \ z),y)),T((y \ 1) \ (y \ z),y) * (y \ 1)) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(2225(a,1),12643(a,2,2))].">
      <j1 rule="para" parents="2225 12643"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,12570,a(flip),b,12687,a),flip(a)].">
      <j1 rule="hyper" parents="370 12570 12687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      T(T(x,y),K(z,(z \ 1) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(12689(a,2),9496(a,1))].">
      <j1 rule="para" parents="12689 9496"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * T(y,x) = T(y,x) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[para(6711(a,1),12512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6711 12512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      L(T(x \ 1,y) \ 1,1 / x,y) = y \ (T(y,x \ 1) / (1 / x))
    ]]></literal>
    <justification jstring="[para(4332(a,1),12514(a,1,1))].">
      <j1 rule="para" parents="4332 12514"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      L(T(x,x \ y) \ z,x,x \ y) = (x * (y / x)) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(5753(a,1),12517(a,1,1,1))].">
      <j1 rule="para" parents="5753 12517"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),x,u) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(273(a,1),12518(a,2,2))].">
      <j1 rule="para" parents="273 12518"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      L(T(x \ 1,y) \ 1,x \ 1,y) = y \ (T(y,x \ 1) / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(3536,a,12692,a)].">
      <j1 rule="hyper" parents="3536 12692"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * z) = (x * (x \ y)) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12489,a(flip),b,12693,a),flip(a)].">
      <j1 rule="hyper" parents="60 12489 12693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * z) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,176,a(flip),b,12696,a),flip(a)].">
      <j1 rule="hyper" parents="370 176 12696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      x \ (T(x,y \ 1) / (1 / y)) = ((y \ 1) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(6718,a,12695,a),flip(a)].">
      <j1 rule="hyper" parents="6718 12695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      x / ((x \ y) * (y \ x)) = R(x,y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(3418(a,1),12429(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3418 12429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      R(x,y \ x,x \ y) = R(x,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1403,a,12700,a),flip(a)].">
      <j1 rule="hyper" parents="1403 12700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12382,a(flip),b,12431,a),flip(a)].">
      <j1 rule="hyper" parents="60 12382 12431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      L(x,y \ z,y / (z / y)) = L(x,y \ z,(z / y) \ y)
    ]]></literal>
    <justification jstring="[para(9032(a,1),12503(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9032 12503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * x) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(9324(a,1),12529(a,1))].">
      <j1 rule="para" parents="9324 12529"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      K((x * x) * (y * z),T(u,z)) = K(z * (x * ((x \ 1) \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6656,a(flip),b,12584,a)].">
      <j1 rule="hyper" parents="60 6656 12584"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      K(x * (y * ((y \ 1) \ z)),u) = K(x * ((y * y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(12612,a,12705,a),flip(a)].">
      <j1 rule="hyper" parents="12612 12705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      x / ((y * z) * K(u,z * y)) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(12552(a,1),12589(a,1,2,2))].">
      <j1 rule="para" parents="12552 12589"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8142,a(flip),b,12649,a),flip(a)].">
      <j1 rule="hyper" parents="370 8142 12649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,933,a(flip),b,12708,a),flip(a)].">
      <j1 rule="hyper" parents="370 933 12708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(8473,a,12709,a)].">
      <j1 rule="hyper" parents="8473 12709"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(12154,a,12710,a)].">
      <j1 rule="hyper" parents="12154 12710"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      T(x,T(x,y) * (1 / y)) = L(T(x,y \ 1),y,x)
    ]]></literal>
    <justification jstring="[para(9611(a,1),12674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9611 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      (x * T(y,z)) * T(K(y,u),w) = x * (T(K(y,u),w) * T(y,z))
    ]]></literal>
    <justification jstring="[para(4919(a,1),12438(a,1,2))].">
      <j1 rule="para" parents="4919 12438"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      (x \ y) * (T(K(x,z),y) * T(x,u)) = K(x,z) * ((x \ y) * T(x,u))
    ]]></literal>
    <justification jstring="[hyper(9288,a,12714,a),flip(a)].">
      <j1 rule="hyper" parents="9288 12714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      K(x,y) * ((x \ z) * T(x,z)) = (x \ z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7999(a,1),12715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7999 12715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12718">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) * ((((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * K((z \ 1) \ (x / z),y)) = (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u)
    ]]></literal>
    <justification jstring="[para(7465(a,1),12717(a,1,2,2))].">
      <j1 rule="para" parents="7465 12717"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      L(T(x,(y * (z * x)) \ ((y * z) * u)),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a,b,12369,a)].">
      <j1 rule="hyper" parents="60 20 12369"/>
    </justification>
  </clause>

  <clause id="12720">
    <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(60,a,22,a,b,12377,a)].">
      <j1 rule="hyper" parents="60 22 12377"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12423(a,2),6933(a,1))].">
      <j1 rule="para" parents="12423 6933"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,1 / z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(4443(a,1),12519(a,1,2,1,1))].">
      <j1 rule="para" parents="4443 12519"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      L(T(x,(y * z) \ (x \ ((y * z) * u))),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(11768(a,1),12719(a,1,1))].">
      <j1 rule="para" parents="11768 12719"/>
    </justification>
  </clause>

  <clause id="12724">
    <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(370,a,5753,a(flip),b,12720,a),flip(a)].">
      <j1 rule="hyper" parents="370 5753 12720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(1488(a,1),12722(a,1,2))].">
      <j1 rule="para" parents="1488 12722"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(12364(a,1),12723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12364 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(164,a,12726,a)].">
      <j1 rule="hyper" parents="164 12726"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(12726(a,1),308(a,1,2))].">
      <j1 rule="para" parents="12726 308"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = (x \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,108,a(flip),b,12728,a),flip(a)].">
      <j1 rule="hyper" parents="370 108 12728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ T(x,x \ 1) = x * (L(x,y,z) \ (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(12728(a,1),2196(a,1,2))].">
      <j1 rule="para" parents="12728 2196"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ T(x,x \ 1) = L(x,y,z) \ (L(x,y,z) \ (x * 1))
    ]]></literal>
    <justification jstring="[para(12728(a,1),2201(a,1,2))].">
      <j1 rule="para" parents="12728 2201"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      x / L((y \ x) \ x,z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(12732(a,1),425(a,1,2,1))].">
      <j1 rule="para" parents="12732 425"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      (x * y) / L(T(x,y),z,u) = L(x,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12729(a,1,2,1,2))].">
      <j1 rule="para" parents="4 12729"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,12738,a),flip(a)].">
      <j1 rule="hyper" parents="215 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(77(a,1),12738(a,1,2,1,1))].">
      <j1 rule="para" parents="77 12738"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      x / L(L(x,y,z),u,w) = L(L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[para(3939(a,1),12738(a,1,2,1))].">
      <j1 rule="para" parents="3939 12738"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      (x * y) * ((L(z,y,x) \ u) \ u) = x * (y * ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12742,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 12742 13"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      L(L(((x \ y) \ y) \ 1,z,u) \ w,(x \ y) \ y,(x \ y) \ y) = ((x \ y) \ y) * (((x \ y) \ y) * (((L(x,z,u) \ y) \ y) \ w))
    ]]></literal>
    <justification jstring="[para(12742(a,1),4020(a,2,2,2,1))].">
      <j1 rule="para" parents="12742 4020"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      L(T(x \ 1,x * y),z,u) = (L(x \ 1,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7579(a,2),12742(a,1,1))].">
      <j1 rule="para" parents="7579 12742"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      L(x / y,y,y) \ x = x / ((1 / y) * x)
    ]]></literal>
    <justification jstring="[para(586(a,1),12743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="586 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      L(x / (y \ z),y \ z,y) \ x = x / (z \ (y * x))
    ]]></literal>
    <justification jstring="[para(656(a,1),12743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      L((x * y) / K(x,y),z,u) \ (x * y) = (x * y) / L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(7475(a,1),12743(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7475 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      (x * y) / L(T(x,y),z,u) = x * (L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,12739,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 12739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      L(L(1 / x,x,x),y,z) \ (1 / x) = (1 / x) / L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1229(a,1),12744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1229 12744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,12754,a)].">
      <j1 rule="hyper" parents="215 12754"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(2822,a,12756,a(flip))].">
      <j1 rule="hyper" parents="2822 12756"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = x / T(x,u)
    ]]></literal>
    <justification jstring="[para(12757(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="12757 5701"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,12759,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 12759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[para(2161(a,1),12761(a,1,1))].">
      <j1 rule="para" parents="2161 12761"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(9019,a,12762,a)].">
      <j1 rule="hyper" parents="9019 12762"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = (x \ y) \ (1 / (y \ (x * 1)))
    ]]></literal>
    <justification jstring="[hyper(125,a,12751,a(flip),b,3864,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 12751 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      L(T(x \ 1,x * y),x,y) = T(y * x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(6487(a,1),12748(a,2,1))].">
      <j1 rule="para" parents="6487 12748"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ z) \ u) \ u) = x * (y * (((y \ (x \ z)) \ u) \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),12745(a,1,2,1,1))].">
      <j1 rule="para" parents="344 12745"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      (1 / x) / L(x \ 1,y,z) = L(x \ 1,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1229(a,1),12755(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1229 12755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = (x \ y) \ (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(3(a,1),12765(a,2,2,2,2))].">
      <j1 rule="para" parents="3 12765"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      (x * y) / L(y * x,z,u) = L(y * x,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(212(a,1),12753(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="212 12753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <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(370,a,22,a,b,12724,a),flip(a)].">
      <j1 rule="hyper" parents="370 22 12724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12772">
    <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(12664(a,1),12771(a,1,1))].">
      <j1 rule="para" parents="12664 12771"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),12772(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 12772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(817,a,12773,a),flip(a)].">
      <j1 rule="hyper" parents="817 12773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,1650,a(flip),b,12774,a)].">
      <j1 rule="hyper" parents="60 1650 12774"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12774(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 12774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[para(9391(a,1),12774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9391 12774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      x / R((y \ x) \ x,z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(221,a,12775,a(flip))].">
      <j1 rule="hyper" parents="221 12775"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(77(a,1),12775(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 12775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <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(6259(a,1),12775(a,2,1))].">
      <j1 rule="para" parents="6259 12775"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      R(x / (x / y),z,u) \ x = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[para(220(a,1),12778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="220 12778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(12779(a,1),7191(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12779 7191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      R(x / (x / y),z,u) = x / (x / R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(221,a,12783,a),flip(a)].">
      <j1 rule="hyper" parents="221 12783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      x / (x / R(y,z,u)) = R(y,z,u) * K(y \ x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6744,a(flip),b,12787,a),flip(a)].">
      <j1 rule="hyper" parents="60 6744 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1955(a,1),12776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1955 12776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(10633(a,1),12777(a,1,1))].">
      <j1 rule="para" parents="10633 12777"/>
    </justification>
  </clause>

  <clause id="12792">
    <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(12789(a,1),5842(a,1,1))].">
      <j1 rule="para" parents="12789 5842"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(8019(a,2),12791(a,2,1))].">
      <j1 rule="para" parents="8019 12791"/>
    </justification>
  </clause>

  <clause id="12794">
    <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(9080(a,1),12793(a,2,1))].">
      <j1 rule="para" parents="9080 12793"/>
    </justification>
  </clause>

  <clause id="12795">
    <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(370,a,270,a(flip),b,12790,a),flip(a)].">
      <j1 rule="hyper" parents="370 270 12790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(R(T(x,u),y,z),u,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),12795(a,2,1))].">
      <j1 rule="para" parents="22 12795"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,894,a(flip),b,12796,a),flip(a)].">
      <j1 rule="hyper" parents="370 894 12796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      R(T(x,x * y),z,u) \ R(x,z,u) = K(R(x,z,u) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12797(a,1),5725(a,1,1))].">
      <j1 rule="para" parents="12797 5725"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5831,a,12798,a),flip(a)].">
      <j1 rule="hyper" parents="5831 12798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9253,a,12799,a)].">
      <j1 rule="hyper" parents="9253 12799"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,12010,a,b,12800,a),flip(a)].">
      <j1 rule="hyper" parents="370 12010 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      ((x \ y) * x) \ (((x \ y) * z) * x) = y \ (((y / x) * z) * x)
    ]]></literal>
    <justification jstring="[para(8203(a,1),12524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8203 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(1378(a,1),12670(a,1,1))].">
      <j1 rule="para" parents="1378 12670"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(8474,a,12803,a),flip(a)].">
      <j1 rule="hyper" parents="8474 12803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      (x \ (L(x,y,z) * L(x,y,z))) \ 1 = x * (L(x,y,z) \ (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(1633,a,12734,a)].">
      <j1 rule="hyper" parents="1633 12734"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = x * (L(x,y,z) \ (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(2156(a,1),12806(a,1,1))].">
      <j1 rule="para" parents="2156 12806"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = x / (L(x,y,z) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,603,a(flip),b,12808,a),flip(a)].">
      <j1 rule="hyper" parents="370 603 12808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      (x \ (L(x,y,z) * L(x,y,z))) \ 1 = L(x,y,z) \ (L(x,y,z) \ (x * 1))
    ]]></literal>
    <justification jstring="[hyper(1633,a,12735,a)].">
      <j1 rule="hyper" parents="1633 12735"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = L(x,y,z) \ (L(x,y,z) \ (x * 1))
    ]]></literal>
    <justification jstring="[para(2156(a,1),12810(a,1,1))].">
      <j1 rule="para" parents="2156 12810"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3(a,1),12812(a,2,2,2))].">
      <j1 rule="para" parents="3 12812"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      x / (L(x,y,z) * L(x,y,z)) = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12809,a(flip),b,12813,a)].">
      <j1 rule="hyper" parents="60 12809 12813"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ (L(z,u,w) \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12814(a,1),3382(a,1,3))].">
      <j1 rule="para" parents="12814 3382"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(T(x,y),K(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(9051(a,1),12361(a,2,2))].">
      <j1 rule="para" parents="9051 12361"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(8587(a,1),12816(a,1,2))].">
      <j1 rule="para" parents="8587 12816"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      ((x * y) * L(y,x,z)) \ (y * (x * L(y,x,z))) = K(L(y,x,z),y * T(x,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),12425(a,1,1,1))].">
      <j1 rule="para" parents="107 12425"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2478,a,12819,a),flip(a)].">
      <j1 rule="hyper" parents="2478 12819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),12820(a,1,2))].">
      <j1 rule="para" parents="107 12820"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6772,a,12821,a),flip(a)].">
      <j1 rule="hyper" parents="6772 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(12822(a,1),6765(a,1,1))].">
      <j1 rule="para" parents="12822 6765"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(9648,a,12824,a),flip(a)].">
      <j1 rule="hyper" parents="9648 12824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(12825(a,1),11948(a,1,1))].">
      <j1 rule="para" parents="12825 11948"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9646(a,1),12826(a,1,1))].">
      <j1 rule="para" parents="9646 12826"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11945,a(flip),b,12827,a)].">
      <j1 rule="hyper" parents="60 11945 12827"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(12827(a,2),5866(a,1,2))].">
      <j1 rule="para" parents="12827 5866"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(11175,a,12829,a)].">
      <j1 rule="hyper" parents="11175 12829"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(2160(a,1),12829(a,1,2))].">
      <j1 rule="para" parents="2160 12829"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(12829(a,1),11168(a,1))].">
      <j1 rule="para" parents="12829 11168"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4216(a,2),12832(a,1,2,1))].">
      <j1 rule="para" parents="4216 12832"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(11014,a,12830,a)].">
      <j1 rule="hyper" parents="11014 12830"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6557,a,b,12837,a),flip(a)].">
      <j1 rule="hyper" parents="370 6557 12837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11621,a(flip),b,12837,a)].">
      <j1 rule="hyper" parents="60 11621 12837"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6557(a,2),12838(a,1,1))].">
      <j1 rule="para" parents="6557 12838"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      (x * y) * K(y * z,z) = x * (y * K(y * z,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,12840,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 12840 13"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,12840,a(flip),b,11895,a),flip(a)].">
      <j1 rule="hyper" parents="124 12840 11895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(11160,a,12839,a)].">
      <j1 rule="hyper" parents="11160 12839"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(11107,a,12839,a)].">
      <j1 rule="hyper" parents="11107 12839"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(11105,a,12839,a),flip(a)].">
      <j1 rule="hyper" parents="11105 12839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6762,a,12839,a)].">
      <j1 rule="hyper" parents="6762 12839"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12839(a,1),11448(a,1,2))].">
      <j1 rule="para" parents="12839 11448"/>
    </justification>
  </clause>

  <clause id="12850">
    <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(11242,a,12836,a)].">
      <j1 rule="hyper" parents="11242 12836"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(12849(a,1),11484(a,1))].">
      <j1 rule="para" parents="12849 11484"/>
    </justification>
  </clause>

  <clause id="12852">
    <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(1951(a,1),12850(a,1,2,1))].">
      <j1 rule="para" parents="1951 12850"/>
    </justification>
  </clause>

  <clause id="12853">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(200(a,1),12852(a,1,2,2))].">
      <j1 rule="para" parents="200 12852"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12625,a,12853,a)].">
      <j1 rule="hyper" parents="12625 12853"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = (x * (R(x,z,u) * y)) / (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(1947(a,1),12673(a,2,1))].">
      <j1 rule="para" parents="1947 12673"/>
    </justification>
  </clause>

  <clause id="12856">
    <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(370,a,9120,a(flip),b,12782,a),flip(a)].">
      <j1 rule="hyper" parents="370 9120 12782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <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(8585(a,1),12856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8585 12856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <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(12857(a,1),12058(a,1,2))].">
      <j1 rule="para" parents="12857 12058"/>
    </justification>
  </clause>

  <clause id="12859">
    <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(6099(a,1),12792(a,1,1))].">
      <j1 rule="para" parents="6099 12792"/>
    </justification>
  </clause>

  <clause id="12860">
    <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(60,a,22,a,b,12859,a)].">
      <j1 rule="hyper" parents="60 22 12859"/>
    </justification>
  </clause>

  <clause id="12861">
    <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(5362(a,1),12860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5362 12860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12862">
    <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(370,a,24,a(flip),b,12861,a),flip(a)].">
      <j1 rule="hyper" parents="370 24 12861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12863">
    <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(12862(a,1),3190(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12862 3190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,6,a(flip),b,12855,a),flip(a)].">
      <j1 rule="hyper" parents="370 6 12855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      L(R(x,y,R(x,z,u)),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(12400(a,1),12864(a,1,1))].">
      <j1 rule="para" parents="12400 12864"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = L(y * K(x,y),z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7136(a,1),12499(a,1,1))].">
      <j1 rule="para" parents="7136 12499"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      T(x * L(L(y,z,u),x,y),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5986,a(flip),b,12867,a),flip(a)].">
      <j1 rule="hyper" parents="370 5986 12867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y * K(x,y)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(25(a,1),12868(a,1,1,2))].">
      <j1 rule="para" parents="25 12868"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),T(y,x)) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,8857,a(flip),b,12869,a)].">
      <j1 rule="hyper" parents="60 8857 12869"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9549,a(flip),b,12870,a)].">
      <j1 rule="hyper" parents="60 9549 12870"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      K(x,L(L(x,y,x),z,u) / (y \ 1)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12871(a,1),8256(a,1,2,2))].">
      <j1 rule="para" parents="12871 8256"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      L(T(x,x \ K(x,y)) \ z,x,x \ K(x,y)) = K(x,y) \ ((((y * x) / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(108(a,2),12654(a,1,1,1))].">
      <j1 rule="para" parents="108 12654"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x \ K(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(11281(a,1),12873(a,1,1,1))].">
      <j1 rule="para" parents="11281 12873"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(L(x,y,x),z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8131(a,1),12872(a,1,1))].">
      <j1 rule="para" parents="8131 12872"/>
    </justification>
  </clause>

  <clause id="12877">
    <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(12417,a,12240,a),flip(a)].">
      <j1 rule="hyper" parents="12417 12240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(12721,a,12877,a),flip(a)].">
      <j1 rule="hyper" parents="12721 12877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12879">
    <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(60,a,12435,a(flip),b,12878,a),flip(a)].">
      <j1 rule="hyper" parents="60 12435 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      K(x \ ((x \ (L(x,y,z) \ u)) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12434,a(flip),b,12878,a),flip(a)].">
      <j1 rule="hyper" parents="60 12434 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12881">
    <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(60,a,12712,a(flip),b,12879,a)].">
      <j1 rule="hyper" parents="60 12712 12879"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6643,a(flip),b,12881,a)].">
      <j1 rule="hyper" parents="60 6643 12881"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9253,a,12882,a)].">
      <j1 rule="hyper" parents="9253 12882"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11884,a(flip),b,12883,a),flip(a)].">
      <j1 rule="hyper" parents="370 11884 12883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(62(a,1),12884(a,2,1))].">
      <j1 rule="para" parents="62 12884"/>
    </justification>
  </clause>

  <clause id="12886">
    <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(12885(a,1),5356(a,1,1,2))].">
      <j1 rule="para" parents="12885 5356"/>
    </justification>
  </clause>

  <clause id="12887">
    <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(6096(a,1),12886(a,1,1))].">
      <j1 rule="para" parents="6096 12886"/>
    </justification>
  </clause>

  <clause id="12888">
    <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(6557(a,1),12887(a,1,1,1,2))].">
      <j1 rule="para" parents="6557 12887"/>
    </justification>
  </clause>

  <clause id="12889">
    <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(370,a,5536,a,b,12888,a),flip(a)].">
      <j1 rule="hyper" parents="370 5536 12888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12890">
    <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(60,a,20,a,b,12889,a)].">
      <j1 rule="hyper" parents="60 20 12889"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5502(a,1),12890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5502 12890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(5543,a,12891,a)].">
      <j1 rule="hyper" parents="5543 12891"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(165,a,12892,a)].">
      <j1 rule="hyper" parents="165 12892"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12892(a,1),7323(a,1,2))].">
      <j1 rule="para" parents="12892 7323"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      R(1 / x,y,L(x,z,u)) = R(1 / x,y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(4013,a,12893,a)].">
      <j1 rule="hyper" parents="4013 12893"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5356,a,b,12893,a)].">
      <j1 rule="hyper" parents="370 5356 12893"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(12893(a,1),10241(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12893 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12899">
    <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(12893(a,1),12196(a,1,1,2,2))].">
      <j1 rule="para" parents="12893 12196"/>
    </justification>
  </clause>

  <clause id="12900">
    <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(12801(a,1),12896(a,1,1,2))].">
      <j1 rule="para" parents="12801 12896"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      R(1 / x,y,L(x,z,u)) = R(1 / x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2712,a(flip),b,12895,a),flip(a)].">
      <j1 rule="hyper" parents="370 2712 12895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      T((x / y) * K(y \ 1,x),L(1 / y,y,x)) = x * L(R(1 / y,x,y),y,x)
    ]]></literal>
    <justification jstring="[para(12901(a,1),7252(a,2,2,1))].">
      <j1 rule="para" parents="12901 7252"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      K(L(x,y * (x \ z),u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12238(a,1),12894(a,1))].">
      <j1 rule="para" parents="12238 12894"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8154,a(flip),b,12898,a),flip(a)].">
      <j1 rule="hyper" parents="370 8154 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11470,a,b,12904,a),flip(a)].">
      <j1 rule="hyper" parents="370 11470 12904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12243,a(flip),b,12904,a)].">
      <j1 rule="hyper" parents="60 12243 12904"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5993,a(flip),b,12907,a),flip(a)].">
      <j1 rule="hyper" parents="370 5993 12907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12244,a(flip),b,12909,a)].">
      <j1 rule="hyper" parents="60 12244 12909"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(12909(a,1),11852(a,1,1,2))].">
      <j1 rule="para" parents="12909 11852"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,12846,a(flip),b,12910,a),flip(a)].">
      <j1 rule="hyper" parents="370 12846 12910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(92(a,1),12914(a,1,1,2))].">
      <j1 rule="para" parents="92 12914"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(11162,a,12915,a)].">
      <j1 rule="hyper" parents="11162 12915"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11221,a(flip),b,12915,a)].">
      <j1 rule="hyper" parents="60 11221 12915"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12845,a(flip),b,12916,a),flip(a)].">
      <j1 rule="hyper" parents="370 12845 12916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11974,a(flip),b,12918,a)].">
      <j1 rule="hyper" parents="60 11974 12918"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13(a,2),12919(a,2,1))].">
      <j1 rule="para" parents="13 12919"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(12903,a,12920,a),flip(a)].">
      <j1 rule="hyper" parents="12903 12920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12453,a,12921,a)].">
      <j1 rule="hyper" parents="12453 12921"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12921(a,1),12453(a,1))].">
      <j1 rule="para" parents="12921 12453"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(11673,a,12922,a)].">
      <j1 rule="hyper" parents="11673 12922"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      K(x,L(y,z * y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11585,a,12922,a),flip(a)].">
      <j1 rule="hyper" parents="11585 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(11353,a,12922,a),flip(a)].">
      <j1 rule="hyper" parents="11353 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,y \ 1,y)) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(8378,a,12922,a),flip(a)].">
      <j1 rule="hyper" parents="8378 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6918,a,12922,a)].">
      <j1 rule="hyper" parents="6918 12922"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,9123,a,b,12922,a)].">
      <j1 rule="hyper" parents="370 9123 12922"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      x * L(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12922,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 12922 5230"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11895,a,b,12922,a)].">
      <j1 rule="hyper" parents="60 11895 12922"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11380,a,b,12922,a)].">
      <j1 rule="hyper" parents="60 11380 12922"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      K(x,L(y,L(y,z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12242,a(flip),b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="60 12242 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,11127,a(flip),b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="60 11127 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10351,a(flip),b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="60 10351 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6753,a(flip),b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="60 6753 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      L(K(x,T(y \ z,u * y)),y,u) = K(x,(u * z) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(9023,a,12922,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9023 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,L(z,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(129,a,12922,a(flip),b,11130,a)].">
      <j1 rule="hyper" parents="129 12922 11130"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12922,a(flip),b,12480,a(flip))].">
      <j1 rule="hyper" parents="129 12922 12480"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12922,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 12922 13"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(344(a,1),12922(a,2,2))].">
      <j1 rule="para" parents="344 12922"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(656(a,1),12922(a,2,2))].">
      <j1 rule="para" parents="656 12922"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      K(x,y) \ (K(x,L(y,z,u)) \ (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(12922(a,1),2179(a,1,2,1))].">
      <j1 rule="para" parents="12922 2179"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * K(L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(12922(a,2),6291(a,1,2))].">
      <j1 rule="para" parents="12922 6291"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      K(x,L((y \ z) \ 1,u,w)) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6463(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6463 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12922(a,1),11891(a,1,2))].">
      <j1 rule="para" parents="12922 11891"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(12922(a,1),11894(a,1,2))].">
      <j1 rule="para" parents="12922 11894"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12922(a,1),11896(a,1,1))].">
      <j1 rule="para" parents="12922 11896"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) / (u * (y \ z))) = w
    ]]></literal>
    <justification jstring="[para(12922(a,1),12014(a,1))].">
      <j1 rule="para" parents="12922 12014"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) = L(K(x,z * y),u,w)
    ]]></literal>
    <justification jstring="[para(12552(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12552 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      L(K(x,((y \ z) \ z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(12522(a,1),12922(a,2,2))].">
      <j1 rule="para" parents="12522 12922"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      K(x,K(y,L(z,u * x,w))) = K(z,K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(12925(a,1),9523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12925 9523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(12922(a,1),12923(a,1,2))].">
      <j1 rule="para" parents="12922 12923"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      K(x,L((T(y,z) \ u) \ 1,y,z)) = K(x,((y * z) \ (z * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(12489(a,1),12926(a,2,2,1))].">
      <j1 rule="para" parents="12489 12926"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      (x * K(y \ 1,L(z,u,w))) \ (x * z) = T(z,L(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(12928(a,1),5853(a,1,1,2))].">
      <j1 rule="para" parents="12928 5853"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      ((x * y) / x) * K(y,L(x,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,12932,a(flip),b,8336,a)].">
      <j1 rule="hyper" parents="129 12932 8336"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      T(x,L(y,z / T(y,u),w)) = x * K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,12933,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 12933 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(11133,a,12946,a)].">
      <j1 rule="hyper" parents="11133 12946"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(L(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(791,a,12946,a)].">
      <j1 rule="hyper" parents="791 12946"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12922,a(flip),b,12964,a),flip(a)].">
      <j1 rule="hyper" parents="60 12922 12964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12964,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 12964 13"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(344(a,1),12964(a,2,1))].">
      <j1 rule="para" parents="344 12964"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(12964(a,1),11896(a,1,1))].">
      <j1 rule="para" parents="12964 11896"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      K((x \ y) / z,L(u,z,x)) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(9009,a,12966,a),flip(a)].">
      <j1 rule="hyper" parents="9009 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w \ 1)) \ v5) = K(x,L((u * (1 / w)) \ v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(6080,a,12966,a)].">
      <j1 rule="hyper" parents="6080 12966"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(344(a,1),12966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="344 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(655(a,1),12966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="655 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(656(a,1),12966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="656 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),L(u,x,y)) = K(((1 / y) * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(1489(a,1),12966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1489 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(x * y,y,x)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(12966(a,1),628(a,1,2))].">
      <j1 rule="para" parents="12966 628"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      (x * K(y,L(z,u,w))) \ (x * z) = T(z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(12966(a,1),5853(a,1,1,2))].">
      <j1 rule="para" parents="12966 5853"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      (x / y) * K(z,L(y,u,w)) = x / T(y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(12966(a,1),5855(a,1,2))].">
      <j1 rule="para" parents="12966 5855"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(u,y,x)) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12966(a,1),6930(a,1,2))].">
      <j1 rule="para" parents="12966 6930"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(12966(a,1),11913(a,1,1))].">
      <j1 rule="para" parents="12966 11913"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(12489(a,1),12966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12489 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12966(a,2),12923(a,1))].">
      <j1 rule="para" parents="12966 12923"/>
    </justification>
  </clause>

  <clause id="12984">
    <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(8636(a,2),12983(a,1))].">
      <j1 rule="para" parents="8636 12983"/>
    </justification>
  </clause>

  <clause id="12986">
    <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(12948(a,1),2902(a,1))].">
      <j1 rule="para" parents="12948 2902"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12948(a,1),7276(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12948 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12988">
    <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(12948(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12948 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <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(12949(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12949 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12991">
    <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(10466(a,1),12949(a,1,2,2))].">
      <j1 rule="para" parents="10466 12949"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,11914,a(flip),b,12950,a)].">
      <j1 rule="hyper" parents="60 11914 12950"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),12992(a,1,3))].">
      <j1 rule="para" parents="8636 12992"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,10268,a,b,12969,a)].">
      <j1 rule="hyper" parents="60 10268 12969"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11913,a(flip),b,12969,a)].">
      <j1 rule="hyper" parents="60 11913 12969"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(12996(a,1),11990(a,2,2))].">
      <j1 rule="para" parents="12996 11990"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      K(L(x,y,z) / x,u) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(8906,a,12995,a)].">
      <j1 rule="hyper" parents="8906 12995"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(3839(a,1),12998(a,1,1))].">
      <j1 rule="para" parents="3839 12998"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12998(a,1),11342(a,1,2,2,2))].">
      <j1 rule="para" parents="12998 11342"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(12941(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="12941 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(z,y * z,x)) = x * (y * (z * K(u,z)))
    ]]></literal>
    <justification jstring="[para(5630(a,1),12941(a,2,2))].">
      <j1 rule="para" parents="5630 12941"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x),z) = w
    ]]></literal>
    <justification jstring="[para(12941(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="12941 6305"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(L(u,y,x),z)) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(12965(a,1),108(a,1,2))].">
      <j1 rule="para" parents="12965 108"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      (x * y) * K(z * z,u) = x * (y * K(z * z,u))
    ]]></literal>
    <justification jstring="[para(613(a,1),12967(a,1,2,1))].">
      <j1 rule="para" parents="613 12967"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      K((x * y) \ z,T(y,u)) = K(y \ (x \ z),T(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,8099,a(flip),b,12968,a),flip(a)].">
      <j1 rule="hyper" parents="60 8099 12968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      K((x * y) \ z,T(u,x \ z)) = K((x \ z) / y,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(9017,a,12972,a),flip(a)].">
      <j1 rule="hyper" parents="9017 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ z)),L(u,x,y)) = K((y * x) \ ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[para(2073(a,1),12972(a,1,1,2))].">
      <j1 rule="para" parents="2073 12972"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,K(x,(z * y) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(12972(a,2),8668(a,1,2))].">
      <j1 rule="para" parents="12972 8668"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(655(a,1),12973(a,1,2))].">
      <j1 rule="para" parents="655 12973"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(12072(a,1),13000(a,1,2,2))].">
      <j1 rule="para" parents="12072 13000"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      K(x,L((y \ z) \ 1,u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,12947,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 12947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      K(x,K((y * z) \ (u \ w),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9525,a(flip),b,12955,a),flip(a)].">
      <j1 rule="hyper" parents="60 9525 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      T(x,L(y,z / T(y,u),w)) = T(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,12963,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      T(x,L(y,y \ z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(308(a,1),13014(a,1,2,2))].">
      <j1 rule="para" parents="308 13014"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      K(K(x,L(y,z,u)),w) * ((v5 / T(y,L(x,z,u))) / (v5 / y)) = T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(12978(a,1),5629(a,1,2,1))].">
      <j1 rule="para" parents="12978 5629"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(32,a,12950,a,b,12981,a)].">
      <j1 rule="hyper" parents="32 12950 12981"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),13017(a,1,2,2))].">
      <j1 rule="para" parents="5 13017"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,u,y)) = K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z)
    ]]></literal>
    <justification jstring="[para(12450(a,1),13018(a,2,2))].">
      <j1 rule="para" parents="12450 13018"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,10522,a,b,12987,a)].">
      <j1 rule="hyper" parents="60 10522 12987"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),13010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13020(a,1),5316(a,1,1))].">
      <j1 rule="para" parents="13020 5316"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),x * u) = L(T(x,L(u,z,y)),u,x)
    ]]></literal>
    <justification jstring="[para(13020(a,1),5363(a,1,1))].">
      <j1 rule="para" parents="13020 5363"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ ((x \ 1) \ y),z) = K(y,((1 / x) \ 1) \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5585,a,b,13025,a),flip(a)].">
      <j1 rule="hyper" parents="370 5585 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12936,a(flip),b,13025,a),flip(a)].">
      <j1 rule="hyper" parents="60 12936 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2508(a,2),13027(a,1,2))].">
      <j1 rule="para" parents="2508 13027"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12533,a(flip),b,13028,a)].">
      <j1 rule="hyper" parents="60 12533 13028"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11548,a(flip),b,12924,a),flip(a)].">
      <j1 rule="hyper" parents="60 11548 12924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13031">
    <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(60,a,13025,a(flip),b,12937,a)].">
      <j1 rule="hyper" parents="60 13025 12937"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11895(a,1),12988(a,1))].">
      <j1 rule="para" parents="11895 12988"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(T(u,x * y),y,x)) = w
    ]]></literal>
    <justification jstring="[para(8838(a,2),13033(a,1))].">
      <j1 rule="para" parents="8838 13033"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,u,y)) = w
    ]]></literal>
    <justification jstring="[para(11125(a,1),13033(a,1))].">
      <j1 rule="para" parents="11125 13033"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12964(a,1),13033(a,1))].">
      <j1 rule="para" parents="12964 13033"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      K((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),L(u,y,x)) = w
    ]]></literal>
    <justification jstring="[para(12968(a,1),13033(a,1))].">
      <j1 rule="para" parents="12968 13033"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      K(x,L(T(y \ z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12930(a,2),13033(a,1))].">
      <j1 rule="para" parents="12930 13033"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12952(a,2),13033(a,1))].">
      <j1 rule="para" parents="12952 13033"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11902(a,1),12990(a,1))].">
      <j1 rule="para" parents="11902 12990"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(12981(a,2),13041(a,1))].">
      <j1 rule="para" parents="12981 13041"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,12978,a(flip),b,12961,a)].">
      <j1 rule="hyper" parents="60 12978 12961"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      (x * L(y,x,y)) / T(T(x,y),L(T(y,x * y),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y)))
    ]]></literal>
    <justification jstring="[para(6629(a,1),13044(a,1,1))].">
      <j1 rule="para" parents="6629 13044"/>
    </justification>
  </clause>

  <clause id="13046">
    <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(12997(a,1),9980(a,2,2))].">
      <j1 rule="para" parents="12997 9980"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11130(a,1),13003(a,1))].">
      <j1 rule="para" parents="11130 13003"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(12922(a,1),13047(a,1))].">
      <j1 rule="para" parents="12922 13047"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(6054,a,13011,a)].">
      <j1 rule="hyper" parents="6054 13011"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      K(x,((y * z) * y) \ ((z * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = w
    ]]></literal>
    <justification jstring="[para(1173(a,1),13035(a,1,2,1))].">
      <j1 rule="para" parents="1173 13035"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12102,a,b,13049,a)].">
      <j1 rule="hyper" parents="60 12102 13049"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      L(K(x,T(y \ z,K(u,w) \ y)),y,K(w,u)) = K(x,(K(w,u) * z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[para(7506(a,2),12938(a,1,1,2,2))].">
      <j1 rule="para" parents="7506 12938"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      K((x * y) \ ((1 / x) \ z),L(u,x * y,x)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(2069(a,1),12975(a,2,1,1))].">
      <j1 rule="para" parents="2069 12975"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      K(x,L(T(((y / z) \ 1) \ u,z / y),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u / ((y / z) \ 1),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(9704(a,1),13038(a,1,2,1))].">
      <j1 rule="para" parents="9704 13038"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u)) = T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,12977,a(flip),b,12958,a)].">
      <j1 rule="hyper" parents="60 12977 12958"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      T(x / (L(y,z,u) \ 1),L(y \ 1,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (L(y,z,u) \ 1) \ x = w
    ]]></literal>
    <justification jstring="[para(13055(a,2),494(a,1))].">
      <j1 rule="para" parents="13055 494"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      T(x,L((y \ z) \ 1,y,y)) = T(x,((1 / y) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(586(a,1),13055(a,2,2,1))].">
      <j1 rule="para" parents="586 13055"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      T(x,L((y \ z) \ 1,y,y)) = T(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4677,a(flip),b,13057,a),flip(a)].">
      <j1 rule="hyper" parents="370 4677 13057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      x * (T(y / (x \ 1),z) \ y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(655(a,1),12927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="655 12927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ (1 / (1 / K(z,(1 / x) * y)))
    ]]></literal>
    <justification jstring="[para(13059(a,1),5083(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13059 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(x,L((T(y,z) \ u) \ 1,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) \ (y * z)) = w
    ]]></literal>
    <justification jstring="[para(12957(a,2),6464(a,1))].">
      <j1 rule="para" parents="12957 6464"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(z,y,x)) = x * (y * (z * K(u,z)))
    ]]></literal>
    <justification jstring="[para(12925(a,1),13002(a,1,2))].">
      <j1 rule="para" parents="12925 13002"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12052,a(flip),b,12899,a)].">
      <j1 rule="hyper" parents="60 12052 12899"/>
    </justification>
  </clause>

  <clause id="13067">
    <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(7(a,1),13065(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 13065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6689(a,1),12911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6689 12911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6268,a(flip),b,13068,a),flip(a)].">
      <j1 rule="hyper" parents="370 6268 13068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(2156(a,1),13069(a,1,1))].">
      <j1 rule="para" parents="2156 13069"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(13070(a,1),10217(a,2,2))].">
      <j1 rule="para" parents="13070 10217"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,6278,a,b,13071,a),flip(a)].">
      <j1 rule="hyper" parents="370 6278 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      K(x,L((y * (1 / z)) \ u,w,v5)) = K(x,L((y * (z \ 1)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(13036,a,12971,a),flip(a)].">
      <j1 rule="hyper" parents="13036 12971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      K(x,L(y \ T(z,u),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (z * u)) = w
    ]]></literal>
    <justification jstring="[para(13012(a,1),13061(a,1))].">
      <j1 rule="para" parents="13012 13061"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(x,K(y \ (z \ (u \ w)),L(z,y,u))) = K(x,K(z,(u * (y * z)) \ w))
    ]]></literal>
    <justification jstring="[para(12007(a,1),13013(a,1,2))].">
      <j1 rule="para" parents="12007 13013"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,(z * (y * w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12164,a(flip),b,13076,a)].">
      <j1 rule="hyper" parents="60 12164 13076"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(13009,a,13077,a),flip(a)].">
      <j1 rule="hyper" parents="13009 13077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(8634,a,13078,a)].">
      <j1 rule="hyper" parents="8634 13078"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = K(x,K(y,(z * u) \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,11971,a(flip),b,13079,a)].">
      <j1 rule="hyper" parents="60 11971 13079"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,10003,a(flip),b,13080,a),flip(a)].">
      <j1 rule="hyper" parents="370 10003 13080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(262(a,1),13081(a,1,2,2,3))].">
      <j1 rule="para" parents="262 13081"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(13083(a,1),8616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13083 8616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(127,a,13085,a(flip),b,8945,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="127 13085 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13086,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 13086 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      K(x,((1 / y) \ 1) \ ((y \ 1) \ z)) = K(y \ ((y \ 1) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6725,a,13026,a),flip(a)].">
      <j1 rule="hyper" parents="6725 13026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,x \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(77(a,1),13089(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 13089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      K((L(x,y,z) \ u) \ w,L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12712,a(flip),b,12880,a)].">
      <j1 rule="hyper" parents="60 12712 12880"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      K(L(x,y,z) * (u \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12844,a(flip),b,13091,a)].">
      <j1 rule="hyper" parents="60 12844 13091"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      K(L(x,y,z) * (u \ w),L(x,y,z)) = K(u \ (x * w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,12005,a(flip),b,13092,a),flip(a)].">
      <j1 rule="hyper" parents="370 12005 13092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      K((x \ y) * L(z,u,w),L(z,u,w)) = K(x \ (z * y),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(9253,a,13093,a)].">
      <j1 rule="hyper" parents="9253 13093"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,12885,a(flip),b,13094,a),flip(a)].">
      <j1 rule="hyper" parents="60 12885 13094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,12005,a,b,13095,a)].">
      <j1 rule="hyper" parents="60 12005 13095"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11883,a,b,13095,a)].">
      <j1 rule="hyper" parents="60 11883 13095"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,11386,a(flip),b,13095,a),flip(a)].">
      <j1 rule="hyper" parents="60 11386 13095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,11884,a,b,13097,a)].">
      <j1 rule="hyper" parents="60 11884 13097"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13030,a(flip),b,13099,a),flip(a)].">
      <j1 rule="hyper" parents="60 13030 13099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12917,a(flip),b,13098,a),flip(a)].">
      <j1 rule="hyper" parents="370 12917 13098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13103">
    <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(6099(a,1),12900(a,1,1))].">
      <j1 rule="para" parents="6099 12900"/>
    </justification>
  </clause>

  <clause id="13104">
    <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(6557(a,1),13103(a,1,1,1,2))].">
      <j1 rule="para" parents="6557 13103"/>
    </justification>
  </clause>

  <clause id="13105">
    <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(60,a,22,a,b,13104,a)].">
      <j1 rule="hyper" parents="60 22 13104"/>
    </justification>
  </clause>

  <clause id="13106">
    <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(5502(a,1),13105(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5502 13105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12893,a(flip),b,13106,a)].">
      <j1 rule="hyper" parents="60 12893 13106"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(169,a,13107,a)].">
      <j1 rule="hyper" parents="169 13107"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11446,a,b,13108,a),flip(a)].">
      <j1 rule="hyper" parents="370 11446 13108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(13108(a,1),12866(a,1,1))].">
      <j1 rule="para" parents="13108 12866"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12112,a,13109,a)].">
      <j1 rule="hyper" parents="12112 13109"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      K(x,y) \ (K(L(y,z,u),x) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(7506(a,1),12944(a,1,2))].">
      <j1 rule="para" parents="7506 12944"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      K(x,y) \ (K(y,L(x,z,u)) * (w * K(x,y))) = L(K(x,y),z,u) \ T(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(12966(a,1),13116(a,1,2,1))].">
      <j1 rule="para" parents="12966 13116"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      K(x,y) \ (T(y,L(x,z,u)) * K(x,y)) = L(K(x,y),z,u) \ T(y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7864(a,1),13117(a,1,2))].">
      <j1 rule="para" parents="7864 13117"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      L(K(x,y),z,u) \ T(y,K(x,y)) = K(x,y) \ (y * a(u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(12987(a,1),13118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12987 13118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,L(u,y,x))) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(8728,a,13004,a)].">
      <j1 rule="hyper" parents="8728 13004"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(((y \ z) \ u) * x,L(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,13096,a(flip),b,13019,a),flip(a)].">
      <j1 rule="hyper" parents="60 13096 13019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13122">
    <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(13072(a,1),13046(a,1,2))].">
      <j1 rule="para" parents="13072 13046"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(8431,a,13122,a),flip(a)].">
      <j1 rule="hyper" parents="8431 13122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,12969,a(flip),b,13123,a),flip(a)].">
      <j1 rule="hyper" parents="370 12969 13123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(386,a,13124,a)].">
      <j1 rule="hyper" parents="386 13124"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),13125(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 13125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5673(a,1),13125(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5673 13125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,u * z))
    ]]></literal>
    <justification jstring="[para(5400(a,1),13125(a,1,3))].">
      <j1 rule="para" parents="5400 13125"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(y * x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,12948,a,b,13127,a)].">
      <j1 rule="hyper" parents="370 12948 13127"/>
    </justification>
  </clause>

  <clause id="13131">
    <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(13127(a,2),11930(a,1,1))].">
      <j1 rule="para" parents="13127 11930"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,7277,a(flip),b,13128,a),flip(a)].">
      <j1 rule="hyper" parents="370 7277 13128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = K(x * y,y) \ (y * a(u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(13128(a,1),13119(a,2,2,2))].">
      <j1 rule="para" parents="13128 13119"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,13132,a)].">
      <j1 rule="hyper" parents="49 13132"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(13134(a,1),8049(a,2,1))].">
      <j1 rule="para" parents="13134 8049"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11933,a,13131,a)].">
      <j1 rule="hyper" parents="11933 13131"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13129,a,b,13136,a)].">
      <j1 rule="hyper" parents="60 13129 13136"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),13136(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 13136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(6822(a,1),13138(a,1,3))].">
      <j1 rule="para" parents="6822 13138"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13137,a(flip),b,13139,a),flip(a)].">
      <j1 rule="hyper" parents="60 13137 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6410(a,1),13140(a,1,3))].">
      <j1 rule="para" parents="6410 13140"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(11302(a,1),13135(a,1,2,2))].">
      <j1 rule="para" parents="11302 13135"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(8047,a,13142,a),flip(a)].">
      <j1 rule="hyper" parents="8047 13142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11499,a(flip),b,13143,a),flip(a)].">
      <j1 rule="hyper" parents="60 11499 13143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(11466(a,1),13144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11466 13144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13101,a(flip),b,13121,a),flip(a)].">
      <j1 rule="hyper" parents="370 13101 13121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12924,a(flip),b,13146,a)].">
      <j1 rule="hyper" parents="60 12924 13146"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13096,a(flip),b,13147,a)].">
      <j1 rule="hyper" parents="60 13096 13147"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13100,a(flip),b,13148,a)].">
      <j1 rule="hyper" parents="60 13100 13148"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),13149(a,2,1,2))].">
      <j1 rule="para" parents="17 13149"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12843,a(flip),b,13150,a)].">
      <j1 rule="hyper" parents="60 12843 13150"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(13151(a,1),7511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13151 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      T(x,x * K(y * T(z,u),y)) \ T(K(y,y * ((z \ u) \ u)) * x,x) = K(y,T(y * ((z \ u) \ u),x))
    ]]></literal>
    <justification jstring="[para(13151(a,1),12288(a,1,1,2,2))].">
      <j1 rule="para" parents="13151 12288"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,7511,a(flip),b,13152,a),flip(a)].">
      <j1 rule="hyper" parents="370 7511 13152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = T(y,x * y) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7907,a(flip),b,13133,a),flip(a)].">
      <j1 rule="hyper" parents="370 7907 13133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13156">
    <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(2508(a,2),13031(a,1,2))].">
      <j1 rule="para" parents="2508 13031"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(K(z,y) * u,K(z,y)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(9604(a,1),12391(a,1,1,2))].">
      <j1 rule="para" parents="9604 12391"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * z) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),12631(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="62 12631"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ ((x * z) / x),T(u,y))
    ]]></literal>
    <justification jstring="[para(2(a,1),13158(a,2,1,2))].">
      <j1 rule="para" parents="2 13158"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x * z) / x) / y,u) = w
    ]]></literal>
    <justification jstring="[para(13159(a,2),8906(a,1))].">
      <j1 rule="para" parents="13159 8906"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(z,K(y,u)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(9265(a,1),13157(a,1,2))].">
      <j1 rule="para" parents="9265 13157"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      (x * (y * (T(T(y,z),z) \ u))) * K(y,K(z,u)) = x * (K(z,y) * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(8630(a,1),13161(a,1,2))].">
      <j1 rule="para" parents="8630 13161"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * (w * K(u,x))))) = K(x,y * (z * (x * (T(T(x,u),u) \ w))))
    ]]></literal>
    <justification jstring="[para(13162(a,1),11341(a,1,2,2))].">
      <j1 rule="para" parents="13162 11341"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * (w * K(u,x))))
    ]]></literal>
    <justification jstring="[hyper(60,a,11347,a(flip),b,13164,a),flip(a)].">
      <j1 rule="hyper" parents="60 11347 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,11349,a(flip),b,13165,a),flip(a)].">
      <j1 rule="hyper" parents="370 11349 13165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <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(370,a,12669,a(flip),b,11165,a),flip(a)].">
      <j1 rule="hyper" parents="370 12669 11165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13170">
    <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(4654(a,1),13169(a,2,2))].">
      <j1 rule="para" parents="4654 13169"/>
    </justification>
  </clause>

  <clause id="13171">
    <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(370,a,11305,a(flip),b,13170,a),flip(a)].">
      <j1 rule="hyper" parents="370 11305 13170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9477,a(flip),b,13171,a),flip(a)].">
      <j1 rule="hyper" parents="370 9477 13171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12413,a,13172,a),flip(a)].">
      <j1 rule="hyper" parents="12413 13172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,9671,a,b,13173,a)].">
      <j1 rule="hyper" parents="370 9671 13173"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,4852,a,b,13173,a)].">
      <j1 rule="hyper" parents="370 4852 13173"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(13173(a,1),8056(a,1,1))].">
      <j1 rule="para" parents="13173 8056"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(13175(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13175 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5871,a,13177,a)].">
      <j1 rule="hyper" parents="5871 13177"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      K((x \ y) \ z,T(x \ y,x)) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12465,a(flip),b,13179,a),flip(a)].">
      <j1 rule="hyper" parents="60 12465 13179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      K((x \ y) \ z,y / x) = K(y \ (z * x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(8904,a,13180,a)].">
      <j1 rule="hyper" parents="8904 13180"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ (1 * x),x \ y) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(13181(a,1),10190(a,1,2))].">
      <j1 rule="para" parents="13181 10190"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,9952,a(flip),b,13178,a),flip(a)].">
      <j1 rule="hyper" parents="60 9952 13178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(13183(a,2),8527(a,1,2))].">
      <j1 rule="para" parents="13183 8527"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(328,a,13184,a)].">
      <j1 rule="hyper" parents="328 13184"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(13185(a,1),9838(a,1,1))].">
      <j1 rule="para" parents="13185 9838"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      K(x,x \ y) * K(y \ x,x \ y) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(2(a,1),13182(a,1,2,1,2))].">
      <j1 rule="para" parents="2 13182"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      (x / y) / T(y \ x,x \ y) = (x / y) * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,5854,a(flip),b,13187,a)].">
      <j1 rule="hyper" parents="60 5854 13187"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      T(x \ y,y \ x) \ (y / x) = (y / x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(10002,a,13188,a)].">
      <j1 rule="hyper" parents="10002 13188"/>
    </justification>
  </clause>

  <clause id="13190">
    <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(11543(a,1),11800(a,1,1))].">
      <j1 rule="para" parents="11543 11800"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      K(x,(y * ((((z \ x) / x) * z) * (1 / z))) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(11363,a,13190,a),flip(a)].">
      <j1 rule="hyper" parents="11363 13190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      K(x,(y * ((z \ x) / x)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2578(a,1),13191(a,1,2,1,2))].">
      <j1 rule="para" parents="2578 13191"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12310,a(flip),b,13192,a)].">
      <j1 rule="hyper" parents="60 12310 13192"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,7188,a(flip),b,13193,a),flip(a)].">
      <j1 rule="hyper" parents="60 7188 13193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13195">
    <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(6102(a,1),13194(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 13194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13196">
    <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(11012(a,1),11936(a,1,2))].">
      <j1 rule="para" parents="11012 11936"/>
    </justification>
  </clause>

  <clause id="13197">
    <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(6591(a,1),13196(a,2,3))].">
      <j1 rule="para" parents="6591 13196"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      ((K(x,y) * z) * ((K(y,x) \ 1) \ 1)) * K(u,y) = ((1 / (1 / K(y,x))) \ z) * (K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7506(a,1),11407(a,1,1,1))].">
      <j1 rule="para" parents="7506 11407"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(x,u) * z)) * z)) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,13167,a(flip),b,11805,a)].">
      <j1 rule="hyper" parents="60 13167 11805"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),z,z \ 1))) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(9346(a,1),13199(a,1,2,2))].">
      <j1 rule="para" parents="9346 13199"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,11344,a(flip),b,13200,a),flip(a)].">
      <j1 rule="hyper" parents="60 11344 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,6160,a(flip),b,13201,a)].">
      <j1 rule="hyper" parents="60 6160 13201"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,10411,a,b,13203,a)].">
      <j1 rule="hyper" parents="60 10411 13203"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(13203(a,2),9425(a,2,2))].">
      <j1 rule="para" parents="13203 9425"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,13051,a,b,13204,a)].">
      <j1 rule="hyper" parents="60 13051 13204"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,((y * K(x,z)) * u) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,10908,a,b,13207,a)].">
      <j1 rule="hyper" parents="60 10908 13207"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(9448,a,13205,a),flip(a)].">
      <j1 rule="hyper" parents="9448 13205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,y)))) = K(x,K(y,(z * u) * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(9211(a,1),13210(a,1,2))].">
      <j1 rule="para" parents="9211 13210"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,y)))) = K(x,K(y,R(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(304(a,1),13211(a,2,2,2))].">
      <j1 rule="para" parents="304 13211"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(z,K(x,R(y,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10733,a,b,13212,a)].">
      <j1 rule="hyper" parents="60 10733 13212"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(z,R(y,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,13213,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 13213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,R(y * K(x,z),u,u \ 1))
    ]]></literal>
    <justification jstring="[para(304(a,1),13209(a,2,2))].">
      <j1 rule="para" parents="304 13209"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      K(x,R(R(y,K(x,z),u),u,(K(x,z) * u) \ 1)) = K(x,R(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,10881,a(flip),b,13216,a),flip(a)].">
      <j1 rule="hyper" parents="370 10881 13216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,10909,a(flip),b,13217,a)].">
      <j1 rule="hyper" parents="60 10909 13217"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = x \ (((x / y) * (y * K(x,z))) * K(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11935(a,2,1))].">
      <j1 rule="para" parents="7 11935"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      T(((x / y) * (y * K(x,z))) / T(x,z),x) = ((x / y) * (y * K(z,x))) \ ((z * x) / z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5911,a,b,13221,a)].">
      <j1 rule="hyper" parents="370 5911 13221"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(13186(a,1),13222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13186 13222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9834,a(flip),b,13223,a),flip(a)].">
      <j1 rule="hyper" parents="370 9834 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,5359,a(flip),b,13224,a),flip(a)].">
      <j1 rule="hyper" parents="60 5359 13224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      a(K(x * y,z),y,y \ (x * y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),13225(a,2,1))].">
      <j1 rule="para" parents="6 13225"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      a(K(x * y,z),y,T(x,y)) = a(x,y,K(z,x * y))
    ]]></literal>
    <justification jstring="[para(17(a,2),13226(a,1,3))].">
      <j1 rule="para" parents="17 13226"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13227(a,1),5310(a,1,2))].">
      <j1 rule="para" parents="13227 5310"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11924,a(flip),b,13228,a),flip(a)].">
      <j1 rule="hyper" parents="60 11924 13228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      T(K(x * y,z) * y,T(x,y)) = T(y,x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(275,a,13229,a,b,7946,a)].">
      <j1 rule="hyper" parents="275 13229 7946"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(12587(a,2),13229(a,2,2))].">
      <j1 rule="para" parents="12587 13229"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      T(x * K(x * y,z),T(y,x)) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12586(a,1),13230(a,1,1))].">
      <j1 rule="para" parents="12586 13230"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6287,a,b,13232,a)].">
      <j1 rule="hyper" parents="60 6287 13232"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8045,a,b,13234,a),flip(a)].">
      <j1 rule="hyper" parents="370 8045 13234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,92,a,b,13235,a),flip(a)].">
      <j1 rule="hyper" parents="370 92 13235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(7183,a,13236,a)].">
      <j1 rule="hyper" parents="7183 13236"/>
    </justification>
  </clause>

  <clause id="13238">
    <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(13237(a,1),9373(a,2,2))].">
      <j1 rule="para" parents="13237 9373"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(4047,a,12666,a),flip(a)].">
      <j1 rule="hyper" parents="4047 12666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13241">
    <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(9583(a,1),12794(a,1,1))].">
      <j1 rule="para" parents="9583 12794"/>
    </justification>
  </clause>

  <clause id="13242">
    <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(6872(a,1),12858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6872 12858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ (1 / (1 / K(z,(x \ 1) * y)))
    ]]></literal>
    <justification jstring="[para(5572(a,1),13060(a,2,2,2,2))].">
      <j1 rule="para" parents="5572 13060"/>
    </justification>
  </clause>

  <clause id="13244">
    <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(370,a,6171,a(flip),b,13195,a),flip(a)].">
      <j1 rule="hyper" parents="370 6171 13195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = ((K(y,x) * z) * K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(4059(a,1),13198(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4059 13198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z,K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(6296(a,1),13245(a,2,1))].">
      <j1 rule="para" parents="6296 13245"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,10049,a,b,13246,a),flip(a)].">
      <j1 rule="hyper" parents="370 10049 13246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(4060(a,1),13247(a,1,1,1))].">
      <j1 rule="para" parents="4060 13247"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(7506(a,1),13248(a,1,1))].">
      <j1 rule="para" parents="7506 13248"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),K(x,u)) = z * K(K(u,x) * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(11526,a,13249,a),flip(a)].">
      <j1 rule="hyper" parents="11526 13249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(8705(a,1),13250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8705 13250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13252">
    <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(8758(a,1),13241(a,1,1,2))].">
      <j1 rule="para" parents="8758 13241"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7621,a,13252,a),flip(a)].">
      <j1 rule="hyper" parents="7621 13252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11188(a,1),13253(a,1,1))].">
      <j1 rule="para" parents="11188 13253"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9773,a(flip),b,13254,a)].">
      <j1 rule="hyper" parents="60 9773 13254"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8003,a(flip),b,13255,a),flip(a)].">
      <j1 rule="hyper" parents="370 8003 13255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12278,a,b,13257,a)].">
      <j1 rule="hyper" parents="60 12278 13257"/>
    </justification>
  </clause>

  <clause id="13259">
    <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(13258(a,1),9018(a,1))].">
      <j1 rule="para" parents="13258 9018"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(13259,a,12909,a)].">
      <j1 rule="hyper" parents="13259 12909"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4060(a,1),13243(a,2,2))].">
      <j1 rule="para" parents="4060 13243"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / x,z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),13261(a,1,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="77 13261"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * (1 / (1 / K(y,x \ z)))
    ]]></literal>
    <justification jstring="[para(8315(a,1),13262(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8315 13262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(4060(a,1),13263(a,2,2))].">
      <j1 rule="para" parents="4060 13263"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      x * K(y,x \ ((x \ 1) \ z)) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),13264(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 13264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(13264(a,2),40(a,1))].">
      <j1 rule="para" parents="13264 40"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = ((1 / x) \ K(z,y)) \ x
    ]]></literal>
    <justification jstring="[para(13265(a,1),6294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13265 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ z)) = ((1 / y) \ K(z,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,13090,a(flip),b,13267,a)].">
      <j1 rule="hyper" parents="60 13090 13267"/>
    </justification>
  </clause>

  <clause id="13269">
    <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(74(a,1),13244(a,2,2,1,2))].">
      <j1 rule="para" parents="74 13244"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6463(a,1),13269(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6463 13269"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12319,a(flip),b,13271,a),flip(a)].">
      <j1 rule="hyper" parents="60 12319 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,12273,a(flip),b,13272,a),flip(a)].">
      <j1 rule="hyper" parents="60 12273 13272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12001,a(flip),b,13273,a),flip(a)].">
      <j1 rule="hyper" parents="60 12001 13273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,11378,a(flip),b,13274,a),flip(a)].">
      <j1 rule="hyper" parents="60 11378 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(11628,a,13275,a),flip(a)].">
      <j1 rule="hyper" parents="11628 13275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(13033,a,13276,a),flip(a)].">
      <j1 rule="hyper" parents="13033 13276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(13033,a,13277,a),flip(a)].">
      <j1 rule="hyper" parents="13033 13277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(12494(a,1),13278(a,2,2))].">
      <j1 rule="para" parents="12494 13278"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13156,a(flip),b,13279,a),flip(a)].">
      <j1 rule="hyper" parents="60 13156 13279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13029,a(flip),b,13280,a),flip(a)].">
      <j1 rule="hyper" parents="60 13029 13280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6727,a,13281,a)].">
      <j1 rule="hyper" parents="6727 13281"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6910,a(flip),b,13281,a)].">
      <j1 rule="hyper" parents="60 6910 13281"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),13284(a,1,1,2))].">
      <j1 rule="para" parents="77 13284"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = (y / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(135,a,13287,a)].">
      <j1 rule="hyper" parents="135 13287"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = ((1 / z) \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[para(13288(a,2),6210(a,2,1))].">
      <j1 rule="para" parents="13288 6210"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(13282(a,1),7170(a,2,1))].">
      <j1 rule="para" parents="13282 7170"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5720,a(flip),b,13291,a),flip(a)].">
      <j1 rule="hyper" parents="370 5720 13291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(33,a,206,a,b,13291,a),flip(a)].">
      <j1 rule="hyper" parents="33 206 13291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      T(x,y * L(y \ 1,y,z)) / ((1 / (y * L(y \ 1,y,z))) \ x) = 1 / (y * ((z * y) \ z))
    ]]></literal>
    <justification jstring="[para(9873(a,1),13292(a,2,2))].">
      <j1 rule="para" parents="9873 13292"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      (1 / T(x,y)) \ x = (1 / x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5259(a,2),13293(a,1,1,2))].">
      <j1 rule="para" parents="5259 13293"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      (1 / (x / y)) \ T(x / y,y) = (1 / (y \ x)) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),13296(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      ((1 / x) \ K(y * x,z)) \ x = K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(6(a,1),13290(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6 13290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      K(x,y \ ((y \ 1) \ (z * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,13268,a,b,13298,a)].">
      <j1 rule="hyper" parents="60 13268 13298"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(13299(a,1),13265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13299 13265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),13300(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 13300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      (1 / (x / y)) \ (y \ x) = (1 / (y \ x)) \ (x / y)
    ]]></literal>
    <justification jstring="[para(109(a,1),13297(a,1,2))].">
      <j1 rule="para" parents="109 13297"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      (x \ y) * (((y / x) \ 1) \ 1) = (1 / (x \ y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10078,a,b,13302,a)].">
      <j1 rule="hyper" parents="60 10078 13302"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      (x \ y) * T(y / x,y \ x) = (1 / (x \ y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(4566(a,2),13303(a,1,2))].">
      <j1 rule="para" parents="4566 13303"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((1 / (y * L(y \ 1,y,z))) \ (L(y \ 1,y,x) \ 1)) = 1 / (y * ((z * y) \ z))
    ]]></literal>
    <justification jstring="[para(6794(a,1),13295(a,1,1))].">
      <j1 rule="para" parents="6794 13295"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6745,a,11308,a),flip(a)].">
      <j1 rule="hyper" parents="6745 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13307">
    <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(5351(a,1),13306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5351 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13308">
    <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(2614(a,2),11481(a,1,2,2))].">
      <j1 rule="para" parents="2614 11481"/>
    </justification>
  </clause>

  <clause id="13309">
    <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(10285(a,1),12225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10285 12225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13310">
    <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(8025(a,1),13309(a,2,2))].">
      <j1 rule="para" parents="8025 13309"/>
    </justification>
  </clause>

  <clause id="13312">
    <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(12122,a,13310,a),flip(a)].">
      <j1 rule="hyper" parents="12122 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13313">
    <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(18(a,1),13312(a,1,1,2))].">
      <j1 rule="para" parents="18 13312"/>
    </justification>
  </clause>

  <clause id="13314">
    <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(5438(a,1),12226(a,1,1))].">
      <j1 rule="para" parents="5438 12226"/>
    </justification>
  </clause>

  <clause id="13315">
    <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(11451(a,1),12662(a,1,1,1))].">
      <j1 rule="para" parents="11451 12662"/>
    </justification>
  </clause>

  <clause id="13316">
    <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(689(a,1),13315(a,1,1))].">
      <j1 rule="para" parents="689 13315"/>
    </justification>
  </clause>

  <clause id="13317">
    <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(13108(a,1),13316(a,1,1,1,1))].">
      <j1 rule="para" parents="13108 13316"/>
    </justification>
  </clause>

  <clause id="13318">
    <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(13317(a,1),12049(a,1))].">
      <j1 rule="para" parents="13317 12049"/>
    </justification>
  </clause>

  <clause id="13320">
    <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(370,a,3190,a(flip),b,12863,a),flip(a)].">
      <j1 rule="hyper" parents="370 3190 12863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <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(22(a,2),13320(a,2,3))].">
      <j1 rule="para" parents="22 13320"/>
    </justification>
  </clause>

  <clause id="13322">
    <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(92(a,1),13308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="92 13308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13323">
    <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(12271(a,1),13314(a,1,1))].">
      <j1 rule="para" parents="12271 13314"/>
    </justification>
  </clause>

  <clause id="13324">
    <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(8215(a,1),13323(a,1,2))].">
      <j1 rule="para" parents="8215 13323"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(9127(a,1),13324(a,1,2))].">
      <j1 rule="para" parents="9127 13324"/>
    </justification>
  </clause>

  <clause id="13326">
    <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(11408(a,1),11527(a,2,2))].">
      <j1 rule="para" parents="11408 11527"/>
    </justification>
  </clause>

  <clause id="13327">
    <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(8700(a,1),13326(a,2,2,1))].">
      <j1 rule="para" parents="8700 13326"/>
    </justification>
  </clause>

  <clause id="13328">
    <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(10048(a,1),13327(a,2,2,1))].">
      <j1 rule="para" parents="10048 13327"/>
    </justification>
  </clause>

  <clause id="13329">
    <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(8705(a,1),13328(a,2,2))].">
      <j1 rule="para" parents="8705 13328"/>
    </justification>
  </clause>

  <clause id="13330">
    <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(370,a,10835,a(flip),b,13329,a),flip(a)].">
      <j1 rule="hyper" parents="370 10835 13329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13331">
    <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(370,a,259,a(flip),b,13330,a),flip(a)].">
      <j1 rule="hyper" parents="370 259 13330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / x = T(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,11405,a(flip),b,13331,a)].">
      <j1 rule="hyper" parents="128 11405 13331"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * K(u,K(x,y) * K(z,x)) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(5240,a,13332,a)].">
      <j1 rule="hyper" parents="5240 13332"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,13333,a)].">
      <j1 rule="hyper" parents="31 5256 13333"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,13334,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 13334 5230"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2894(a,1),13335(a,1,2,1))].">
      <j1 rule="para" parents="2894 13335"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,13251,a(flip),b,13336,a)].">
      <j1 rule="hyper" parents="60 13251 13336"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8714,a,13337,a)].">
      <j1 rule="hyper" parents="8714 13337"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(1146,a,13337,a)].">
      <j1 rule="hyper" parents="1146 13337"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,R(y,w,v5))) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10778,a,b,13337,a)].">
      <j1 rule="hyper" parents="60 10778 13337"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2894(a,1),13337(a,2,2))].">
      <j1 rule="para" parents="2894 13337"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(2894(a,1),13339(a,2,2))].">
      <j1 rule="para" parents="2894 13339"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,R(K(u,y),w,v5)),K(y,z))
    ]]></literal>
    <justification jstring="[para(10016(a,1),13339(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10016 13339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13345">
    <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(13339(a,1),12158(a,2,1))].">
      <j1 rule="para" parents="13339 12158"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,13337,a(flip),b,13340,a)].">
      <j1 rule="hyper" parents="60 13337 13340"/>
    </justification>
  </clause>

  <clause id="13347">
    <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(13342(a,1),10095(a,1,1))].">
      <j1 rule="para" parents="13342 10095"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5313,a,13346,a)].">
      <j1 rule="hyper" parents="5313 13346"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(31,a,13336,a,b,13348,a)].">
      <j1 rule="hyper" parents="31 13336 13348"/>
    </justification>
  </clause>

  <clause id="13350">
    <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(13348(a,1),5265(a,1))].">
      <j1 rule="para" parents="13348 5265"/>
    </justification>
  </clause>

  <clause id="13351">
    <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(13337(a,2),13350(a,1))].">
      <j1 rule="para" parents="13337 13350"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(5710,a,13347,a),flip(a)].">
      <j1 rule="hyper" parents="5710 13347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,13349,a(flip),b,13353,a),flip(a)].">
      <j1 rule="hyper" parents="370 13349 13353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13356">
    <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(10648(a,1),13353(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10648 13353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13334,a,b,13355,a),flip(a)].">
      <j1 rule="hyper" parents="370 13334 13355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13358">
    <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(60,a,10889,a,b,13355,a)].">
      <j1 rule="hyper" parents="60 10889 13355"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,13343,a(flip),b,13341,a),flip(a)].">
      <j1 rule="hyper" parents="60 13343 13341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <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(370,a,5699,a,b,13345,a),flip(a)].">
      <j1 rule="hyper" parents="370 5699 13345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13361">
    <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(7506(a,1),13360(a,1,2))].">
      <j1 rule="para" parents="7506 13360"/>
    </justification>
  </clause>

  <clause id="13362">
    <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(370,a,13334,a(flip),b,13361,a),flip(a)].">
      <j1 rule="hyper" parents="370 13334 13361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(13350,a,13359,a)].">
      <j1 rule="hyper" parents="13350 13359"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(z,R(y,u,w))) = T(x,K(y,R(z,u,w)) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,13363,a)].">
      <j1 rule="hyper" parents="370 5256 13363"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,K(y,R(u,w,v5))),K(y,z))
    ]]></literal>
    <justification jstring="[para(10777(a,1),13344(a,2,1))].">
      <j1 rule="para" parents="10777 13344"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w)) * K(z,y)) = K(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,13364,a)].">
      <j1 rule="hyper" parents="31 5256 13364"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(370,a,13340,a(flip),b,13365,a),flip(a)].">
      <j1 rule="hyper" parents="370 13340 13365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      T(x,K(y,z) * R(K(u,y),w,v5)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[para(10016(a,1),13367(a,1,2,2))].">
      <j1 rule="para" parents="10016 13367"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * R(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,13346,a,b,13368,a)].">
      <j1 rule="hyper" parents="370 13346 13368"/>
    </justification>
  </clause>

  <clause id="13370">
    <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(8630(a,1),13358(a,1,2,2,2))].">
      <j1 rule="para" parents="8630 13358"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(8273,a,13370,a)].">
      <j1 rule="hyper" parents="8273 13370"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(8630(a,1),13371(a,1,1))].">
      <j1 rule="para" parents="8630 13371"/>
    </justification>
  </clause>

  <clause id="13373">
    <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(10731(a,1),13356(a,2,2))].">
      <j1 rule="para" parents="10731 13356"/>
    </justification>
  </clause>

  <clause id="13374">
    <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(370,a,13353,a(flip),b,13373,a),flip(a)].">
      <j1 rule="hyper" parents="370 13353 13373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <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(10648(a,1),13374(a,1,1,2))].">
      <j1 rule="para" parents="10648 13374"/>
    </justification>
  </clause>

  <clause id="13376">
    <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(11565(a,1),11984(a,1,1))].">
      <j1 rule="para" parents="11565 11984"/>
    </justification>
  </clause>

  <clause id="13377">
    <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(8413(a,1),13376(a,1,1))].">
      <j1 rule="para" parents="8413 13376"/>
    </justification>
  </clause>

  <clause id="13378">
    <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(13377(a,1),385(a,1)),flip(b)].">
      <j1 rule="para" parents="13377 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),T((y \ 1) \ (y \ z),y) * (y \ 1)) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(8700(a,1),12688(a,1,1))].">
      <j1 rule="para" parents="8700 12688"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      T(x,x * K(y * T(z,u),y)) \ T(K(y,y * T(z,u)) * x,x) = K(y,T(y * ((z \ u) \ u),x))
    ]]></literal>
    <justification jstring="[para(13154(a,1),13153(a,1,2,1,1))].">
      <j1 rule="para" parents="13154 13153"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12288,a(flip),b,13380,a),flip(a)].">
      <j1 rule="hyper" parents="60 12288 13380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      T(x / R(y * K(z,y),u,y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(11737(a,1),11738(a,1,1,2))].">
      <j1 rule="para" parents="11737 11738"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),T(R((u * y) / u,z,y),y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(7412(a,1),13382(a,1,1))].">
      <j1 rule="para" parents="7412 13382"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(T((u * y) / u,y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(22(a,2),13383(a,1,2))].">
      <j1 rule="para" parents="22 13383"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R((u * y) / u,z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(317(a,1),13384(a,1,2,1))].">
      <j1 rule="para" parents="317 13384"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(u / (u / y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,9965,a(flip),b,13385,a)].">
      <j1 rule="hyper" parents="60 9965 13385"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),u / (u / y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,10833,a(flip),b,13386,a)].">
      <j1 rule="hyper" parents="60 10833 13386"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7649,a(flip),b,13387,a),flip(a)].">
      <j1 rule="hyper" parents="60 7649 13387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(7385(a,1),13389(a,2,2))].">
      <j1 rule="para" parents="7385 13389"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8389,a(flip),b,13390,a),flip(a)].">
      <j1 rule="hyper" parents="370 8389 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(11736(a,1),13391(a,1,1,1))].">
      <j1 rule="para" parents="11736 13391"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(11737(a,1),13392(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11737 13392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      R(x * K(y,x),z,x) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(13393(a,1),7916(a,1))].">
      <j1 rule="para" parents="13393 7916"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      (x * L(y,x,y)) / T(T(x,y),L(T(y,x),z,u)) = T(y,x * y) * a(u,z,K(T(x,y),T(y,x * y)))
    ]]></literal>
    <justification jstring="[para(10082(a,1),13045(a,1,2))].">
      <j1 rule="para" parents="10082 13045"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,L(x,u,z)),x)
    ]]></literal>
    <justification jstring="[para(5896(a,1),13395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5896 13395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13397">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = (y * L(x,y,x)) / T(T(y,x),L(x,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),13396(a,2,2))].">
      <j1 rule="para" parents="18 13396"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(L(x,u,z),y) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8300,a(flip),b,13397,a),flip(a)].">
      <j1 rule="hyper" parents="370 8300 13397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = K(x,L(y,u,z)) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(12966(a,1),13398(a,2,1))].">
      <j1 rule="para" parents="12966 13398"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y * x))) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7292,a(flip),b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="370 7292 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(T(y,x),T(x,y))) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(7340(a,1),13400(a,1,2,3))].">
      <j1 rule="para" parents="7340 13400"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      T(x,y * x) * a(z,u,K(y,x)) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(5764(a,1),13401(a,1,2,3))].">
      <j1 rule="para" parents="5764 13401"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      L(K(x * y,y),z,u) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,13155,a,b,13402,a)].">
      <j1 rule="hyper" parents="60 13155 13402"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) \ T(y,K(x * y,y)) = L(T(y,L(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(12922(a,1),13403(a,1,1))].">
      <j1 rule="para" parents="12922 13403"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(4745(a,1),13404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4745 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,13405,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 13405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(12966(a,1),13406(a,2,1))].">
      <j1 rule="para" parents="12966 13406"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,13407,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 13407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,13024,a,b,13408,a)].">
      <j1 rule="hyper" parents="60 13024 13408"/>
    </justification>
  </clause>

  <clause id="13410">
    <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(370,a,92,a(flip),b,13238,a),flip(a)].">
      <j1 rule="hyper" parents="370 92 13238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13411">
    <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(370,a,8045,a(flip),b,13410,a),flip(a)].">
      <j1 rule="hyper" parents="370 8045 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13412">
    <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(4(a,1),13307(a,2,1,1))].">
      <j1 rule="para" parents="4 13307"/>
    </justification>
  </clause>

  <clause id="13413">
    <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(370,a,10008,a(flip),b,13412,a),flip(a)].">
      <j1 rule="hyper" parents="370 10008 13412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <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(4(a,1),13413(a,1,1,1))].">
      <j1 rule="para" parents="4 13413"/>
    </justification>
  </clause>

  <clause id="13416">
    <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(4(a,1),13415(a,1,2,2))].">
      <j1 rule="para" parents="4 13415"/>
    </justification>
  </clause>

  <clause id="13417">
    <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(6591(a,1),13416(a,1,2,1,3))].">
      <j1 rule="para" parents="6591 13416"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(T(x,x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,7296,a(flip),b,12216,a),flip(a)].">
      <j1 rule="hyper" parents="370 7296 12216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12215,a(flip),b,13418,a),flip(a)].">
      <j1 rule="hyper" parents="370 12215 13418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13422">
    <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(12309(a,1),12318(a,1,2,1,1))].">
      <j1 rule="para" parents="12309 12318"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(60,a,12288,a(flip),b,13422,a),flip(a)].">
      <j1 rule="hyper" parents="60 12288 13422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9858,a,13423,a),flip(a)].">
      <j1 rule="hyper" parents="9858 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8904,a,13424,a)].">
      <j1 rule="hyper" parents="8904 13424"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11244,a,13425,a),flip(a)].">
      <j1 rule="hyper" parents="11244 13425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(13426(a,1),12408(a,1,1))].">
      <j1 rule="para" parents="13426 12408"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,12407,a(flip),b,13427,a)].">
      <j1 rule="hyper" parents="60 12407 13427"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(12639,a,13428,a),flip(a)].">
      <j1 rule="hyper" parents="12639 13428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,10938,a(flip),b,13429,a),flip(a)].">
      <j1 rule="hyper" parents="60 10938 13429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(15(a,2),13430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15 13430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      R(K(x,R(1 / y,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(713(a,1),13431(a,2,2,1))].">
      <j1 rule="para" parents="713 13431"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5614(a,1),13431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5614 13431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7344(a,1),13431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7344 13431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13435">
    <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(12786(a,1),13431(a,1,1))].">
      <j1 rule="para" parents="12786 13431"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(7107,a,13433,a)].">
      <j1 rule="hyper" parents="7107 13433"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ x) = x * R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,13433,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 13433 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      R(K(x,x * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(13436(a,1),6083(a,1))].">
      <j1 rule="para" parents="13436 6083"/>
    </justification>
  </clause>

  <clause id="13439">
    <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(13434(a,1),13435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13434 13435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      R(K(x,R(y \ 1,y,z) \ x),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(5593(a,1),13432(a,1,1))].">
      <j1 rule="para" parents="5593 13432"/>
    </justification>
  </clause>

  <clause id="13441">
    <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(7506(a,1),11596(a,1,1,2,2))].">
      <j1 rule="para" parents="7506 11596"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K(x * y,K(z,(T(x * y,u) * w) \ L(w,y,x))) = K(z,K(x * y,a(x,y,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,11066,a(flip),b,11646,a),flip(a)].">
      <j1 rule="hyper" parents="60 11066 11646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K(x,K(y * z,(T(y * z,u) * w) \ L(w,z,y))) = K(x,K(y * z,a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(8634,a,13442,a)].">
      <j1 rule="hyper" parents="8634 13442"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      K(x,K(y * z,u \ ((y * z) \ L(u,z,y)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(11266(a,1),13443(a,1,2))].">
      <j1 rule="para" parents="11266 13443"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x,K(y * z,u \ L(u,z,y))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12383,a,13445,a)].">
      <j1 rule="hyper" parents="12383 13445"/>
    </justification>
  </clause>

  <clause id="13447">
    <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(7892(a,1),13441(a,1,1,2))].">
      <j1 rule="para" parents="7892 13441"/>
    </justification>
  </clause>

  <clause id="13448">
    <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(12187(a,1),13447(a,1,2))].">
      <j1 rule="para" parents="12187 13447"/>
    </justification>
  </clause>

  <clause id="13449">
    <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(11383(a,1),13448(a,1,2))].">
      <j1 rule="para" parents="11383 13448"/>
    </justification>
  </clause>

  <clause id="13451">
    <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(7506(a,1),13449(a,2,2,1,1))].">
      <j1 rule="para" parents="7506 13449"/>
    </justification>
  </clause>

  <clause id="13452">
    <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(8705(a,1),13451(a,2,2,1))].">
      <j1 rule="para" parents="8705 13451"/>
    </justification>
  </clause>

  <clause id="13453">
    <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(8601(a,2),13452(a,2,2))].">
      <j1 rule="para" parents="8601 13452"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),13453(a,2,2,1))].">
      <j1 rule="para" parents="7 13453"/>
    </justification>
  </clause>

  <clause id="13455">
    <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(13454(a,1),9667(a,1,1,2))].">
      <j1 rule="para" parents="13454 9667"/>
    </justification>
  </clause>

  <clause id="13456">
    <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(11518(a,1),11515(a,1,1,2))].">
      <j1 rule="para" parents="11518 11515"/>
    </justification>
  </clause>

  <clause id="13457">
    <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(11508(a,1),13456(a,1,2,1))].">
      <j1 rule="para" parents="11508 13456"/>
    </justification>
  </clause>

  <clause id="13458">
    <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(2014(a,1),13457(a,1,2,2))].">
      <j1 rule="para" parents="2014 13457"/>
    </justification>
  </clause>

  <clause id="13459">
    <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(7767(a,1),13458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7767 13458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13461">
    <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(11508(a,1),13459(a,1,2,1))].">
      <j1 rule="para" parents="11508 13459"/>
    </justification>
  </clause>

  <clause id="13463">
    <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(11518(a,1),13461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11518 13461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <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(11508(a,1),13463(a,2,3))].">
      <j1 rule="para" parents="11508 13463"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,12057,a(flip),b,13464,a),flip(a)].">
      <j1 rule="hyper" parents="370 12057 13464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) * ((v5 / T(y,L(x,z,u))) / (v5 / y)) = T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(8605(a,1),13016(a,1,1))].">
      <j1 rule="para" parents="8605 13016"/>
    </justification>
  </clause>

  <clause id="13468">
    <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(13(a,2),2522(a,1,1))].">
      <j1 rule="para" parents="13 2522"/>
    </justification>
  </clause>

  <clause id="13469">
    <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(13(a,2),13468(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13 13468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13470">
    <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(15(a,2),2527(a,2,2,1,1))].">
      <j1 rule="para" parents="15 2527"/>
    </justification>
  </clause>

  <clause id="13471">
    <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(2567(a,1),13470(a,1,1))].">
      <j1 rule="para" parents="2567 13470"/>
    </justification>
  </clause>

  <clause id="13472">
    <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(2568(a,1),13471(a,1,1,1))].">
      <j1 rule="para" parents="2568 13471"/>
    </justification>
  </clause>

  <clause id="13473">
    <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(693,a,13472,a),flip(a)].">
      <j1 rule="hyper" parents="693 13472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13474">
    <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(60,a,1968,a(flip),b,13473,a),flip(a)].">
      <j1 rule="hyper" parents="60 1968 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <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(910(a,1),13473(a,2,1,2))].">
      <j1 rule="para" parents="910 13473"/>
    </justification>
  </clause>

  <clause id="13476">
    <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(5889(a,1),13473(a,2,1,2,1))].">
      <j1 rule="para" parents="5889 13473"/>
    </justification>
  </clause>

  <clause id="13477">
    <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(10816(a,1),13473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10816 13473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1750,a,13475,a),flip(a)].">
      <j1 rule="hyper" parents="1750 13475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = R(x * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),13478(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2 13478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5393,a(flip),b,13479,a),flip(a)].">
      <j1 rule="hyper" parents="370 5393 13479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13481">
    <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(129,a,13480,a(flip),b,250,a)].">
      <j1 rule="hyper" parents="129 13480 250"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5380,a,13481,a),flip(a)].">
      <j1 rule="hyper" parents="5380 13481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(2624(a,1),13482(a,1,1))].">
      <j1 rule="para" parents="2624 13482"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,4219,a(flip),b,13483,a),flip(a)].">
      <j1 rule="hyper" parents="370 4219 13483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4216(a,1),13484(a,1,1))].">
      <j1 rule="para" parents="4216 13484"/>
    </justification>
  </clause>

  <clause id="13486">
    <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(13485(a,1),389(a,1,2))].">
      <j1 rule="para" parents="13485 389"/>
    </justification>
  </clause>

  <clause id="13487">
    <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(2040(a,1),13474(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2040 13474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3333,a,13487,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3333 13487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,10540,a(flip),b,13488,a)].">
      <j1 rule="hyper" parents="60 10540 13488"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,13489,a(flip),b,3289,a)].">
      <j1 rule="hyper" parents="125 13489 3289"/>
    </justification>
  </clause>

  <clause id="13492">
    <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(13489(a,1),6811(a,1,2,1,1))].">
      <j1 rule="para" parents="13489 6811"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4905(a,1),13492(a,1,2))].">
      <j1 rule="para" parents="4905 13492"/>
    </justification>
  </clause>

  <clause id="13494">
    <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(13493(a,1),10283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13493 10283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,13494,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 13494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(7518,a,13495,a)].">
      <j1 rule="hyper" parents="7518 13495"/>
    </justification>
  </clause>

  <clause id="13497">
    <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(1628(a,1),13496(a,1,2,2))].">
      <j1 rule="para" parents="1628 13496"/>
    </justification>
  </clause>

  <clause id="13498">
    <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(10598(a,1),13496(a,1,1))].">
      <j1 rule="para" parents="10598 13496"/>
    </justification>
  </clause>

  <clause id="13499">
    <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(10734(a,1),13496(a,1,1))].">
      <j1 rule="para" parents="10734 13496"/>
    </justification>
  </clause>

  <clause id="13500">
    <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(7883,a,13498,a)].">
      <j1 rule="hyper" parents="7883 13498"/>
    </justification>
  </clause>

  <clause id="13501">
    <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(10965(a,1),13498(a,1,2,2))].">
      <j1 rule="para" parents="10965 13498"/>
    </justification>
  </clause>

  <clause id="13502">
    <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(13500(a,1),12110(a,1))].">
      <j1 rule="para" parents="13500 12110"/>
    </justification>
  </clause>

  <clause id="13503">
    <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(12114(a,1),13501(a,1,2))].">
      <j1 rule="para" parents="12114 13501"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(7538,a,13503,a),flip(a)].">
      <j1 rule="hyper" parents="7538 13503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(13502,a,13504,a)].">
      <j1 rule="hyper" parents="13502 13504"/>
    </justification>
  </clause>

  <clause id="13507">
    <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(7377(a,1),13497(a,1,1))].">
      <j1 rule="para" parents="7377 13497"/>
    </justification>
  </clause>

  <clause id="13508">
    <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(5230(a,2),13507(a,1,2))].">
      <j1 rule="para" parents="5230 13507"/>
    </justification>
  </clause>

  <clause id="13510">
    <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(6883(a,1),13508(a,1,1))].">
      <j1 rule="para" parents="6883 13508"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9791,a(flip),b,13510,a),flip(a)].">
      <j1 rule="hyper" parents="370 9791 13510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(T(x,y),z) * K(x * z,T(x,y)) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(2902,a,13511,a)].">
      <j1 rule="hyper" parents="2902 13511"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      (x * (K(T(y,z),u) * K(y * u,T(y,z)))) * (y \ L(y,u,y)) = x
    ]]></literal>
    <justification jstring="[para(13512(a,2),13465(a,1,1,2))].">
      <j1 rule="para" parents="13512 13465"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      K(x,T(y,z)) * K(T(y,z),y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(11523,a,13514,a)].">
      <j1 rule="hyper" parents="11523 13514"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(y * x,z)) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(9137,a,13515,a)].">
      <j1 rule="hyper" parents="9137 13515"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = (y \ L(y,x,y)) * y
    ]]></literal>
    <justification jstring="[para(13516(a,1),6268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13516 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3838,a(flip),b,13517,a),flip(a)].">
      <j1 rule="hyper" parents="370 3838 13517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z)
    ]]></literal>
    <justification jstring="[para(12580(a,1),13518(a,1,1))].">
      <j1 rule="para" parents="12580 13518"/>
    </justification>
  </clause>

  <clause id="13520">
    <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(10505(a,1),13519(a,1,1,1))].">
      <j1 rule="para" parents="10505 13519"/>
    </justification>
  </clause>

  <clause id="13521">
    <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(8019(a,2),13499(a,1,2,2,1))].">
      <j1 rule="para" parents="8019 13499"/>
    </justification>
  </clause>

  <clause id="13522">
    <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(7506(a,1),13521(a,1,2))].">
      <j1 rule="para" parents="7506 13521"/>
    </justification>
  </clause>

  <clause id="13523">
    <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(13522(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="13522 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13524">
    <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(10816(a,1),13477(a,2,2,1,1))].">
      <j1 rule="para" parents="10816 13477"/>
    </justification>
  </clause>

  <clause id="13525">
    <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(5865(a,1),13524(a,2,2,1))].">
      <j1 rule="para" parents="5865 13524"/>
    </justification>
  </clause>

  <clause id="13527">
    <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(5865(a,1),13525(a,1,1,2,1))].">
      <j1 rule="para" parents="5865 13525"/>
    </justification>
  </clause>

  <clause id="13528">
    <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(60,a,7545,a(flip),b,13527,a)].">
      <j1 rule="hyper" parents="60 7545 13527"/>
    </justification>
  </clause>

  <clause id="13529">
    <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(13527(a,1),683(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13527 683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <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(13527(a,2),7657(a,1,1))].">
      <j1 rule="para" parents="13527 7657"/>
    </justification>
  </clause>

  <clause id="13532">
    <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(8605(a,1),13530(a,1,1,1,2,1))].">
      <j1 rule="para" parents="8605 13530"/>
    </justification>
  </clause>

  <clause id="13533">
    <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(10729(a,1),13532(a,1,1,1,2))].">
      <j1 rule="para" parents="10729 13532"/>
    </justification>
  </clause>

  <clause id="13534">
    <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(13372(a,1),13533(a,1,1,1))].">
      <j1 rule="para" parents="13372 13533"/>
    </justification>
  </clause>

  <clause id="13535">
    <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(15(a,2),2585(a,2,2,1,1))].">
      <j1 rule="para" parents="15 2585"/>
    </justification>
  </clause>

  <clause id="13536">
    <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(2552(a,1),13535(a,1,1))].">
      <j1 rule="para" parents="2552 13535"/>
    </justification>
  </clause>

  <clause id="13537">
    <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(2553(a,1),13536(a,1,1,1))].">
      <j1 rule="para" parents="2553 13536"/>
    </justification>
  </clause>

  <clause id="13538">
    <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(693,a,13537,a),flip(a)].">
      <j1 rule="hyper" parents="693 13537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(1069(a,1),13538(a,2,1,2))].">
      <j1 rule="para" parents="1069 13538"/>
    </justification>
  </clause>

  <clause id="13540">
    <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(1970(a,1),13539(a,1,2))].">
      <j1 rule="para" parents="1970 13539"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),13540(a,2,1,2))].">
      <j1 rule="para" parents="222 13540"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1709(a,2),13541(a,2,1))].">
      <j1 rule="para" parents="1709 13541"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3646,a(flip),b,13542,a),flip(a)].">
      <j1 rule="hyper" parents="370 3646 13542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,7116,a,b,13543,a),flip(a)].">
      <j1 rule="hyper" parents="31 7116 13543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(13545(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13545 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(13546,a,7121,a),flip(a)].">
      <j1 rule="hyper" parents="13546 7121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(13486,a,13547,a)].">
      <j1 rule="hyper" parents="13486 13547"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,13490,a(flip),b,13547,a)].">
      <j1 rule="hyper" parents="60 13490 13547"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      (x \ (y * R(y \ x,z,u))) \ 1 = R(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(2514(a,1),13549(a,1,1))].">
      <j1 rule="para" parents="2514 13549"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(12109(a,1),13549(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12109 13549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,13548,a)].">
      <j1 rule="hyper" parents="52 13548"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(13552(a,1),6133(a,1,1,1))].">
      <j1 rule="para" parents="13552 6133"/>
    </justification>
  </clause>

  <clause id="13554">
    <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(13553(a,1),2945(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13553 2945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13555">
    <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(9538(a,1),13551(a,2,1))].">
      <j1 rule="para" parents="9538 13551"/>
    </justification>
  </clause>

  <clause id="13556">
    <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(10224(a,1),13555(a,1,1))].">
      <j1 rule="para" parents="10224 13555"/>
    </justification>
  </clause>

  <clause id="13557">
    <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(12141(a,1),13556(a,2,1))].">
      <j1 rule="para" parents="12141 13556"/>
    </justification>
  </clause>

  <clause id="13558">
    <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(60,a,13551,a(flip),b,13557,a)].">
      <j1 rule="hyper" parents="60 13551 13557"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(13505(a,1),13558(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13505 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(326,a,13559,a),flip(a)].">
      <j1 rule="hyper" parents="326 13559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13562">
    <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(370,a,9800,a,b,13560,a)].">
      <j1 rule="hyper" parents="370 9800 13560"/>
    </justification>
  </clause>

  <clause id="13564">
    <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(13553(a,1),13554(a,2,2,1,1))].">
      <j1 rule="para" parents="13553 13554"/>
    </justification>
  </clause>

  <clause id="13565">
    <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(77(a,1),13564(a,2,2,1))].">
      <j1 rule="para" parents="77 13564"/>
    </justification>
  </clause>

  <clause id="13567">
    <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(370,a,2012,a(flip),b,13565,a),flip(a)].">
      <j1 rule="hyper" parents="370 2012 13565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),13567(a,1,1,2,1))].">
      <j1 rule="para" parents="77 13567"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2012(a,1),13568(a,1,1))].">
      <j1 rule="para" parents="2012 13568"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3736,a,13569,a)].">
      <j1 rule="hyper" parents="3736 13569"/>
    </justification>
  </clause>

  <clause id="13571">
    <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(13570(a,1),7112(a,1,1,1))].">
      <j1 rule="para" parents="13570 7112"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(13549(a,1),13570(a,1,1))].">
      <j1 rule="para" parents="13549 13570"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(156,a,13572,a)].">
      <j1 rule="hyper" parents="156 13572"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x \ R(x,y,z),R(x,y,z) \ x) = 1 \ ((R(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(13573(a,1),94(a,2,1))].">
      <j1 rule="para" parents="13573 94"/>
    </justification>
  </clause>

  <clause id="13575">
    <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(1144,a,13571,a)].">
      <j1 rule="hyper" parents="1144 13571"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(103(a,1),13575(a,1,1,2))].">
      <j1 rule="para" parents="103 13575"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),13576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 13576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,12069,a(flip),b,13577,a)].">
      <j1 rule="hyper" parents="370 12069 13577"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,2),13578(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 13578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),a(y,z,u)) = L(a(y,z,u),a(y,z,u),x) \ x
    ]]></literal>
    <justification jstring="[para(13579(a,1),7001(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13579 7001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <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(7212(a,1),13562(a,1,1,2))].">
      <j1 rule="para" parents="7212 13562"/>
    </justification>
  </clause>

  <clause id="13583">
    <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(872(a,1),13582(a,1,1))].">
      <j1 rule="para" parents="872 13582"/>
    </justification>
  </clause>

  <clause id="13584">
    <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(274(a,1),13583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="274 13583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13585">
    <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(370,a,3190,a(flip),b,13584,a),flip(a)].">
      <j1 rule="hyper" parents="370 3190 13584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13586">
    <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(22(a,2),13585(a,2,3))].">
      <j1 rule="para" parents="22 13585"/>
    </justification>
  </clause>

  <clause id="13587">
    <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(60,a,13560,a(flip),b,13586,a)].">
      <j1 rule="hyper" parents="60 13560 13586"/>
    </justification>
  </clause>

  <clause id="13588">
    <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(60,a,13505,a(flip),b,13587,a)].">
      <j1 rule="hyper" parents="60 13505 13587"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12151,a(flip),b,13588,a),flip(a)].">
      <j1 rule="hyper" parents="60 12151 13588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13592">
    <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(60,a,13321,a,b,13590,a)].">
      <j1 rule="hyper" parents="60 13321 13590"/>
    </justification>
  </clause>

  <clause id="13593">
    <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(11493,a,13592,a)].">
      <j1 rule="hyper" parents="11493 13592"/>
    </justification>
  </clause>

  <clause id="13594">
    <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(13593(a,1),13242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13593 13242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13595">
    <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(17(a,2),13594(a,2,2,2))].">
      <j1 rule="para" parents="17 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <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(12150(a,1),13595(a,2,2))].">
      <j1 rule="para" parents="12150 13595"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      (x * y) * L(((x \ 1) * y) \ ((x \ 1) * (x \ 1)),z,u) = ((x \ 1) * y) \ L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2093(a,1),4269(a,1,1))].">
      <j1 rule="para" parents="2093 4269"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      (x * y) * L(((x \ 1) * y) \ (x \ (1 / x)),z,u) = ((x \ 1) * y) \ L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(1211(a,1),13597(a,1,2,1,2))].">
      <j1 rule="para" parents="1211 13597"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      (x * y) * L((x * y) \ ((1 / x) \ (1 / x)),z,u) = ((x \ 1) * y) \ L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2113(a,1),13598(a,1,2,1))].">
      <j1 rule="para" parents="2113 13598"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      ((x \ 1) * y) \ L((x \ 1) * y,z,u) = (x * y) * L((x * y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(63(a,1),13599(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="63 13599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      ((x \ 1) * y) \ L((x \ 1) * y,z,u) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3816,a(flip),b,13600,a),flip(a)].">
      <j1 rule="hyper" parents="370 3816 13600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      a(x,y,(z * u) \ L(z * u,u,z)) = a(x,y,(z \ 1) * (u * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(13601(a,1),4010(a,1,3))].">
      <j1 rule="para" parents="13601 4010"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * ((z \ 1) * u))) = a(x,y,z * (u * ((z * u) \ 1)))
    ]]></literal>
    <justification jstring="[para(3822(a,1),13603(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3822 13603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13605">
    <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(7208(a,1),10246(a,1,1,1))].">
      <j1 rule="para" parents="7208 10246"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(5748(a,1),13605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5748 13605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7374,a(flip),b,13606,a),flip(a)].">
      <j1 rule="hyper" parents="370 7374 13606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13609">
    <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(370,a,689,a(flip),b,10315,a),flip(a)].">
      <j1 rule="hyper" parents="370 689 10315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13610">
    <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(60,a,2567,a(flip),b,13609,a)].">
      <j1 rule="hyper" parents="60 2567 13609"/>
    </justification>
  </clause>

  <clause id="13611">
    <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(7533(a,1),13610(a,1,1,2,1))].">
      <j1 rule="para" parents="7533 13610"/>
    </justification>
  </clause>

  <clause id="13612">
    <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(6526(a,1),13611(a,1,1,2,1))].">
      <j1 rule="para" parents="6526 13611"/>
    </justification>
  </clause>

  <clause id="13613">
    <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(8791(a,1),13612(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8791 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <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(60,a,7832,a(flip),b,13613,a),flip(a)].">
      <j1 rule="hyper" parents="60 7832 13613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <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(13614(a,1),1985(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13614 1985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13617">
    <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(7506(a,1),13616(a,1,1))].">
      <j1 rule="para" parents="7506 13616"/>
    </justification>
  </clause>

  <clause id="13618">
    <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(10375(a,1),13617(a,1,1))].">
      <j1 rule="para" parents="10375 13617"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,13618,a),flip(a)].">
      <j1 rule="hyper" parents="333 13618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13622">
    <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(60,a,10645,a(flip),b,13619,a)].">
      <j1 rule="hyper" parents="60 10645 13619"/>
    </justification>
  </clause>

  <clause id="13623">
    <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(370,a,8130,a(flip),b,13622,a),flip(a)].">
      <j1 rule="hyper" parents="370 8130 13622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,10687,a(flip),b,13623,a),flip(a)].">
      <j1 rule="hyper" parents="60 10687 13623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,11307,a(flip),b,13624,a),flip(a)].">
      <j1 rule="hyper" parents="370 11307 13624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9028,a,13626,a)].">
      <j1 rule="hyper" parents="9028 13626"/>
    </justification>
  </clause>

  <clause id="13629">
    <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(5865(a,1),10571(a,2,1,2,1))].">
      <j1 rule="para" parents="5865 10571"/>
    </justification>
  </clause>

  <clause id="13630">
    <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(11891(a,1),13629(a,2,1))].">
      <j1 rule="para" parents="11891 13629"/>
    </justification>
  </clause>

  <clause id="13631">
    <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(11010(a,1),13630(a,1,2,2,2,1))].">
      <j1 rule="para" parents="11010 13630"/>
    </justification>
  </clause>

  <clause id="13632">
    <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(60,a,10570,a(flip),b,13631,a)].">
      <j1 rule="hyper" parents="60 10570 13631"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,13197,a(flip),b,13632,a)].">
      <j1 rule="hyper" parents="60 13197 13632"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(12922(a,1),13633(a,1,3))].">
      <j1 rule="para" parents="12922 13633"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(T(x,x \ y),y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,7296,a(flip),b,12217,a),flip(a)].">
      <j1 rule="hyper" parents="60 7296 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      (x \ 1) \ ((y / (x * x)) * R((y / (x * x)) \ (x \ 1),z,u)) = T(y / x,x \ 1) \ R(T(y / x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(1127(a,1),2517(a,2,2,1))].">
      <j1 rule="para" parents="1127 2517"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      (x \ 1) * (R(y,x,x) * (((x \ 1) \ 1) * ((x \ 1) \ 1))) = T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(401,a,4487,a)].">
      <j1 rule="hyper" parents="401 4487"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1)) = (x \ 1) * (R(y,x,x) * ((x \ 1) \ (1 / (x \ 1))))
    ]]></literal>
    <justification jstring="[para(1211(a,1),13638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1211 13638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1)) = (x \ 1) * (R(y,x,x) * ((x \ 1) \ x))
    ]]></literal>
    <justification jstring="[para(74(a,1),13640(a,2,2,2,2))].">
      <j1 rule="para" parents="74 13640"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1)) = (x \ 1) * (R(y,x,x) * (x * x))
    ]]></literal>
    <justification jstring="[para(311(a,1),13641(a,2,2,2))].">
      <j1 rule="para" parents="311 13641"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      T(R(x * y,x,x),((x \ 1) \ 1) * ((x \ 1) \ 1)) = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[para(103(a,1),13643(a,2,2))].">
      <j1 rule="para" parents="103 13643"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      T(R(x * y,x,x),(x \ 1) \ (1 / (x \ 1))) = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[para(1211(a,1),13644(a,1,2))].">
      <j1 rule="para" parents="1211 13644"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      T(R(x * y,x,x),(x \ 1) \ x) = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[para(74(a,1),13645(a,1,2,2))].">
      <j1 rule="para" parents="74 13645"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      T(R(x * y,x,x),x * x) = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[para(311(a,1),13646(a,1,2))].">
      <j1 rule="para" parents="311 13646"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      R(T(x * y,x * x),x,x) = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a,b,13648,a)].">
      <j1 rule="hyper" parents="60 22 13648"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      (((1 / x) * y) * x) * x = (x \ 1) * ((y * x) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1866,a(flip),b,13649,a)].">
      <j1 rule="hyper" parents="60 1866 13649"/>
    </justification>
  </clause>

  <clause id="13651">
    <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(11418(a,1),11422(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11418 11422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13652">
    <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(4(a,1),13651(a,2,1,2,1))].">
      <j1 rule="para" parents="4 13651"/>
    </justification>
  </clause>

  <clause id="13654">
    <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(11418(a,1),13652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11418 13652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <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(2898(a,1),13654(a,2,2))].">
      <j1 rule="para" parents="2898 13654"/>
    </justification>
  </clause>

  <clause id="13656">
    <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(60,a,11873,a,b,13655,a)].">
      <j1 rule="hyper" parents="60 11873 13655"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      R(x * (K(y,z) * R(K(z,y),u,u \ 1)),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(13655(a,1),10698(a,1,1))].">
      <j1 rule="para" parents="13655 10698"/>
    </justification>
  </clause>

  <clause id="13658">
    <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(294,a,13656,a),flip(a)].">
      <j1 rule="hyper" parents="294 13656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      R(x * a(K(y,z),u,u \ 1),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7515(a,1),13657(a,1,1,2))].">
      <j1 rule="para" parents="7515 13657"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(11430,a,13659,a),flip(a)].">
      <j1 rule="hyper" parents="11430 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(10489,a,13660,a)].">
      <j1 rule="hyper" parents="10489 13660"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(13661(a,1),12210(a,1,2))].">
      <j1 rule="para" parents="13661 12210"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,13663,a)].">
      <j1 rule="hyper" parents="53 13663"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3094(a,1),13664(a,1,2))].">
      <j1 rule="para" parents="3094 13664"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,13665,a)].">
      <j1 rule="hyper" parents="51 13665"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = K(x,y) \ R(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3056,a,b,13666,a),flip(a)].">
      <j1 rule="hyper" parents="370 3056 13666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13668">
    <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(7531(a,2),13667(a,1,1))].">
      <j1 rule="para" parents="7531 13667"/>
    </justification>
  </clause>

  <clause id="13669">
    <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(60,a,10171,a,b,13668,a)].">
      <j1 rule="hyper" parents="60 10171 13668"/>
    </justification>
  </clause>

  <clause id="13670">
    <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(60,a,9301,a,b,13669,a)].">
      <j1 rule="hyper" parents="60 9301 13669"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13523,a,13670,a)].">
      <j1 rule="hyper" parents="13523 13670"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2730(a,1),13671(a,1,2,2))].">
      <j1 rule="para" parents="2730 13671"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,13672,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 13672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13214,a,b,13672,a)].">
      <j1 rule="hyper" parents="60 13214 13672"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      T(x,K(y,R(z,u,u \ 1))) = x * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(13672(a,1),8638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13672 8638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(706(a,1),13673(a,1,2,2))].">
      <j1 rule="para" parents="706 13673"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(77(a,1),13676(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="77 13676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5565(a,2),13676(a,1,2))].">
      <j1 rule="para" parents="5565 13676"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5568(a,1),13676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5568 13676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9472,a,13677,a)].">
      <j1 rule="hyper" parents="9472 13677"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9472,a,13679,a)].">
      <j1 rule="hyper" parents="9472 13679"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8678,a,13679,a)].">
      <j1 rule="hyper" parents="8678 13679"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(8058(a,1),13679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8058 13679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13684">
    <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(13680(a,1),12994(a,1,3))].">
      <j1 rule="para" parents="13680 12994"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),13681(a,2,2,2))].">
      <j1 rule="para" parents="7 13681"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8634,a,13685,a)].">
      <j1 rule="hyper" parents="8634 13685"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9435,a(flip),b,13686,a)].">
      <j1 rule="hyper" parents="60 9435 13686"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(13687(a,1),10022(a,1,1))].">
      <j1 rule="para" parents="13687 10022"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(13687(a,1),10233(a,1,1))].">
      <j1 rule="para" parents="13687 10233"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8648(a,1),13690(a,1,1))].">
      <j1 rule="para" parents="8648 13690"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10732,a(flip),b,13691,a)].">
      <j1 rule="hyper" parents="60 10732 13691"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(74(a,1),13693(a,1,2,2,2))].">
      <j1 rule="para" parents="74 13693"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(8680,a,13689,a)].">
      <j1 rule="hyper" parents="8680 13689"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(74(a,1),13689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 13689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(8606(a,1),13695(a,1,1))].">
      <j1 rule="para" parents="8606 13695"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8636(a,1),13696(a,2,1))].">
      <j1 rule="para" parents="8636 13696"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(10024,a,13698,a)].">
      <j1 rule="hyper" parents="10024 13698"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,13699,a)].">
      <j1 rule="hyper" parents="215 13699"/>
    </justification>
  </clause>

  <clause id="13702">
    <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(7690(a,1),13700(a,1,1,1,1))].">
      <j1 rule="para" parents="7690 13700"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5309,a,13701,a)].">
      <j1 rule="hyper" parents="5309 13701"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,13703,a)].">
      <j1 rule="hyper" parents="50 13703"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),13704(a,1,3))].">
      <j1 rule="para" parents="4 13704"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(6218(a,2),13704(a,1,1))].">
      <j1 rule="para" parents="6218 13704"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(8606(a,1),13705(a,1,1))].">
      <j1 rule="para" parents="8606 13705"/>
    </justification>
  </clause>

  <clause id="13708">
    <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(370,a,8652,a,b,13706,a),flip(a)].">
      <j1 rule="hyper" parents="370 8652 13706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      T(x,K(y,R(z,u,u \ 1))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8616,a(flip),b,13675,a),flip(a)].">
      <j1 rule="hyper" parents="370 8616 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      T(x,K(y,T(z * (u \ 1),u))) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10780,a(flip),b,13710,a)].">
      <j1 rule="hyper" parents="60 10780 13710"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(8024(a,1),13683(a,1,2))].">
      <j1 rule="para" parents="8024 13683"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,x \ z))
    ]]></literal>
    <justification jstring="[hyper(8052,a,13711,a)].">
      <j1 rule="hyper" parents="8052 13711"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      T(x,K(T(y,z),z \ u)) = T(x,K(y,u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(8766(a,1),13711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8766 13711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9105,a(flip),b,13713,a),flip(a)].">
      <j1 rule="hyper" parents="370 9105 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5568(a,1),13716(a,1,2))].">
      <j1 rule="para" parents="5568 13716"/>
    </justification>
  </clause>

  <clause id="13718">
    <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(13717(a,1),5776(a,1,1))].">
      <j1 rule="para" parents="13717 5776"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12551(a,1),13712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12551 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9467,a,13719,a)].">
      <j1 rule="hyper" parents="9467 13719"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),13719(a,2,2,2))].">
      <j1 rule="para" parents="7 13719"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,11631,a(flip),b,13720,a),flip(a)].">
      <j1 rule="hyper" parents="60 11631 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(13721(a,1),9629(a,2,2))].">
      <j1 rule="para" parents="13721 9629"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8794(a,1),13715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8794 13715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(9461,a,13725,a),flip(a)].">
      <j1 rule="hyper" parents="9461 13725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8603,a,13726,a),flip(a)].">
      <j1 rule="hyper" parents="8603 13726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(9496,a,13727,a)].">
      <j1 rule="hyper" parents="9496 13727"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,13728,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 13728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(5289,a,13729,a)].">
      <j1 rule="hyper" parents="5289 13729"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      R(K(x,T(y,(z * x) / z)),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(13730(a,1),12680(a,1,1))].">
      <j1 rule="para" parents="13730 12680"/>
    </justification>
  </clause>

  <clause id="13732">
    <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(13694(a,1),13708(a,2,2))].">
      <j1 rule="para" parents="13694 13708"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(9415,a,13722,a),flip(a)].">
      <j1 rule="hyper" parents="9415 13722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(9467,a,13733,a)].">
      <j1 rule="hyper" parents="9467 13733"/>
    </justification>
  </clause>

  <clause id="13735">
    <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(5514(a,2),13734(a,2,2))].">
      <j1 rule="para" parents="5514 13734"/>
    </justification>
  </clause>

  <clause id="13736">
    <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(8636(a,2),13732(a,2,2))].">
      <j1 rule="para" parents="8636 13732"/>
    </justification>
  </clause>

  <clause id="13737">
    <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(6218(a,1),13736(a,1,1))].">
      <j1 rule="para" parents="6218 13736"/>
    </justification>
  </clause>

  <clause id="13738">
    <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(370,a,13355,a(flip),b,13737,a)].">
      <j1 rule="hyper" parents="370 13355 13737"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,13707,a(flip),b,13738,a),flip(a)].">
      <j1 rule="hyper" parents="370 13707 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,13366,a(flip),b,13739,a)].">
      <j1 rule="hyper" parents="60 13366 13739"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),13740(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4 13740"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      R(K(x,T(y,T(x,z))),z * x,z \ 1) = K(x,((y \ (z * x)) * (z \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(8855(a,1),13731(a,1,1,2))].">
      <j1 rule="para" parents="8855 13731"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(7054(a,1),13742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7054 13742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,10017,a(flip),b,13743,a),flip(a)].">
      <j1 rule="hyper" parents="370 10017 13743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      K(R(x,y,y \ 1),R(z,z \ y,x)) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(675(a,1),13744(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="675 13744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10654,a(flip),b,13746,a)].">
      <j1 rule="hyper" parents="60 10654 13746"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,7662,a(flip),b,13747,a),flip(a)].">
      <j1 rule="hyper" parents="60 7662 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11993,a(flip),b,13748,a)].">
      <j1 rule="hyper" parents="60 11993 13748"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(63(a,1),13750(a,1,2,2))].">
      <j1 rule="para" parents="63 13750"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10722,a(flip),b,13751,a)].">
      <j1 rule="hyper" parents="60 10722 13751"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(13752(a,2),5865(a,1,1))].">
      <j1 rule="para" parents="13752 5865"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(10637,a,13754,a)].">
      <j1 rule="hyper" parents="10637 13754"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(304(a,2),13755(a,2,2)),flip(a)].">
      <j1 rule="para" parents="304 13755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(12561,a,13756,a)].">
      <j1 rule="hyper" parents="12561 13756"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,9859,a(flip),b,13757,a),flip(a)].">
      <j1 rule="hyper" parents="60 9859 13757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,13755,a(flip),b,13758,a)].">
      <j1 rule="hyper" parents="60 13755 13758"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,13219,a,b,13759,a)].">
      <j1 rule="hyper" parents="60 13219 13759"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(706(a,1),13759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="706 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13762">
    <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(13759(a,1),7680(a,2,2))].">
      <j1 rule="para" parents="13759 7680"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      L(K(x,y / z),z,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12923,a,13761,a)].">
      <j1 rule="hyper" parents="12923 13761"/>
    </justification>
  </clause>

  <clause id="13764">
    <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(4905(a,1),13762(a,2,2))].">
      <j1 rule="para" parents="4905 13762"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7754(a,1),13764(a,2,2))].">
      <j1 rule="para" parents="7754 13764"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[hyper(370,a,87,a(flip),b,13765,a),flip(a)].">
      <j1 rule="hyper" parents="370 87 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(1121(a,1),13766(a,1,1,1))].">
      <j1 rule="para" parents="1121 13766"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y) = y * x
    ]]></literal>
    <justification jstring="[para(1121(a,1),13768(a,1,2))].">
      <j1 rule="para" parents="1121 13768"/>
    </justification>
  </clause>

  <clause id="13770">
    <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(8223(a,2),13702(a,1,1))].">
      <j1 rule="para" parents="8223 13702"/>
    </justification>
  </clause>

  <clause id="13771">
    <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(8880,a,13770,a)].">
      <j1 rule="hyper" parents="8880 13770"/>
    </justification>
  </clause>

  <clause id="13772">
    <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(60,a,13682,a(flip),b,13771,a)].">
      <j1 rule="hyper" parents="60 13682 13771"/>
    </justification>
  </clause>

  <clause id="13773">
    <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(7(a,1),13772(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 13772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <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(13773(a,1),8617(a,1))].">
      <j1 rule="para" parents="13773 8617"/>
    </justification>
  </clause>

  <clause id="13775">
    <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(13(a,2),13735(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13776">
    <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(2795(a,1),11633(a,2,1,2))].">
      <j1 rule="para" parents="2795 11633"/>
    </justification>
  </clause>

  <clause id="13777">
    <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(921(a,1),13776(a,1,1,2,2))].">
      <j1 rule="para" parents="921 13776"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3743(a,1),13777(a,1,1,2))].">
      <j1 rule="para" parents="3743 13777"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6044,a(flip),b,13778,a),flip(a)].">
      <j1 rule="hyper" parents="60 6044 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13780">
    <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(8605(a,1),13718(a,1,2,1,2))].">
      <j1 rule="para" parents="8605 13718"/>
    </justification>
  </clause>

  <clause id="13781">
    <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(9426(a,1),13780(a,1,2,1,2))].">
      <j1 rule="para" parents="9426 13780"/>
    </justification>
  </clause>

  <clause id="13782">
    <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(8805(a,1),13781(a,1,2,1,2))].">
      <j1 rule="para" parents="8805 13781"/>
    </justification>
  </clause>

  <clause id="13783">
    <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(5297(a,2),13782(a,1,2,1))].">
      <j1 rule="para" parents="5297 13782"/>
    </justification>
  </clause>

  <clause id="13784">
    <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(9136,a,13783,a)].">
      <j1 rule="hyper" parents="9136 13783"/>
    </justification>
  </clause>

  <clause id="13785">
    <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(9438(a,1),13784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9438 13784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13786">
    <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(2246(a,1),13785(a,2,2))].">
      <j1 rule="para" parents="2246 13785"/>
    </justification>
  </clause>

  <clause id="13787">
    <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(370,a,8683,a(flip),b,13786,a),flip(a)].">
      <j1 rule="hyper" parents="370 8683 13786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <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(370,a,4205,a(flip),b,13787,a),flip(a)].">
      <j1 rule="hyper" parents="370 4205 13787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13789">
    <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(1769(a,1),13788(a,1,1))].">
      <j1 rule="para" parents="1769 13788"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * R(((z * x) * y) \ (x * y),u,w)) = R(T(z,x * y),x,y) \ R(R(T(z,x * y),x,y),u,w)
    ]]></literal>
    <justification jstring="[para(880(a,1),2518(a,2,2,1))].">
      <j1 rule="para" parents="880 2518"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      R(T(x,y * z),y,z) \ R(R(T(x,y * z),y,z),u,w) = (y * z) \ (((x * y) * R((x * y) \ y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(2567(a,1),13790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2567 13790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13792">
    <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(7506(a,1),10141(a,1,1,1))].">
      <j1 rule="para" parents="7506 10141"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      L(T(x * (y \ 1),y),z,u) \ (((y \ 1) \ 1) \ R(x,y,y)) = L(T(x * y,y \ 1),z,u) \ ((y \ 1) \ R(x,y,y))
    ]]></literal>
    <justification jstring="[para(4476(a,1),10195(a,1,1,1))].">
      <j1 rule="para" parents="4476 10195"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      L(T(x * y,y \ 1),z,u) \ ((y \ 1) \ R(x,y,y)) = L(T(x * (y \ 1),y),z,u) \ T(x * (y \ 1),y)
    ]]></literal>
    <justification jstring="[para(4476(a,1),13793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4476 13793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13795">
    <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(4(a,1),11630(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13796">
    <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(370,a,8025,a(flip),b,13795,a),flip(a)].">
      <j1 rule="hyper" parents="370 8025 13795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13798">
    <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(370,a,10745,a(flip),b,13796,a),flip(a)].">
      <j1 rule="hyper" parents="370 10745 13796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13799">
    <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(8181,a,13798,a)].">
      <j1 rule="hyper" parents="8181 13798"/>
    </justification>
  </clause>

  <clause id="13800">
    <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(60,a,9857,a(flip),b,13799,a)].">
      <j1 rule="hyper" parents="60 9857 13799"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(10751,a,13800,a)].">
      <j1 rule="hyper" parents="10751 13800"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8911,a,13801,a),flip(a)].">
      <j1 rule="hyper" parents="8911 13801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10700,a(flip),b,13802,a)].">
      <j1 rule="hyper" parents="60 10700 13802"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8464,a,13804,a),flip(a)].">
      <j1 rule="hyper" parents="8464 13804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10740,a,b,13805,a)].">
      <j1 rule="hyper" parents="60 10740 13805"/>
    </justification>
  </clause>

  <clause id="13807">
    <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(60,a,10979,a,b,13806,a)].">
      <j1 rule="hyper" parents="60 10979 13806"/>
    </justification>
  </clause>

  <clause id="13808">
    <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(15(a,2),13807(a,2,2,1))].">
      <j1 rule="para" parents="15 13807"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10862,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="60 10862 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <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(13527(a,1),13792(a,1,1))].">
      <j1 rule="para" parents="13527 13792"/>
    </justification>
  </clause>

  <clause id="13812">
    <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(7527,a,13811,a)].">
      <j1 rule="hyper" parents="7527 13811"/>
    </justification>
  </clause>

  <clause id="13814">
    <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(60,a,13375,a(flip),b,13812,a)].">
      <j1 rule="hyper" parents="60 13375 13812"/>
    </justification>
  </clause>

  <clause id="13815">
    <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(60,a,13362,a(flip),b,13814,a),flip(a)].">
      <j1 rule="hyper" parents="60 13362 13814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13816">
    <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(370,a,13366,a(flip),b,13815,a),flip(a)].">
      <j1 rule="hyper" parents="370 13366 13815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,13741,a(flip),b,13816,a),flip(a)].">
      <j1 rule="hyper" parents="370 13741 13816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(7527,a,13817,a)].">
      <j1 rule="hyper" parents="7527 13817"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13818(a,1),5940(a,1,1))].">
      <j1 rule="para" parents="13818 5940"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13528(a,1),13820(a,1,2))].">
      <j1 rule="para" parents="13528 13820"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,13821,a)].">
      <j1 rule="hyper" parents="131 13821"/>
    </justification>
  </clause>

  <clause id="13823">
    <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(8647(a,1),13821(a,1,2,1))].">
      <j1 rule="para" parents="8647 13821"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(7518,a,13822,a)].">
      <j1 rule="hyper" parents="7518 13822"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2904,a,13822,a)].">
      <j1 rule="hyper" parents="2904 13822"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(13822(a,1),7657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13822 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(10615(a,1),13822(a,1,2))].">
      <j1 rule="para" parents="10615 13822"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(10797(a,1),13822(a,1,2))].">
      <j1 rule="para" parents="10797 13822"/>
    </justification>
  </clause>

  <clause id="13830">
    <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(13822(a,1),13369(a,2,2))].">
      <j1 rule="para" parents="13822 13369"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      K(K(x,y) * K(y,R(x,z,u)),w) = K(a(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(13822(a,1),13375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13822 13375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(13822(a,1),13658(a,1,1,2))].">
      <j1 rule="para" parents="13822 13658"/>
    </justification>
  </clause>

  <clause id="13833">
    <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(13824(a,1),10275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13824 10275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13834">
    <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(13825(a,1),11872(a,2,2))].">
      <j1 rule="para" parents="13825 11872"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(7518,a,13827,a)].">
      <j1 rule="hyper" parents="7518 13827"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13349,a(flip),b,13831,a)].">
      <j1 rule="hyper" parents="60 13349 13831"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(13822(a,1),13832(a,1,2))].">
      <j1 rule="para" parents="13822 13832"/>
    </justification>
  </clause>

  <clause id="13841">
    <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(125,a,108,a(flip),b,13839,a)].">
      <j1 rule="hyper" parents="125 108 13839"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(13839(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="13839 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      K(x,x * y) * (a(K(x,y),z,u) * x) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11730,a(flip),b,13835,a)].">
      <j1 rule="hyper" parents="60 11730 13835"/>
    </justification>
  </clause>

  <clause id="13844">
    <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(13838(a,1),13534(a,1,1,1))].">
      <j1 rule="para" parents="13838 13534"/>
    </justification>
  </clause>

  <clause id="13845">
    <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(10732(a,1),13823(a,1,2,2))].">
      <j1 rule="para" parents="10732 13823"/>
    </justification>
  </clause>

  <clause id="13846">
    <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(13372(a,1),13845(a,1,2))].">
      <j1 rule="para" parents="13372 13845"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      K(x,x * y) * (x * a(K(x,y),z,u)) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9835(a,1),13843(a,1,2))].">
      <j1 rule="para" parents="9835 13843"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = R(K(x,y),z,u) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7900,a,13847,a)].">
      <j1 rule="hyper" parents="7900 13847"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(x * R(K(x,y),z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,10929,a,b,13848,a),flip(a)].">
      <j1 rule="hyper" parents="370 10929 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <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(370,a,13834,a(flip),b,13833,a),flip(a)].">
      <j1 rule="hyper" parents="370 13834 13833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13851">
    <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(448(a,1),13844(a,1,1)),flip(a)].">
      <j1 rule="para" parents="448 13844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13852">
    <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(370,a,9839,a(flip),b,13851,a),flip(a)].">
      <j1 rule="hyper" parents="370 9839 13851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13853">
    <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(8605(a,1),13852(a,1,2,1,1))].">
      <j1 rule="para" parents="8605 13852"/>
    </justification>
  </clause>

  <clause id="13854">
    <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(10729(a,1),13853(a,1,2,1))].">
      <j1 rule="para" parents="10729 13853"/>
    </justification>
  </clause>

  <clause id="13855">
    <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(5275(a,2),13854(a,1,2))].">
      <j1 rule="para" parents="5275 13854"/>
    </justification>
  </clause>

  <clause id="13856">
    <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(60,a,10781,a,b,13855,a)].">
      <j1 rule="hyper" parents="60 10781 13855"/>
    </justification>
  </clause>

  <clause id="13857">
    <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(8639(a,1),13856(a,1,1))].">
      <j1 rule="para" parents="8639 13856"/>
    </justification>
  </clause>

  <clause id="13858">
    <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(13351,a,13857,a)].">
      <j1 rule="hyper" parents="13351 13857"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13830,a(flip),b,13858,a),flip(a)].">
      <j1 rule="hyper" parents="60 13830 13858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,13859,a),flip(a)].">
      <j1 rule="hyper" parents="31 5256 13859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13861">
    <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(60,a,13838,a,b,13860,a)].">
      <j1 rule="hyper" parents="60 13838 13860"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(13861(a,1),13846(a,1,2))].">
      <j1 rule="para" parents="13861 13846"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,13862,a),flip(a)].">
      <j1 rule="hyper" parents="131 13862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,13860,a,b,13863,a),flip(a)].">
      <j1 rule="hyper" parents="370 13860 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8630(a,1),13863(a,1,1))].">
      <j1 rule="para" parents="8630 13863"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8630(a,1),13864(a,1,1))].">
      <j1 rule="para" parents="8630 13864"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      x * T(((x * L(y,z,u)) / L(y,z,u)) \ (x * y),w) = ((x * L(y,z,u)) * T(y,w)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),2490(a,1,1))].">
      <j1 rule="para" parents="6 2490"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(x \ (x * y),w)
    ]]></literal>
    <justification jstring="[para(6(a,1),13867(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      ((x * L(y,z,u)) * T(y,w)) / L(y,z,u) = x * T(y,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),13868(a,2,2,1))].">
      <j1 rule="para" parents="4 13868"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      (x * T(y,z)) * L(y,u,w) = (x * L(y,u,w)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(155,a,13869,a)].">
      <j1 rule="hyper" parents="155 13869"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(756,a,13870,a),flip(a)].">
      <j1 rule="hyper" parents="756 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13872">
    <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(13871(a,1),11432(a,1,2))].">
      <j1 rule="para" parents="13871 11432"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1029,a,13872,a),flip(a)].">
      <j1 rule="hyper" parents="1029 13872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9841,a,13873,a)].">
      <j1 rule="hyper" parents="9841 13873"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(13873(a,1),9840(a,1,2))].">
      <j1 rule="para" parents="13873 9840"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11074(a,2),13874(a,1,1))].">
      <j1 rule="para" parents="11074 13874"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y * L(z,u,w))) = x / a(z,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(13874(a,1),11524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13874 11524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,12906,a(flip),b,13875,a),flip(a)].">
      <j1 rule="hyper" parents="31 12906 13875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      a(x,x,L(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3947,a,b,13878,a),flip(a)].">
      <j1 rule="hyper" parents="370 3947 13878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13878(a,2),12051(a,2,2))].">
      <j1 rule="para" parents="13878 12051"/>
    </justification>
  </clause>

  <clause id="13882">
    <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(13107(a,1),13880(a,1,2))].">
      <j1 rule="para" parents="13107 13880"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10012,a(flip),b,13876,a)].">
      <j1 rule="hyper" parents="60 10012 13876"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13878,a(flip),b,13883,a),flip(a)].">
      <j1 rule="hyper" parents="370 13878 13883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,11510,a,b,13884,a),flip(a)].">
      <j1 rule="hyper" parents="36 11510 13884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      L(x \ y,z,x \ y) = L(x \ y,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(3519,a,13886,a),flip(a)].">
      <j1 rule="hyper" parents="3519 13886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(13886(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13886 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <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(13886(a,1),10440(a,1,1))].">
      <j1 rule="para" parents="13886 10440"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,y * x))) * (x \ y) = L(x \ y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(13887(a,1),4046(a,1,1,2,2))].">
      <j1 rule="para" parents="13887 4046"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      L(x \ y,x,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(13887(a,1),10167(a,1))].">
      <j1 rule="para" parents="13887 10167"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      (L(x,y,z) \ L(L(x,u,x),y,z)) \ w = w * a(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13888(a,1),11706(a,1,1,2))].">
      <j1 rule="para" parents="13888 11706"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,71,a(flip),b,13877,a),flip(a)].">
      <j1 rule="hyper" parents="125 71 13877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      L(x \ y,z,y \ x) = L(x \ y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(4047,a,13892,a),flip(a)].">
      <j1 rule="hyper" parents="4047 13892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13898">
    <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(13886(a,1),13890(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13886 13890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13899">
    <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(370,a,10440,a(flip),b,13898,a),flip(a)].">
      <j1 rule="hyper" parents="370 10440 13898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13901">
    <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(60,a,13596,a(flip),b,13882,a),flip(a)].">
      <j1 rule="hyper" parents="60 13596 13882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13902">
    <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(614(a,1),13901(a,1,2,3))].">
      <j1 rule="para" parents="614 13901"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(11707,a,13902,a)].">
      <j1 rule="hyper" parents="11707 13902"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(13318,a,13903,a)].">
      <j1 rule="hyper" parents="13318 13903"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13593,a(flip),b,13903,a),flip(a)].">
      <j1 rule="hyper" parents="60 13593 13903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13904(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13114,a(flip),b,13906,a),flip(a)].">
      <j1 rule="hyper" parents="60 13114 13906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12138,a(flip),b,13907,a),flip(a)].">
      <j1 rule="hyper" parents="60 12138 13907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ 1 = z \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,13907,a(flip),b,1110,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 13907 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(13907(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13907 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(13907(a,1),327(a,1,1))].">
      <j1 rule="para" parents="13907 327"/>
    </justification>
  </clause>

  <clause id="13916">
    <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(6096(a,1),13911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6096 13911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3747,a,13913,a)].">
      <j1 rule="hyper" parents="3747 13913"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(755,a,13913,a),flip(a)].">
      <j1 rule="hyper" parents="755 13913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,13913,a)].">
      <j1 rule="hyper" parents="125 70 13913"/>
    </justification>
  </clause>

  <clause id="13920">
    <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(13913(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13913 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(13913(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13913 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13922">
    <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(13913(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13913 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(13913(a,1),755(a,1))].">
      <j1 rule="para" parents="13913 755"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(11680(a,1),13913(a,1,1))].">
      <j1 rule="para" parents="11680 13913"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(13917(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="13917 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(13917(a,1),47(a,2))].">
      <j1 rule="para" parents="13917 47"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(13917(a,1),727(a,1,2))].">
      <j1 rule="para" parents="13917 727"/>
    </justification>
  </clause>

  <clause id="13928">
    <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(13917(a,1),622(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13917 622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      (a(x,y,x) * z) \ (a(x,y,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z \ u = w
    ]]></literal>
    <justification jstring="[para(94(a,1),13925(a,1)),flip(b)].">
      <j1 rule="para" parents="94 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,13145,a(flip),b,13924,a),flip(a)].">
      <j1 rule="hyper" parents="370 13145 13924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      L(x,a(y,z,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,13930,a)].">
      <j1 rule="hyper" parents="625 13930"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(13378,a,13931,a)].">
      <j1 rule="hyper" parents="13378 13931"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(5886,a,13932,a)].">
      <j1 rule="hyper" parents="5886 13932"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(y,x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,8391,a(flip),b,13933,a)].">
      <j1 rule="hyper" parents="60 8391 13933"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(13905(a,1),12171(a,1,1))].">
      <j1 rule="para" parents="13905 12171"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,13088,a(flip),b,13936,a)].">
      <j1 rule="hyper" parents="60 13088 13936"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(13114(a,1),13937(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13114 13937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,11486,a(flip),b,13938,a),flip(a)].">
      <j1 rule="hyper" parents="370 11486 13938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(12165,a,13939,a),flip(a)].">
      <j1 rule="hyper" parents="12165 13939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12420,a(flip),b,13941,a)].">
      <j1 rule="hyper" parents="60 12420 13941"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13627,a(flip),b,13942,a)].">
      <j1 rule="hyper" parents="60 13627 13942"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13809,a(flip),b,13943,a)].">
      <j1 rule="hyper" parents="60 13809 13943"/>
    </justification>
  </clause>

  <clause id="13949">
    <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(60,a,13417,a(flip),b,13947,a),flip(a)].">
      <j1 rule="hyper" parents="60 13417 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13950">
    <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(60,a,13322,a(flip),b,13916,a)].">
      <j1 rule="hyper" parents="60 13322 13916"/>
    </justification>
  </clause>

  <clause id="13951">
    <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(60,a,13439,a(flip),b,13949,a)].">
      <j1 rule="hyper" parents="60 13439 13949"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(8363(a,1),13951(a,1,1))].">
      <j1 rule="para" parents="8363 13951"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      R(x * K(R(y,z,u),x),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(13952(a,1),10696(a,1,1,1,2))].">
      <j1 rule="para" parents="13952 10696"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (R(x,w,x) \ R(x,w,x)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(13394,a,13957,a)].">
      <j1 rule="hyper" parents="13394 13957"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(233,a,13960,a),flip(a)].">
      <j1 rule="hyper" parents="233 13960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13960(a,1),232(a,1)),flip(b)].">
      <j1 rule="para" parents="13960 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,13760,a(flip),b,13961,a),flip(a)].">
      <j1 rule="hyper" parents="370 13760 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13952,a(flip),b,13961,a)].">
      <j1 rule="hyper" parents="60 13952 13961"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13961(a,1),13822(a,1,2))].">
      <j1 rule="para" parents="13961 13822"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(x * K(x,R(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(13961(a,1),13849(a,2,1,2))].">
      <j1 rule="para" parents="13961 13849"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10924,a,13965,a),flip(a)].">
      <j1 rule="hyper" parents="10924 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13952(a,1),13962(a,1))].">
      <j1 rule="para" parents="13952 13962"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13829,a(flip),b,13969,a)].">
      <j1 rule="hyper" parents="60 13829 13969"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(13976(a,2),13864(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13976 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,13866,a,b,13977,a)].">
      <j1 rule="hyper" parents="60 13866 13977"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(13964(a,1),10765(a,1,2,1))].">
      <j1 rule="para" parents="13964 10765"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13975,a,13971,a)].">
      <j1 rule="hyper" parents="13975 13971"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(7520,a,13980,a),flip(a)].">
      <j1 rule="hyper" parents="7520 13980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,12966,a(flip),b,13982,a)].">
      <j1 rule="hyper" parents="125 12966 13982"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(13984(a,1),9893(a,1,2,1))].">
      <j1 rule="para" parents="13984 9893"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(8016(a,1),13985(a,1,2,1,1))].">
      <j1 rule="para" parents="8016 13985"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6170,a(flip),b,13986,a)].">
      <j1 rule="hyper" parents="60 6170 13986"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2217(a,1),13987(a,1,2,1,1))].">
      <j1 rule="para" parents="2217 13987"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      K(x,((y / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11265,a(flip),b,13988,a),flip(a)].">
      <j1 rule="hyper" parents="60 11265 13988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,13988,a(flip),b,11265,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 13988 11265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (T(z,y) / x) \ z = u
    ]]></literal>
    <justification jstring="[para(13989(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13989 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13301,a(flip),b,13990,a),flip(a)].">
      <j1 rule="hyper" parents="370 13301 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(74(a,1),13992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,L(L(x,z,u),w,v5) / y)
    ]]></literal>
    <justification jstring="[para(13993(a,2),8131(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13993 8131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (T(z,y) / x) \ z = u
    ]]></literal>
    <justification jstring="[para(13301(a,1),13991(a,1))].">
      <j1 rule="para" parents="13301 13991"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(T(x,R(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(5256(a,2),13970(a,2,1))].">
      <j1 rule="para" parents="5256 13970"/>
    </justification>
  </clause>

  <clause id="13998">
    <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(13913(a,1),13922(a,1,2))].">
      <j1 rule="para" parents="13913 13922"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = (w * y) \ (w * (y * x))
    ]]></literal>
    <justification jstring="[hyper(13929,a,13998,a),flip(a)].">
      <j1 rule="hyper" parents="13929 13998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a,b,13999,a),flip(a)].">
      <j1 rule="hyper" parents="370 13 13999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11451(a,1),14000(a,1,3))].">
      <j1 rule="para" parents="11451 14000"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(11468(a,1),14000(a,1,3))].">
      <j1 rule="para" parents="11468 14000"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(11474(a,1),14000(a,1,3))].">
      <j1 rule="para" parents="11474 14000"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(11438(a,1),14000(a,1,3))].">
      <j1 rule="para" parents="11438 14000"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6572,a(flip),b,14001,a)].">
      <j1 rule="hyper" parents="60 6572 14001"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,L(z,w,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14005,a,b,14005,a)].">
      <j1 rule="hyper" parents="370 14005 14005"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      L(x,y,L(L(z,u,z),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(13888(a,1),14005(a,1,3))].">
      <j1 rule="para" parents="13888 14005"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),w,a(v5,v6,v5)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,13917,a,b,14002,a)].">
      <j1 rule="hyper" parents="370 13917 14002"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      L(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,8240,a(flip),b,14002,a),flip(a)].">
      <j1 rule="hyper" parents="370 8240 14002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(6558(a,1),14010(a,1,3))].">
      <j1 rule="para" parents="6558 14010"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(14011(a,1),7975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14011 7975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),14003(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5 14003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8246,a,14004,a)].">
      <j1 rule="hyper" parents="8246 14004"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = (x \ y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7522,a(flip),b,14014,a)].">
      <j1 rule="hyper" parents="60 7522 14014"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,w / (T(w,z) / z))
    ]]></literal>
    <justification jstring="[para(9060(a,1),14006(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9060 14006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      L(x,y,z * (u / z)) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,6666,a(flip),b,14013,a)].">
      <j1 rule="hyper" parents="60 6666 14013"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ 1) / u,z)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7068,a(flip),b,14019,a),flip(a)].">
      <j1 rule="hyper" parents="60 7068 14019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(7518,a,14012,a)].">
      <j1 rule="hyper" parents="7518 14012"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10877,a,14021,a)].">
      <j1 rule="hyper" parents="10877 14021"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14022(a,1,2))].">
      <j1 rule="para" parents="4 14022"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(13438,a,14023,a)].">
      <j1 rule="hyper" parents="13438 14023"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[para(14023(a,1),13437(a,2,2))].">
      <j1 rule="para" parents="14023 13437"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(14025(a,1),13440(a,1,1))].">
      <j1 rule="para" parents="14025 13440"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,14026,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 14026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4665,a(flip),b,14028,a)].">
      <j1 rule="hyper" parents="60 4665 14028"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(7(a,1),14029(a,1,2,1,2))].">
      <j1 rule="para" parents="7 14029"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11315,a,b,14030,a)].">
      <j1 rule="hyper" parents="60 11315 14030"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,14031,a)].">
      <j1 rule="hyper" parents="370 5256 14031"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,14032,a)].">
      <j1 rule="hyper" parents="31 5256 14032"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(11244,a,14033,a)].">
      <j1 rule="hyper" parents="11244 14033"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x))
    ]]></literal>
    <justification jstring="[para(14033(a,1),8822(a,1,1,2))].">
      <j1 rule="para" parents="14033 8822"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(14034(a,1),9753(a,1,1))].">
      <j1 rule="para" parents="14034 9753"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14009(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="14009 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(8973,a,14035,a),flip(a)].">
      <j1 rule="hyper" parents="8973 14035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10712,a(flip),b,14038,a)].">
      <j1 rule="hyper" parents="60 10712 14038"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(11881,a,14039,a)].">
      <j1 rule="hyper" parents="11881 14039"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(x,y,z),x * (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(14036(a,1),9941(a,1))].">
      <j1 rule="para" parents="14036 9941"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14034,a(flip),b,14027,a),flip(a)].">
      <j1 rule="hyper" parents="370 14034 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,2),14042(a,2,2,2))].">
      <j1 rule="para" parents="15 14042"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13962,a,14044,a)].">
      <j1 rule="hyper" parents="13962 14044"/>
    </justification>
  </clause>

  <clause id="14046">
    <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(13913(a,1),13928(a,2,1))].">
      <j1 rule="para" parents="13913 13928"/>
    </justification>
  </clause>

  <clause id="14047">
    <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(370,a,13927,a(flip),b,14046,a),flip(a)].">
      <j1 rule="hyper" parents="370 13927 14046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14048">
    <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(15(a,2),14047(a,2,2))].">
      <j1 rule="para" parents="15 14047"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(13917(a,1),14048(a,1,2))].">
      <j1 rule="para" parents="13917 14048"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14049(a,2),13913(a,1,1))].">
      <j1 rule="para" parents="14049 13913"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(11680(a,1),14050(a,1,1,1))].">
      <j1 rule="para" parents="11680 14050"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11810,a(flip),b,14051,a),flip(a)].">
      <j1 rule="hyper" parents="60 11810 14051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(12045,a,14052,a)].">
      <j1 rule="hyper" parents="12045 14052"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,11474,a,b,14052,a)].">
      <j1 rule="hyper" parents="32 11474 14052"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(14054(a,1),11494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14054 11494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      (R(x,y,z) * R(u,x,u)) \ ((u * R(x,y,z)) * u) = T(u,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(14053(a,2),5808(a,1,1))].">
      <j1 rule="para" parents="14053 5808"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11494,a(flip),b,14055,a),flip(a)].">
      <j1 rule="hyper" parents="370 11494 14055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,R(y,z,u))) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12053,a(flip),b,14056,a)].">
      <j1 rule="hyper" parents="60 12053 14056"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(13913(a,1),13921(a,1,2,1))].">
      <j1 rule="para" parents="13913 13921"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5364(a,1),13950(a,2,2))].">
      <j1 rule="para" parents="5364 13950"/>
    </justification>
  </clause>

  <clause id="14061">
    <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(11482,a,14060,a)].">
      <j1 rule="hyper" parents="11482 14060"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(13913(a,1),14059(a,1,2))].">
      <j1 rule="para" parents="13913 14059"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1201,a,14062,a)].">
      <j1 rule="hyper" parents="1201 14062"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(13926,a,14063,a),flip(a)].">
      <j1 rule="hyper" parents="13926 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(14063(a,1),13925(a,1)),flip(b)].">
      <j1 rule="para" parents="14063 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),14064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(11451(a,1),14064(a,1,1))].">
      <j1 rule="para" parents="11451 14064"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11438(a,1),14064(a,1,1))].">
      <j1 rule="para" parents="11438 14064"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(11680(a,1),14064(a,1,1))].">
      <j1 rule="para" parents="11680 14064"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      a(L(x,y,x) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(11703(a,1),14064(a,1,1))].">
      <j1 rule="para" parents="11703 14064"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      a(L(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(11716(a,1),14064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11716 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(12440(a,1),14068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12440 14068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      a(L(L(x,y,x),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(13888(a,1),14073(a,1,1))].">
      <j1 rule="para" parents="13888 14073"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11437(a,1),14067(a,1,1))].">
      <j1 rule="para" parents="11437 14067"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(11476(a,1),14067(a,1,1))].">
      <j1 rule="para" parents="11476 14067"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5675(a,1),14075(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5675 14075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      a(L((x \ L(y,z,y)) \ u,x \ L(y,z,y),x),w,v5) = a(y \ (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(656(a,2),14071(a,1,1))].">
      <j1 rule="para" parents="656 14071"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(11680(a,1),14065(a,1,1))].">
      <j1 rule="para" parents="11680 14065"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14069,a(flip),b,14077,a),flip(a)].">
      <j1 rule="hyper" parents="370 14069 14077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7344(a,1),14081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7344 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14076,a,b,14082,a)].">
      <j1 rule="hyper" parents="60 14076 14082"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4905(a,1),14083(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4905 14083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14085">
    <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(12671(a,2),14083(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12671 14083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13828,a,b,14084,a)].">
      <j1 rule="hyper" parents="60 13828 14084"/>
    </justification>
  </clause>

  <clause id="14087">
    <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(13965(a,1),14084(a,2,1))].">
      <j1 rule="para" parents="13965 14084"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      a(L(L(x \ y,z,x \ y),x,x),u,w) = a((1 / x) * y,u,w)
    ]]></literal>
    <justification jstring="[para(586(a,1),14074(a,2,1))].">
      <j1 rule="para" parents="586 14074"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      a(K(R(x,y,z),u),w,v5) = a(K(x,R(u,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,14084,a(flip),b,14087,a)].">
      <j1 rule="hyper" parents="60 14084 14087"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      a(L((1 / x) * y,z,x \ y),u,w) = a((1 / x) * y,u,w)
    ]]></literal>
    <justification jstring="[para(593(a,1),14088(a,1,1))].">
      <j1 rule="para" parents="593 14088"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      a(L(x * y,z,x \ y),u,w) = a((1 / x) * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3975,a(flip),b,14090,a)].">
      <j1 rule="hyper" parents="60 3975 14090"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      a(L(x * y,z,x \ y),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2958,a(flip),b,14091,a),flip(a)].">
      <j1 rule="hyper" parents="370 2958 14091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14093">
    <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(10665(a,1),14085(a,2,1))].">
      <j1 rule="para" parents="10665 14085"/>
    </justification>
  </clause>

  <clause id="14094">
    <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(370,a,14083,a(flip),b,14093,a),flip(a)].">
      <j1 rule="hyper" parents="370 14083 14093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14095">
    <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(12671(a,1),14094(a,1,1))].">
      <j1 rule="para" parents="12671 14094"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,14089,a(flip),b,14095,a),flip(a)].">
      <j1 rule="hyper" parents="370 14089 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      K(x,(1 / (y \ T(L(L(x,z,u),w,v5),v6))) \ K(v6,L(L(x,z,u),w,v5))) = K(x,y \ L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,8131,a(flip),b,13995,a),flip(a)].">
      <j1 rule="hyper" parents="370 8131 13995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      K(x,(1 / (y \ L(T(L(x,z,u),w),v5,v6))) \ K(w,L(L(x,z,u),v5,v6))) = K(x,y \ L(L(x,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(20(a,2),14097(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20 14097"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(20(a,2),14098(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="20 14098"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      K(x,(1 / (y \ L(L(T(x,z),u,w),v5,v6))) \ 1) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,12213,a(flip),b,14099,a)].">
      <j1 rule="hyper" parents="60 12213 14099"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      K(x,y \ L(L(T(x,z),u,w),v5,v6)) = K(x,y \ L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(77(a,1),14100(a,1,2))].">
      <j1 rule="para" parents="77 14100"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) = K(x,z \ L(L(x,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,13635,a,b,14102,a)].">
      <j1 rule="hyper" parents="60 13635 14102"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,13420,a(flip),b,14103,a),flip(a)].">
      <j1 rule="hyper" parents="60 13420 14103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      K(x,(y \ 1) \ L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(14106(a,1),12876(a,1,1))].">
      <j1 rule="para" parents="14106 12876"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,1 \ (y * L(x,z,u))) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12247(a,1),14108(a,1,1))].">
      <j1 rule="para" parents="12247 14108"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (y \ (T(y,x) * L(x,z,u))) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(62(a,1),14109(a,1,1,2))].">
      <j1 rule="para" parents="62 14109"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) * (K(y,x) * L(x,z,u)) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7857(a,1),14111(a,1,2))].">
      <j1 rule="para" parents="7857 14111"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      ((x \ T(x * (y / (z * y)),y / (z * y))) * (z * y)) / y = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,9543,a(flip),b,6143,a),flip(a)].">
      <j1 rule="hyper" parents="60 9543 6143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      K((((x \ 1) * (y * z)) / z) \ 1,z / (y * z)) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6961,a(flip),b,14113,a)].">
      <j1 rule="hyper" parents="60 6961 14113"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),((z * y) / y) \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,10216,a(flip),b,14115,a)].">
      <j1 rule="hyper" parents="60 10216 14115"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),14116(a,1,2,1))].">
      <j1 rule="para" parents="6 14116"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,11220,a(flip),b,14117,a)].">
      <j1 rule="hyper" parents="60 11220 14117"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,11199,a(flip),b,14118,a),flip(a)].">
      <j1 rule="hyper" parents="370 11199 14118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,11965,a(flip),b,14119,a)].">
      <j1 rule="hyper" parents="60 11965 14119"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(9259,a,14120,a),flip(a)].">
      <j1 rule="hyper" parents="9259 14120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,6646,a(flip),b,14121,a),flip(a)].">
      <j1 rule="hyper" parents="370 6646 14121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,13779,a,b,14123,a)].">
      <j1 rule="hyper" parents="60 13779 14123"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(14124(a,1),7215(a,1,1,1))].">
      <j1 rule="para" parents="14124 7215"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6947,a(flip),b,14126,a),flip(a)].">
      <j1 rule="hyper" parents="60 6947 14126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),14127(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 14127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14130">
    <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(14129(a,1),11714(a,2,2))].">
      <j1 rule="para" parents="14129 11714"/>
    </justification>
  </clause>

  <clause id="14131">
    <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(370,a,1744,a(flip),b,14130,a),flip(a)].">
      <j1 rule="hyper" parents="370 1744 14130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(370,a,2526,a(flip),b,14131,a),flip(a)].">
      <j1 rule="hyper" parents="370 2526 14131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(7648(a,1),14132(a,2,1,2))].">
      <j1 rule="para" parents="7648 14132"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12043,a(flip),b,14133,a),flip(a)].">
      <j1 rule="hyper" parents="370 12043 14133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(3093(a,1),14134(a,1,1))].">
      <j1 rule="para" parents="3093 14134"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12071,a(flip),b,14135,a)].">
      <j1 rule="hyper" parents="60 12071 14135"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13325,a,b,14136,a)].">
      <j1 rule="hyper" parents="60 13325 14136"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (((x \ 1) \ 1) * (((L(x,y,z) \ 1) \ 1) \ u)) = L(L(1 / x,y,z) \ u,(x \ 1) \ 1,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1307(a,1),12747(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 12747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (((x \ 1) \ 1) * (((L(x,y,z) \ 1) \ 1) \ u)) = L(L(1 / x,y,z) \ u,(x \ 1) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,10149,a(flip),b,14138,a),flip(a)].">
      <j1 rule="hyper" parents="370 10149 14138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (((x \ 1) \ 1) * (((L(x,y,z) \ 1) \ 1) \ u)) = L(L(1 / x,y,z) \ u,x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3406,a(flip),b,14139,a),flip(a)].">
      <j1 rule="hyper" parents="370 3406 14139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (((x \ 1) \ 1) * (L((x \ 1) \ 1,y,z) \ u)) = L(L(1 / x,y,z) \ u,x,x)
    ]]></literal>
    <justification jstring="[para(5066(a,2),14140(a,1,2,2,1))].">
      <j1 rule="para" parents="5066 14140"/>
    </justification>
  </clause>

  <clause id="14142">
    <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(5393(a,1),13476(a,1,1))].">
      <j1 rule="para" parents="5393 13476"/>
    </justification>
  </clause>

  <clause id="14143">
    <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(5393(a,1),14142(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5393 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14144">
    <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(5865(a,1),14143(a,2,2,1))].">
      <j1 rule="para" parents="5865 14143"/>
    </justification>
  </clause>

  <clause id="14145">
    <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(10615(a,1),14144(a,2,2))].">
      <j1 rule="para" parents="10615 14144"/>
    </justification>
  </clause>

  <clause id="14146">
    <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(5251(a,1),14145(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5251 14145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14147">
    <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(10615(a,1),14146(a,2,1,2))].">
      <j1 rule="para" parents="10615 14146"/>
    </justification>
  </clause>

  <clause id="14148">
    <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(60,a,13828,a(flip),b,14147,a),flip(a)].">
      <j1 rule="hyper" parents="60 13828 14147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14149">
    <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(370,a,14087,a(flip),b,14148,a),flip(a)].">
      <j1 rule="hyper" parents="370 14087 14148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(14086(a,1),14149(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14086 14149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14151">
    <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(8215(a,1),13520(a,1,1))].">
      <j1 rule="para" parents="8215 13520"/>
    </justification>
  </clause>

  <clause id="14152">
    <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(5(a,1),14151(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5 14151"/>
    </justification>
  </clause>

  <clause id="14154">
    <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(9664(a,1),14152(a,1,2))].">
      <j1 rule="para" parents="9664 14152"/>
    </justification>
  </clause>

  <clause id="14155">
    <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(14040(a,1),14154(a,1,2))].">
      <j1 rule="para" parents="14040 14154"/>
    </justification>
  </clause>

  <clause id="14156">
    <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(8311(a,1),14155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8311 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14157">
    <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(14156(a,2),8526(a,1))].">
      <j1 rule="para" parents="14156 8526"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ (x / x) = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4565(a,1,2,1))].">
      <j1 rule="para" parents="7 4565"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ 1 = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(71(a,1),14158(a,1,2))].">
      <j1 rule="para" parents="71 14158"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(397,a,14159,a),flip(a)].">
      <j1 rule="hyper" parents="397 14159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(7794(a,1),14161(a,1,1))].">
      <j1 rule="para" parents="7794 14161"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7785,a(flip),b,14164,a),flip(a)].">
      <j1 rule="hyper" parents="60 7785 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,4082,a(flip),b,14165,a),flip(a)].">
      <j1 rule="hyper" parents="370 4082 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,4083,a(flip),b,14166,a),flip(a)].">
      <j1 rule="hyper" parents="370 4083 14166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14166(a,2),7786(a,1,1))].">
      <j1 rule="para" parents="14166 7786"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1769(a,1),14167(a,1,2))].">
      <j1 rule="para" parents="1769 14167"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,14169,a)].">
      <j1 rule="hyper" parents="215 14169"/>
    </justification>
  </clause>

  <clause id="14171">
    <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(14169(a,1),552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14169 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) \ x) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(14169(a,1),4145(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14169 4145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14169(a,1),5248(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14169 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u)) = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(14169(a,1),9923(a,1,2,2,1))].">
      <j1 rule="para" parents="14169 9923"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(1362(a,1),14170(a,1,1))].">
      <j1 rule="para" parents="1362 14170"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ L(L(x,y,z) \ x,u,w) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(14170(a,1),3907(a,1,1,1))].">
      <j1 rule="para" parents="14170 3907"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,z)) = a(z,z,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,3823,a(flip),b,14176,a)].">
      <j1 rule="hyper" parents="370 3823 14176"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      (x \ (x \ y)) \ L(x \ (x \ y),x,x) = (y \ (x \ ((1 / x) \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(2117(a,1),14176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2117 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * y = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(14176(a,2),3838(a,1,1))].">
      <j1 rule="para" parents="14176 3838"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ 1 = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14176(a,2),10449(a,1,1,1))].">
      <j1 rule="para" parents="14176 10449"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      L(x,a(y,y,z) * z,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(14180(a,1),3464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14180 3464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      L(x,a(y,y,(y \ 1) * z) * ((y \ 1) * z),u) = L(x,(1 / y) * L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(2086(a,1),14182(a,2,2))].">
      <j1 rule="para" parents="2086 14182"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,13579,a,b,14181,a),flip(a)].">
      <j1 rule="hyper" parents="36 13579 14181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = L(K(x,x \ 1) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(13879(a,1),14181(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13879 14181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <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(14184(a,2),45(a,1))].">
      <j1 rule="para" parents="14184 45"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = L(K(x \ 1,x) * 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(3617(a,1),14185(a,2,1,1))].">
      <j1 rule="para" parents="3617 14185"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = L(K(x,x \ 1) * 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(1716(a,1),14187(a,2,1,1,1))].">
      <j1 rule="para" parents="1716 14187"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = L(K(x,x \ 1),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(3(a,1),14188(a,2,1,1))].">
      <j1 rule="para" parents="3 14188"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x,x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4585(a,1),14189(a,2,1))].">
      <j1 rule="para" parents="4585 14189"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x \ 1,x) * 1
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,14190,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x,x \ 1) * 1
    ]]></literal>
    <justification jstring="[para(1716(a,1),14191(a,2,1))].">
      <j1 rule="para" parents="1716 14191"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,14193,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 14193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14195">
    <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(370,a,8648,a,b,14173,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 14173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(14168(a,1),13305(a,1,2))].">
      <j1 rule="para" parents="14168 13305"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,6909,a(flip),b,14197,a)].">
      <j1 rule="hyper" parents="60 6909 14197"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,9869,a(flip),b,14198,a),flip(a)].">
      <j1 rule="hyper" parents="370 9869 14198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(215,a,14199,a)].">
      <j1 rule="hyper" parents="215 14199"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,7806,a(flip),b,14199,a),flip(a)].">
      <j1 rule="hyper" parents="60 7806 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(14200(a,1),4947(a,1,2,1))].">
      <j1 rule="para" parents="14200 4947"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9869,a(flip),b,14202,a),flip(a)].">
      <j1 rule="hyper" parents="370 9869 14202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(14201(a,1),14203(a,1,1))].">
      <j1 rule="para" parents="14201 14203"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10180,a,b,14204,a)].">
      <j1 rule="hyper" parents="60 10180 14204"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6433(a,1),14205(a,1,1))].">
      <j1 rule="para" parents="6433 14205"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,6136,a(flip),b,14206,a),flip(a)].">
      <j1 rule="hyper" parents="60 6136 14206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,9876,a(flip),b,14207,a)].">
      <j1 rule="hyper" parents="60 9876 14207"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,14208,a)].">
      <j1 rule="hyper" parents="215 14208"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(14209(a,1),4338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14209 4338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(14210(a,2),11171(a,1,2,1))].">
      <j1 rule="para" parents="14210 11171"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = (y \ (y \ x)) \ ((y * y) \ x)
    ]]></literal>
    <justification jstring="[para(344(a,1),14179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="344 14179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = ((y \ 1) \ (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,973,a(flip),b,14212,a),flip(a)].">
      <j1 rule="hyper" parents="370 973 14212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = (y \ ((1 / y) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(2104(a,1),14213(a,2,1))].">
      <j1 rule="para" parents="2104 14213"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) \ 1 = (x \ ((1 / x) \ y)) \ y
    ]]></literal>
    <justification jstring="[para(2117(a,2),14214(a,1,1))].">
      <j1 rule="para" parents="2117 14214"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) / L(y \ L(y,z,u),(L(y,z,u) \ y) * (L(y,z,u) \ y),x) = x * ((L(y,z,u) \ y) / (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(14172(a,1),12452(a,1,2,2))].">
      <j1 rule="para" parents="14172 12452"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(11146,a,14211,a)].">
      <j1 rule="hyper" parents="11146 14211"/>
    </justification>
  </clause>

  <clause id="14218">
    <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(13789(a,1),14195(a,1,2))].">
      <j1 rule="para" parents="13789 14195"/>
    </justification>
  </clause>

  <clause id="14219">
    <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(60,a,14195,a(flip),b,14218,a),flip(a)].">
      <j1 rule="hyper" parents="60 14195 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(u,K(w,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8636,a,b,14219,a),flip(a)].">
      <j1 rule="hyper" parents="370 8636 14219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <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(60,a,13773,a(flip),b,14220,a)].">
      <j1 rule="hyper" parents="60 13773 14220"/>
    </justification>
  </clause>

  <clause id="14222">
    <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(370,a,8630,a,b,14221,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 14221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14223">
    <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(13774,a,14222,a)].">
      <j1 rule="hyper" parents="13774 14222"/>
    </justification>
  </clause>

  <clause id="14224">
    <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(60,a,13775,a,b,14223,a)].">
      <j1 rule="hyper" parents="60 13775 14223"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ u) = ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(9916(a,2),14171(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9916 14171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14226">
    <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(370,a,13446,a(flip),b,14224,a),flip(a)].">
      <j1 rule="hyper" parents="370 13446 14224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14227">
    <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(8889,a,14226,a)].">
      <j1 rule="hyper" parents="8889 14226"/>
    </justification>
  </clause>

  <clause id="14228">
    <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(14226(a,1),8889(a,1))].">
      <j1 rule="para" parents="14226 8889"/>
    </justification>
  </clause>

  <clause id="14229">
    <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(60,a,8806,a,b,14227,a)].">
      <j1 rule="hyper" parents="60 8806 14227"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) / (y \ L(y,z,u)) = x * ((L(y,z,u) \ y) / (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(614(a,1),14216(a,1,2))].">
      <j1 rule="para" parents="614 14216"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x * K(y,z * x)))
    ]]></literal>
    <justification jstring="[para(8019(a,2),10058(a,2,2))].">
      <j1 rule="para" parents="8019 10058"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(u,w) \ ((u \ 1) \ K(v5,u))) = K((x * (K(y,x) / T(x,z))) \ 1,u * (K(v5,u) / T(u,w)))
    ]]></literal>
    <justification jstring="[para(10898(a,1),10482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10898 10482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ ((K(y,x) / T(x,z)) \ 1),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7676,a(flip),b,14233,a),flip(a)].">
      <j1 rule="hyper" parents="370 7676 14233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(x \ (K(x,z) * T(x,y)),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(9660(a,1),14234(a,2,1,2))].">
      <j1 rule="para" parents="9660 14234"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(T(K(x,z),x) * K(x,y),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(8415(a,1),14235(a,2,1))].">
      <j1 rule="para" parents="8415 14235"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),(K(y,x) / T(x,z)) * x)
    ]]></literal>
    <justification jstring="[para(4907(a,1),14236(a,2,1,1))].">
      <j1 rule="para" parents="4907 14236"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = K(K(x,z) * K(x,y),K(y,x) * K(z,x))
    ]]></literal>
    <justification jstring="[para(5850(a,1),14237(a,2,2))].">
      <j1 rule="para" parents="5850 14237"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) / K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9272(a,1),14232(a,2,2))].">
      <j1 rule="para" parents="9272 14232"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = (K(y,z * x) * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8088,a(flip),b,14239,a),flip(a)].">
      <j1 rule="hyper" parents="370 8088 14239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (x * K(z,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,11089,a(flip),b,14240,a),flip(a)].">
      <j1 rule="hyper" parents="370 11089 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      (x * K(y,z * x)) / T(T(K(y,z),x * K(y,z * x)),x * K(y,z * x)) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8045,a(flip),b,14242,a),flip(a)].">
      <j1 rule="hyper" parents="370 8045 14242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(8750(a,1),14243(a,1,2))].">
      <j1 rule="para" parents="8750 14243"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(6304,a,14244,a)].">
      <j1 rule="hyper" parents="6304 14244"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      K(x,y * z) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z * (K(x,y * z) * K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(14245(a,1),11397(a,1))].">
      <j1 rule="para" parents="14245 11397"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      L(x,y,z) * (K(x,u * L(x,y,z)) * K(u,x)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(14247,a,14112,a)].">
      <j1 rule="hyper" parents="14247 14112"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * K(x,u * L(x,y,z))) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(2894(a,1),14248(a,1,2))].">
      <j1 rule="para" parents="2894 14248"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      L(x,y,z) * (a(x,u,L(x,y,z)) \ 1) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(13895(a,1),14249(a,1,2))].">
      <j1 rule="para" parents="13895 14249"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,x),y,z) = a(x,u,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,14250,a)].">
      <j1 rule="hyper" parents="135 14250"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      x * a(L(y,z,u),w,L(y,z,u)) = (a(y,w,L(y,z,u)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(14251(a,1),13894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14251 13894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,14252,a,b,13579,a(flip))].">
      <j1 rule="hyper" parents="123 14252 13579"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13878,a(flip),b,14253,a),flip(a)].">
      <j1 rule="hyper" parents="370 13878 14253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13067,a(flip),b,14255,a)].">
      <j1 rule="hyper" parents="60 13067 14255"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13911,a,b,14257,a)].">
      <j1 rule="hyper" parents="60 13911 14257"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      a(x,y,a(z,u,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,14257,a)].">
      <j1 rule="hyper" parents="50 14257"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,14257,a(flip),b,9147,a)].">
      <j1 rule="hyper" parents="129 14257 9147"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(14257(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="14257 617"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) / a(y,z,y) = x * u
    ]]></literal>
    <justification jstring="[para(14257(a,1),11700(a,1,2))].">
      <j1 rule="para" parents="14257 11700"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(14257(a,1),14061(a,1,1))].">
      <j1 rule="para" parents="14257 14061"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      x * a(y,z,a(u,w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,14261,a,b,63,a)].">
      <j1 rule="hyper" parents="129 14261 63"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7178,a,14268,a)].">
      <j1 rule="hyper" parents="7178 14268"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(12160,a,14269,a)].">
      <j1 rule="hyper" parents="12160 14269"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(14269(a,1),48(a,2))].">
      <j1 rule="para" parents="14269 48"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(u,w,u)) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(14269(a,1),726(a,1,1))].">
      <j1 rule="para" parents="14269 726"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7942,a,14260,a)].">
      <j1 rule="hyper" parents="7942 14260"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(5279(a,1),14260(a,1,2))].">
      <j1 rule="para" parents="5279 14260"/>
    </justification>
  </clause>

  <clause id="14279">
    <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(370,a,13313,a,b,14275,a),flip(a)].">
      <j1 rule="hyper" parents="370 13313 14275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      a(x,R(y / z,u,w),x) = a(x,R(z \ y,u,w),x)
    ]]></literal>
    <justification jstring="[para(286(a,1),14275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="286 14275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      a(x,R(y / z,z,u),x) = a(x,(z * u) \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(711(a,1),14275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="711 14275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,y / z) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(11455,a,14277,a)].">
      <j1 rule="hyper" parents="11455 14277"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(11692,a,14262,a)].">
      <j1 rule="hyper" parents="11692 14262"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(14262(a,1),685(a,1,1))].">
      <j1 rule="para" parents="14262 685"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      x * (y * (z * a(x,x,x))) = L(x,x,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(14262(a,1),4461(a,1,2))].">
      <j1 rule="para" parents="14262 4461"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      a(x * (y * a(z,u,z)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(14262(a,1),14070(a,1,1))].">
      <j1 rule="para" parents="14262 14070"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      (x \ (y \ z)) * a(y,u,y) = x \ (L(y,u,y) \ z)
    ]]></literal>
    <justification jstring="[para(11565(a,1),14264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11565 14264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11680(a,2),14264(a,1,2))].">
      <j1 rule="para" parents="11680 14264"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) = x \ u
    ]]></literal>
    <justification jstring="[para(11687(a,1),14264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11687 14264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(11711,a,14266,a)].">
      <j1 rule="hyper" parents="11711 14266"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      a(x,y,x) \ (z * (a(x,y,x) * u)) = z * u
    ]]></literal>
    <justification jstring="[hyper(11690,a,14266,a)].">
      <j1 rule="hyper" parents="11690 14266"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      (x / (y * a(z,u,z))) * y = a(z,u,z) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,7,a(flip),b,14284,a),flip(a)].">
      <j1 rule="hyper" parents="125 7 14284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(11687(a,1),14284(a,2,2))].">
      <j1 rule="para" parents="11687 14284"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = a(y,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,11680,a,b,14289,a),flip(a)].">
      <j1 rule="hyper" parents="370 11680 14289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(11699,a,14290,a)].">
      <j1 rule="hyper" parents="11699 14290"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(13914,a,14291,a)].">
      <j1 rule="hyper" parents="13914 14291"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      a(x,y,x) * (z \ 1) = z \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(483,a,14291,a),flip(a)].">
      <j1 rule="hyper" parents="483 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,14291,a)].">
      <j1 rule="hyper" parents="125 172 14291"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      x * (a(y,z,y) \ (x \ u)) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(125,a,70,a(flip),b,14291,a),flip(a)].">
      <j1 rule="hyper" parents="125 70 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13924,a,b,14291,a)].">
      <j1 rule="hyper" parents="60 13924 14291"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) * w = a(y,z,y) * ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(14291(a,1),13913(a,1,1))].">
      <j1 rule="para" parents="14291 13913"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(14291(a,1),13919(a,1,1))].">
      <j1 rule="para" parents="14291 13919"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,u) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(14291(a,1),14000(a,1,3))].">
      <j1 rule="para" parents="14291 14000"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      a(x * (a(y,z,y) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(14291(a,1),14064(a,1,1))].">
      <j1 rule="para" parents="14291 14064"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      a(x,y,x) \ (z \ a(x,y,x)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(135,a,14299,a)].">
      <j1 rule="hyper" parents="135 14299"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      x / (y * a(x,z,x)) = L(x,z,x) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,11507,a(flip),b,14294,a),flip(a)].">
      <j1 rule="hyper" parents="128 11507 14294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(13923,a,14295,a),flip(a)].">
      <j1 rule="hyper" parents="13923 14295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      a(x * (a(y,z,y) \ u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(14295(a,1),14064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14295 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      a(x,y,x) * (z \ x) = z \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(11451(a,1),14296(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11451 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(11507(a,1),14297(a,2,2))].">
      <j1 rule="para" parents="11507 14297"/>
    </justification>
  </clause>

  <clause id="14315">
    <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(12192,a,14300,a),flip(a)].">
      <j1 rule="hyper" parents="12192 14300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      (x / y) / a(z,u,z) = x / (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(808,a,14302,a),flip(a)].">
      <j1 rule="hyper" parents="808 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      (x / y) * (a(y,z,y) * u) = (x / L(y,z,y)) * u
    ]]></literal>
    <justification jstring="[para(11563(a,1),14302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11563 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      a(x,((a(y,z,y) \ u) \ 1) * w,v5) = a(x,u * (a(y,z,y) \ w),v5)
    ]]></literal>
    <justification jstring="[para(14311(a,1),3061(a,2,2))].">
      <j1 rule="para" parents="14311 3061"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      a(x,y,(((a(z,u,z) \ w) \ 1) * v5) * v6) = a(x,y,(w * (a(z,u,z) \ v5)) * v6)
    ]]></literal>
    <justification jstring="[para(14311(a,1),3138(a,2,3,1))].">
      <j1 rule="para" parents="14311 3138"/>
    </justification>
  </clause>

  <clause id="14322">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * w = (x \ u) * (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(14297(a,1),14311(a,1,1))].">
      <j1 rule="para" parents="14297 14311"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) * w = (x * u) * (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(14300(a,1),14311(a,1,1))].">
      <j1 rule="para" parents="14300 14311"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      x / (a(y,z,y) * u) = a(y,z,y) \ (x / u)
    ]]></literal>
    <justification jstring="[hyper(11690,a,14317,a),flip(a)].">
      <j1 rule="hyper" parents="11690 14317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(11451(a,1),14324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11451 14324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[para(11680(a,1),14324(a,1,2))].">
      <j1 rule="para" parents="11680 14324"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,14310,a(flip),b,14326,a),flip(a)].">
      <j1 rule="hyper" parents="60 14310 14326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      R(x,y,x) \ (x / z) = x \ (L(x,y,x) / z)
    ]]></literal>
    <justification jstring="[para(14327(a,1),12031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14327 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(13926,a,14270,a),flip(a)].">
      <j1 rule="hyper" parents="13926 14270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(14270(a,1),13925(a,1)),flip(b)].">
      <j1 rule="para" parents="14270 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,14329,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 14329 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      T(x,(y * z) * y) = T(x,y * (z * y))
    ]]></literal>
    <justification jstring="[para(82(a,1),14329(a,1,2))].">
      <j1 rule="para" parents="82 14329"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(11477(a,1),14329(a,1,2))].">
      <j1 rule="para" parents="11477 14329"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(11572(a,1),14329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11572 14329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(11680(a,2),14329(a,1,2))].">
      <j1 rule="para" parents="11680 14329"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      T(x,R(y,z,y) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(12059(a,1),14329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12059 14329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(14262(a,1),14329(a,1,2))].">
      <j1 rule="para" parents="14262 14329"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      T(x,y \ (z * a(u,w,u))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(14264(a,2),14329(a,1,2))].">
      <j1 rule="para" parents="14264 14329"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = u / T(u,z)
    ]]></literal>
    <justification jstring="[para(14336(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="14336 5701"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      T(x,(y \ R(y,z,y)) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(11439(a,1),14336(a,1,2,1))].">
      <j1 rule="para" parents="11439 14336"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(11500(a,1),14336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11500 14336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(14313(a,1),14336(a,1,2))].">
      <j1 rule="para" parents="14313 14336"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      K(T(x,y) / y,z) = z / T(z,y \ x)
    ]]></literal>
    <justification jstring="[para(14334(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="14334 5701"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(5747(a,1),14334(a,1,2))].">
      <j1 rule="para" parents="5747 14334"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      T(x,y / (y \ z)) = T(x,(z / y) \ y)
    ]]></literal>
    <justification jstring="[para(5790(a,1),14334(a,1,2))].">
      <j1 rule="para" parents="5790 14334"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      T(x,T(y,z \ u) / ((u \ z) \ 1)) = T(x,((u \ z) \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(6446(a,1),14334(a,1,2,1))].">
      <j1 rule="para" parents="6446 14334"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      K(x,T(T(y,z) / z,u)) = (u * T(x,z \ y)) / (u * x)
    ]]></literal>
    <justification jstring="[para(14334(a,1),8981(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14334 8981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,14332,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 14332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(14332(a,2),5290(a,1))].">
      <j1 rule="para" parents="14332 5290"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      K(x,y * (z \ R(z,u,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11439(a,1),14350(a,1,2,2))].">
      <j1 rule="para" parents="11439 14350"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(11477(a,1),14350(a,1,2))].">
      <j1 rule="para" parents="11477 14350"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11680(a,2),14350(a,1,2))].">
      <j1 rule="para" parents="11680 14350"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12042(a,1),14350(a,1,2))].">
      <j1 rule="para" parents="12042 14350"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(12048(a,1),14350(a,1,2))].">
      <j1 rule="para" parents="12048 14350"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(12059(a,1),14350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12059 14350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(14289(a,2),14350(a,1,2))].">
      <j1 rule="para" parents="14289 14350"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      a((a(x,x,x) * y) * K(x \ 1,y),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(14354(a,1),6031(a,1,1,2))].">
      <j1 rule="para" parents="14354 6031"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(11505(a,1),14354(a,1,2))].">
      <j1 rule="para" parents="11505 14354"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(13918(a,1),14354(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13918 14354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(14291(a,1),14354(a,1,2))].">
      <j1 rule="para" parents="14291 14354"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(5747(a,1),14353(a,1,2))].">
      <j1 rule="para" parents="5747 14353"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      K(T(x,y),x \ y) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(14353(a,1),8534(a,1,1))].">
      <j1 rule="para" parents="14353 8534"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(14353(a,1),12595(a,1,1,2))].">
      <j1 rule="para" parents="14353 12595"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      K(x,T(y * z,T(y,u) * (1 / u)) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(12486(a,1),14353(a,2,2))].">
      <j1 rule="para" parents="12486 14353"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      K(x,L(y / T(z,y),u,w)) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(14363(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14363 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      T(x,(y / z) * (z * (z \ y))) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(12501(a,1),14335(a,1,2))].">
      <j1 rule="para" parents="12501 14335"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(13607(a,1),14335(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13607 14335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      T(x,T(y,y * z) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5985(a,1),14337(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5985 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,14340,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      K(K(x,x * y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(11500(a,1),14371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11500 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11680(a,1),14371(a,1,1))].">
      <j1 rule="para" parents="11680 14371"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(11716(a,1),14371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11716 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      K(R(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(12038(a,1),14371(a,1,1))].">
      <j1 rule="para" parents="12038 14371"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      K(x \ R(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(14313(a,1),14371(a,1,1))].">
      <j1 rule="para" parents="14313 14371"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(11477(a,1),14373(a,1,1))].">
      <j1 rule="para" parents="11477 14373"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10214,a(flip),b,14378,a)].">
      <j1 rule="hyper" parents="60 10214 14378"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      K(L(T(x,y),z,u) / y,w) = K(y \ L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(20(a,2),14378(a,1,1,1))].">
      <j1 rule="para" parents="20 14378"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(14378(a,1),10213(a,2,2))].">
      <j1 rule="para" parents="14378 10213"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      K(x / L(T(y,x),z,u),w) = K(L(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),14380(a,1,1,2))].">
      <j1 rule="para" parents="20 14380"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      T(x,y \ R(z \ 1,u,z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(2711(a,1),14344(a,1,2,2))].">
      <j1 rule="para" parents="2711 14344"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7378(a,1),14344(a,1,2,2))].">
      <j1 rule="para" parents="7378 14344"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      K(x,y / (z \ R(z,u,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),14352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 14352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5985(a,1),14355(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5985 14355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7378(a,1),14355(a,1,2,2))].">
      <j1 rule="para" parents="7378 14355"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7378(a,1),14356(a,1,2,1))].">
      <j1 rule="para" parents="7378 14356"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6195(a,1),14357(a,1,2,1))].">
      <j1 rule="para" parents="6195 14357"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7378(a,1),14357(a,1,2,1))].">
      <j1 rule="para" parents="7378 14357"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(14357(a,1),11355(a,1,1))].">
      <j1 rule="para" parents="14357 11355"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w) \ v5) = K(x,L(y,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(12892(a,1),14357(a,1,2,1))].">
      <j1 rule="para" parents="12892 14357"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      K(T(x,x \ y) * z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(6195(a,1),14376(a,1,1,1))].">
      <j1 rule="para" parents="6195 14376"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5985(a,1),14377(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5985 14377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(x \ ((y \ z) \ z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7378(a,1),14377(a,1,1,2))].">
      <j1 rule="para" parents="7378 14377"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11695(a,1),14386(a,1,2))].">
      <j1 rule="para" parents="11695 14386"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(y * (u \ R(u,w,u))) \ z)
    ]]></literal>
    <justification jstring="[para(14399(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="14399 11126"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      T(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(11477(a,1),14330(a,1,2))].">
      <j1 rule="para" parents="11477 14330"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      T(x,L(y,z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(11565(a,1),14330(a,1,2))].">
      <j1 rule="para" parents="11565 14330"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      K(T(x,y) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(14345(a,2),5734(a,1))].">
      <j1 rule="para" parents="14345 5734"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      T(x,(y / z) \ z) = T(x,z * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4664,a(flip),b,14347,a),flip(a)].">
      <j1 rule="hyper" parents="60 4664 14347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      T(x / (x \ y),T(z,(y / x) \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(14347(a,1),5742(a,1,2))].">
      <j1 rule="para" parents="14347 5742"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(11477(a,1),14351(a,1,2))].">
      <j1 rule="para" parents="11477 14351"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      T(x,y * ((z * y) \ y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(6(a,1),14405(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 14405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,T(u,y * (x \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((x / y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(14405(a,1),8906(a,1,2))].">
      <j1 rule="para" parents="14405 8906"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      T(x,y * ((z * u) * z)) = T(x,y * (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(82(a,1),14338(a,1,2,2))].">
      <j1 rule="para" parents="82 14338"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11473(a,1),14338(a,1,2,2))].">
      <j1 rule="para" parents="11473 14338"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(11477(a,1),14338(a,1,2,2))].">
      <j1 rule="para" parents="11477 14338"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,u))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(11572(a,1),14338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11572 14338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      T(x,y \ T(z * u,z)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11473(a,1),14339(a,1,2,2))].">
      <j1 rule="para" parents="11473 14339"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      T(x,y \ (T(z,u) / u)) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(11477(a,1),14339(a,1,2,2))].">
      <j1 rule="para" parents="11477 14339"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      T(x,y \ (R(z,u,z) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(12059(a,1),14339(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12059 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11474(a,1),14358(a,1,2,2))].">
      <j1 rule="para" parents="11474 14358"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(12036(a,1),14358(a,1,2,2))].">
      <j1 rule="para" parents="12036 14358"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11454(a,1),14361(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11454 14361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11437(a,1),14361(a,1,2,1))].">
      <j1 rule="para" parents="11437 14361"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(11704(a,1),14361(a,1,2,1))].">
      <j1 rule="para" parents="11704 14361"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      K(x,(y / R(z,u,z)) * w) = K(x,(y / z) * w)
    ]]></literal>
    <justification jstring="[para(14325(a,1),14361(a,1,2,1))].">
      <j1 rule="para" parents="14325 14361"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11474(a,1),14362(a,1,2,2))].">
      <j1 rule="para" parents="11474 14362"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(11716(a,1),14362(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11716 14362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      K(x,y * (z * R(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(12036(a,1),14362(a,1,2,2))].">
      <j1 rule="para" parents="12036 14362"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5747(a,1),14402(a,1,2))].">
      <j1 rule="para" parents="5747 14402"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      K(x / T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5747(a,1),14404(a,1,1))].">
      <j1 rule="para" parents="5747 14404"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      K(T(x,y / z) / T(z \ y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z \ y,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(8874(a,1),14404(a,1,1,1))].">
      <j1 rule="para" parents="8874 14404"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      T(x,y * T(z,z \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(108(a,2),14369(a,1,2,2))].">
      <j1 rule="para" parents="108 14369"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      T(x,K(y * z,y) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7873(a,2),14370(a,1,2))].">
      <j1 rule="para" parents="7873 14370"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(14382(a,1),12106(a,1,1,2))].">
      <j1 rule="para" parents="14382 12106"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      T(x,y \ T(z \ 1,u * z)) = T(x,y \ T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(6851(a,2),14385(a,1,2,2))].">
      <j1 rule="para" parents="6851 14385"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ ((u * z) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(6536(a,1),14385(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6536 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,14387,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 14387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) * K(x,y / (z * ((u \ w) \ w))) = K(x,(z * ((u \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(14388(a,1),9364(a,1,1,2))].">
      <j1 rule="para" parents="14388 9364"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      K((x * y) / x,T(z,u) * w) = K(y,T(((z \ u) \ u) * w,x))
    ]]></literal>
    <justification jstring="[hyper(8790,a,14390,a),flip(a)].">
      <j1 rule="hyper" parents="8790 14390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,14390,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 14390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(77(a,1),14390(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 14390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14391,a,b,14392,a)].">
      <j1 rule="hyper" parents="370 14391 14392"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a,b,14392,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 14392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(77(a,1),14392(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 14392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      L(K(x,T(y,z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14392(a,1),12953(a,1,1))].">
      <j1 rule="para" parents="14392 12953"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(77(a,1),14398(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1317(a,1),14403(a,1,2,1))].">
      <j1 rule="para" parents="1317 14403"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = x * K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,14412,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 14412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      T(x,y * (z / T(u,z))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(5747(a,1),14412(a,1,2,2))].">
      <j1 rule="para" parents="5747 14412"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      T(x,T(y,z * (u \ w)) * (z * (T(w,u) / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * (T(w,u) / u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(14412(a,1),12606(a,1,2,1))].">
      <j1 rule="para" parents="14412 12606"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),14414(a,1,2,2,1))].">
      <j1 rule="para" parents="107 14414"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      T(x,L(y,z,u) \ T(w * y,w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(2160(a,1),14414(a,2,2))].">
      <j1 rule="para" parents="2160 14414"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(5747(a,1),14415(a,1,2,2))].">
      <j1 rule="para" parents="5747 14415"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),14417(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,14419,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 14419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7864(a,1),14420(a,2,2))].">
      <j1 rule="para" parents="7864 14420"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(8210(a,1),14420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 14420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      T(T(x,y),K(y,(z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,T(u / z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(14442(a,1),8603(a,1,2))].">
      <j1 rule="para" parents="14442 8603"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(14445(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14445 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      T(x,y \ (z / T(T(u,u \ z),z))) = T(x,y \ T(u \ z,u))
    ]]></literal>
    <justification jstring="[para(5794(a,1),14454(a,2,2,2))].">
      <j1 rule="para" parents="5794 14454"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) = K(x,y \ ((z \ 1) \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(2874(a,1),14455(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2874 14455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      a(x * (L(y,z,y) \ u),w,v5) = a(x * (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(11565(a,1),14287(a,1,1,2))].">
      <j1 rule="para" parents="11565 14287"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(14306(a,1),3528(a,1))].">
      <j1 rule="para" parents="14306 3528"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11446(a,1),14464(a,1,3))].">
      <j1 rule="para" parents="11446 14464"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(11473(a,1),14464(a,1,3))].">
      <j1 rule="para" parents="11473 14464"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(6572(a,1),14465(a,1))].">
      <j1 rule="para" parents="6572 14465"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,z)) = u
    ]]></literal>
    <justification jstring="[para(12440(a,1),14465(a,1,3))].">
      <j1 rule="para" parents="12440 14465"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(5978(a,1),14467(a,1,3))].">
      <j1 rule="para" parents="5978 14467"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      T(x,y * (z * L(1 / u,w,v5))) = T(x,y * (z * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(5099(a,1),14413(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5099 14413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      T(x,y \ ((z \ T(u * z,u)) \ w)) = T(x,y \ (u \ w))
    ]]></literal>
    <justification jstring="[para(5536(a,2),14416(a,1,2,2,1))].">
      <j1 rule="para" parents="5536 14416"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      T(x,y \ (T(z,z * u) \ w)) = T(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5985(a,1),14416(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5985 14416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      K(x,y \ (z * T(u,u * w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5985(a,1),14418(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5985 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      K(x,((y * z) * y) * u) = K(x,(y * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(92(a,1),14421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="92 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      K(x,(y * L(1 / z,u,w)) * v5) = K(x,(y * L(z \ 1,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(5099(a,1),14421(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5099 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(6723(a,1),14421(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6723 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(13607(a,1),14421(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13607 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(5545(a,1),14422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5545 14422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      K(x,y * (T(z / u,z) * w)) = K(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5978(a,1),14424(a,1,2,2,1))].">
      <j1 rule="para" parents="5978 14424"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(13607(a,1),14424(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13607 14424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      K(x,y * (z * ((u \ w) \ w))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7378(a,1),14425(a,1,2,2,2))].">
      <j1 rule="para" parents="7378 14425"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(3501(a,1),14448(a,1,2,1))].">
      <j1 rule="para" parents="3501 14448"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      L(x,y,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12479(a,1),14469(a,1))].">
      <j1 rule="para" parents="12479 14469"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(5537(a,1),14478(a,1,2,1))].">
      <j1 rule="para" parents="5537 14478"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      K(x,(y * L(z \ 1,u,z)) * w) = K(x,(y * (1 / z)) * w)
    ]]></literal>
    <justification jstring="[para(6990(a,1),14478(a,1,2,1,2))].">
      <j1 rule="para" parents="6990 14478"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      K(x,(y * z) * z) = K(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(12637,a,14487,a),flip(a)].">
      <j1 rule="hyper" parents="12637 14487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14487(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) * u) = K(x,((y \ z) * (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(1566(a,1),14487(a,1,2,1))].">
      <j1 rule="para" parents="1566 14487"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      K(x,T(y / (y \ z),y) * u) = K(x,((((z \ y) \ 1) \ 1) * y) * u)
    ]]></literal>
    <justification jstring="[para(3510(a,1),14487(a,1,2,1,1))].">
      <j1 rule="para" parents="3510 14487"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      K(x,(y * z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(14487(a,1),12637(a,1))].">
      <j1 rule="para" parents="14487 12637"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * y)) = K(x,z * (y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),14489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      L(x,x,x) * (y * (z * x)) = x * (y * (z * R(x,x,x)))
    ]]></literal>
    <justification jstring="[para(12042(a,1),14286(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12042 14286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      a(x \ (L(y,z,y) \ u),w,v5) = a(x \ (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(14288(a,1),14070(a,1,1))].">
      <j1 rule="para" parents="14288 14070"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      L(x,y,(z / L(u,w,u)) * v5) = L(x,y,(z / u) * v5)
    ]]></literal>
    <justification jstring="[para(14319(a,1),14306(a,1,3))].">
      <j1 rule="para" parents="14319 14306"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      K(x,L(y / T(z,y),u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,14367,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 14367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      T(x,(y / z) * y) = T(x,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14368(a,1,2,2))].">
      <j1 rule="para" parents="5 14368"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      T(x,(T(y,z \ y) / T(z,y)) * (y * (T(y,z) / z))) = T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z))))
    ]]></literal>
    <justification jstring="[para(9240(a,1),14500(a,1,2,1))].">
      <j1 rule="para" parents="9240 14500"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (z \ (w * K(z,u))))) = T(x,y * ((K(z,u) * w) * K(z,u)))
    ]]></literal>
    <justification jstring="[para(7860(a,2),14410(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7860 14410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14437(a,2),5290(a,1))].">
      <j1 rule="para" parents="14437 5290"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(5264,a,14441,a)].">
      <j1 rule="hyper" parents="5264 14441"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14441(a,2),5290(a,1))].">
      <j1 rule="para" parents="14441 5290"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      T(x,T(y / z,y) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(77(a,1),14505(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 14505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      T(x,(y \ z) * z) = T(x,z * (z / y))
    ]]></literal>
    <justification jstring="[hyper(12606,a,14507,a),flip(a)].">
      <j1 rule="hyper" parents="12606 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      T(x,(y \ z) * (K(T(z / y,z),u) * w)) = T(x,T(T(z / y,z),u) * w)
    ]]></literal>
    <justification jstring="[para(7839(a,1),14507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7839 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      ((x \ y) * y) * T(z,y * (y / x)) = z * ((x \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,14508,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 14508 17"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(5289,a,14449,a)].">
      <j1 rule="hyper" parents="5289 14449"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(14449(a,2),5265(a,1))].">
      <j1 rule="para" parents="14449 5265"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      K(x,y * ((z \ u) / z)) = K(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),14513(a,1,2,2,1))].">
      <j1 rule="para" parents="109 14513"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(5747(a,1),14513(a,1,2,2))].">
      <j1 rule="para" parents="5747 14513"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,(z * (w / T(u,w))) / x) = K(y,x \ (z * (w / T(u,w))))
    ]]></literal>
    <justification jstring="[para(14516(a,1),9362(a,1,1,2))].">
      <j1 rule="para" parents="14516 9362"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5264,a,14456,a)].">
      <j1 rule="hyper" parents="5264 14456"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(14456(a,2),5290(a,1))].">
      <j1 rule="para" parents="14456 5290"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14518(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(14518(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="14518 5701"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      K(x,(((y \ z) * y) * (y \ z)) * u) = K(x,((y \ z) * z) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14476(a,2,2,1,2))].">
      <j1 rule="para" parents="5 14476"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      K(x,L(T(y,z) / z,u,w)) = K(x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(5747(a,2),14499(a,1,2,1))].">
      <j1 rule="para" parents="5747 14499"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,14521,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 14521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14524(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(6557(a,2),14524(a,1,1,1))].">
      <j1 rule="para" parents="6557 14524"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(K(y,x) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(12097(a,1),14525(a,1,1))].">
      <j1 rule="para" parents="12097 14525"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      K(K(x,y) * (((x * y) * y) \ z),u) = K((y * (x * y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(12083(a,1),14526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12083 14526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14280,a(flip),b,14281,a)].">
      <j1 rule="hyper" parents="60 14280 14281"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,T(z \ y,y)) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(8767(a,2),14282(a,1,2))].">
      <j1 rule="para" parents="8767 14282"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      a(x,y \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z / y,x) = u
    ]]></literal>
    <justification jstring="[para(14282(a,1),11483(a,1))].">
      <j1 rule="para" parents="14282 11483"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      L(x,y,((z * u) / z) * w) = L(x,y,(z * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(727(a,1),14498(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="727 14498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(108(a,2),14506(a,1,2,1))].">
      <j1 rule="para" parents="108 14506"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      K(x,L((y \ 1) \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(L(y,z,u),1) * w) = v5
    ]]></literal>
    <justification jstring="[para(5066(a,2),14506(a,1,2,1))].">
      <j1 rule="para" parents="5066 14506"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      K(x,K(y * z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(6557(a,2),14519(a,1,2,1))].">
      <j1 rule="para" parents="6557 14519"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14054,a(flip),b,14530,a),flip(a)].">
      <j1 rule="hyper" parents="60 14054 14530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      a(x,y \ z,x) = a(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3066,a(flip),b,14538,a),flip(a)].">
      <j1 rule="hyper" parents="60 3066 14538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),14538(a,1,2,2))].">
      <j1 rule="para" parents="2 14538"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(14538(a,1),11713(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14538 11713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      x \ R(x,y * z,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11441,a,b,14540,a)].">
      <j1 rule="hyper" parents="370 11441 14540"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(14532,a,14541,a)].">
      <j1 rule="hyper" parents="14532 14541"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      R(x,y \ z,x) = R(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,11441,a,b,14543,a)].">
      <j1 rule="hyper" parents="35 11441 14543"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      a(x,y \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,x) = u
    ]]></literal>
    <justification jstring="[para(14543(a,1),11460(a,1))].">
      <j1 rule="para" parents="14543 11460"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      R(x,x * y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5540,a(flip),b,14545,a),flip(a)].">
      <j1 rule="hyper" parents="60 5540 14545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      T(x,y) / R(y,y * x,y) = y \ x
    ]]></literal>
    <justification jstring="[para(14545(a,1),5545(a,1,2))].">
      <j1 rule="para" parents="14545 5545"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      (x / y) / R(x,x * (T(x,y \ x) / y),x) = x \ (T(x,y \ x) / y)
    ]]></literal>
    <justification jstring="[para(5473(a,1),14548(a,1,1))].">
      <j1 rule="para" parents="5473 14548"/>
    </justification>
  </clause>

  <clause id="14550">
    <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(5189(a,1),14544(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5189 14544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (a(y,z,y) * ((x * u) * w)) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(14304(a,1),13920(a,1,2))].">
      <j1 rule="para" parents="14304 13920"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      (x * y) \ (a(z,u,z) \ (x * (a(z,u,z) * (y * w)))) = L(L(w,y,a(z,u,z)),a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(1199,a,14305,a),flip(a)].">
      <j1 rule="hyper" parents="1199 14305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      K(x,T(T(y,z) / z,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8981,a(flip),b,14349,a),flip(a)].">
      <j1 rule="hyper" parents="370 8981 14349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      K(x,T(y / T(z,y),u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(5747(a,1),14553(a,1,2,1))].">
      <j1 rule="para" parents="5747 14553"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(14444(a,2),6305(a,1))].">
      <j1 rule="para" parents="14444 6305"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,14460,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),14557(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 14557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(108(a,2),14558(a,1,1,1))].">
      <j1 rule="para" parents="108 14558"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      K(T(x,y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(14558(a,1),9018(a,1))].">
      <j1 rule="para" parents="14558 9018"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) * a(w,v5,K(T(y,z) \ u,x)) = K(x,L(((y \ z) \ z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(14558(a,1),12932(a,1,2,3))].">
      <j1 rule="para" parents="14558 12932"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      K(x \ T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5749(a,1),14560(a,1,1))].">
      <j1 rule="para" parents="5749 14560"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * ((u * z) * (1 / z))) * w)
    ]]></literal>
    <justification jstring="[para(6536(a,1),14479(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6536 14479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      K(x,y * (T(z,z \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(108(a,2),14482(a,1,2,2,1))].">
      <j1 rule="para" parents="108 14482"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,u))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(77(a,1),14483(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 14483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * ((w * u) * (1 / u))))
    ]]></literal>
    <justification jstring="[para(6536(a,1),14483(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6536 14483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      L(x,x,x) * (y * (z * x)) = x * (y * (z * L(x,x,x)))
    ]]></literal>
    <justification jstring="[para(1342(a,1),14495(a,2,2,2,2))].">
      <j1 rule="para" parents="1342 14495"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,14277,a(flip),b,14267,a),flip(a)].">
      <j1 rule="hyper" parents="370 14277 14267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11363,a,14393,a),flip(a)].">
      <j1 rule="hyper" parents="11363 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(14393(a,1),11363(a,1))].">
      <j1 rule="para" parents="14393 11363"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14570(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(9164,a,14573,a),flip(a)].">
      <j1 rule="hyper" parents="9164 14573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(14573(a,1),9164(a,1))].">
      <j1 rule="para" parents="14573 9164"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(5749(a,1),14574(a,1,2))].">
      <j1 rule="para" parents="5749 14574"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      K(x,T(y * z,y) \ T(u,z * y)) = K(x,u / T(y * z,y))
    ]]></literal>
    <justification jstring="[para(12567(a,1),14576(a,1,2,2))].">
      <j1 rule="para" parents="12567 14576"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(14576(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14576 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) \ z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z / L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),14575(a,1,2,1))].">
      <j1 rule="para" parents="20 14575"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5749(a,1),14575(a,1,2))].">
      <j1 rule="para" parents="5749 14575"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14578(a,2),13033(a,1))].">
      <j1 rule="para" parents="14578 13033"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13033,a,14446,a)].">
      <j1 rule="hyper" parents="13033 14446"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      K(x,(y * L(z \ 1,u,z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * w) = v5
    ]]></literal>
    <justification jstring="[para(14488(a,2),6063(a,1))].">
      <j1 rule="para" parents="14488 6063"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      K(x * (y \ z),T(x,z)) = K(x * (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(32,a,12222,a,b,14531,a)].">
      <j1 rule="hyper" parents="32 12222 14531"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13(a,2),14568(a,2,2))].">
      <j1 rule="para" parents="13 14568"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14257,a(flip),b,14586,a),flip(a)].">
      <j1 rule="hyper" parents="60 14257 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11441,a,b,14587,a),flip(a)].">
      <j1 rule="hyper" parents="370 11441 14587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(344(a,1),14587(a,1,2))].">
      <j1 rule="para" parents="344 14587"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(14587(a,1),11507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14587 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11450,a,14589,a)].">
      <j1 rule="hyper" parents="11450 14589"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      a(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(14589(a,2),11460(a,1))].">
      <j1 rule="para" parents="14589 11460"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      R(x,(y * z) \ u,x) = R(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(344(a,1),14592(a,1,2))].">
      <j1 rule="para" parents="344 14592"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11507,a(flip),b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="370 11507 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      L(x,y \ z,x) = L(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(4130,a,14595,a),flip(a)].">
      <j1 rule="hyper" parents="4130 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(456(a,1),14595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="456 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      L(x,(y \ z) \ u,x) = L(x,z \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(656(a,1),14595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(2660(a,2),14595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2660 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      L(x,y \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,x) = u
    ]]></literal>
    <justification jstring="[para(14595(a,1),4130(a,1))].">
      <j1 rule="para" parents="14595 4130"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      L(x \ y,x * y,x \ y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1328,a,14596,a),flip(a)].">
      <j1 rule="hyper" parents="1328 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5362,a,b,14596,a)].">
      <j1 rule="hyper" parents="60 5362 14596"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      L(x,x * y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9060,a(flip),b,14596,a),flip(a)].">
      <j1 rule="hyper" parents="60 9060 14596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      x / L(y,y * z,y) = x / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[hyper(57,a,14603,a)].">
      <j1 rule="hyper" parents="57 14603"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ u),x) = w
    ]]></literal>
    <justification jstring="[para(344(a,1),14593(a,1,2))].">
      <j1 rule="para" parents="344 14593"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,12180,a,b,14597,a)].">
      <j1 rule="hyper" parents="60 12180 14597"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x)
    ]]></literal>
    <justification jstring="[para(5(a,2),14606(a,1,2))].">
      <j1 rule="para" parents="5 14606"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      T(x,y) != L(z,z * y,z)
    ]]></literal>
    <literal><![CDATA[
      z * K(z \ y,z) = x
    ]]></literal>
    <justification jstring="[para(14602(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="14602 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,(z * y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(14546,a,14590,a),flip(a)].">
      <j1 rule="hyper" parents="14546 14590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      R(x,y \ (z \ u),x) = R(x,(z * y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14545,a(flip),b,14594,a),flip(a)].">
      <j1 rule="hyper" parents="60 14545 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      L(x,(y \ z) \ u,x) = L(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,14596,a(flip),b,14598,a),flip(a)].">
      <j1 rule="hyper" parents="370 14596 14598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      a(x,(y * z) * u,x) = a(x,z * (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(14546,a,14609,a),flip(a)].">
      <j1 rule="hyper" parents="14546 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      R(x,(y * z) * u,x) = R(x,z * (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14545,a(flip),b,14610,a),flip(a)].">
      <j1 rule="hyper" parents="60 14545 14610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      L(x,(y \ z) * u,x) = L(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(14600,a,14611,a)].">
      <j1 rule="hyper" parents="14600 14611"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(14157,a,14607,a)].">
      <j1 rule="hyper" parents="14157 14607"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) = T(x \ y,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,9386,a(flip),b,14615,a),flip(a)].">
      <j1 rule="hyper" parents="370 9386 14615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(74(a,1),14615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 14615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14619">
    <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(2022(a,2),14615(a,1,2))].">
      <j1 rule="para" parents="2022 14615"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(5349(a,2),14615(a,1,2))].">
      <j1 rule="para" parents="5349 14615"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(6544(a,1),14618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6544 14618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(6099(a,1),14623(a,1,2))].">
      <j1 rule="para" parents="6099 14623"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,y \ x) = z
    ]]></literal>
    <justification jstring="[para(14617(a,2),9388(a,1))].">
      <j1 rule="para" parents="14617 9388"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      K(x,(y * (z \ R(z,u,z))) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(5650,a,14400,a),flip(a)].">
      <j1 rule="hyper" parents="5650 14400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(11710(a,1),14627(a,1,2,1))].">
      <j1 rule="para" parents="11710 14627"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(11468(a,1),14629(a,1,2,1))].">
      <j1 rule="para" parents="11468 14629"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(11716(a,1),14629(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11716 14629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(14284(a,1),14629(a,1,2,1))].">
      <j1 rule="para" parents="14284 14629"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14630(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(11464(a,1),14632(a,1,2,1,2))].">
      <j1 rule="para" parents="11464 14632"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      K(x,T(((y \ z) \ z) * u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(8790,a,14440,a),flip(a)].">
      <j1 rule="hyper" parents="8790 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      K(x,T(T(y,y * z) * u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(363(a,2),14635(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="363 14635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      K(x,T(T(T(y,T(y,z) * u),T(z,y)) * w,v5)) = K(x,T(T(T(y,z),u) * w,v5))
    ]]></literal>
    <justification jstring="[para(5750(a,2),14636(a,1,2,1,1))].">
      <j1 rule="para" parents="5750 14636"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (y * w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14414,a(flip),b,14453,a)].">
      <j1 rule="hyper" parents="60 14414 14453"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (y \ w))) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(5(a,1),14638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 14638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) = T(x,y \ (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[para(8410(a,1),14461(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8410 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      K(x,(y * T(z \ y,z)) * u) = K(x,((z \ y) * y) * u)
    ]]></literal>
    <justification jstring="[para(1174(a,1),14522(a,1,2,1))].">
      <j1 rule="para" parents="1174 14522"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11713,a(flip),b,14542,a),flip(a)].">
      <j1 rule="hyper" parents="370 11713 14542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,y * z)) = K(x,u / T(z * y,z))
    ]]></literal>
    <justification jstring="[hyper(14571,a,14577,a)].">
      <j1 rule="hyper" parents="14571 14577"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14580,a,14643,a),flip(a)].">
      <j1 rule="hyper" parents="14580 14643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(14643(a,1),14580(a,1))].">
      <j1 rule="para" parents="14643 14580"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      K(x,y / ((z \ u) * z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),14644(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      K(x / T(y * z,y),u) = (w * K(u,x / (z * y))) \ w
    ]]></literal>
    <justification jstring="[para(14644(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14644 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      T(x,y / ((z \ u) * z)) = x * K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,14646,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 14646 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      T(x,y / ((z \ u) * z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,14648,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 14648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      T(x,y / T(z * u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14649(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 14649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      K(x / T(y * z,y),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,14647,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 14647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      K(x / T(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(14647(a,2),6305(a,1))].">
      <j1 rule="para" parents="14647 6305"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      K(x / ((y \ z) * y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),14651(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(14262(a,1),14273(a,1,2))].">
      <j1 rule="para" parents="14262 14273"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z))
    ]]></literal>
    <justification jstring="[hyper(12227,a,14279,a)].">
      <j1 rule="hyper" parents="12227 14279"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a(flip),b,14655,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 14655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14657">
    <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(9341(a,2),14656(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9341 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14658">
    <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(6557(a,2),14657(a,1,1,1))].">
      <j1 rule="para" parents="6557 14657"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14624,a(flip),b,14620,a),flip(a)].">
      <j1 rule="hyper" parents="60 14624 14620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14642,a(flip),b,14659,a),flip(a)].">
      <j1 rule="hyper" parents="60 14642 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14661(a,2,2))].">
      <j1 rule="para" parents="4 14661"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(14262(a,1),14654(a,1,2,2))].">
      <j1 rule="para" parents="14262 14654"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(629,a,14664,a)].">
      <j1 rule="hyper" parents="629 14664"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3933,a,14665,a),flip(a)].">
      <j1 rule="hyper" parents="3933 14665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      a(x,(y \ a(z,u,z)) * w,v5) = a(x,y * (a(z,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(13912(a,1),14320(a,1,2,1))].">
      <j1 rule="para" parents="13912 14320"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      T(x,y * (z * L(1 / z,u,w))) = T(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(3816(a,1),14472(a,2,2,2))].">
      <j1 rule="para" parents="3816 14472"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      K(x,((((y \ z) \ 1) \ 1) * z) * u) = K(x,((z \ y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14442,a(flip),b,14492,a),flip(a)].">
      <j1 rule="hyper" parents="60 14442 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14670">
    <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(14666(a,2),14315(a,1,2))].">
      <j1 rule="para" parents="14666 14315"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) = L(y,K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14434(a,1,1))].">
      <j1 rule="para" parents="4 14434"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8817,a,14671,a),flip(a)].">
      <j1 rule="hyper" parents="8817 14671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(77(a,1),14672(a,1,2,1))].">
      <j1 rule="para" parents="77 14672"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10264,a(flip),b,14674,a)].">
      <j1 rule="hyper" parents="60 10264 14674"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      (K(x,y) * z) * z = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,14675,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 14675 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5402(a,1),14675(a,1,1))].">
      <j1 rule="para" parents="5402 14675"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(6963,a,14679,a)].">
      <j1 rule="hyper" parents="6963 14679"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(14308(a,1),14670(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14308 14670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3816,a(flip),b,14681,a),flip(a)].">
      <j1 rule="hyper" parents="370 3816 14681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13899,a,b,14682,a)].">
      <j1 rule="hyper" parents="60 13899 14682"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      a(x,y,x \ L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,14682,a)].">
      <j1 rule="hyper" parents="50 14682"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      x * ((x \ y) * (x \ L(x,z,u))) = y * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,14682,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="129 14682 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      (x * y) * (x \ L(x,z,u)) = x * (y * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(129,a,14682,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 14682 5160"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),w,x) = T(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14682(a,1),20(a,2,1))].">
      <j1 rule="para" parents="14682 20"/>
    </justification>
  </clause>

  <clause id="14690">
    <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(14682(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14682 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) != x \ w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14682(a,2),44(a,1))].">
      <j1 rule="para" parents="14682 44"/>
    </justification>
  </clause>

  <clause id="14692">
    <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(14682(a,1),336(a,1,2))].">
      <j1 rule="para" parents="14682 336"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      (x * y) * L(x \ L(x,z,u),w,v5) = x * (y * L(x \ L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(14682(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="14682 528"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14682(a,1),3519(a,1,3))].">
      <j1 rule="para" parents="14682 3519"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w),v5,x) = (x \ L(x,y,z)) \ L(L(x \ L(x,y,z),v5,x),u,w)
    ]]></literal>
    <justification jstring="[para(14682(a,1),10440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14682 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      (1 / L(x,y,z)) \ (x \ L(x,u,w)) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(125,a,14685,a(flip),b,2075,a)].">
      <j1 rule="hyper" parents="125 14685 2075"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,L(x,v6,v7)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14685(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14685 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14700">
    <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="[para(14685(a,1),727(a,1,2))].">
      <j1 rule="para" parents="14685 727"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) = (L(x,y,z) \ (x * (x \ L(x,y,z)))) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(14685(a,1),4046(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14685 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <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(31,a,3825,a,b,14687,a),flip(a)].">
      <j1 rule="hyper" parents="31 3825 14687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(14687(a,1),3383(a,1,3,2))].">
      <j1 rule="para" parents="14687 3383"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      L(((x \ y) \ y) \ L((x \ y) \ y,z,u),x,x \ y) = L(y \ ((x \ y) * L((x \ y) \ y,z,u)),w,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(12522(a,1),14690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12522 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      R(x,L(y,z,u) * L(y \ 1,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(14702(a,1),682(a,1,2))].">
      <j1 rule="para" parents="14702 682"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      a((L(x,y,z) * L(x \ 1,y,z)) \ u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(14702(a,1),2952(a,1,1,1))].">
      <j1 rule="para" parents="14702 2952"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * L(z \ 1,u,w)) \ v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14702(a,1),3077(a,1,3,1))].">
      <j1 rule="para" parents="14702 3077"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(14702(a,1),14171(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14702 14171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ u) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(14702(a,1),14225(a,2,1))].">
      <j1 rule="para" parents="14702 14225"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      K(x,y / x) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(8778(a,1),14364(a,1,1))].">
      <j1 rule="para" parents="8778 14364"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      K(x,x \ y) * (((T(y,x) / x) \ y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(5692(a,1),14710(a,1,1))].">
      <j1 rule="para" parents="5692 14710"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      K(x,x \ y) * (T(x,y) \ z) = (y / (T(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[para(5784(a,1),14711(a,1,2,1))].">
      <j1 rule="para" parents="5784 14711"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ y) = (y / (T(y,x) / x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(10064,a,14712,a)].">
      <j1 rule="hyper" parents="10064 14712"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y \ z,u) * w)) = T(x,T(T(z / y,z),u) * w)
    ]]></literal>
    <justification jstring="[para(7293(a,1),14509(a,1,2,2,1))].">
      <j1 rule="para" parents="7293 14509"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      T(x,T(T(y / z,y),u) * w) = T(x,T(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(7839(a,1),14714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7839 14714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      R(x,y,L(x \ L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,14693,a)].">
      <j1 rule="hyper" parents="2810 14693"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * L(x \ L(x,u,w),v5,v6)) = (L(x,y,z) \ x) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2162(a,1),14693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2162 14693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      T(x * L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w) \ 1) = (L(x \ L(x,y,z),u,w) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(14716(a,1),1120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14716 1120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      a(a(x,x,x) * (y * K(x \ 1,y)),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(5630(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="5630 14359"/>
    </justification>
  </clause>

  <clause id="14721">
    <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(13912(a,1),14321(a,1,3,1,1))].">
      <j1 rule="para" parents="13912 14321"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      a(x,y,((z \ a(u,w,u)) * v5) * v6) = a(x,y,(z * v5) * (a(u,w,u) \ v6))
    ]]></literal>
    <justification jstring="[para(14323(a,1),14721(a,2,3))].">
      <j1 rule="para" parents="14323 14721"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (z \ (w * K(z,u))))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,14410,a(flip),b,14503,a),flip(a)].">
      <j1 rule="hyper" parents="370 14410 14503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <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(9(a,2),14619(a,2,2))].">
      <j1 rule="para" parents="9 14619"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14663,a(flip),b,14724,a)].">
      <j1 rule="hyper" parents="60 14663 14724"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      K(x,T(T(T(y,y * z),T(u,y)) * w,v5)) = K(x,T(T(T(y,u),z) * w,v5))
    ]]></literal>
    <justification jstring="[para(9175(a,1),14637(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9175 14637"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * u) * w,v5)) = K(x,T(T(T(y,z),u) * w,v5))
    ]]></literal>
    <justification jstring="[para(5750(a,1),14727(a,1,2,1,1))].">
      <j1 rule="para" parents="5750 14727"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      K(x,T(T(T(y \ 1,z),y) * u,w)) = K(x,T(T(y \ 1,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4362(a,1),14728(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4362 14728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ ((L(x,y,z) \ x) \ u) = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,14174,a(flip),b,14708,a),flip(a)].">
      <j1 rule="hyper" parents="60 14174 14708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ (u * w)) = ((L(x,y,z) * L(x \ 1,y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(14708(a,1),9921(a,2,1))].">
      <j1 rule="para" parents="14708 9921"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z \ w) * K(z,u)))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(7270(a,1),14723(a,1,2,2,2))].">
      <j1 rule="para" parents="7270 14723"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ T(u,L(x,y,z) \ x) = (x \ L(x,y,z)) \ (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),14731(a,1,2))].">
      <j1 rule="para" parents="17 14731"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      L((a(x,y,x) \ (z * (a(x,y,x) * (u * w)))) \ ((z * u) * w),a(x,y,x) \ (z * (a(x,y,x) * (u * w))),a(x,y,x)) = a(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[hyper(1207,a,14551,a)].">
      <j1 rule="hyper" parents="1207 14551"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * ((w * u) * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(370,a,6163,a(flip),b,14566,a),flip(a)].">
      <j1 rule="hyper" parents="370 6163 14566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      K(x,y * (z * T((u * w) * (1 / u),u * w))) = K(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(1111(a,1),14736(a,2,2,2,2))].">
      <j1 rule="para" parents="1111 14736"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(14262(a,1),14285(a,1,2))].">
      <j1 rule="para" parents="14262 14285"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) = R(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(693,a,14738,a),flip(a)].">
      <j1 rule="hyper" parents="693 14738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14272,a,14739,a),flip(a)].">
      <j1 rule="hyper" parents="14272 14739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      R(x,y,T(z,u) / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(11477(a,1),14740(a,1,3))].">
      <j1 rule="para" parents="11477 14740"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      R(x,y,z / T(u,z)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(5747(a,1),14742(a,1,3))].">
      <j1 rule="para" parents="5747 14742"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * a(w,v5,K(T(y,z) \ u,x)) = K(x,L(((y \ z) \ z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(14392(a,1),14561(a,1,1))].">
      <j1 rule="para" parents="14392 14561"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(12988,a,14744,a),flip(a)].">
      <j1 rule="hyper" parents="12988 14744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14744(a,1),12988(a,1))].">
      <j1 rule="para" parents="14744 12988"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(((z * y) * (1 / y)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(6536(a,1),14745(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6536 14745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) = 1 * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(295(a,1),14701(a,2,1))].">
      <j1 rule="para" parents="295 14701"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,14748,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 14748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,14748,a(flip),b,14005,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 14748 14005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,14748,a(flip),b,2391,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="123 14748 2391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = v6
    ]]></literal>
    <justification jstring="[para(14748(a,2),130(a,1)),flip(b)].">
      <j1 rule="para" parents="14748 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      L(x * y,y,x) \ (x * y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(2661,a,14750,a),flip(a)].">
      <j1 rule="hyper" parents="2661 14750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      (x * y) * (L(x,z,u) \ x) = x * (y * (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(129,a,14750,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 14750 5160"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),v5,x) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14750(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14750 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      x \ (y * (L(x,z,u) \ x)) = (x \ y) * (L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(14750(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="14750 617"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) \ x) = x * (y / (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(14750(a,1),727(a,1,2))].">
      <j1 rule="para" parents="14750 727"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      (x * y) * (L(x,z,u) \ x) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * (L(x,z,u) \ x)) = w
    ]]></literal>
    <justification jstring="[para(14750(a,1),336(a,1,2))].">
      <j1 rule="para" parents="14750 336"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      x * (y * T(L(x,z,u) \ x,x * y)) = (L(x,z,u) \ x) * (x * y)
    ]]></literal>
    <justification jstring="[para(14750(a,1),869(a,2,1))].">
      <j1 rule="para" parents="14750 869"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ x) \ u) = ((x * L(x,y,z)) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(14751(a,1),975(a,1,2,1))].">
      <j1 rule="para" parents="14751 975"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(14751(a,1),2735(a,1,3))].">
      <j1 rule="para" parents="14751 2735"/>
    </justification>
  </clause>

  <clause id="14764">
    <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(14751(a,1),3532(a,1,3))].">
      <j1 rule="para" parents="14751 3532"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      (x * y) \ a(x,y,x * y) = L(x * y,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,14754,a(flip),b,2162,a)].">
      <j1 rule="hyper" parents="125 14754 2162"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(14754(a,1),14170(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14754 14170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),v5,L(x,v6,v7)) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14749(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14749 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(3827,a,14766,a)].">
      <j1 rule="hyper" parents="3827 14766"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ x)) = L(x \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,3909,a(flip),b,14755,a),flip(a)].">
      <j1 rule="hyper" parents="60 3909 14755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      (x \ y) * ((x \ y) * (L(x \ y,x \ y,x) \ (x \ y))) = (y \ (x * 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(656(a,1),14769(a,2,1))].">
      <j1 rule="para" parents="656 14769"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x * (L(x,u,w) \ x))) = L(x,y,z) \ (L(x \ 1,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(14769(a,1),2160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14769 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      (x * x) * ((x \ y) * (L(x,z,u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ (y * (L(x,z,u) \ x)) = w
    ]]></literal>
    <justification jstring="[para(14757(a,1),960(a,1,2))].">
      <j1 rule="para" parents="14757 960"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      (1 / x) \ ((x * y) * (L(1 / x,z,u) \ (1 / x))) = (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(2077(a,1),14757(a,2,1))].">
      <j1 rule="para" parents="2077 14757"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,L(x,y,z),z * y),u,x) = (z * (y * x)) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,669,a(flip),b,14756,a),flip(a)].">
      <j1 rule="hyper" parents="370 669 14756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      (x * L(x,y,z)) \ 1 = L(x,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1472,a,14762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1472 14762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      (x * L(x,y,z)) \ 1 = x \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,2178,a(flip),b,14776,a),flip(a)].">
      <j1 rule="hyper" parents="370 2178 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      a(x,y \ (L(y,z,u) \ 1),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(14777(a,1),3058(a,1,2))].">
      <j1 rule="para" parents="14777 3058"/>
    </justification>
  </clause>

  <clause id="14779">
    <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(3112(a,1),14778(a,1))].">
      <j1 rule="para" parents="3112 14778"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ (L(x,u,w) \ x))) = L(x,y,z) \ (L(x \ 1,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(2160(a,1),14771(a,1,2))].">
      <j1 rule="para" parents="2160 14771"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(2660(a,2),14775(a,1,1))].">
      <j1 rule="para" parents="2660 14775"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9,a,b,14781,a),flip(a)].">
      <j1 rule="hyper" parents="370 9 14781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      L(a(x,y,z),u,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14781(a,2),1029(a,1))].">
      <j1 rule="para" parents="14781 1029"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      L(a(x,y,z),u,z) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(14781(a,2),1030(a,1))].">
      <j1 rule="para" parents="14781 1030"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      a(x,y,a(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,14782,a)].">
      <j1 rule="hyper" parents="50 14782"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,14782,a(flip),b,5160,a(flip))].">
      <j1 rule="hyper" parents="129 14782 5160"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,14782,a(flip),b,3399,a),flip(a)].">
      <j1 rule="hyper" parents="125 14782 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      (1 / x) \ a(y,z,x) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,14782,a(flip),b,2075,a)].">
      <j1 rule="hyper" parents="125 14782 2075"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,z)
    ]]></literal>
    <literal><![CDATA[
      a(u,w,z) = x
    ]]></literal>
    <justification jstring="[para(14782(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="14782 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      x \ (y * a(z,u,x)) = (x \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(14782(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="14782 617"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      (x * y) / a(z,u,x) = x * (y / a(z,u,x))
    ]]></literal>
    <justification jstring="[para(14782(a,1),727(a,1,2))].">
      <j1 rule="para" parents="14782 727"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      (x * y) * a(z,u,x) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * a(z,u,x)) = w
    ]]></literal>
    <justification jstring="[para(14782(a,1),336(a,1,2))].">
      <j1 rule="para" parents="14782 336"/>
    </justification>
  </clause>

  <clause id="14793">
    <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(14787(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14787 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),z \ 1) = (z \ a(x,y,z)) \ ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(14787(a,1),94(a,2,1))].">
      <j1 rule="para" parents="14787 94"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      R(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2810,a,14786,a)].">
      <j1 rule="hyper" parents="2810 14786"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      (x * a(y,z,x)) \ x = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,14795,a(flip),b,1111,a)].">
      <j1 rule="hyper" parents="125 14795 1111"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(14795(a,1),688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14795 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      L(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3747,a,14797,a)].">
      <j1 rule="hyper" parents="3747 14797"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),z) = (z \ a(x,y,z)) \ ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(3522,a,14794,a)].">
      <j1 rule="hyper" parents="3522 14794"/>
    </justification>
  </clause>

  <clause id="14801">
    <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(370,a,3050,a(flip),b,14793,a),flip(a)].">
      <j1 rule="hyper" parents="370 3050 14793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      (x \ y) * ((x \ y) * ((x \ y) \ (1 / (y \ x)))) = (y \ (x * 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(12769(a,1),14770(a,1,2,2))].">
      <j1 rule="para" parents="12769 14770"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      (x \ (y * 1)) \ (y \ x) = (y \ x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(387,a,14802,a),flip(a)].">
      <j1 rule="hyper" parents="387 14802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      (x \ y) * (1 / (y \ x)) = (y \ x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(3(a,1),14803(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3 14803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) \ z,u,w) = a(((y \ x) * (x \ y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(14805(a,1),2999(a,1,1,1))].">
      <j1 rule="para" parents="14805 2999"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(((z * y) * (y \ 1)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,13073,a(flip),b,14747,a),flip(a)].">
      <j1 rule="hyper" parents="370 13073 14747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      K(x,L(T((y * z) * (1 / y),y * z) \ u,w,v5)) = K(x,L(R(z,y,y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(1111(a,1),14807(a,2,2,1,1))].">
      <j1 rule="para" parents="1111 14807"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      (x * y) \ (a(z,u,z) \ (x * (a(z,u,z) * (y * w)))) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(13917(a,1),14552(a,2,1))].">
      <j1 rule="para" parents="13917 14552"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = (w * u) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(14292(a,1),14809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14292 14809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,13,a,b,14810,a),flip(a)].">
      <j1 rule="hyper" parents="370 13 14810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),14811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(11451(a,1),14811(a,1,2))].">
      <j1 rule="para" parents="11451 14811"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(11474(a,1),14811(a,1,2))].">
      <j1 rule="para" parents="11474 14811"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      L(x,y * a(z,u,z),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(11680(a,1),14811(a,1,2))].">
      <j1 rule="para" parents="11680 14811"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12440(a,1),14814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12440 14814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      L(x,L(y,z,y),L(u,w,u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(14468,a,14817,a)].">
      <j1 rule="hyper" parents="14468 14817"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,L(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14817,a,b,14817,a)].">
      <j1 rule="hyper" parents="370 14817 14817"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,L(y,w,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14814,a,b,14817,a)].">
      <j1 rule="hyper" parents="370 14814 14817"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      x * L(1 / L(y,z,y),y,x) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,14817,a(flip),b,3417,a(flip))].">
      <j1 rule="hyper" parents="129 14817 3417"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      L(x,T(y / z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5978(a,1),14817(a,1,2))].">
      <j1 rule="para" parents="5978 14817"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      L(x,L(y,z,y),L(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = v5
    ]]></literal>
    <justification jstring="[para(14817(a,2),14467(a,1))].">
      <j1 rule="para" parents="14817 14467"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      L(x,y * L(z,u,z),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(11704(a,1),14813(a,1,2))].">
      <j1 rule="para" parents="11704 14813"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      L(x,y \ L(z,u,z),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(14314(a,1),14813(a,1,2))].">
      <j1 rule="para" parents="14314 14813"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      L(x,((y \ z) * y) * (y \ z),u) = L(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[para(1027(a,1),14816(a,1,2))].">
      <j1 rule="para" parents="1027 14816"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(12506,a,14815,a),flip(a)].">
      <j1 rule="hyper" parents="12506 14815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,w / (T(w,y) / y),u)
    ]]></literal>
    <justification jstring="[para(9060(a,1),14819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9060 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      L(T(R(x,y,x),z) \ u,L(x,w,x),z) = (R(x,y,x) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12489,a(flip),b,14820,a),flip(a)].">
      <j1 rule="hyper" parents="60 12489 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      L(x,y / z,y) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(12506,a,14822,a)].">
      <j1 rule="hyper" parents="12506 14822"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      a(L((x \ L(y,z,y)) \ u,x \ y,x),w,v5) = a(y \ (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(14826(a,1),14078(a,1,1))].">
      <j1 rule="para" parents="14826 14078"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      x * L(R(1 / y,z,y),y,x) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(11719(a,2),14821(a,1,2,1))].">
      <j1 rule="para" parents="11719 14821"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      L(x,L(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(614(a,1),14824(a,1,3))].">
      <j1 rule="para" parents="614 14824"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      L(x,T(y / z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5978(a,1),14835(a,1,2))].">
      <j1 rule="para" parents="5978 14835"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      L(x,L(L(y,z,y),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(13888(a,1),14835(a,1,2))].">
      <j1 rule="para" parents="13888 14835"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,L(y,u,y),x / (T(x,y) / y)) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,14830,a,b,2074,a)].">
      <j1 rule="hyper" parents="125 14830 2074"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      T((x / y) * K(y \ 1,x),L(1 / y,y,x)) = x / L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12902,a,b,14834,a)].">
      <j1 rule="hyper" parents="60 12902 14834"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      L(x,y * T(z \ y,z),u) = L(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[para(1174(a,1),14827(a,1,2))].">
      <j1 rule="para" parents="1174 14827"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      L(x,L(L(y,z,u),w,y),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u),v5) = v6
    ]]></literal>
    <justification jstring="[para(25(a,1),14838(a,1,2))].">
      <j1 rule="para" parents="25 14838"/>
    </justification>
  </clause>

  <clause id="14843">
    <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(3873(a,1),14838(a,1))].">
      <j1 rule="para" parents="3873 14838"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      T(L(1 / x,x,y) * y,L(1 / x,x,y)) = y / L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5404(a,1),14840(a,1,1))].">
      <j1 rule="para" parents="5404 14840"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      L(R(T(x,y),z,x) \ u,L(x,w,x),y) = (R(x,z,x) * y) \ (y * u)
    ]]></literal>
    <justification jstring="[para(22(a,2),14831(a,1,1,1))].">
      <j1 rule="para" parents="22 14831"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      L(R(T(x,y),x \ y,x) \ z,L(x,u,x),y) = ((x * (y / x)) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(12410(a,1),14846(a,2,1))].">
      <j1 rule="para" parents="12410 14846"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      L(T(x,x \ y) \ z,L(x,u,x),y) = ((x * (y / x)) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5496(a,1),14848(a,1,1,1))].">
      <j1 rule="para" parents="5496 14848"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      ((x * (y / x)) * x) \ (y * z) = L(T(x,x \ y) \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(14835,a,14849,a),flip(a)].">
      <j1 rule="hyper" parents="14835 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,y) = y \ ((y / T(x,x \ y)) * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10560,a(flip),b,14850,a),flip(a)].">
      <j1 rule="hyper" parents="60 10560 14850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,L(y,u,y),L(y,w,y)) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[para(14018(a,2),14839(a,1,2))].">
      <j1 rule="para" parents="14018 14839"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,y,y) = ((x / (T(x,y) / y)) \ 1) * z
    ]]></literal>
    <justification jstring="[para(14818(a,1),14852(a,1,2))].">
      <j1 rule="para" parents="14818 14852"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(L(x \ L(x,u,w),v5,v6),L(x,y,z) \ 1,L(x,y,z))) = (L(x,y,z) \ x) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(511(a,2),14717(a,1,2))].">
      <j1 rule="para" parents="511 14717"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (u * w) = ((L(x,y,z) * L(x \ 1,y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(60,a,14709,a(flip),b,14732,a)].">
      <j1 rule="hyper" parents="60 14709 14732"/>
    </justification>
  </clause>

  <clause id="14857">
    <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(12851,a,14550,a)].">
      <j1 rule="hyper" parents="12851 14550"/>
    </justification>
  </clause>

  <clause id="14858">
    <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(14605,a,14857,a)].">
      <j1 rule="hyper" parents="14605 14857"/>
    </justification>
  </clause>

  <clause id="14859">
    <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(13(a,2),14858(a,1,2,2))].">
      <j1 rule="para" parents="13 14858"/>
    </justification>
  </clause>

  <clause id="14860">
    <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(5040(a,1),14859(a,1,2))].">
      <j1 rule="para" parents="5040 14859"/>
    </justification>
  </clause>

  <clause id="14861">
    <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(7639,a,14860,a)].">
      <j1 rule="hyper" parents="7639 14860"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1725(a,1),14861(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1725 14861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <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(14862(a,1),12159(a,1,1,2))].">
      <j1 rule="para" parents="14862 12159"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = L(T(y \ L(y,z,u),y \ x),y,x)
    ]]></literal>
    <justification jstring="[para(4205(a,1),14851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4205 14851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x)) = (1 / x) \ ((x * y) * (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(3985(a,1),14774(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3985 14774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x)) = (1 / x) \ (x * (y * (L(x,z,u) \ x)))
    ]]></literal>
    <justification jstring="[para(14755(a,1),14865(a,2,2))].">
      <j1 rule="para" parents="14755 14865"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x)) = x * ((x \ 1) \ (y * (L(x,z,u) \ x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,2077,a(flip),b,14866,a),flip(a)].">
      <j1 rule="hyper" parents="370 2077 14866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w),v5,x) = (x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14682(a,1),14695(a,2,2,1))].">
      <j1 rule="para" parents="14682 14695"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w),v5,x) = x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3823,a(flip),b,14868,a),flip(a)].">
      <j1 rule="hyper" parents="370 3823 14868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) = L(x,y,z) * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(4157,a,14869,a)].">
      <j1 rule="hyper" parents="4157 14869"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w),v5,x) = L(x,y,z) * (x \ L(L(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,2156,a(flip),b,14869,a),flip(a)].">
      <j1 rule="hyper" parents="370 2156 14869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(L(x,y,z) \ x,u,w)) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,2157,a,b,14871,a)].">
      <j1 rule="hyper" parents="31 2157 14871"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w),v5,x) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,14873,a(flip),b,14872,a),flip(a)].">
      <j1 rule="hyper" parents="370 14873 14872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      L(x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w)),v5,x) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3823(a,1),14874(a,1,1))].">
      <j1 rule="para" parents="3823 14874"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      L(L(x,y,z) * (x \ L(L(x,y,z) \ x,u,w)),v5,x) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2156(a,1),14875(a,1,1))].">
      <j1 rule="para" parents="2156 14875"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ L(x \ L(x,y,z),u,w)),v5,x) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14873(a,1),14876(a,1,1))].">
      <j1 rule="para" parents="14873 14876"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      a(x,y,x * (L(x,z,u) \ L(x \ L(x,z,u),w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,14877,a)].">
      <j1 rule="hyper" parents="50 14877"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      L(((x \ y) \ y) \ L((x \ y) \ y,z,u),x,x \ y) = L(y \ (L(x,z,u) * (x \ y)),w,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(876(a,1),14704(a,2,1,2))].">
      <j1 rule="para" parents="876 14704"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x \ L(x,u,w),v5,v6) = x * (L(x,y,z) \ L(x \ L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(14698(a,1),14855(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14698 14855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14882">
    <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(8630(a,1),10882(a,1,1,3,1))].">
      <j1 rule="para" parents="8630 10882"/>
    </justification>
  </clause>

  <clause id="14883">
    <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(6460(a,1),10899(a,1,2,1))].">
      <j1 rule="para" parents="6460 10899"/>
    </justification>
  </clause>

  <clause id="14884">
    <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(6695(a,1),14883(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6695 14883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <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(8985(a,1),14884(a,2,2))].">
      <j1 rule="para" parents="8985 14884"/>
    </justification>
  </clause>

  <clause id="14886">
    <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(4(a,1),14885(a,2,2,1))].">
      <j1 rule="para" parents="4 14885"/>
    </justification>
  </clause>

  <clause id="14887">
    <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(10516(a,1),14886(a,1,1,2))].">
      <j1 rule="para" parents="10516 14886"/>
    </justification>
  </clause>

  <clause id="14888">
    <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(10720(a,1),14887(a,1,1))].">
      <j1 rule="para" parents="10720 14887"/>
    </justification>
  </clause>

  <clause id="14889">
    <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(10516(a,1),14888(a,1,2,1))].">
      <j1 rule="para" parents="10516 14888"/>
    </justification>
  </clause>

  <clause id="14891">
    <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(5579(a,1),14889(a,1,2))].">
      <j1 rule="para" parents="5579 14889"/>
    </justification>
  </clause>

  <clause id="14892">
    <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(8504(a,1),14891(a,1,2))].">
      <j1 rule="para" parents="8504 14891"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9768(a,1),14892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9768 14892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8393,a,b,14893,a),flip(a)].">
      <j1 rule="hyper" parents="370 8393 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14896">
    <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(14275(a,1),11488(a,1,1))].">
      <j1 rule="para" parents="14275 11488"/>
    </justification>
  </clause>

  <clause id="14897">
    <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(11850(a,1),14896(a,1,1))].">
      <j1 rule="para" parents="11850 14896"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),z * ((y * z) \ u))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(14450(a,1),12681(a,1,2))].">
      <j1 rule="para" parents="14450 12681"/>
    </justification>
  </clause>

  <clause id="14900">
    <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(9280(a,1),14882(a,1,1,3))].">
      <j1 rule="para" parents="9280 14882"/>
    </justification>
  </clause>

  <clause id="14901">
    <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(8057(a,2),14900(a,1,1,3))].">
      <j1 rule="para" parents="8057 14900"/>
    </justification>
  </clause>

  <clause id="14903">
    <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(8630(a,1),14901(a,1,2,1,1))].">
      <j1 rule="para" parents="8630 14901"/>
    </justification>
  </clause>

  <clause id="14904">
    <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(10835(a,1),14903(a,1,2))].">
      <j1 rule="para" parents="10835 14903"/>
    </justification>
  </clause>

  <clause id="14905">
    <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(8630(a,1),14904(a,2,2,1))].">
      <j1 rule="para" parents="8630 14904"/>
    </justification>
  </clause>

  <clause id="14906">
    <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(9280(a,1),14905(a,2,2))].">
      <j1 rule="para" parents="9280 14905"/>
    </justification>
  </clause>

  <clause id="14907">
    <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(8057(a,2),14906(a,2,2))].">
      <j1 rule="para" parents="8057 14906"/>
    </justification>
  </clause>

  <clause id="14909">
    <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(11421(a,1),14907(a,1,1))].">
      <j1 rule="para" parents="11421 14907"/>
    </justification>
  </clause>

  <clause id="14910">
    <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(10834,a,14909,a),flip(a)].">
      <j1 rule="hyper" parents="10834 14909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,T(T(x,y),x \ 1),T(T(x,y),x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,218,a(flip),b,4346,a),flip(a)].">
      <j1 rule="hyper" parents="370 218 4346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14914">
    <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(11377(a,1),9959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11377 9959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <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(370,a,8359,a,b,14914,a),flip(a)].">
      <j1 rule="hyper" parents="370 8359 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <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(7864(a,1),14915(a,2,1))].">
      <j1 rule="para" parents="7864 14915"/>
    </justification>
  </clause>

  <clause id="14918">
    <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(14592(a,1),14917(a,1,2,1))].">
      <j1 rule="para" parents="14592 14917"/>
    </justification>
  </clause>

  <clause id="14919">
    <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(14592(a,1),14918(a,1,2,2,1))].">
      <j1 rule="para" parents="14592 14918"/>
    </justification>
  </clause>

  <clause id="14921">
    <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(5485(a,2),14919(a,1,2))].">
      <j1 rule="para" parents="5485 14919"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      L(x,y,z) * T(R(u,x,u),T(u * x,u)) = T(T(u,u * x) * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5537(a,1),14921(a,1,2,2))].">
      <j1 rule="para" parents="5537 14921"/>
    </justification>
  </clause>

  <clause id="14924">
    <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(12567(a,1),14923(a,1,2))].">
      <j1 rule="para" parents="12567 14923"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1163(a,1),14924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1163 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10196,a(flip),b,14925,a)].">
      <j1 rule="hyper" parents="60 10196 14925"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) = K(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,14926,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 14926 5256"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(11434,a,14927,a),flip(a)].">
      <j1 rule="hyper" parents="11434 14927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(12990,a,14929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12990 14929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[para(7(a,1),14930(a,1,1))].">
      <j1 rule="para" parents="7 14930"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11544,a(flip),b,14931,a)].">
      <j1 rule="hyper" parents="60 11544 14931"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(12763(a,1),14932(a,2,3))].">
      <j1 rule="para" parents="12763 14932"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,13125,a(flip),b,14933,a),flip(a)].">
      <j1 rule="hyper" parents="370 13125 14933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,12834,a(flip),b,14934,a)].">
      <j1 rule="hyper" parents="60 12834 14934"/>
    </justification>
  </clause>

  <clause id="14937">
    <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(60,a,8188,a,b,14936,a)].">
      <j1 rule="hyper" parents="60 8188 14936"/>
    </justification>
  </clause>

  <clause id="14938">
    <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(7(a,1),14936(a,1,2))].">
      <j1 rule="para" parents="7 14936"/>
    </justification>
  </clause>

  <clause id="14939">
    <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(8459,a,14938,a)].">
      <j1 rule="hyper" parents="8459 14938"/>
    </justification>
  </clause>

  <clause id="14940">
    <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(60,a,12846,a(flip),b,14939,a)].">
      <j1 rule="hyper" parents="60 12846 14939"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(13260(a,1),14940(a,2,3))].">
      <j1 rule="para" parents="13260 14940"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(77(a,1),14941(a,2,3,1))].">
      <j1 rule="para" parents="77 14941"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(14942(a,1),7511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14942 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,11929,a(flip),b,14945,a),flip(a)].">
      <j1 rule="hyper" parents="370 11929 14945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,14946,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 14946 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z)))
    ]]></literal>
    <justification jstring="[para(14946(a,1),13136(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14946 13136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,13141,a,b,14948,a)].">
      <j1 rule="hyper" parents="60 13141 14948"/>
    </justification>
  </clause>

  <clause id="14950">
    <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(14948(a,1),12991(a,1,1))].">
      <j1 rule="para" parents="14948 12991"/>
    </justification>
  </clause>

  <clause id="14951">
    <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(14949(a,1),11918(a,1,2))].">
      <j1 rule="para" parents="14949 11918"/>
    </justification>
  </clause>

  <clause id="14952">
    <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(14599(a,1),14937(a,1,2))].">
      <j1 rule="para" parents="14599 14937"/>
    </justification>
  </clause>

  <clause id="14953">
    <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(7851,a,14952,a)].">
      <j1 rule="hyper" parents="7851 14952"/>
    </justification>
  </clause>

  <clause id="14954">
    <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(8485,a,14953,a)].">
      <j1 rule="hyper" parents="8485 14953"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(11940(a,1),14951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11940 14951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,14955,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 14955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(14956(a,1),7511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14956 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,7511,a(flip),b,14958,a),flip(a)].">
      <j1 rule="hyper" parents="370 7511 14958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x * K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,14959,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 14959 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,14960,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 14960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14962">
    <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(14961(a,1),14954(a,1,2,1))].">
      <j1 rule="para" parents="14961 14954"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5383,a,14962,a)].">
      <j1 rule="hyper" parents="5383 14962"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11941(a,1),14950(a,1,1))].">
      <j1 rule="para" parents="11941 14950"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,14964,a)].">
      <j1 rule="hyper" parents="131 14964"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6935,a(flip),b,14965,a)].">
      <j1 rule="hyper" parents="60 6935 14965"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      x * K(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,14967,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 14967 5230"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(5265,a,14969,a),flip(a)].">
      <j1 rule="hyper" parents="5265 14969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14973">
    <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(14969(a,1),5265(a,1))].">
      <j1 rule="para" parents="14969 5265"/>
    </justification>
  </clause>

  <clause id="14974">
    <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(14972(a,2),891(a,1,1))].">
      <j1 rule="para" parents="14972 891"/>
    </justification>
  </clause>

  <clause id="14975">
    <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(370,a,14947,a(flip),b,14974,a),flip(a)].">
      <j1 rule="hyper" parents="370 14947 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14976">
    <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(11377(a,1),9960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11377 9960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <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(370,a,8359,a,b,14976,a),flip(a)].">
      <j1 rule="hyper" parents="370 8359 14976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14979">
    <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(7864(a,1),14977(a,2,1))].">
      <j1 rule="para" parents="7864 14977"/>
    </justification>
  </clause>

  <clause id="14980">
    <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(370,a,10197,a(flip),b,14979,a),flip(a)].">
      <j1 rule="hyper" parents="370 10197 14979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14981">
    <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(5487(a,2),14980(a,1,2))].">
      <j1 rule="para" parents="5487 14980"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,u * x),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(11373(a,1),14981(a,1,2,1))].">
      <j1 rule="para" parents="11373 14981"/>
    </justification>
  </clause>

  <clause id="14983">
    <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(5485(a,2),14982(a,1,2,1))].">
      <j1 rule="para" parents="5485 14982"/>
    </justification>
  </clause>

  <clause id="14985">
    <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(14057(a,1),14983(a,1,2))].">
      <j1 rule="para" parents="14057 14983"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1165(a,1),14985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1165 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(14986(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14986 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14989">
    <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(60,a,14894,a(flip),b,14988,a)].">
      <j1 rule="hyper" parents="60 14894 14988"/>
    </justification>
  </clause>

  <clause id="14990">
    <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(13829(a,1),14989(a,1,1))].">
      <j1 rule="para" parents="13829 14989"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      (((x \ 1) \ K(y,x)) \ T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(7062(a,1),10481(a,1,1,1))].">
      <j1 rule="para" parents="7062 10481"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(10478(a,1),14991(a,1,1))].">
      <j1 rule="para" parents="10478 14991"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ K(x,y)) \ 1)) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(10478(a,1),14992(a,1,2,1))].">
      <j1 rule="para" parents="10478 14992"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1 / (((x \ K(x,y)) \ 1) \ T(x,z))
    ]]></literal>
    <justification jstring="[para(7062(a,1),14993(a,1,2,2,2))].">
      <j1 rule="para" parents="7062 14993"/>
    </justification>
  </clause>

  <clause id="14995">
    <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(11521(a,1),11530(a,2,2,1,1))].">
      <j1 rule="para" parents="11521 11530"/>
    </justification>
  </clause>

  <clause id="14996">
    <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(370,a,2516,a(flip),b,14995,a),flip(a)].">
      <j1 rule="hyper" parents="370 2516 14995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14997">
    <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(2926(a,1),14996(a,2,2))].">
      <j1 rule="para" parents="2926 14996"/>
    </justification>
  </clause>

  <clause id="14998">
    <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(1600(a,1),14997(a,2,2,1))].">
      <j1 rule="para" parents="1600 14997"/>
    </justification>
  </clause>

  <clause id="14999">
    <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(1965(a,1),14998(a,2,2,1,2))].">
      <j1 rule="para" parents="1965 14998"/>
    </justification>
  </clause>

  <clause id="15000">
    <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(2516(a,1),14999(a,1,1))].">
      <j1 rule="para" parents="2516 14999"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      T(x \ R(a(y,x \ 1,y) * (a(y,x \ 1,y) \ x),z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(14049(a,2),15000(a,1,1,2))].">
      <j1 rule="para" parents="14049 15000"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(5(a,1),15001(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15003">
    <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(370,a,9956,a(flip),b,10021,a),flip(a)].">
      <j1 rule="hyper" parents="370 9956 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15004">
    <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(370,a,8636,a(flip),b,15003,a),flip(a)].">
      <j1 rule="hyper" parents="370 8636 15003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15005">
    <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(370,a,14229,a(flip),b,15004,a),flip(a)].">
      <j1 rule="hyper" parents="370 14229 15004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15006">
    <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(10497,a,15005,a)].">
      <j1 rule="hyper" parents="10497 15005"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),a(u,w,u) \ (x * (a(u,w,u) * (y * z))),a(u,w,u)) = a(x,a(u,w,u) * y,z)
    ]]></literal>
    <justification jstring="[para(14292(a,1),14735(a,1,1,1))].">
      <j1 rule="para" parents="14292 14735"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,u) \ (x * (a(u,w,u) * (y * z))),a(u,w,u)) = a(x,a(u,w,u) * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,2),15007(a,1,1))].">
      <j1 rule="para" parents="9 15007"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(13926,a,15008,a),flip(a)].">
      <j1 rule="hyper" parents="13926 15008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(11451(a,1),15010(a,1,2))].">
      <j1 rule="para" parents="11451 15010"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      a(x,y * (a(z,u,z) \ w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(14295(a,1),15010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14295 15010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7378(a,1),15012(a,1,2))].">
      <j1 rule="para" parents="7378 15012"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(12440(a,1),15012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12440 15012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      a(x,L(L(y,z,y),u,w),v5) = a(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(13888(a,1),15015(a,1,2))].">
      <j1 rule="para" parents="13888 15015"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      a(x,(y \ a(z,u,z)) * w,v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,14667,a,b,15013,a)].">
      <j1 rule="hyper" parents="60 14667 15013"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * (y * (x * x))) / ((x \ 1) \ (x * x))) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[para(519(a,1),2531(a,1,1,1,2))].">
      <j1 rule="para" parents="519 2531"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * (y * (x * x))) / ((x * x) * x)) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[para(939(a,1),15019(a,1,1,1,2))].">
      <j1 rule="para" parents="939 15019"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * y) / (((x * x) * x) / (x * x))) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[para(1097(a,1),15020(a,1,1,1))].">
      <j1 rule="para" parents="1097 15020"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * y) / R(x,x,x)) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[para(15(a,2),15021(a,1,1,1,2))].">
      <j1 rule="para" parents="15 15021"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      (((((x \ 1) \ 1) * y) / L(x,x,x)) * ((x \ 1) \ 1)) * (x * x) = (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x))
    ]]></literal>
    <justification jstring="[para(1342(a,1),15022(a,1,1,1,2))].">
      <j1 rule="para" parents="1342 15022"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = (((x * y) / x) * ((x \ 1) \ 1)) * (x * x)
    ]]></literal>
    <justification jstring="[para(4527(a,1),15023(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4527 15023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = ((x * y) * K(x,x \ 1)) * (x * x)
    ]]></literal>
    <justification jstring="[para(3671(a,1),15024(a,2,1))].">
      <j1 rule="para" parents="3671 15024"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = (x * (y * K(x,x \ 1))) * (x * x)
    ]]></literal>
    <justification jstring="[para(4138(a,1),15025(a,2,1))].">
      <j1 rule="para" parents="4138 15025"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = (L(x,x,x) * y) * (x * x)
    ]]></literal>
    <justification jstring="[para(4460(a,1),15026(a,2,1))].">
      <j1 rule="para" parents="4460 15026"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = L(x,x,x) * (y * (x * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,30,a(flip),b,15027,a),flip(a)].">
      <j1 rule="hyper" parents="370 30 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = x * (y * (x * L(x,x,x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14567,a(flip),b,15028,a),flip(a)].">
      <j1 rule="hyper" parents="370 14567 15028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      (x * x) * (x * T(R(y,(x \ 1) \ 1,x * x),x * x)) = x * (y * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(1325(a,1),15029(a,2,2,2))].">
      <j1 rule="para" parents="1325 15029"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      (x * x) * (x * T(y,x * x)) = x * (y * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[para(681(a,1),15030(a,1,2,2,1))].">
      <j1 rule="para" parents="681 15030"/>
    </justification>
  </clause>

  <clause id="15032">
    <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(9640(a,1),13455(a,1,2))].">
      <j1 rule="para" parents="9640 13455"/>
    </justification>
  </clause>

  <clause id="15033">
    <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(370,a,4,a(flip),b,13529,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 13529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(13527(a,1),15033(a,1,3))].">
      <j1 rule="para" parents="13527 15033"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(13822(a,1),15035(a,1,3))].">
      <j1 rule="para" parents="13822 15035"/>
    </justification>
  </clause>

  <clause id="15038">
    <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(1838,a,15037,a),flip(a)].">
      <j1 rule="hyper" parents="1838 15037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <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(60,a,13850,a(flip),b,15038,a),flip(a)].">
      <j1 rule="hyper" parents="60 13850 15038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7500(a,1),15039(a,1,2))].">
      <j1 rule="para" parents="7500 15039"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8763(a,1),15040(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8763 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(276,a,15041,a),flip(a)].">
      <j1 rule="hyper" parents="276 15041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15043">
    <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(370,a,14990,a(flip),b,15042,a)].">
      <j1 rule="hyper" parents="370 14990 15042"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(200(a,1),15043(a,2,1,2))].">
      <j1 rule="para" parents="200 15043"/>
    </justification>
  </clause>

  <clause id="15045">
    <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(8370,a,15044,a)].">
      <j1 rule="hyper" parents="8370 15044"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15044(a,1,1))].">
      <j1 rule="para" parents="7 15044"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,11776,a(flip),b,15046,a)].">
      <j1 rule="hyper" parents="60 11776 15046"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12854,a(flip),b,15047,a)].">
      <j1 rule="hyper" parents="60 12854 15047"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5674(a,1),15048(a,2,1))].">
      <j1 rule="para" parents="5674 15048"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14075,a(flip),b,15049,a),flip(a)].">
      <j1 rule="hyper" parents="370 14075 15049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15051">
    <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(60,a,8188,a,b,15050,a)].">
      <j1 rule="hyper" parents="60 8188 15050"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      (x \ T(x * (y \ R(y,z,u)),x)) \ (x \ (x * (y \ R(y,z,u)))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6639,a(flip),b,15050,a)].">
      <j1 rule="hyper" parents="60 6639 15050"/>
    </justification>
  </clause>

  <clause id="15053">
    <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(15044(a,1),15045(a,1,1))].">
      <j1 rule="para" parents="15044 15045"/>
    </justification>
  </clause>

  <clause id="15054">
    <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(60,a,14150,a,b,15053,a)].">
      <j1 rule="hyper" parents="60 14150 15053"/>
    </justification>
  </clause>

  <clause id="15055">
    <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(60,a,14096,a(flip),b,15054,a)].">
      <j1 rule="hyper" parents="60 14096 15054"/>
    </justification>
  </clause>

  <clause id="15056">
    <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(14725(a,1),15051(a,1,2))].">
      <j1 rule="para" parents="14725 15051"/>
    </justification>
  </clause>

  <clause id="15057">
    <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(7851,a,15056,a)].">
      <j1 rule="hyper" parents="7851 15056"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (u \ (u * (x \ R(x,y,z)))) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(15002(a,1),15052(a,1,1))].">
      <j1 rule="para" parents="15002 15052"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) \ (x \ R(x,y,z)) = a(K(u,x),y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),15058(a,1,2))].">
      <j1 rule="para" parents="4 15058"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5710,a,15059,a),flip(a)].">
      <j1 rule="hyper" parents="5710 15059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      a(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15059(a,1),5710(a,1))].">
      <j1 rule="para" parents="15059 5710"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(15060(a,1),13865(a,2,2))].">
      <j1 rule="para" parents="15060 13865"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      a(K(x,y),z * y,u) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(15060(a,2),15057(a,1,1))].">
      <j1 rule="para" parents="15060 15057"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,13978,a(flip),b,15063,a),flip(a)].">
      <j1 rule="hyper" parents="60 13978 15063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,11637,a,b,15065,a)].">
      <j1 rule="hyper" parents="60 11637 15065"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8636(a,2),15066(a,2,1))].">
      <j1 rule="para" parents="8636 15066"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(11762,a,15067,a)].">
      <j1 rule="hyper" parents="11762 15067"/>
    </justification>
  </clause>

  <clause id="15069">
    <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(60,a,10952,a(flip),b,15068,a)].">
      <j1 rule="hyper" parents="60 10952 15068"/>
    </justification>
  </clause>

  <clause id="15070">
    <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(8648(a,1),15069(a,2,1))].">
      <j1 rule="para" parents="8648 15069"/>
    </justification>
  </clause>

  <clause id="15071">
    <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(12354(a,1),15070(a,2,1,2))].">
      <j1 rule="para" parents="12354 15070"/>
    </justification>
  </clause>

  <clause id="15072">
    <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(10957,a,15071,a)].">
      <j1 rule="hyper" parents="10957 15071"/>
    </justification>
  </clause>

  <clause id="15075">
    <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(60,a,10959,a(flip),b,15072,a)].">
      <j1 rule="hyper" parents="60 10959 15072"/>
    </justification>
  </clause>

  <clause id="15077">
    <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(60,a,15006,a(flip),b,15075,a),flip(a)].">
      <j1 rule="hyper" parents="60 15006 15075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(10753(a,1),15077(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10753 15077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,13707,a(flip),b,15078,a),flip(a)].">
      <j1 rule="hyper" parents="370 13707 15078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(14228,a,15079,a)].">
      <j1 rule="hyper" parents="14228 15079"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      (1 / K(x,a(y,z,u))) * ((y * (z * u)) / (K(x,a(y,z,u)) \ 1)) = 1 * (y * (z * u))
    ]]></literal>
    <justification jstring="[para(15080(a,1),8729(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15080 8729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ a(K(x,y),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(12041,a,15064,a)].">
      <j1 rule="hyper" parents="12041 15064"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(192,a,15084,a),flip(a)].">
      <j1 rule="hyper" parents="192 15084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,15085,a)].">
      <j1 rule="hyper" parents="49 15085"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = w
    ]]></literal>
    <justification jstring="[para(15085(a,2),190(a,1,1))].">
      <j1 rule="para" parents="15085 190"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,13111,a(flip),b,15086,a),flip(a)].">
      <j1 rule="hyper" parents="60 13111 15086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(15086(a,1),5548(a,1,1,1))].">
      <j1 rule="para" parents="15086 5548"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      L(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(11507(a,1),15088(a,1))].">
      <j1 rule="para" parents="11507 15088"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10162(a,1),15092(a,1)),flip(b)].">
      <j1 rule="para" parents="10162 15092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      (1 / K(x,a(y,z,u))) * ((y * (z * u)) / (K(x,a(y,z,u)) \ 1)) = y * (z * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,15083,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 15083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      K(x,a(y,z,u)) * (y * (z * u)) = (y * (z * u)) * K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15094(a,1),8943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15094 8943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      K(x,T(a(y,z,u),y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8111,a,15095,a)].">
      <j1 rule="hyper" parents="8111 15095"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9022,a,15096,a)].">
      <j1 rule="hyper" parents="9022 15096"/>
    </justification>
  </clause>

  <clause id="15098">
    <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(60,a,10804,a,b,15097,a)].">
      <j1 rule="hyper" parents="60 10804 15097"/>
    </justification>
  </clause>

  <clause id="15099">
    <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(15060(a,2),15098(a,1,1))].">
      <j1 rule="para" parents="15060 15098"/>
    </justification>
  </clause>

  <clause id="15100">
    <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(60,a,14150,a,b,15099,a)].">
      <j1 rule="hyper" parents="60 14150 15099"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15055,a(flip),b,15100,a)].">
      <j1 rule="hyper" parents="60 15055 15100"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ K(x,a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(15101(a,1),15084(a,1,2))].">
      <j1 rule="para" parents="15101 15084"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(12035,a,15103,a)].">
      <j1 rule="hyper" parents="12035 15103"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(5383,a,15104,a)].">
      <j1 rule="hyper" parents="5383 15104"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15101,a(flip),b,15106,a),flip(a)].">
      <j1 rule="hyper" parents="370 15101 15106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,13976,a(flip),b,15106,a),flip(a)].">
      <j1 rule="hyper" parents="370 13976 15106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14963,a(flip),b,15107,a)].">
      <j1 rule="hyper" parents="60 14963 15107"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(15109(a,1),11928(a,2,1))].">
      <j1 rule="para" parents="15109 11928"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14963,a(flip),b,15108,a),flip(a)].">
      <j1 rule="hyper" parents="60 14963 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      a(K(x,y),z,z) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,5642,a(flip),b,15111,a),flip(a)].">
      <j1 rule="hyper" parents="370 5642 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,8245,a(flip),b,15111,a),flip(a)].">
      <j1 rule="hyper" parents="60 8245 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15114">
    <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(15111(a,1),13841(a,1,1,2))].">
      <j1 rule="para" parents="15111 13841"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      L(x,x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,15112,a)].">
      <j1 rule="hyper" parents="49 15112"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      K(x \ L(x,y,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,12999,a,b,15113,a)].">
      <j1 rule="hyper" parents="60 12999 15113"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,15113,a)].">
      <j1 rule="hyper" parents="49 15113"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,15115,a(flip),b,2481,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 15115 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      L(L(x,y,z),x,K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15115(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15115 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      (K(x,y) * z) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * z) = u
    ]]></literal>
    <justification jstring="[para(15115(a,1),336(a,1,2))].">
      <j1 rule="para" parents="15115 336"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(15115(a,1),2483(a,1,2))].">
      <j1 rule="para" parents="15115 2483"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      T(x \ L(x,y,y),z) = x \ L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,15116,a)].">
      <j1 rule="hyper" parents="53 15116"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      K(L(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(13047,a,15117,a)].">
      <j1 rule="hyper" parents="13047 15117"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      K(x,L(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13033,a,15117,a)].">
      <j1 rule="hyper" parents="13033 15117"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      K(x,(y * z) \ (y * y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11210,a,15117,a)].">
      <j1 rule="hyper" parents="11210 15117"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3531,a,15117,a)].">
      <j1 rule="hyper" parents="3531 15117"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3530,a,15117,a)].">
      <j1 rule="hyper" parents="3530 15117"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      (1 / x) * (x * K(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(993,a,15117,a)].">
      <j1 rule="hyper" parents="993 15117"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K((x * x) \ y,z) = K(x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12968,a(flip),b,15117,a)].">
      <j1 rule="hyper" parents="60 12968 15117"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12942,a(flip),b,15117,a)].">
      <j1 rule="hyper" parents="60 12942 15117"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,15117,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 15117 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,15117,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="125 15117 579"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      L(x * K(y,z),x,x) = L(x,x,x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15117(a,1),1280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15117 1280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      L(x,x,x) * K(y,z) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(15117(a,1),2121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15117 2121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(15117(a,1),3485(a,1,2,2))].">
      <j1 rule="para" parents="15117 3485"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(15117(a,1),12931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15117 12931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(586(a,1),15123(a,1,1))].">
      <j1 rule="para" parents="586 15123"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1492(a,2),15123(a,1,1))].">
      <j1 rule="para" parents="1492 15123"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2082(a,1),15123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2082 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(4020(a,1),15123(a,1,1))].">
      <j1 rule="para" parents="4020 15123"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(x,z) * x
    ]]></literal>
    <justification jstring="[para(15123(a,1),7901(a,2,1))].">
      <j1 rule="para" parents="15123 7901"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),15124(a,1,2))].">
      <j1 rule="para" parents="586 15124"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2082(a,1),15124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2082 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x,(y * y) * z) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(2096(a,1),15124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2096 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(2084(a,1),15124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2084 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K((x * y) \ 1,z) = K(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(7137,a,15127,a)].">
      <j1 rule="hyper" parents="7137 15127"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13763,a(flip),b,15128,a)].">
      <j1 rule="hyper" parents="60 13763 15128"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      T(x,L(y,z,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,15140,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 15140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(15140(a,2),5265(a,1))].">
      <j1 rule="para" parents="15140 5265"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,13058,a(flip),b,15156,a)].">
      <j1 rule="hyper" parents="60 13058 15156"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      L(x,y,y) * T(z,x) = z * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,15156,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 15156 17"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),15156(a,1,2))].">
      <j1 rule="para" parents="586 15156"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      T(x,(y * y) \ z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(344(a,1),15156(a,1,2))].">
      <j1 rule="para" parents="344 15156"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(591(a,1),15156(a,1,2))].">
      <j1 rule="para" parents="591 15156"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2082(a,1),15156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2082 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(2096(a,1),15156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2096 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,15144,a(flip),b,13982,a),flip(a)].">
      <j1 rule="hyper" parents="125 15144 13982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,15118,a)].">
      <j1 rule="hyper" parents="215 15118"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(7518,a,15121,a)].">
      <j1 rule="hyper" parents="7518 15121"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      a(K(x,y) / z,u,w) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(15121(a,1),2996(a,1,1))].">
      <j1 rule="para" parents="15121 2996"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      L(x,K(y,z) / u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(15121(a,1),3770(a,1,2))].">
      <j1 rule="para" parents="15121 3770"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * x) = (K(x,y) / z) * x
    ]]></literal>
    <justification jstring="[para(15121(a,1),7444(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15121 7444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(15121(a,1),7464(a,1,1))].">
      <j1 rule="para" parents="15121 7464"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      (K(x,y) / z) * K(y,x) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(15121(a,1),8705(a,1,1))].">
      <j1 rule="para" parents="15121 8705"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      T(K(x * y,x) / z,K(x,y)) = (1 / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(15121(a,1),8952(a,1,1))].">
      <j1 rule="para" parents="15121 8952"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,13287,a,b,15129,a)].">
      <j1 rule="hyper" parents="31 13287 15129"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,13284,a,b,15129,a),flip(a)].">
      <j1 rule="hyper" parents="31 13284 15129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(15129(a,1),134(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15129 134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(6302,a,15133,a)].">
      <j1 rule="hyper" parents="6302 15133"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      (((x * x) \ y) \ 1) * K(z,u) = y \ ((x * x) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,849,a(flip),b,15133,a),flip(a)].">
      <j1 rule="hyper" parents="370 849 15133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      (x * x) \ K(y,z) = x \ (x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,15133,a(flip),b,944,a),flip(a)].">
      <j1 rule="hyper" parents="125 15133 944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(15133(a,1),3438(a,1,3))].">
      <j1 rule="para" parents="15133 3438"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(15133(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="15133 6294"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(15133(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="15133 6305"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(15133(a,1),8704(a,1,1))].">
      <j1 rule="para" parents="15133 8704"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(15133(a,1),8719(a,1,1))].">
      <j1 rule="para" parents="15133 8719"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      (K(x,T(y,z \ 1)) * z) * (1 / z) = (z \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(15133(a,1),8823(a,2,1))].">
      <j1 rule="para" parents="15133 8823"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(13996,a,15134,a)].">
      <j1 rule="hyper" parents="13996 15134"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13266,a,15134,a),flip(a)].">
      <j1 rule="hyper" parents="13266 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      (1 / (x / ((y * z) / y))) \ K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(370,a,6441,a(flip),b,15134,a),flip(a)].">
      <j1 rule="hyper" parents="370 6441 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,13993,a(flip),b,15134,a),flip(a)].">
      <j1 rule="hyper" parents="60 13993 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      L(x \ (y * K(z,u)),x,y) = ((1 / y) * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(15134(a,1),1489(a,1,1,2))].">
      <j1 rule="para" parents="15134 1489"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      L(x,y * (z \ K(u,w)),v5) = L(x,y * (z * K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(15134(a,1),3773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15134 3773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(7018,a,15141,a)].">
      <j1 rule="hyper" parents="7018 15141"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 15141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) * y)) * K(x \ y,z) = (1 / x) * T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(15141(a,1),6349(a,1,2))].">
      <j1 rule="para" parents="15141 6349"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x \ y,x * x) = K(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6999,a(flip),b,15145,a)].">
      <j1 rule="hyper" parents="60 6999 15145"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,15145,a(flip),b,6404,a),flip(a)].">
      <j1 rule="hyper" parents="129 15145 6404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,z) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,15145,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 15145 5230"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),z) = K(T(((x \ 1) \ y) / (x \ 1),(x \ 1) \ 1),z)
    ]]></literal>
    <justification jstring="[para(2648(a,1),15145(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2648 15145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      K(T((x \ 1) \ 1,y) * z,u) = K((1 / T(x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(4335(a,1),15145(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4335 15145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(15145(a,1),6406(a,1,2,2))].">
      <j1 rule="para" parents="15145 6406"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(15145(a,1),6521(a,1,1,2))].">
      <j1 rule="para" parents="15145 6521"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(15145(a,1),6725(a,1))].">
      <j1 rule="para" parents="15145 6725"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,(z \ (y \ 1)) * (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(15145(a,1),6913(a,1,1,2))].">
      <j1 rule="para" parents="15145 6913"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(15145(a,1),11851(a,1,1,2))].">
      <j1 rule="para" parents="15145 11851"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(6078,a,15148,a),flip(a)].">
      <j1 rule="hyper" parents="6078 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      K(x,y \ ((1 / y) \ z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15148(a,1),6078(a,1))].">
      <j1 rule="para" parents="15148 6078"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * y) = K(x,y * (z * y))
    ]]></literal>
    <justification jstring="[hyper(12628,a,15150,a)].">
      <j1 rule="hyper" parents="12628 15150"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = x * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,15150,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 15150 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      (1 / x) \ K(y,z * u) = x * K(y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,15150,a(flip),b,15129,a)].">
      <j1 rule="hyper" parents="125 15150 15129"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(15150(a,1),6062(a,1))].">
      <j1 rule="para" parents="15150 6062"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[para(15150(a,1),11632(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15150 11632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      L(K(x,y * (z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(15150(a,1),11363(a,1,1))].">
      <j1 rule="para" parents="15150 11363"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(15150(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15150 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6075,a,15155,a)].">
      <j1 rule="hyper" parents="6075 15155"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(6056,a,15155,a),flip(a)].">
      <j1 rule="hyper" parents="6056 15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      x \ T(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5373,a,15155,a)].">
      <j1 rule="hyper" parents="5373 15155"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      L(K(x,y / z),u,u \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,15128,a,b,15155,a)].">
      <j1 rule="hyper" parents="370 15128 15155"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(77(a,1),15155(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,y / ((z * z) \ u)) = K(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(578(a,1),15155(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="578 15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ (z * z))) = K(x,y / L(1 / z,u,w))
    ]]></literal>
    <justification jstring="[para(3799(a,1),15155(a,1,2,2))].">
      <j1 rule="para" parents="3799 15155"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15155(a,1),6056(a,1))].">
      <j1 rule="para" parents="15155 6056"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      K(x,L(y * (z \ 1),u,w)) = L(K(x,y / z),u,w)
    ]]></literal>
    <justification jstring="[para(15155(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15155 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      T(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(586(a,1),15157(a,1,2))].">
      <j1 rule="para" parents="586 15157"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(344(a,1),15157(a,1,2))].">
      <j1 rule="para" parents="344 15157"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      T(x,T((y * y) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(745(a,1),15157(a,1,2))].">
      <j1 rule="para" parents="745 15157"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4657,a(flip),b,15161,a),flip(a)].">
      <j1 rule="hyper" parents="60 4657 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4652,a(flip),b,15161,a)].">
      <j1 rule="hyper" parents="60 4652 15161"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      T(x,(1 / (y / (z * z))) * u) = T(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(512(a,1),15161(a,2,2))].">
      <j1 rule="para" parents="512 15161"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * T(w,z \ u))) = T(x,y * (w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(15161(a,1),4991(a,1,2,2,2))].">
      <j1 rule="para" parents="15161 4991"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      T(x,T(y,z \ u) / ((u \ z) \ 1)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,14348,a,b,15165,a)].">
      <j1 rule="hyper" parents="60 14348 15165"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      T(x,(y * y) / z) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9708,a(flip),b,15165,a)].">
      <j1 rule="hyper" parents="60 9708 15165"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      ((x \ 1) \ y) * T(z,x * y) = z * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,15165,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 15165 17"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      K(x,T(y,z * u) * ((z \ 1) \ u)) = K(x,((z \ 1) \ u) * y)
    ]]></literal>
    <justification jstring="[para(15165(a,1),12605(a,1,2,1))].">
      <j1 rule="para" parents="15165 12605"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(15165(a,1),14448(a,1))].">
      <j1 rule="para" parents="15165 14448"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ 1 = K(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,15168,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(221,a,15168,a)].">
      <j1 rule="hyper" parents="221 15168"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      a(x \ K(y,z),u,w) = a(K(z,y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(15168(a,1),2962(a,1,1))].">
      <j1 rule="para" parents="15168 2962"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      L(x,y \ (z \ K(u,w)),v5) = L(x,y \ (K(w,u) * z),v5)
    ]]></literal>
    <justification jstring="[para(15168(a,1),3724(a,1,2,2))].">
      <j1 rule="para" parents="15168 3724"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(15168(a,1),15133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15168 15133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(15168(a,1),15155(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15168 15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(y,z) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(8939(a,1),15169(a,1,1))].">
      <j1 rule="para" parents="8939 15169"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(15170(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15170 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(221,a,15178,a)].">
      <j1 rule="hyper" parents="221 15178"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(214(a,1),15178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="214 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,15179,a(flip),b,6269,a)].">
      <j1 rule="hyper" parents="128 15179 6269"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      (x \ (y * K(z,y))) * K(y * K(z,y),y * z) = x \ L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5353(a,1),15179(a,2,2))].">
      <j1 rule="para" parents="5353 15179"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(15179(a,1),7501(a,1,1))].">
      <j1 rule="para" parents="15179 7501"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(841,a,15182,a),flip(a)].">
      <j1 rule="hyper" parents="841 15182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(221,a,15199,a)].">
      <j1 rule="hyper" parents="221 15199"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,y) = (K(y,z) / x) \ y
    ]]></literal>
    <justification jstring="[para(13291(a,1),15199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13291 15199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      K((x * y) / x,z \ u) = K(y,T((z \ 1) * u,x))
    ]]></literal>
    <justification jstring="[hyper(8790,a,15200,a),flip(a)].">
      <j1 rule="hyper" parents="8790 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      (x * K(y \ z,u)) \ x = K(u,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a,b,15200,a)].">
      <j1 rule="hyper" parents="370 6294 15200"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      K(x,y \ (z * T(u / w,u))) = K(x,(y \ 1) * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14565,a(flip),b,15200,a),flip(a)].">
      <j1 rule="hyper" parents="60 14565 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      K(x,y \ (T(z,z \ u) * w)) = K(x,(y \ 1) * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14564,a(flip),b,15200,a),flip(a)].">
      <j1 rule="hyper" parents="60 14564 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,(y \ 1) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14481,a(flip),b,15200,a),flip(a)].">
      <j1 rule="hyper" parents="60 14481 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,((y * y) * (z \ 1)) * u) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[para(512(a,1),15200(a,1,2,1))].">
      <j1 rule="para" parents="512 15200"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      K(x,y * (((1 / y) * z) * u)) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1254(a,1),15200(a,1,2))].">
      <j1 rule="para" parents="1254 15200"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15200(a,1),6060(a,1))].">
      <j1 rule="para" parents="15200 6060"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      (x \ T(y * x,z)) \ T(y,x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,17,a,b,15203,a)].">
      <j1 rule="hyper" parents="125 17 15203"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(15203(a,1),6310(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15203 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(12579,a,15208,a),flip(a)].">
      <j1 rule="hyper" parents="12579 15208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 15208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      (x * ((y \ 1) * z)) * K(y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T((y \ 1) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15208(a,1),6372(a,1,2))].">
      <j1 rule="para" parents="15208 6372"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      K(x,y * ((y \ 1) \ z)) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(2077(a,1),15226(a,1,2))].">
      <j1 rule="para" parents="2077 15226"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      K(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(15226(a,1),6077(a,1))].">
      <j1 rule="para" parents="15226 6077"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * K(z,x \ ((1 / x) \ y)) = x \ (((1 / x) \ y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(15227(a,1),5637(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15227 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(14506,a,15237,a),flip(a)].">
      <j1 rule="hyper" parents="14506 15237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(15238(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15238 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      K(x,(y * z) * z) = K(x,y * (z * z))
    ]]></literal>
    <justification jstring="[para(855(a,1),15241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="855 15241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(15241(a,1),6057(a,1))].">
      <j1 rule="para" parents="15241 6057"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      T(x / ((1 / y) \ z),y * y) = (y \ 1) * (y \ (x / (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10530,a(flip),b,15251,a),flip(a)].">
      <j1 rule="hyper" parents="60 10530 15251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      T(((1 / x) \ y) * z,x * x) = (x \ y) * (z * ((1 / x) \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4295,a(flip),b,15251,a),flip(a)].">
      <j1 rule="hyper" parents="60 4295 15251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(2077(a,1),15251(a,1,2))].">
      <j1 rule="para" parents="2077 15251"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      (x \ 1) * (x \ (y / (z * (1 / x)))) = T(y,x * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(15251(a,1),3350(a,2,1))].">
      <j1 rule="para" parents="15251 3350"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      T(1 / x,x * y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(15251(a,1),5607(a,1,1))].">
      <j1 rule="para" parents="15251 5607"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = (x \ y) \ T(z * (x \ 1),x * x)
    ]]></literal>
    <justification jstring="[para(15251(a,1),10566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15251 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      K(x,T(y,z * u) * ((z \ 1) \ u)) = K(x,((1 / z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(15251(a,1),12608(a,1,2,1))].">
      <j1 rule="para" parents="15251 12608"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,15252,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 15252 17"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      T(x,y \ ((y \ 1) \ z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 15252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,(y \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[para(573(a,1),15252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="573 15252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(15252(a,2),5289(a,1))].">
      <j1 rule="para" parents="15252 5289"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(15252(a,2),5313(a,1))].">
      <j1 rule="para" parents="15252 5313"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      T(x,((1 / L(y,z,u)) * y) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(9917(a,1),15252(a,1,2,1))].">
      <j1 rule="para" parents="9917 15252"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      K(x,T(y,z \ u) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(15252(a,1),14407(a,1,2,1))].">
      <j1 rule="para" parents="15252 14407"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,(u \ K(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(15168(a,1),15252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15168 15252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      z \ K(y,x) = u
    ]]></literal>
    <justification jstring="[para(15262(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15262 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(15262(a,1),13293(a,1,1))].">
      <j1 rule="para" parents="15262 13293"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      x / (y * K(x * K(z,x),z)) = (x * K(z,x)) / y
    ]]></literal>
    <justification jstring="[para(5280(a,1),15273(a,1,1))].">
      <j1 rule="para" parents="5280 15273"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      T(x,y) / (z / T(y,x)) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5855(a,1),15273(a,1,2))].">
      <j1 rule="para" parents="5855 15273"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[hyper(221,a,15284,a)].">
      <j1 rule="hyper" parents="221 15284"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(15284(a,1),5592(a,2,2,1,2))].">
      <j1 rule="para" parents="15284 5592"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(15284(a,1),12267(a,1,1,1,2))].">
      <j1 rule="para" parents="15284 12267"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6279(a,1),15287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6279 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      (x \ y) * K(y,z) = (1 / x) * T(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[para(15309(a,1),6437(a,1,2))].">
      <j1 rule="para" parents="15309 6437"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      T(x,y \ (y \ L(y,z,u))) = T(x,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3820(a,1),15330(a,1,2,2))].">
      <j1 rule="para" parents="3820 15330"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(T(x,y) * (z \ ((z \ 1) \ y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z \ ((z \ 1) \ y)) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15330(a,1),12601(a,1,1,1))].">
      <j1 rule="para" parents="15330 12601"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ ((u \ 1) \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ ((u \ 1) \ z)) * y) = w
    ]]></literal>
    <justification jstring="[para(15330(a,1),12637(a,1,2,1))].">
      <j1 rule="para" parents="15330 12637"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ (((z \ ((1 / z) \ y)) \ y) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14214(a,1),15330(a,1,2,2,1))].">
      <j1 rule="para" parents="14214 15330"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x,T(y,z) \ (u \ ((u \ 1) \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ ((u \ 1) \ z)) / y) = w
    ]]></literal>
    <justification jstring="[para(15330(a,1),14575(a,1,2,1))].">
      <j1 rule="para" parents="15330 14575"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[para(7500(a,1),15339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 15339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      (T(x,y) \ z) \ x = (x \ z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(7873(a,1),15339(a,1,1))].">
      <j1 rule="para" parents="7873 15339"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      (((x * y) / x) * z) \ T(x,y) = (y * z) \ x
    ]]></literal>
    <justification jstring="[para(8385(a,1),15339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8385 15339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = (x * K(z,y)) \ y
    ]]></literal>
    <justification jstring="[para(15339(a,1),9554(a,1,1))].">
      <j1 rule="para" parents="15339 9554"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      a(x * (K(y,z) / u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (u * K(z,y)),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(15343(a,1),3006(a,1,1,2))].">
      <j1 rule="para" parents="15343 3006"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(221,a,15360,a)].">
      <j1 rule="hyper" parents="221 15360"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(77(a,1),15369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 15369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(15369(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15369 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(7518,a,15370,a)].">
      <j1 rule="hyper" parents="7518 15370"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      T(x,y) * (x / z) = x * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,15370,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 15370 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[para(15273(a,1),15372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15273 15372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      R(K(x,y),z,L(L(z,u,w),z,K(x,y))) = (K(x,y) * (z * L(z,u,w))) / (z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(15119(a,1),623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15119 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      T(x,y \ L(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,15122,a)].">
      <j1 rule="hyper" parents="51 15122"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      x / (y \ L(y,z,z)) = (y \ L(y,z,z)) \ x
    ]]></literal>
    <justification jstring="[para(15122(a,1),308(a,1,2))].">
      <j1 rule="para" parents="15122 308"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      T(x,a(y,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,14972,a,b,15378,a)].">
      <j1 rule="hyper" parents="60 14972 15378"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      K(x,y * ((z \ L(z,u,u)) * w)) = K(x,y * (w * (z \ L(z,u,u))))
    ]]></literal>
    <justification jstring="[para(15378(a,1),14423(a,1,2,2))].">
      <j1 rule="para" parents="15378 14423"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      K(x,K(y,z \ (z \ u))) * x = T(x,K((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(15130(a,2),8687(a,2,2))].">
      <j1 rule="para" parents="15130 8687"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      1 / (x \ K(y \ (z \ 1),x)) = T(x,(z * y) \ 1)
    ]]></literal>
    <justification jstring="[para(15153(a,1),5767(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15153 5767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      L(x,y,y) * (x \ T(z,x)) = x \ (z * L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(125,a,15160,a(flip),b,2157,a),flip(a)].">
      <j1 rule="hyper" parents="125 15160 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      x \ ((y * y) * (z * ((y * y) \ x))) = T(z,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(1441,a,15162,a)].">
      <j1 rule="hyper" parents="1441 15162"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      T(x,y \ ((y \ 1) * z)) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(942(a,2),15162(a,1,2))].">
      <j1 rule="para" parents="942 15162"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,((y * y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(514(a,1),15162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="514 15162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(1766,a,15166,a)].">
      <j1 rule="hyper" parents="1766 15166"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      x * (y \ (y \ K(y \ 1,z))) = (x / y) * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(15185(a,1),6875(a,1,2))].">
      <j1 rule="para" parents="15185 6875"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      K(x * 1,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(15214(a,1),9037(a,1,1))].">
      <j1 rule="para" parents="15214 9037"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(15215(a,1),653(a,1,1))].">
      <j1 rule="para" parents="15215 653"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15231(a,2),5265(a,1))].">
      <j1 rule="para" parents="15231 5265"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5230,a(flip),b,15239,a),flip(a)].">
      <j1 rule="hyper" parents="35 5230 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      1 / (x \ K(y / z,x)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,5767,a(flip),b,15398,a)].">
      <j1 rule="hyper" parents="370 5767 15398"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4646,a,b,15398,a)].">
      <j1 rule="hyper" parents="60 4646 15398"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,15252,a(flip),b,15398,a),flip(a)].">
      <j1 rule="hyper" parents="60 15252 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      T(x,(1 / y) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,15161,a(flip),b,15398,a),flip(a)].">
      <j1 rule="hyper" parents="60 15161 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      T(x,T(y / z,y) / u) = T(x,(z \ y) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,14507,a(flip),b,15398,a),flip(a)].">
      <j1 rule="hyper" parents="60 14507 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4649,a(flip),b,15398,a),flip(a)].">
      <j1 rule="hyper" parents="60 4649 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(77(a,1),15398(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      T(x,y / ((z * z) \ u)) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(578(a,1),15398(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="578 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      T(x,y / (z \ (u \ ((1 / u) \ z)))) = T(x,y * ((u \ ((1 / u) \ z)) \ z))
    ]]></literal>
    <justification jstring="[para(14214(a,1),15398(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14214 15398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12713,a(flip),b,15400,a)].">
      <j1 rule="hyper" parents="60 12713 15400"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * (1 / u)) = T(x,(y / (1 / z)) / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4696,a(flip),b,15400,a)].">
      <j1 rule="hyper" parents="60 4696 15400"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      K(x * (1 / y),z) = z / T(z,x / y)
    ]]></literal>
    <justification jstring="[para(15400(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="15400 5701"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      K(x,T(y * z,T(y,u) / u) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(15400(a,1),14366(a,1,2,1))].">
      <j1 rule="para" parents="15400 14366"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      T(x,y / (z \ L(z,u,u))) = T(x,y * a(u,u,z))
    ]]></literal>
    <justification jstring="[para(14176(a,1),15404(a,1,2,2))].">
      <j1 rule="para" parents="14176 15404"/>
    </justification>
  </clause>

  <clause id="15414">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15165,a,b,15405,a),flip(a)].">
      <j1 rule="hyper" parents="370 15165 15405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      T(x,T(y * z,y * y) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * (y * y),y)) = u
    ]]></literal>
    <justification jstring="[para(15405(a,1),10083(a,1))].">
      <j1 rule="para" parents="15405 10083"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8897,a,15306,a),flip(a)].">
      <j1 rule="hyper" parents="8897 15306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(15306(a,1),8897(a,1))].">
      <j1 rule="para" parents="15306 8897"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6729,a,15416,a)].">
      <j1 rule="hyper" parents="6729 15416"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      K((1 / x) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15141,a(flip),b,15416,a),flip(a)].">
      <j1 rule="hyper" parents="60 15141 15416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),15416(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 15416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(x * (u \ K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(15168(a,1),15416(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15168 15416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15418(a,1),6728(a,1))].">
      <j1 rule="para" parents="15418 6728"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z / u,y))) / x) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[para(15418(a,1),9748(a,1,2,1,2,2))].">
      <j1 rule="para" parents="15418 9748"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15145,a,b,15420,a),flip(a)].">
      <j1 rule="hyper" parents="370 15145 15420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,y * (z * z)) = K(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(14493,a,15318,a),flip(a)].">
      <j1 rule="hyper" parents="14493 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      T(x,x \ 1) / (y / (1 / x)) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(955(a,1),15341(a,1,2,2))].">
      <j1 rule="para" parents="955 15341"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x / y,T(x,z))) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(15374(a,1),12972(a,2,1,1))].">
      <j1 rule="para" parents="15374 12972"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(1146,a,15388,a)].">
      <j1 rule="hyper" parents="1146 15388"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      T(x,((y * y) * ((z \ 1) \ 1)) / u) = T(x,(z \ (y \ (y \ 1))) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(1139(a,1),15401(a,1,2,1))].">
      <j1 rule="para" parents="1139 15401"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(15411(a,2),5734(a,1))].">
      <j1 rule="para" parents="15411 5734"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(K(y \ (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(15419(a,1),8226(a,2,1))].">
      <j1 rule="para" parents="15419 8226"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,(y \ z) * (y * y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15425(a,2,2,2))].">
      <j1 rule="para" parents="5 15425"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,y * (y * (z * (u \ 1)))) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[para(574(a,1),15425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="574 15425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      K(x,y * (y * (z \ (u * (w / y))))) = K(x,z \ (u * (w / (1 / y))))
    ]]></literal>
    <justification jstring="[para(1444(a,1),15425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1444 15425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      T(x,x * (x * y)) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,741,a(flip),b,15429,a),flip(a)].">
      <j1 rule="hyper" parents="60 741 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      L(T(x,x \ y),x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(5(a,1),15437(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      T((x \ 1) \ 1,x \ y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1323,a,b,15438,a)].">
      <j1 rule="hyper" parents="60 1323 15438"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      (x \ 1) * T(x,x \ y) = x \ T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(125,a,15438,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 15438 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x,x * y) \ L(L(T(x,x \ y),x,x),z,u)
    ]]></literal>
    <justification jstring="[para(15438(a,1),10440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15438 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(x,(y \ z) * (y * y)) = x \ T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,15434,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      T(x,x * y) = (((x \ y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,8422,a(flip),b,15439,a),flip(a)].">
      <j1 rule="hyper" parents="60 8422 15439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      1 / T(x,x \ y) = T(x,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(15439(a,1),4335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15439 4335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T((x \ 1) \ 1,x \ z))
    ]]></literal>
    <justification jstring="[para(15439(a,1),5454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15439 5454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      L(x,T(y,y * z),u) = L(x,(y \ z) \ z,u)
    ]]></literal>
    <justification jstring="[para(15443(a,2),3406(a,1,2))].">
      <j1 rule="para" parents="15443 3406"/>
    </justification>
  </clause>

  <clause id="15447">
    <literal><![CDATA[
      L(x,T(y,y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15443(a,2),3534(a,1,2))].">
      <j1 rule="para" parents="15443 3534"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * (1 / (((w \ v5) \ v5) \ 1)))))
    ]]></literal>
    <justification jstring="[para(15443(a,2),4709(a,2,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15443 4709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      x * (1 / T(x,x \ y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,15444,a,b,5721,a(flip))].">
      <j1 rule="hyper" parents="129 15444 5721"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      T((x \ 1) \ 1,x * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(33,a,8399,a,b,15444,a)].">
      <j1 rule="hyper" parents="33 8399 15444"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      K(x * (x * y),x) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),15449(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      (x \ 1) \ K(x \ y,x) = K(x * y,x) * x
    ]]></literal>
    <justification jstring="[para(15449(a,1),7616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15449 7616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      K(K((x / (1 / y)) * ((x / (1 / y)) * z),x / (1 / y)),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(15451(a,2),6019(a,1,1))].">
      <j1 rule="para" parents="15451 6019"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6002(a,2),15221(a,1))].">
      <j1 rule="para" parents="6002 15221"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9982(a,1),15221(a,1))].">
      <j1 rule="para" parents="9982 15221"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      K(x,((y * y) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ (y * y)) * u) = w
    ]]></literal>
    <justification jstring="[para(575(a,1),15228(a,1,2,1))].">
      <j1 rule="para" parents="575 15228"/>
    </justification>
  </clause>

  <clause id="15459">
    <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(14169(a,1),15228(a,1,2,1))].">
      <j1 rule="para" parents="14169 15228"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * z) * u)) = w
    ]]></literal>
    <justification jstring="[para(573(a,1),15233(a,1,2))].">
      <j1 rule="para" parents="573 15233"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5572(a,2),15233(a,1))].">
      <j1 rule="para" parents="5572 15233"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(14176(a,1),15233(a,1,2,1))].">
      <j1 rule="para" parents="14176 15233"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5566(a,2),15244(a,1))].">
      <j1 rule="para" parents="5566 15244"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      T(x,(1 / y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(15398(a,1),15247(a,1))].">
      <j1 rule="para" parents="15398 15247"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(5720(a,2),15270(a,1,2))].">
      <j1 rule="para" parents="5720 15270"/>
    </justification>
  </clause>

  <clause id="15467">
    <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(15343(a,1),15270(a,1,2))].">
      <j1 rule="para" parents="15343 15270"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      K(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(939(a,1),15300(a,1,2))].">
      <j1 rule="para" parents="939 15300"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12702(a,2),15300(a,1))].">
      <j1 rule="para" parents="12702 15300"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      x * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y \ T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),15303(a,1,1))].">
      <j1 rule="para" parents="4 15303"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      K(x,y * ((y \ 1) \ (z * (1 / u)))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = w
    ]]></literal>
    <justification jstring="[para(1657(a,1),15319(a,1,2))].">
      <j1 rule="para" parents="1657 15319"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5565(a,1),15319(a,1))].">
      <j1 rule="para" parents="5565 15319"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(939(a,1),15396(a,1,2))].">
      <j1 rule="para" parents="939 15396"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      T(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4654(a,2),15396(a,1))].">
      <j1 rule="para" parents="4654 15396"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      T(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ 1) * z) = u
    ]]></literal>
    <justification jstring="[para(4656(a,1),15396(a,1))].">
      <j1 rule="para" parents="4656 15396"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15252(a,2),15396(a,1))].">
      <j1 rule="para" parents="15252 15396"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      T(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15414(a,2),15396(a,1))].">
      <j1 rule="para" parents="15414 15396"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,14334,a(flip),b,15408,a),flip(a)].">
      <j1 rule="hyper" parents="370 14334 15408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <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(15478(a,1),15093(a,1))].">
      <j1 rule="para" parents="15478 15093"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ K(y,z)),u) = w
    ]]></literal>
    <justification jstring="[para(5972(a,1),15422(a,1,1,2))].">
      <j1 rule="para" parents="5972 15422"/>
    </justification>
  </clause>

  <clause id="15482">
    <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(15262(a,1),15422(a,1,1,2))].">
      <j1 rule="para" parents="15262 15422"/>
    </justification>
  </clause>

  <clause id="15483">
    <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(15343(a,1),15422(a,1,1,2))].">
      <j1 rule="para" parents="15343 15422"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15424(a,1),15422(a,1))].">
      <j1 rule="para" parents="15424 15422"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      K((x * x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(552(a,1),15455(a,1,1))].">
      <j1 rule="para" parents="552 15455"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      K(x,(K(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(5720(a,2),15461(a,1,2,1))].">
      <j1 rule="para" parents="5720 15461"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      K(x,y * ((z * z) * ((u * w) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * (w / (z * z)))) = v5
    ]]></literal>
    <justification jstring="[para(1102(a,1),15472(a,1,2,2))].">
      <j1 rule="para" parents="1102 15472"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(2077(a,1),15474(a,1,2))].">
      <j1 rule="para" parents="2077 15474"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ K(z,y)) * w) = v5
    ]]></literal>
    <justification jstring="[para(15262(a,1),15474(a,1,2,1))].">
      <j1 rule="para" parents="15262 15474"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      T(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(4647(a,1),15477(a,1))].">
      <j1 rule="para" parents="4647 15477"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(6004(a,2),15484(a,1))].">
      <j1 rule="para" parents="6004 15484"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(15398(a,2),15492(a,1))].">
      <j1 rule="para" parents="15398 15492"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7573,a,15110,a),flip(a)].">
      <j1 rule="hyper" parents="7573 15110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (1 / w) = K(a(x,y,z),u) / w
    ]]></literal>
    <justification jstring="[hyper(129,a,15170,a(flip),b,15110,a)].">
      <j1 rule="hyper" parents="129 15170 15110"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      T(x,a(y,z,u)) \ x = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5699,a(flip),b,15496,a)].">
      <j1 rule="hyper" parents="370 5699 15496"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(129,a,15496,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 15496 5230"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      K(a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,15113,a(flip),b,15496,a),flip(a)].">
      <j1 rule="hyper" parents="60 15113 15496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      K(a(x,y,z),y) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,5642,a(flip),b,15496,a),flip(a)].">
      <j1 rule="hyper" parents="60 5642 15496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(15496(a,2),5280(a,1,1,2))].">
      <j1 rule="para" parents="15496 5280"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(15496(a,2),5265(a,1,2))].">
      <j1 rule="para" parents="15496 5265"/>
    </justification>
  </clause>

  <clause id="15504">
    <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(15496(a,2),5334(a,1,2))].">
      <j1 rule="para" parents="15496 5334"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15496(a,2),5855(a,1,2))].">
      <j1 rule="para" parents="15496 5855"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x \ y))) = y * K(a(z,u,w),x \ y)
    ]]></literal>
    <justification jstring="[para(15496(a,2),5643(a,1,2,2))].">
      <j1 rule="para" parents="15496 5643"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = w * a(x,y,K(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(15496(a,2),8064(a,2,2))].">
      <j1 rule="para" parents="15496 8064"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,15501,a)].">
      <j1 rule="hyper" parents="53 15501"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(15498(a,1),5710(a,1))].">
      <j1 rule="para" parents="15498 5710"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      L(x * K(y,z),x,x) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15137,a(flip),b,15135,a),flip(a)].">
      <j1 rule="hyper" parents="370 15137 15135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,15147,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 15147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      L(T(x,y),z,z) * a(z,z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(20(a,2),15511(a,1,1))].">
      <j1 rule="para" parents="20 15511"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      a(x,x,T(y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(1363,a,15513,a)].">
      <j1 rule="hyper" parents="1363 15513"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6446,a(flip),b,15159,a),flip(a)].">
      <j1 rule="hyper" parents="370 6446 15159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      T(x,(y * z) \ (y * y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4966,a(flip),b,15516,a)].">
      <j1 rule="hyper" parents="60 4966 15516"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      T(x,T((y \ 1) \ z,u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),15163(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 15163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      a(K(x,y) / ((K(x,y) \ 1) \ z),u,w) = a((K(x,y) \ (1 / K(x,y))) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1213(a,2),15171(a,2,1))].">
      <j1 rule="para" parents="1213 15171"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      ((x * x) \ y) * x = (K(y,x) / x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,9041,a(flip),b,15173,a)].">
      <j1 rule="hyper" parents="60 9041 15173"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      R(1 / (K(x,y) / y),K(x,y) / y,x) = x / (((y * y) \ x) * y)
    ]]></literal>
    <justification jstring="[para(15520(a,2),253(a,2,2))].">
      <j1 rule="para" parents="15520 253"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(15174(a,1),11743(a,1,1))].">
      <j1 rule="para" parents="15174 11743"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(15343(a,2),15174(a,1,1))].">
      <j1 rule="para" parents="15343 15174"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x * K(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12874,a(flip),b,15190,a),flip(a)].">
      <j1 rule="hyper" parents="60 12874 15190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ T(x / z,1 / (x / ((y * z) / y))) = (x / z) * (1 / (x / ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(15201(a,1),6485(a,2,1))].">
      <j1 rule="para" parents="15201 6485"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10844,a,b,15261,a)].">
      <j1 rule="hyper" parents="60 10844 15261"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,9951,a,b,15269,a)].">
      <j1 rule="hyper" parents="60 9951 15269"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(L(x,x,x) * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(1324(a,1),15274(a,1,2,1))].">
      <j1 rule="para" parents="1324 15274"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15282,a(flip),b,15364,a),flip(a)].">
      <j1 rule="hyper" parents="60 15282 15364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(15475,a,15386,a)].">
      <j1 rule="hyper" parents="15475 15386"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      T(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(15399(a,1),5768(a,1))].">
      <j1 rule="para" parents="15399 5768"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(4646(a,2),15531(a,1))].">
      <j1 rule="para" parents="4646 15531"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      T(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5721(a,1),15531(a,1,2,2))].">
      <j1 rule="para" parents="5721 15531"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      T(x,y \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ 1) / z) = u
    ]]></literal>
    <justification jstring="[para(15252(a,1),15531(a,1))].">
      <j1 rule="para" parents="15252 15531"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      (x \ 1) * T(x,x \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,15440,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 15440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      K(x,x * y) / x = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,15535,a(flip),b,6286,a)].">
      <j1 rule="hyper" parents="128 15535 6286"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      (x \ K(x,x \ y)) * K(z,x) = K(x,x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[para(15536(a,1),5855(a,1,1))].">
      <j1 rule="para" parents="15536 5855"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      T(x,(y \ z) * (y * y)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(5264,a,15442,a)].">
      <j1 rule="hyper" parents="5264 15442"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),15538(a,1,2,1))].">
      <j1 rule="para" parents="4 15538"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,y * (z * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15429,a,b,15539,a)].">
      <j1 rule="hyper" parents="370 15429 15539"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15388,a,b,15539,a)].">
      <j1 rule="hyper" parents="370 15388 15539"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15323,a,b,15539,a)].">
      <j1 rule="hyper" parents="370 15323 15539"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      T(x,y \ (z * (u * u))) = T(x,u * (u * (y \ z)))
    ]]></literal>
    <justification jstring="[para(513(a,2),15539(a,1,2))].">
      <j1 rule="para" parents="513 15539"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(x,z * (y \ (1 / y)))
    ]]></literal>
    <justification jstring="[para(1211(a,1),15539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1211 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      T(x,T(y,z) * ((1 / z) * (1 / z))) = T(x,(1 / z) * (((z * z) \ y) * z))
    ]]></literal>
    <justification jstring="[para(1276(a,2),15539(a,2,2,2))].">
      <j1 rule="para" parents="1276 15539"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,(1 / y) * (z * y)),u)
    ]]></literal>
    <justification jstring="[para(4435(a,1),15446(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4435 15446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      (x \ 1) \ K(x \ y,x) = x * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4746,a(flip),b,15452,a),flip(a)].">
      <j1 rule="hyper" parents="370 4746 15452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      (x / K(y,z)) \ 1 = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,15196,a(flip),b,15527,a),flip(a)].">
      <j1 rule="hyper" parents="60 15196 15527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6291(a,1),15549(a,1,1))].">
      <j1 rule="para" parents="6291 15549"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      1 / (1 / (x * K(y,z))) = (K(z,y) * (x \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(15550(a,1),1313(a,2,1))].">
      <j1 rule="para" parents="15550 1313"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * (v5 \ 1))) = L(x,y,z * (v5 * K(w,u)))
    ]]></literal>
    <justification jstring="[para(15550(a,1),3426(a,1,3,2))].">
      <j1 rule="para" parents="15550 3426"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ 1) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(15133(a,1),15550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15133 15550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      K((K(x,y) * (z \ 1)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(y,x)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(15550(a,1),15484(a,1,1,1))].">
      <j1 rule="para" parents="15550 15484"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,u * (y * y))) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[para(15542(a,1),8834(a,1,2))].">
      <j1 rule="para" parents="15542 8834"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      x * K(x * (x * y),x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),15548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K(x,y) * T(T(z,z \ 1),u) = (T(z,u) \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4329(a,2),15553(a,1,2))].">
      <j1 rule="para" parents="4329 15553"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K(x,y) * T((z \ 1) \ 1,u) = (T(z,u) \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4333(a,2),15553(a,1,2))].">
      <j1 rule="para" parents="4333 15553"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      T(x,y) \ T((x \ 1) \ K(z,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (x * z),T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(15557(a,1),6137(a,1,2,1))].">
      <j1 rule="para" parents="15557 6137"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      K(x,y) * (z * z) = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(15120,a,14678,a)].">
      <j1 rule="hyper" parents="15120 14678"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      x \ (K(y,z) * (x * x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(721,a,15562,a)].">
      <j1 rule="hyper" parents="721 15562"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      T(x * K(y,z),x * x) = L(x * K(y,z),x,x)
    ]]></literal>
    <justification jstring="[para(15563(a,1),1238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15563 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(15240(a,1),11072(a,1,2))].">
      <j1 rule="para" parents="15240 11072"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = w
    ]]></literal>
    <justification jstring="[para(514(a,1),15248(a,1,2))].">
      <j1 rule="para" parents="514 15248"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ (w \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(9918(a,1),15464(a,1,2,1))].">
      <j1 rule="para" parents="9918 15464"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(1765(a,2),15473(a,1))].">
      <j1 rule="para" parents="1765 15473"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),15476(a,1,2,1))].">
      <j1 rule="para" parents="108 15476"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(5068(a,1),15476(a,1,2,1))].">
      <j1 rule="para" parents="5068 15476"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(((x * x) \ y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ (y * z)),u) = w
    ]]></literal>
    <justification jstring="[para(514(a,1),15485(a,1,1))].">
      <j1 rule="para" parents="514 15485"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      T(x,y / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(3510(a,1),15495(a,1,2))].">
      <j1 rule="para" parents="3510 15495"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      T(x * K(y,z),x * x) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15510,a(flip),b,15564,a),flip(a)].">
      <j1 rule="hyper" parents="370 15510 15564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      T(x * K(y,z),x * (x * u)) = T((x \ 1) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(15577(a,1),15388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15577 15388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      T(T(x,y),z * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),15569(a,1))].">
      <j1 rule="para" parents="18 15569"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      K((x \ y) \ y,L(z * u,w,v5)) = K(x,T(L((z \ 1) \ u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(8180,a,15152,a),flip(a)].">
      <j1 rule="hyper" parents="8180 15152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      (x \ (R(1 / x,y,z) \ u)) * K(x * (R(x,y,z) \ u),w) = T((x \ 1) \ (R(x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(7702(a,1),15216(a,1,1))].">
      <j1 rule="para" parents="7702 15216"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(32,a,5001,a(flip),b,15225,a),flip(a)].">
      <j1 rule="hyper" parents="32 5001 15225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      x * K(y,(z \ 1) \ (z \ u)) = (1 / x) \ K(y,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),15232(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13001,a,15234,a)].">
      <j1 rule="hyper" parents="13001 15234"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(15587(a,1),9524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15587 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(15587(a,1),12976(a,1,2))].">
      <j1 rule="para" parents="15587 12976"/>
    </justification>
  </clause>

  <clause id="15590">
    <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(15236(a,2),13033(a,1))].">
      <j1 rule="para" parents="15236 13033"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) = K(x,y / ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(551(a,1),15242(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="551 15242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      K(x,L(y * (z \ 1),u,w)) = K(x,L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,15246,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 15246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15593">
    <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(15246(a,2),13033(a,1))].">
      <j1 rule="para" parents="15246 13033"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x * y) = (x * y) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),15257(a,1,2))].">
      <j1 rule="para" parents="106 15257"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(7873(a,1),15268(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 15268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(15289(a,1),8790(a,1))].">
      <j1 rule="para" parents="15289 8790"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,15237,a(flip),b,15316,a),flip(a)].">
      <j1 rule="hyper" parents="370 15237 15316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,15317,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 15317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15599">
    <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(15317(a,2),13033(a,1))].">
      <j1 rule="para" parents="15317 13033"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      (x * K(y,x)) / z = x / (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(5678(a,1),15340(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5678 15340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15376,a(flip),b,15600,a),flip(a)].">
      <j1 rule="hyper" parents="370 15376 15600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      ((x * y) * K(T(z,y),x * y)) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(12578(a,1),15600(a,2,2,2))].">
      <j1 rule="para" parents="12578 15600"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      ((x * y) / x) / z = K(x,y) * (y / z)
    ]]></literal>
    <justification jstring="[para(5233(a,2),15601(a,1,1))].">
      <j1 rule="para" parents="5233 15601"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(5279(a,1),15601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5279 15601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      T(x,(y * z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ 1)) = u
    ]]></literal>
    <justification jstring="[para(15383(a,1),5768(a,1))].">
      <j1 rule="para" parents="15383 5768"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      T(x,y \ (L(z,y,z) \ 1)) = T(x,z / (z * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(15607,a,9707,a)].">
      <j1 rule="hyper" parents="15607 9707"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      T(x,(y * y) * ((z * u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u / (y * y)) \ (z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(1102(a,1),15607(a,1,2))].">
      <j1 rule="para" parents="1102 15607"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(9706(a,2),15607(a,1))].">
      <j1 rule="para" parents="9706 15607"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,((y * y) \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(2156(a,1),15387(a,1,2,2))].">
      <j1 rule="para" parents="2156 15387"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      T(x,T(y / z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) / u) = w
    ]]></literal>
    <justification jstring="[para(15403(a,2),15531(a,1))].">
      <j1 rule="para" parents="15403 15531"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      T(x,(y / z) * (u * u)) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(1082(a,1),15406(a,1,2))].">
      <j1 rule="para" parents="1082 15406"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,u * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(15379(a,1),15413(a,1,2))].">
      <j1 rule="para" parents="15379 15413"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x * ((y / z) \ K(u,y)),w) = K(x / (T(y,u) / z),w)
    ]]></literal>
    <justification jstring="[para(15370(a,1),15421(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15370 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / ((y / ((x \ 1) \ 1)) * (x * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,977,a,b,15427,a),flip(a)].">
      <j1 rule="hyper" parents="370 977 15427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (1 / w) = a(x,y,K(z,u)) / w
    ]]></literal>
    <justification jstring="[para(15496(a,2),15497(a,2,1))].">
      <j1 rule="para" parents="15496 15497"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9557,a(flip),b,15523,a)].">
      <j1 rule="hyper" parents="60 9557 15523"/>
    </justification>
  </clause>

  <clause id="15619">
    <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(15618(a,1),15270(a,1,2))].">
      <j1 rule="para" parents="15618 15270"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,z * z))) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,2),15543(a,1,2,2))].">
      <j1 rule="para" parents="107 15543"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ 1 = 1 / (K(x,y) / z)
    ]]></literal>
    <justification jstring="[para(15343(a,1),15551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15343 15551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      1 / (K(x,y) / z) = (z \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(15338,a,15621,a),flip(a)].">
      <j1 rule="hyper" parents="15338 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      (1 / x) \ K(y,T(z * u,w)) = x * K(y,T((z \ 1) \ u,w))
    ]]></literal>
    <justification jstring="[para(1531(a,1),15585(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1531 15585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      K(x,L(y / (1 / z),u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(77(a,1),15592(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="77 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L(T(z,y \ 1) * (1 / (y \ 1)),u,w))
    ]]></literal>
    <justification jstring="[para(4452(a,1),15592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4452 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x,L(y * (1 / z),u,w)) = K(x,L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(77(a,1),15598(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="77 15598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x,L(T(y,1 / z) * z,u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14523,a(flip),b,15627,a),flip(a)].">
      <j1 rule="hyper" parents="60 14523 15627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      T(x \ a(y,z,K(u,w)),K(a(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(y,z,u),w) * (x \ 1) = v5
    ]]></literal>
    <justification jstring="[para(15496(a,2),15197(a,1,1,2))].">
      <j1 rule="para" parents="15496 15197"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      L(x,L((y * K(z * y,u)) \ 1,z,u) \ w,v5) = L(x,((u * z) \ ((z * y) * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(15393(a,1),4024(a,2,2,1))].">
      <j1 rule="para" parents="15393 4024"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(5565(a,2),15566(a,1,2))].">
      <j1 rule="para" parents="5565 15566"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(5943,a,15589,a)].">
      <j1 rule="hyper" parents="5943 15589"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,15634,a)].">
      <j1 rule="hyper" parents="135 15634"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(15634(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15634 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15637">
    <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(8758(a,1),15636(a,1,1,2))].">
      <j1 rule="para" parents="8758 15636"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      T(x,y \ R(z \ 1,y,z)) = T(x,z / (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(11717(a,2),15608(a,1,2,2))].">
      <j1 rule="para" parents="11717 15608"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      T(x,y / (y * (z * y))) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,14384,a(flip),b,15638,a),flip(a)].">
      <j1 rule="hyper" parents="60 14384 15638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      x \ ((y * y) * K(z,u)) = (x \ (y * y)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(578(a,1),15183(a,1,1)),flip(a)].">
      <j1 rule="para" parents="578 15183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      (x * x) \ ((y \ (x * x)) * K(z,u)) = T(y,x * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(15641(a,1),1570(a,1,2))].">
      <j1 rule="para" parents="15641 1570"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * (1 / z) = (z \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(9477(a,1),15198(a,1,1,1))].">
      <j1 rule="para" parents="9477 15198"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1291,a,15643,a)].">
      <j1 rule="hyper" parents="1291 15643"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      L(x,y * ((z * u) / z),w) = L(x,y * (u * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,5962,a(flip),b,15207,a)].">
      <j1 rule="hyper" parents="60 5962 15207"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(T((x \ 1) \ 1,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15218(a,2),15493(a,1))].">
      <j1 rule="para" parents="15218 15493"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      T(x,((y * y) / z) * u) = T(x,(y * y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(806(a,1),15253(a,1,2,1))].">
      <j1 rule="para" parents="806 15253"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      T(x,((y * y) / z) * u) = T(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15166,a(flip),b,15647,a),flip(a)].">
      <j1 rule="hyper" parents="370 15166 15647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (u \ z)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(15492,a,15255,a)].">
      <j1 rule="hyper" parents="15492 15255"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      T(x,T(y,z) * ((u * z) \ u)) = T(x,((u * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),15649(a,1,2,1,2))].">
      <j1 rule="para" parents="4 15649"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ 1)) = T(x,(z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(62(a,1),15649(a,1,2,1,2))].">
      <j1 rule="para" parents="62 15649"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),(y \ 1) * ((y \ 1) \ (y \ z))) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,13379,a(flip),b,15651,a),flip(a)].">
      <j1 rule="hyper" parents="60 13379 15651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      K(x,(y * y) * ((z \ 1) * u)) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[para(28(a,1),15296(a,1,2))].">
      <j1 rule="para" parents="28 15296"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y * (L(z,y,y) * u))
    ]]></literal>
    <justification jstring="[para(579(a,1),15297(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="579 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,y * (((1 / y) * y) * (z * ((y * y) \ u)))) = K(x,y \ (T(z,y \ (y \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(1762(a,1),15297(a,2,2,2))].">
      <j1 rule="para" parents="1762 15297"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      (1 / x) * T(x \ ((x \ 1) \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(15303,a,15354,a),flip(a)].">
      <j1 rule="hyper" parents="15303 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      (x \ (x \ y)) * ((x \ 1) \ 1) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10549,a(flip),b,15656,a)].">
      <j1 rule="hyper" parents="60 10549 15656"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      x \ (T(y,z \ (z \ 1)) * x) = T(y,z \ (z \ x))
    ]]></literal>
    <justification jstring="[para(1762(a,1),15385(a,1,2))].">
      <j1 rule="para" parents="1762 15385"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(389,a,15659,a)].">
      <j1 rule="hyper" parents="389 15659"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(1146,a,15660,a)].">
      <j1 rule="hyper" parents="1146 15660"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = T(x,y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(1145,a,15660,a)].">
      <j1 rule="hyper" parents="1145 15660"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      T((x * y) / x,z \ (z \ x)) = T(y,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(986,a,15660,a),flip(a)].">
      <j1 rule="hyper" parents="986 15660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      T((x * y) / x,z \ (z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(15660(a,1),986(a,1))].">
      <j1 rule="para" parents="15660 986"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      T(x,y \ (y \ x)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(6703,a,15662,a),flip(a)].">
      <j1 rule="hyper" parents="6703 15662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x \ (x \ 1),y) * (y \ z) = T(y,x \ (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(15662(a,1),7873(a,2,1))].">
      <j1 rule="para" parents="15662 7873"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      T(T(x,y \ (y \ x)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(15662(a,1),15660(a,1,1))].">
      <j1 rule="para" parents="15662 15660"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x,y \ (y \ x)) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5289,a,15665,a)].">
      <j1 rule="hyper" parents="5289 15665"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ (u \ z)),w)) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(15665(a,2),5458(a,1,3,1))].">
      <j1 rule="para" parents="15665 5458"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      T(x,y \ (y \ x)) \ z = K(x,y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(15665(a,2),7846(a,1,1))].">
      <j1 rule="para" parents="15665 7846"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      T(T(x,y),z \ (u \ ((u * z) \ 1))) = T(x,(u * z) \ ((u * z) \ y))
    ]]></literal>
    <justification jstring="[para(1284(a,1),15661(a,1,2))].">
      <j1 rule="para" parents="1284 15661"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(15661(a,1),15660(a,1,1))].">
      <j1 rule="para" parents="15661 15660"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      L(x,y,T(z,u \ (u \ w))) = L(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[para(15667(a,1),15669(a,1,3))].">
      <j1 rule="para" parents="15667 15669"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      L(x,y,T(z,u \ w)) = L(x,y,T(z,u * w))
    ]]></literal>
    <justification jstring="[para(4(a,1),15673(a,1,3,2,2))].">
      <j1 rule="para" parents="4 15673"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z * 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,7067,a,b,15674,a)].">
      <j1 rule="hyper" parents="60 7067 15674"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      K(x \ (x \ y),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(7882,a,15670,a)].">
      <j1 rule="hyper" parents="7882 15670"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15672(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      T(T(x,y),y \ (y \ z)) = T(T(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(63(a,1),15672(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="63 15672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(15672(a,1),225(a,1)),flip(b)].">
      <j1 rule="para" parents="15672 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      T(T(x,a(y,y,z)),a(y,y,z) \ (a(y,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(15380(a,1),15679(a,2,1))].">
      <j1 rule="para" parents="15380 15679"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) * w),L(1 / y,z,u) \ (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(3864(a,1),15678(a,1,2,2))].">
      <j1 rule="para" parents="3864 15678"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      T(T(x,T(y \ z,z \ y) * (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(13189(a,1),15678(a,2,1,2))].">
      <j1 rule="para" parents="13189 15678"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      T(T(x,(L(y,z,u) \ y) * w),(L(y,z,u) \ y) \ (y \ L(y,z,u))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[para(14170(a,1),15678(a,1,2,2))].">
      <j1 rule="para" parents="14170 15678"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      (x / y) * T(y \ 1,z) = x * (y \ T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5260(a,1),15390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5260 15390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      x * (y \ T(y \ 1,y * x)) = (1 / y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(8518,a,15686,a),flip(a)].">
      <j1 rule="hyper" parents="8518 15686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      x * (y \ T(y \ 1,x * y)) = (1 / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(7578(a,2),15687(a,1,2,2))].">
      <j1 rule="para" parents="7578 15687"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      T(x * K((1 / y) * (x / y),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(15688(a,1),5502(a,1,1,2,1))].">
      <j1 rule="para" parents="15688 5502"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      (x \ T(x \ 1,y * x)) * R(y,x \ T(x \ 1,y * x),y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(15688(a,1),5537(a,2,1))].">
      <j1 rule="para" parents="15688 5537"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      T(x,(y / (1 / z)) / u) = T(x,(y / (z \ 1)) / u)
    ]]></literal>
    <justification jstring="[hyper(15532,a,15409,a),flip(a)].">
      <j1 rule="hyper" parents="15532 15409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      T(K(x,x \ y) / T(x,z),x) = K(x,x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(9098,a,15537,a)].">
      <j1 rule="hyper" parents="9098 15537"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      T(x,y * (z \ (1 / z))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,15530,a(flip),b,15544,a),flip(a)].">
      <j1 rule="hyper" parents="60 15530 15544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,u \ (u \ (y * z)))
    ]]></literal>
    <justification jstring="[para(704(a,1),15694(a,1,2))].">
      <j1 rule="para" parents="704 15694"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      T((x \ 1) \ K(x * y,x),y) = L(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(11753,a,15578,a),flip(a)].">
      <j1 rule="hyper" parents="11753 15578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      (x \ 1) \ K(x * y,x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(14608,a,15696,a),flip(a)].">
      <j1 rule="hyper" parents="14608 15696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      x * K(x \ (x \ y),x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),15697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      L(x \ (y * K(y \ z,y)),x,y) = ((y \ 1) * x) \ K(y * z,y)
    ]]></literal>
    <justification jstring="[para(15697(a,1),1501(a,1,1,2))].">
      <j1 rule="para" parents="15697 1501"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x \ (x \ y),x) = K(x * (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(31,a,15557,a,b,15698,a),flip(a)].">
      <j1 rule="hyper" parents="31 15557 15698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      T(x,y) \ T((x \ 1) \ K(z,x),y) = K(x \ (x \ z),T(x,y))
    ]]></literal>
    <justification jstring="[para(15698(a,1),5598(a,1,2,1))].">
      <j1 rule="para" parents="15698 5598"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = T((x \ 1) \ K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(15698(a,1),9061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15698 9061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) = K(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,6174,a(flip),b,15591,a),flip(a)].">
      <j1 rule="hyper" parents="370 6174 15591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(x,y * (((z * K(z * u,z)) \ w) \ K(z * K(z * u,z),u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(5502(a,1),15595(a,2,2,2,1))].">
      <j1 rule="para" parents="5502 15595"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      L(x,y * ((z * u) / z),w) = L(x,y * T(u,z),w)
    ]]></literal>
    <justification jstring="[para(5256(a,2),15645(a,2,2,2))].">
      <j1 rule="para" parents="5256 15645"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      L(x,y * T(z \ u,z),w) = L(x,y * (u / z),w)
    ]]></literal>
    <justification jstring="[para(5(a,1),15705(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      L(x,(y \ z) * z,u) = L(x,z * (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14841,a(flip),b,15706,a)].">
      <j1 rule="hyper" parents="60 14841 15706"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = L(x,z * (z / (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(5957,a,15707,a)].">
      <j1 rule="hyper" parents="5957 15707"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      T(x,T(y,z) * ((y * z) \ y)) = T(x,y * (y / (y * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14508,a(flip),b,15650,a),flip(a)].">
      <j1 rule="hyper" parents="370 14508 15650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,(z / (y * y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(15468,a,15653,a)].">
      <j1 rule="hyper" parents="15468 15653"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      K(x \ (x \ 1),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(32,a,15670,a(flip),b,15666,a),flip(a)].">
      <j1 rule="hyper" parents="32 15670 15666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,(y * z) \ (y * y))) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(107(a,2),15703(a,1,2))].">
      <j1 rule="para" parents="107 15703"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      T(x,y * (y / (y * z))) = T(x,y * ((z * y) \ y))
    ]]></literal>
    <justification jstring="[para(12087(a,1),15709(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12087 15709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      T(x,y * (y / (y * z))) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14408,a(flip),b,15713,a),flip(a)].">
      <j1 rule="hyper" parents="370 14408 15713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15714(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,((z \ y) * (z \ y)) * y)
    ]]></literal>
    <justification jstring="[para(1474(a,1),15715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1474 15715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,(y * y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(512(a,1),15710(a,2,2))].">
      <j1 rule="para" parents="512 15710"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x,y * (y * ((z \ 1) * u))) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15151,a(flip),b,15717,a),flip(a)].">
      <j1 rule="hyper" parents="370 15151 15717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      K(x,y * (y * ((1 / z) \ u))) = K(x,y * (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(77(a,1),15718(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 15718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ (z \ u),y)) = w
    ]]></literal>
    <justification jstring="[para(12548(a,2),15249(a,1))].">
      <j1 rule="para" parents="12548 15249"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y \ 1),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1530(a,2),15593(a,1,2,1))].">
      <j1 rule="para" parents="1530 15593"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K(x,L(y * (z \ K(z,u)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((u * z) / u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5935(a,1),15593(a,1,2,1,2))].">
      <j1 rule="para" parents="5935 15593"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      K(x,L(y * (K(z,y) * (u \ 1)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(7845(a,1),15593(a,1,2,1))].">
      <j1 rule="para" parents="7845 15593"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) * (1 / y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10346(a,1),15593(a,1,2,1))].">
      <j1 rule="para" parents="10346 15593"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (K(w,u) * z),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(15168(a,1),15599(a,1,2,1,2))].">
      <j1 rule="para" parents="15168 15599"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      T((x * y) / x,(z \ x) \ T(z,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z \ x) \ ((z \ x) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),15664(a,1,2,2))].">
      <j1 rule="para" parents="108 15664"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (1 / x)) \ ((z * (x \ 1)) \ (1 / x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(4501(a,1),15664(a,1,2,2))].">
      <j1 rule="para" parents="4501 15664"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ (z * z))) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,5617,a(flip),b,15243,a),flip(a)].">
      <j1 rule="hyper" parents="370 5617 15243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      K(x,y \ (z * T(u / w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(15293(a,2),15233(a,1))].">
      <j1 rule="para" parents="15293 15233"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      K(x,y \ (T(z,z \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,15294,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 15294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <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(15295(a,2),15233(a,1))].">
      <j1 rule="para" parents="15295 15233"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      (x \ (1 / x)) * T(((1 / x) \ 1) * (x \ y),x * x) = T((1 / ((1 / x) \ x)) * y,(1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(15322(a,2),4310(a,1,2))].">
      <j1 rule="para" parents="15322 4310"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      K(x,((1 / y) \ z) * u) = K(x,((y \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15258,a(flip),b,15327,a),flip(a)].">
      <j1 rule="hyper" parents="60 15258 15327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      T(x,((L(y,z,u) \ 1) * y) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,4660,a(flip),b,15334,a)].">
      <j1 rule="hyper" parents="60 4660 15334"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,15526,a)].">
      <j1 rule="hyper" parents="52 15526"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,14238,a,b,15736,a)].">
      <j1 rule="hyper" parents="60 14238 15736"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(10841(a,2),15736(a,1,2))].">
      <j1 rule="para" parents="10841 15736"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(1720,a,15738,a)].">
      <j1 rule="hyper" parents="1720 15738"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      L(x * 1,K(y,z) * K(y,u),(K(y,z) * K(y,u)) \ 1) = ((K(y,z) * K(y,u)) \ 1) * ((K(y,z) * K(y,u)) * x)
    ]]></literal>
    <justification jstring="[para(15739(a,1),5036(a,1,1,2))].">
      <j1 rule="para" parents="15739 5036"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      L(x,y,(z * K(u,z)) * w) = L(x,y,z * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,8201,a(flip),b,15552,a)].">
      <j1 rule="hyper" parents="60 8201 15552"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * w)) = L(x,y,z * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(7845(a,1),15741(a,1,3))].">
      <j1 rule="para" parents="7845 15741"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(12464(a,1),15583(a,1,2))].">
      <j1 rule="para" parents="12464 15583"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),15743(a,1,2,1))].">
      <j1 rule="para" parents="4 15743"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),15744(a,1,1,2))].">
      <j1 rule="para" parents="5 15744"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(210(a,1),15744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="210 15744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(15744(a,1),841(a,1))].">
      <j1 rule="para" parents="15744 841"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      T(x \ (y * z),K(y,z)) = K(y,z) * (x \ (z * y))
    ]]></literal>
    <justification jstring="[para(15744(a,1),8703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15744 8703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      T(x \ (y * z),K(y,z)) * L(u,x \ (z * y),K(y,z)) = K(y,z) * ((x \ (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(15750(a,2),92(a,1,1))].">
      <j1 rule="para" parents="15750 92"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6270,a(flip),b,15747,a),flip(a)].">
      <j1 rule="hyper" parents="370 6270 15747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(221,a,15753,a),flip(a)].">
      <j1 rule="hyper" parents="221 15753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(15180,a,15625,a),flip(a)].">
      <j1 rule="hyper" parents="15180 15625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ x) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(11155,a,15755,a)].">
      <j1 rule="hyper" parents="11155 15755"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(x,1 \ (((y * T(z,u)) \ y) * x)) = K(x,T(((y * z) \ y) * x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14217,a(flip),b,15755,a)].">
      <j1 rule="hyper" parents="60 14217 15755"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) * z,u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(4443(a,1),15630(a,1,2,1,1))].">
      <j1 rule="para" parents="4443 15630"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      ((x * x) \ (y \ (x * x))) * K(z,u) = T(y,x * x) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(851,a,15642,a)].">
      <j1 rule="hyper" parents="851 15642"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(x,y * (z * (L(z,u,w) \ z))) = K(x,y / L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(2160(a,1),15728(a,1,2,2))].">
      <j1 rule="para" parents="2160 15728"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      T(x,(y * (L(y,z,u) \ 1)) * w) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,10388,a(flip),b,15735,a)].">
      <j1 rule="hyper" parents="60 10388 15735"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      T(x \ 1,y * y) * K(z,u) = T(x,y * y) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(572(a,1),15759(a,1,1))].">
      <j1 rule="para" parents="572 15759"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      T(x \ 1,y * y) = T(x,y * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(32,a,15133,a,b,15762,a),flip(a)].">
      <j1 rule="hyper" parents="32 15133 15762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      x * T(x \ 1,y * y) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,15763,a,b,5721,a(flip))].">
      <j1 rule="hyper" parents="129 15763 5721"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      L(x,y,T(z,u * u) * (T(z \ 1,u * u) \ w)) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(15763(a,2),3372(a,1,3,2,1))].">
      <j1 rule="para" parents="15763 3372"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K(x * x,y \ 1) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(5384,a,15764,a),flip(a)].">
      <j1 rule="hyper" parents="5384 15764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      a(x,y,z * K(z,u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15766(a,1),7045(a,1,3,2))].">
      <j1 rule="para" parents="15766 7045"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      a(x,y,T(z,u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5256(a,2),15767(a,1,3))].">
      <j1 rule="para" parents="5256 15767"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * z) = a(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(1286(a,1),15768(a,1,3))].">
      <j1 rule="para" parents="1286 15768"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3081,a(flip),b,15769,a),flip(a)].">
      <j1 rule="hyper" parents="60 3081 15769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,u * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,3163,a(flip),b,15770,a),flip(a)].">
      <j1 rule="hyper" parents="60 3163 15770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      a(x,y,z * (1 / u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(77(a,1),15770(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="77 15770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3081,a(flip),b,15772,a),flip(a)].">
      <j1 rule="hyper" parents="60 3081 15772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(195(a,1),15774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="195 15774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) \ u)) = a(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14751(a,1),15774(a,1,3,2))].">
      <j1 rule="para" parents="14751 15774"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(30(a,1),15776(a,1,3))].">
      <j1 rule="para" parents="30 15776"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      a(x,y,z \ (u / (1 / w))) = a(x,y,z \ (u / w))
    ]]></literal>
    <justification jstring="[para(863(a,1),15776(a,1,3))].">
      <j1 rule="para" parents="863 15776"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(3874(a,2),15776(a,1,3))].">
      <j1 rule="para" parents="3874 15776"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      a(x,y,z * (u / (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15778(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 * v5)))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(30(a,1),15778(a,1,3,2))].">
      <j1 rule="para" parents="30 15778"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      a(x,y,z * (u * (w / (v5 * v5)))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(1098(a,1),15781(a,1,3,2))].">
      <j1 rule="para" parents="1098 15781"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(1101(a,1),15781(a,1,3,2))].">
      <j1 rule="para" parents="1101 15781"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) \ (L(u,w,v5) \ u))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12814(a,1),15781(a,1,3,2))].">
      <j1 rule="para" parents="12814 15781"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      a(x,y,L(z * (u * (w * w)),v5,v6)) = a(x,y,L(z * u,v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),15780(a,1,3,1))].">
      <j1 rule="para" parents="30 15780"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(248(a,1),15780(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="248 15780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ 1) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(3105,a,15787,a)].">
      <j1 rule="hyper" parents="3105 15787"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5))) = a(x,y,L(a(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(14181(a,1),15788(a,1,3))].">
      <j1 rule="para" parents="14181 15788"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,y * (z * a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(1362(a,1),15760(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1362 15760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      L(x,y,z * (T(z \ 1,u * u) \ w)) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,4108,a(flip),b,15765,a)].">
      <j1 rule="hyper" parents="60 4108 15765"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      L(x,y,K(z * z,u \ 1) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7962,a(flip),b,15791,a)].">
      <j1 rule="hyper" parents="60 7962 15791"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      L(x,y,K(z,u * u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(15766(a,1),15793(a,1,3,1))].">
      <j1 rule="para" parents="15766 15793"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      a(x,y,z * (((1 / u) \ w) * L((1 / u) \ w,u,u))) = a(x,y,z * ((T(u,u \ 1) * w) \ ((1 / u) \ w)))
    ]]></literal>
    <justification jstring="[para(3710(a,1),15777(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="3710 15777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(248(a,1),15786(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="248 15786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15798">
    <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(2162(a,1),15797(a,1,3,1))].">
      <j1 rule="para" parents="2162 15797"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      R((x \ 1) \ K(x,y),K(y,x) / x,y) = y / (((x * x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(15622(a,1),15521(a,1,1))].">
      <j1 rule="para" parents="15622 15521"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      ((1 / x) * y) \ K(x \ z,x) = ((x \ 1) * y) \ K(x * z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,15206,a(flip),b,15699,a)].">
      <j1 rule="hyper" parents="60 15206 15699"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      ((x \ 1) * y) \ K(x * y,x) = L(y / x,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,7737,a(flip),b,15800,a),flip(a)].">
      <j1 rule="hyper" parents="60 7737 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(z * u,z)) = L(x,y,L(u / z,z,z) \ 1)
    ]]></literal>
    <justification jstring="[para(15801(a,1),15190(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15801 15190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(222(a,1),15732(a,1,2,2,1))].">
      <j1 rule="para" parents="222 15732"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      R(T(T(x,y),x \ 1),K(y,x) / x,y) = y / (((x * x) \ y) * x)
    ]]></literal>
    <justification jstring="[para(5297(a,2),15799(a,1,1))].">
      <j1 rule="para" parents="5297 15799"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11925,a(flip),b,15114,a),flip(a)].">
      <j1 rule="hyper" parents="60 11925 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      a(L(K(x,y),K(y,x),K(y,x)),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5890,a,15805,a)].">
      <j1 rule="hyper" parents="5890 15805"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,15108,a,b,15805,a)].">
      <j1 rule="hyper" parents="60 15108 15805"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,15111,a(flip),b,15805,a),flip(a)].">
      <j1 rule="hyper" parents="60 15111 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(129,a,15805,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="129 15805 9"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = a(T(x,z),u,K(w,y))
    ]]></literal>
    <justification jstring="[para(8024(a,1),15805(a,1,1))].">
      <j1 rule="para" parents="8024 15805"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(11048(a,1),15805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11048 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      a(K(x,x \ (y \ z)),u,w) = a(x,u,K(w,(y * x) \ z))
    ]]></literal>
    <justification jstring="[para(12334(a,1),15805(a,1,1))].">
      <j1 rule="para" parents="12334 15805"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(12986,a,15808,a)].">
      <j1 rule="hyper" parents="12986 15808"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15805,a,b,15808,a)].">
      <j1 rule="hyper" parents="370 15805 15808"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11896,a,b,15808,a)].">
      <j1 rule="hyper" parents="370 11896 15808"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15109,a(flip),b,15808,a),flip(a)].">
      <j1 rule="hyper" parents="370 15109 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,12842,a(flip),b,15808,a),flip(a)].">
      <j1 rule="hyper" parents="370 12842 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,15808,a,b,4,a)].">
      <j1 rule="hyper" parents="129 15808 4"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13128,a,b,15808,a)].">
      <j1 rule="hyper" parents="60 13128 15808"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,11891,a,b,15808,a)].">
      <j1 rule="hyper" parents="60 11891 15808"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(8631(a,1),15808(a,1,3))].">
      <j1 rule="para" parents="8631 15808"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(z,w)))
    ]]></literal>
    <justification jstring="[para(8645(a,1),15808(a,1,3))].">
      <j1 rule="para" parents="8645 15808"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      a(x,y,K(z,T(u,x) * w)) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[para(9222(a,1),15808(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9222 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(15808(a,1),11903(a,2,1))].">
      <j1 rule="para" parents="15808 11903"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15808(a,2),11923(a,1,2))].">
      <j1 rule="para" parents="15808 11923"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(15808(a,2),11928(a,1,1))].">
      <j1 rule="para" parents="15808 11928"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15808(a,1),12932(a,1,2))].">
      <j1 rule="para" parents="15808 12932"/>
    </justification>
  </clause>

  <clause id="15828">
    <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(15808(a,1),12988(a,1,2))].">
      <j1 rule="para" parents="15808 12988"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      L(K(x * y,z),x,y) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,15817,a)].">
      <j1 rule="hyper" parents="49 15817"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,11898,a,b,15814,a)].">
      <j1 rule="hyper" parents="370 11898 15814"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(w,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,15814,a,b,4,a)].">
      <j1 rule="hyper" parents="129 15814 4"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      x * a(a(y,z,u) \ x,z,K(u,y)) = (a(y,z,u) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,15816,a,b,88,a)].">
      <j1 rule="hyper" parents="129 15816 88"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u) * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,15816,a,b,5231,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 15816 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,15816,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 15816 5230"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      a(x,y,z) \ a(u,y,K(z,x)) = T(a(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,15816,a,b,5719,a(flip))].">
      <j1 rule="hyper" parents="125 15816 5719"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,6362,a(flip),b,15816,a),flip(a)].">
      <j1 rule="hyper" parents="60 6362 15816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = K(x,a(L(w,u,u),y,z))
    ]]></literal>
    <justification jstring="[para(2956(a,1),15816(a,2,2))].">
      <j1 rule="para" parents="2956 15816"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(15816(a,2),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15816 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15816(a,2),5265(a,1,2))].">
      <j1 rule="para" parents="15816 5265"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) * y) / a(z,u,w)) = x * a(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(15816(a,2),6309(a,2,2))].">
      <j1 rule="para" parents="15816 6309"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      L(x,y,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[para(15816(a,2),8240(a,1,3))].">
      <j1 rule="para" parents="15816 8240"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(15816(a,2),12922(a,1,1))].">
      <j1 rule="para" parents="15816 12922"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(15816(a,1),15109(a,2,2))].">
      <j1 rule="para" parents="15816 15109"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,15836,a)].">
      <j1 rule="hyper" parents="53 15836"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      T(x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[para(3091(a,1),15845(a,1,2))].">
      <j1 rule="para" parents="3091 15845"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      a(x,y,y) * z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(3284,a,15846,a),flip(a)].">
      <j1 rule="hyper" parents="3284 15846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      T(a(x,y,y),z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,15846,a)].">
      <j1 rule="hyper" parents="51 15846"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      L(a(x,y,y),z,u) * (u * z) = u * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,15846,a(flip),b,15635,a)].">
      <j1 rule="hyper" parents="129 15846 15635"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      T(x,a(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(15846(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="15846 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      x / a(y,z,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,z) \ x = u
    ]]></literal>
    <justification jstring="[para(15846(a,1),494(a,1))].">
      <j1 rule="para" parents="15846 494"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      x * a(y,z,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,z) * x = u
    ]]></literal>
    <justification jstring="[para(15849(a,1),328(a,1,2))].">
      <j1 rule="para" parents="15849 328"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      L(a(x,y,y),z,u) * (z * u) = u * (T(z,u) * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(15849(a,1),12491(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15849 12491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      (x * a(y,z,z)) / (a(y,z,z) * T(x,u)) = K(u,x)
    ]]></literal>
    <justification jstring="[para(15848(a,2),7927(a,1,2))].">
      <j1 rule="para" parents="15848 7927"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(13033,a,15829,a)].">
      <j1 rule="hyper" parents="13033 15829"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      a(x,y,K(z,u * x)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15808,a(flip),b,15819,a)].">
      <j1 rule="hyper" parents="60 15808 15819"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15805,a(flip),b,15811,a),flip(a)].">
      <j1 rule="hyper" parents="370 15805 15811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) \ w)) = a(x,y,K(z,u \ (x \ w)))
    ]]></literal>
    <justification jstring="[para(344(a,1),15858(a,1,3,2))].">
      <j1 rule="para" parents="344 15858"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) \ w)) = a(x,y,K(z,u \ (x * w)))
    ]]></literal>
    <justification jstring="[para(656(a,1),15858(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="656 15858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ (x * w))) = a(x,y,K(z,T(u,x) \ w))
    ]]></literal>
    <justification jstring="[para(663(a,1),15858(a,1,3,2))].">
      <j1 rule="para" parents="663 15858"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15805,a(flip),b,15810,a),flip(a)].">
      <j1 rule="hyper" parents="60 15805 15810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(15813(a,1),13042(a,1))].">
      <j1 rule="para" parents="15813 13042"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(15111(a,2),15863(a,1))].">
      <j1 rule="para" parents="15111 15863"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(15805(a,2),15863(a,1))].">
      <j1 rule="para" parents="15805 15863"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(15808(a,1),15863(a,1))].">
      <j1 rule="para" parents="15808 15863"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,K(w,z))) = v5
    ]]></literal>
    <justification jstring="[para(8631(a,1),15867(a,1,3))].">
      <j1 rule="para" parents="8631 15867"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(x,u / (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(12381(a,1),15867(a,1,3))].">
      <j1 rule="para" parents="12381 15867"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = L(K(z,x),y,u)
    ]]></literal>
    <justification jstring="[hyper(6302,a,15815,a)].">
      <j1 rule="hyper" parents="6302 15815"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,1),15821(a,2,3))].">
      <j1 rule="para" parents="8636 15821"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = K(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,12949,a(flip),b,15826,a)].">
      <j1 rule="hyper" parents="129 12949 15826"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      x \ (y * (a(z,u,K(w,v5)) * T(a(v5,u,K(w,z)) * (y \ x),v6))) = K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(15826(a,1),6118(a,1,2,2,2,1))].">
      <j1 rule="para" parents="15826 6118"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,y) * a(x,T(z,u),K(w,y))
    ]]></literal>
    <justification jstring="[para(5922(a,1),15827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5922 15827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y \ (w \ v5),T(y,z))) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(13006(a,1),15827(a,1,2,3))].">
      <j1 rule="para" parents="13006 15827"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5 * a(w,u,K(z,y))
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(15831(a,1),41(a,2))].">
      <j1 rule="para" parents="15831 41"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(8630(a,1),15844(a,1,3))].">
      <j1 rule="para" parents="8630 15844"/>
    </justification>
  </clause>

  <clause id="15882">
    <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(15873(a,2),13033(a,1))].">
      <j1 rule="para" parents="15873 13033"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(15808(a,2),15873(a,1,1))].">
      <j1 rule="para" parents="15808 15873"/>
    </justification>
  </clause>

  <clause id="15884">
    <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(12137,a,15875,a)].">
      <j1 rule="hyper" parents="12137 15875"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      K(x,L(y,z,L(u,u,w))) = a(y,z,K(x,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11056(a,1),15876(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="11056 15876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15821,a(flip),b,15881,a)].">
      <j1 rule="hyper" parents="60 15821 15881"/>
    </justification>
  </clause>

  <clause id="15887">
    <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(370,a,9519,a(flip),b,15883,a),flip(a)].">
      <j1 rule="hyper" parents="370 9519 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <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(15883(a,1),41(a,1))].">
      <j1 rule="para" parents="15883 41"/>
    </justification>
  </clause>

  <clause id="15889">
    <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(15883(a,2),9580(a,1))].">
      <j1 rule="para" parents="15883 9580"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      (1 / x) * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(2957(a,1),15839(a,1,2))].">
      <j1 rule="para" parents="2957 15839"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,13634,a,b,15843,a)].">
      <j1 rule="hyper" parents="60 13634 15843"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(7458(a,1),15806(a,1,1))].">
      <j1 rule="para" parents="7458 15806"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(15866,a,15892,a)].">
      <j1 rule="hyper" parents="15866 15892"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(15865,a,15892,a)].">
      <j1 rule="hyper" parents="15865 15892"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(15892(a,1),15865(a,1))].">
      <j1 rule="para" parents="15892 15865"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(15892(a,1),15866(a,1))].">
      <j1 rule="para" parents="15892 15866"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u,x)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15893(a,1),12932(a,1,2))].">
      <j1 rule="para" parents="15893 12932"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,K(x,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(15893(a,1),15499(a,1,2))].">
      <j1 rule="para" parents="15893 15499"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(x,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(15893(a,1),15827(a,1,2))].">
      <j1 rule="para" parents="15893 15827"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15894(a,1),11895(a,1,2))].">
      <j1 rule="para" parents="15894 11895"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15894(a,1),12932(a,1,2))].">
      <j1 rule="para" parents="15894 12932"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      a(x,y,z) * a(u,y,K(z,x)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(15894(a,1),15499(a,1,2))].">
      <j1 rule="para" parents="15894 15499"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      (x / y) * a(y,z,K(u,w)) = x / T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(15894(a,1),15505(a,1,2))].">
      <j1 rule="para" parents="15894 15505"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      a(x,y,z) * a(u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(15894(a,1),15503(a,1,2))].">
      <j1 rule="para" parents="15894 15503"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15894(a,1),15834(a,1,2))].">
      <j1 rule="para" parents="15894 15834"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(15913(a,1),15502(a,1,1))].">
      <j1 rule="para" parents="15913 15502"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) / a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(15913(a,1),15504(a,1))].">
      <j1 rule="para" parents="15913 15504"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * (u / w),y,K(z,x)) = v5
    ]]></literal>
    <justification jstring="[para(12562(a,1),15902(a,1,3))].">
      <j1 rule="para" parents="12562 15902"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(15822(a,1),15903(a,1))].">
      <j1 rule="para" parents="15822 15903"/>
    </justification>
  </clause>

  <clause id="15920">
    <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(15907(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15907 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = L(K(x,y),y * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,11382,a,b,15909,a),flip(a)].">
      <j1 rule="hyper" parents="370 11382 15909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,K(x,u)) = T(a(x,y,z),u * z)
    ]]></literal>
    <justification jstring="[para(15857(a,1),15905(a,1,2))].">
      <j1 rule="para" parents="15857 15905"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(31,a,15908,a,b,15922,a)].">
      <j1 rule="hyper" parents="31 15908 15922"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),15924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 15924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),15924(a,1,3))].">
      <j1 rule="para" parents="8636 15924"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(15867,a,15925,a)].">
      <j1 rule="hyper" parents="15867 15925"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(15863,a,15925,a)].">
      <j1 rule="hyper" parents="15863 15925"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[para(15925(a,1),15827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15925 15827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      a(T(x,y) \ z,T((x \ z) \ z,y),K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[para(8407(a,2),15928(a,1,2))].">
      <j1 rule="para" parents="8407 15928"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),15926(a,2,3))].">
      <j1 rule="para" parents="8636 15926"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15827,a(flip),b,15929,a),flip(a)].">
      <j1 rule="hyper" parents="370 15827 15929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12974,a(flip),b,15932,a),flip(a)].">
      <j1 rule="hyper" parents="60 12974 15932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),15932(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      K(x,L(y,T(z * u,u \ 1),u \ 1)) = K(x,L(y,R(z,u,u),u \ 1))
    ]]></literal>
    <justification jstring="[para(1120(a,1),15932(a,1,2,2))].">
      <j1 rule="para" parents="1120 15932"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      K(x,L(y,T(1 / (z / u),z),(1 / (z / u)) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(7722(a,2),15932(a,1,2,2))].">
      <j1 rule="para" parents="7722 15932"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      K(x,L((y \ z) \ (y * u),u,y)) = K(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,12935,a(flip),b,15934,a),flip(a)].">
      <j1 rule="hyper" parents="60 12935 15934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,L((y * z) \ (y \ u),z,y)) = K(x,(y * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(344(a,1),15934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="344 15934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,((y \ 1) * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1501(a,1),15934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1501 15934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14828(a,2),15934(a,1,2))].">
      <j1 rule="para" parents="14828 15934"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,L(u,y,x \ y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[para(108(a,2),15933(a,1,1,1))].">
      <j1 rule="para" parents="108 15933"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K((x \ (y \ ((1 / z) \ u))) \ w,L(v5,y \ (z \ u),x)) = K((y \ ((1 / z) \ u)) \ (x * w),v5)
    ]]></literal>
    <justification jstring="[para(3723(a,1),15933(a,1,2))].">
      <j1 rule="para" parents="3723 15933"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(15929(a,2),15828(a,1))].">
      <j1 rule="para" parents="15929 15828"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      a(x,y,z) * a(x * (y * z),y,K(z,x)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(82(a,1),15833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 15833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = a(x,y,K(z,L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15816,a,b,15837,a),flip(a)].">
      <j1 rule="hyper" parents="370 15816 15837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ (L(a(z,u,u),y,x) * (y * x)) = T(y,x)
    ]]></literal>
    <justification jstring="[para(15850(a,1),12386(a,1,1,1))].">
      <j1 rule="para" parents="15850 12386"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      ((L(a(x,y,y),z,u) * (z * u)) / u) \ (u * (z * a(x,y,y))) = T(u,z)
    ]]></literal>
    <justification jstring="[para(15850(a,1),12386(a,1,2))].">
      <j1 rule="para" parents="15850 12386"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(w,x))) = v5
    ]]></literal>
    <justification jstring="[para(15893(a,1),15870(a,1))].">
      <j1 rule="para" parents="15893 15870"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,L(y,z,L(u,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15885(a,2),15882(a,1))].">
      <j1 rule="para" parents="15885 15882"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15920,a,13130,a),flip(a)].">
      <j1 rule="hyper" parents="15920 13130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13130(a,1),15920(a,1))].">
      <j1 rule="para" parents="13130 15920"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      T(a(x,y,z),u * z) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15905,a(flip),b,15923,a),flip(a)].">
      <j1 rule="hyper" parents="60 15905 15923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      a(x,y,K(z,u * (u * w))) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[para(15124(a,1),15946(a,2,3))].">
      <j1 rule="para" parents="15124 15946"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      a(x,y,K(z,u \ w)) = a(x,y,K(z,u * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),15957(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x * y)) = T(x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15958(a,1),15913(a,1,2))].">
      <j1 rule="para" parents="15958 15913"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ w)) = a(x,y,K(z,x \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(15865,a,15812,a),flip(a)].">
      <j1 rule="hyper" parents="15865 15812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      a(x,y,K(z,u \ (x \ w))) = a(x,y,K(z,(x * u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,15958,a(flip),b,15859,a),flip(a)].">
      <j1 rule="hyper" parents="60 15958 15859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) \ w)) = a(x,y,K(z,u * (x * w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,15860,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 15860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      a(x,y,K(z,(u * x) \ w)) = a(x,y,K(z,x * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,15961,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) * w)) = a(x,y,K(z,u * (x \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15958,a(flip),b,15962,a),flip(a)].">
      <j1 rule="hyper" parents="60 15958 15962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) * w)) = a(x,y,K(z,u * (x * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15958,a(flip),b,15963,a)].">
      <j1 rule="hyper" parents="60 15958 15963"/>
    </justification>
  </clause>

  <clause id="15968">
    <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(15809(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15809 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      1 / T(x,a(y,z,u)) = T(1 / x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(15890,a,15911,a),flip(a)].">
      <j1 rule="hyper" parents="15890 15911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(x,y,K(z,T(u,x) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,15965,a(flip),b,15861,a)].">
      <j1 rule="hyper" parents="60 15965 15861"/>
    </justification>
  </clause>

  <clause id="15971">
    <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(8648(a,1),15884(a,1,2))].">
      <j1 rule="para" parents="8648 15884"/>
    </justification>
  </clause>

  <clause id="15972">
    <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(93(a,2),15887(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="93 15887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(x,y,K(z,T(u,x) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,15970,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <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(60,a,13357,a(flip),b,15971,a)].">
      <j1 rule="hyper" parents="60 13357 15971"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(11914(a,1),15974(a,1,1))].">
      <j1 rule="para" parents="11914 15974"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),15975(a,2,3))].">
      <j1 rule="para" parents="8648 15975"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      a(x,y,K(z,x * (u \ (x * w)))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15823,a(flip),b,15973,a),flip(a)].">
      <j1 rule="hyper" parents="370 15823 15973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,L(y * (z \ u),z \ u,z)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(15235,a,12922,a),flip(a)].">
      <j1 rule="hyper" parents="15235 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,L(y * (z \ u),u,z)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(15944,a,15978,a)].">
      <j1 rule="hyper" parents="15944 15978"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * (y \ (y \ u)),u,y)) = w
    ]]></literal>
    <justification jstring="[para(15979(a,1),15944(a,1))].">
      <j1 rule="para" parents="15979 15944"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      T(x \ 1,x \ y) \ (y / (1 / x)) = x \ ((x * x) * ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(7721(a,1),15325(a,1,1))].">
      <j1 rule="para" parents="7721 15325"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      K(x,x * x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3(a,1),15391(a,1,1,1))].">
      <j1 rule="para" parents="3 15391"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      a(x,x,x) * (y * K(x \ 1,y)) = ((1 / x) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5602(a,1),15982(a,1,1))].">
      <j1 rule="para" parents="5602 15982"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      a(x,x,x) * (y * K(x \ 1,y)) = ((x \ 1) * y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,9958,a(flip),b,15983,a),flip(a)].">
      <j1 rule="hyper" parents="370 9958 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      a(((x \ 1) * y) / (1 / x),z,u) = a((x \ 1) \ (y * (1 / x)),z,u)
    ]]></literal>
    <justification jstring="[para(15984(a,1),14719(a,1,1))].">
      <j1 rule="para" parents="15984 14719"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x \ y))) = y * a(z,u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[para(15496(a,2),15506(a,2,2))].">
      <j1 rule="para" parents="15496 15506"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      K((x \ y) \ y,L(z * u,w,v5)) = K(x,L(T((z \ 1) \ u,y),w,v5))
    ]]></literal>
    <justification jstring="[para(20(a,2),15580(a,2,2))].">
      <j1 rule="para" parents="20 15580"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      ((x * y) * K(z,y * x)) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(12554(a,1),15603(a,1,1,2))].">
      <j1 rule="para" parents="12554 15603"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,L(1 / y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(3790(a,1),15611(a,2,2,1))].">
      <j1 rule="para" parents="3790 15611"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5074,a(flip),b,15989,a),flip(a)].">
      <j1 rule="hyper" parents="370 5074 15989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[para(2156(a,1),15990(a,1,2))].">
      <j1 rule="para" parents="2156 15990"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,(z \ y) * ((z \ y) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15166,a(flip),b,15716,a),flip(a)].">
      <j1 rule="hyper" parents="370 15166 15716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15994">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(10478(a,1),15737(a,1,1))].">
      <j1 rule="para" parents="10478 15737"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(15994(a,1),14994(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15994 14994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,((y * T(z,u)) \ y) * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),15757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="62 15757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5512,a(flip),b,15996,a),flip(a)].">
      <j1 rule="hyper" parents="370 5512 15996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(12835,a,15997,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12835 15997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,11144,a,b,15998,a),flip(a)].">
      <j1 rule="hyper" parents="370 11144 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),15999(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 15999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(11599,a,16000,a),flip(a)].">
      <j1 rule="hyper" parents="11599 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(12622,a,16001,a)].">
      <j1 rule="hyper" parents="12622 16001"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,11878,a(flip),b,16001,a)].">
      <j1 rule="hyper" parents="60 11878 16001"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13381,a(flip),b,16002,a)].">
      <j1 rule="hyper" parents="60 13381 16002"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),16003(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ T(T(x,u),w),w)) = K(T(x,w),T(z * T(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11555,a,b,16005,a)].">
      <j1 rule="hyper" parents="60 11555 16005"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      R(K(x,T(x * T(y,z),z)),x * u,w) = K(R(x,u,w),((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[para(16004(a,2),9753(a,1,1))].">
      <j1 rule="para" parents="16004 9753"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),L(z,u,w),w * u)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(2660(a,2),15798(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2660 15798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(11923(a,1),15968(a,1))].">
      <j1 rule="para" parents="11923 15968"/>
    </justification>
  </clause>

  <clause id="16010">
    <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(15825(a,1),15968(a,1))].">
      <j1 rule="para" parents="15825 15968"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      T(x \ 1,x \ y) \ (y / (1 / x)) = (x \ 1) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,10040,a(flip),b,15981,a),flip(a)].">
      <j1 rule="hyper" parents="370 10040 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      (x / (1 / y)) * K((y \ 1) \ ((y \ 1) \ x),T(y \ 1,y \ x)) = (T(y \ 1,y \ x) \ (x / (1 / y))) * T(y \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(16011(a,1),353(a,1,2,1))].">
      <j1 rule="para" parents="16011 353"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      a((x \ 1) \ (y * (1 / x)),z,u) = a(((x \ 1) * y) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2993,a,15985,a),flip(a)].">
      <j1 rule="hyper" parents="2993 15985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a((x \ 1) \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2994,a,16013,a),flip(a)].">
      <j1 rule="hyper" parents="2994 16013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a(x \ (y * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2959,a(flip),b,16014,a),flip(a)].">
      <j1 rule="hyper" parents="370 2959 16014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      a(((x \ 1) * y) / x,z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),16015(a,2,1))].">
      <j1 rule="para" parents="17 16015"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x * y))) = y * a(z,u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[para(15958(a,1),15986(a,1,2,2))].">
      <j1 rule="para" parents="15958 15986"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      K(x,L(T((y \ 1) \ z,u),w,v5)) = K(x,T(L(y * z,w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(8180,a,15987,a),flip(a)].">
      <j1 rule="hyper" parents="8180 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      K(x,L(T((y \ 1) \ z,u),w,v5)) = K(x,L(T(y * z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(20(a,2),16018(a,2,2))].">
      <j1 rule="para" parents="20 16018"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,10898,a(flip),b,15995,a),flip(a)].">
      <j1 rule="hyper" parents="370 10898 15995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(7062(a,1),16020(a,1,2,1))].">
      <j1 rule="para" parents="7062 16020"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(10478(a,1),16022(a,1,2))].">
      <j1 rule="para" parents="10478 16022"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,16023,a)].">
      <j1 rule="hyper" parents="215 16023"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      (((x \ K(x,y)) * T(x,z)) \ 1) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(16024(a,1),2122(a,1,1,1))].">
      <j1 rule="para" parents="16024 2122"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,x * y))) = y * a(z,u,K(w,x * y))
    ]]></literal>
    <justification jstring="[para(15958(a,1),16017(a,2,2))].">
      <j1 rule="para" parents="15958 16017"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      x * T(x \ y,a(z,u,w)) = y * a(z,u,K(w,x * y))
    ]]></literal>
    <justification jstring="[para(15960(a,1),16026(a,1,2))].">
      <j1 rule="para" parents="15960 16026"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x \ (x \ y),T(x,z)) = K(x * (x * y),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(15561,a,15701,a),flip(a)].">
      <j1 rule="hyper" parents="15561 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      T(x,(y * y) / (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u / (y * y)) \ (z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(15398(a,1),15609(a,1))].">
      <j1 rule="para" parents="15398 15609"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      T(x,(y / (z * z)) \ (u \ 1)) = T(x,z * (z / (u * y)))
    ]]></literal>
    <justification jstring="[hyper(16029,a,15256,a)].">
      <j1 rule="hyper" parents="16029 15256"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      T(x,(y * y) * (z \ (u \ 1))) = T(x,y * (y / (u * z)))
    ]]></literal>
    <justification jstring="[para(512(a,1),16030(a,1,2))].">
      <j1 rule="para" parents="512 16030"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(z * u,z)) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,15802,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * K(u * z,z)) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[para(6557(a,2),16032(a,1,3,2))].">
      <j1 rule="para" parents="6557 16032"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      L(x,y,(z \ 1) * (u * K(u * z,z))) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[para(12841(a,1),16033(a,1,3))].">
      <j1 rule="para" parents="12841 16033"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      L(x,y,z * (u * K(u * z,z))) = L(x,y,L(u / z,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,3438,a(flip),b,16034,a)].">
      <j1 rule="hyper" parents="60 3438 16034"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      L(x,y,L(z / u,u,u)) = L(x,y,T(u * z,u))
    ]]></literal>
    <justification jstring="[para(6645(a,1),16035(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6645 16035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      L(x,y,T(z * (u * z),z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16036(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      L(x,y,(z * u) * u) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(14466,a,16037,a)].">
      <j1 rule="hyper" parents="14466 16037"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      L(x,y,R(z,u,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(3539,a,16038,a)].">
      <j1 rule="hyper" parents="3539 16038"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2482,a(flip),b,16039,a),flip(a)].">
      <j1 rule="hyper" parents="60 2482 16039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3730,a(flip),b,16040,a),flip(a)].">
      <j1 rule="hyper" parents="370 3730 16040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16042">
    <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(8630(a,1),15889(a,1,1,3))].">
      <j1 rule="para" parents="8630 15889"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      K(x,L(y,T(z * u,u \ 1),u)) = K(x,L(y,R(z,u,u),u \ 1))
    ]]></literal>
    <justification jstring="[para(1492(a,1),15935(a,1,2))].">
      <j1 rule="para" parents="1492 15935"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,(y * ((1 / y) * z)) \ u)
    ]]></literal>
    <justification jstring="[para(951(a,1),15939(a,2,2,1))].">
      <j1 rule="para" parents="951 15939"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ (x * (T(y,x) * a(z,u,u))) = T(y,x)
    ]]></literal>
    <justification jstring="[para(15854(a,1),15947(a,1,2))].">
      <j1 rule="para" parents="15854 15947"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      ((x * (T(y,x) * a(z,u,u))) / x) \ (x * (y * a(z,u,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(15854(a,1),15948(a,1,1,1))].">
      <j1 rule="para" parents="15854 15948"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      ((x * (T(y,x) * a(z,u,u))) / x) \ (x * (a(z,u,u) * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(15848(a,2),16046(a,1,2,2))].">
      <j1 rule="para" parents="15848 16046"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      (1 / x) * T((1 / x) * y,z) = (x \ 1) * T((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(15310,a,15213,a),flip(a)].">
      <j1 rule="hyper" parents="15310 15213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      T(x,y * (z * ((1 / u) * w))) = T(x,y * (z * ((u \ 1) * w)))
    ]]></literal>
    <justification jstring="[para(15329(a,1),15254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15329 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      T(x,T(y,z * ((1 / u) * w)) * (z * ((u \ 1) * w))) = T(x,(z * ((1 / u) * w)) * y)
    ]]></literal>
    <justification jstring="[hyper(12606,a,16049,a),flip(a)].">
      <j1 rule="hyper" parents="12606 16049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = (x \ y) \ ((1 / x) * T(z,x))
    ]]></literal>
    <justification jstring="[para(1337(a,1),15326(a,2,2))].">
      <j1 rule="para" parents="1337 15326"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      ((1 / x) \ y) \ (z * ((x \ 1) \ 1)) = ((x \ 1) \ y) \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1479,a(flip),b,16051,a),flip(a)].">
      <j1 rule="hyper" parents="370 1479 16051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(15423(a,1),9749(a,1))].">
      <j1 rule="para" parents="15423 9749"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) / (1 / y)) / u)
    ]]></literal>
    <justification jstring="[para(1315(a,1),15431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1315 15431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) / (y \ 1)) / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,15691,a(flip),b,16054,a),flip(a)].">
      <j1 rule="hyper" parents="370 15691 16054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,((z * z) * y) / u)
    ]]></literal>
    <justification jstring="[para(527(a,1),16055(a,2,2,1))].">
      <j1 rule="para" parents="527 16055"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,(z * z) * (y / u))
    ]]></literal>
    <justification jstring="[para(853(a,1),16056(a,2,2))].">
      <j1 rule="para" parents="853 16056"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      T(x,(y \ (z \ (z \ 1))) \ (u \ 1)) = T(x,z * (z * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15166,a(flip),b,16057,a),flip(a)].">
      <j1 rule="hyper" parents="370 15166 16057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      T(x,(y * y) * ((z \ 1) \ (u \ 1))) = T(x,y * (y * (z / u)))
    ]]></literal>
    <justification jstring="[para(1139(a,1),16058(a,1,2))].">
      <j1 rule="para" parents="1139 16058"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      T(x,y * (y / (z * (u \ 1)))) = T(x,y * (y * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16031,a(flip),b,16059,a)].">
      <j1 rule="hyper" parents="60 16031 16059"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(y \ (x \ 1),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8637,a(flip),b,15433,a),flip(a)].">
      <j1 rule="hyper" parents="370 8637 15433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      T(x,T(y,z) * ((1 / z) * (z \ 1))) = T(x,(1 / z) * (((z * z) \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4674,a(flip),b,15545,a)].">
      <j1 rule="hyper" parents="60 4674 15545"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(15912,a,15945,a),flip(a)].">
      <j1 rule="hyper" parents="15912 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(T(x,y),T(z * T(x,y),u)) = K(x,T((u / (u * z)) \ x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11556,a(flip),b,16006,a),flip(a)].">
      <j1 rule="hyper" parents="60 11556 16006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(8181,a,16064,a)].">
      <j1 rule="hyper" parents="8181 16064"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10298,a(flip),b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="60 10298 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),z),u)) = K(x,T((z / (y * z)) \ x,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16067(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 16067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),z),y)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,11602,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="370 11602 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9672,a,16070,a)].">
      <j1 rule="hyper" parents="9672 16070"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5593,a(flip),b,16071,a),flip(a)].">
      <j1 rule="hyper" parents="370 5593 16071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / y,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(77(a,1),16072(a,2,2,1,1))].">
      <j1 rule="para" parents="77 16072"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(370,a,13436,a(flip),b,16073,a)].">
      <j1 rule="hyper" parents="370 13436 16073"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      R(R(K(x,x * y),y,z),x * u,w) = K(R(x,u,w),T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[para(16074(a,2),9753(a,1,1))].">
      <j1 rule="para" parents="16074 9753"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),T(x * T(u,w),w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9758,a(flip),b,16076,a)].">
      <j1 rule="hyper" parents="60 9758 16076"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),((u \ w) / w) \ x)
    ]]></literal>
    <justification jstring="[hyper(9941,a,16007,a)].">
      <j1 rule="hyper" parents="9941 16007"/>
    </justification>
  </clause>

  <clause id="16079">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * (w / (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(14041,a,16078,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14041 16078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(74(a,1),16079(a,2,2,2))].">
      <j1 rule="para" parents="74 16079"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16077,a,b,16080,a)].">
      <j1 rule="hyper" parents="60 16077 16080"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(13965(a,1),16082(a,1,1))].">
      <j1 rule="para" parents="13965 16082"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(13962,a,16084,a)].">
      <j1 rule="hyper" parents="13962 16084"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,13965,a(flip),b,16085,a),flip(a)].">
      <j1 rule="hyper" parents="370 13965 16085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13981,a(flip),b,16086,a),flip(a)].">
      <j1 rule="hyper" parents="60 13981 16086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14045,a(flip),b,16087,a),flip(a)].">
      <j1 rule="hyper" parents="60 14045 16087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) * x = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(16089(a,2),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16089 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5276,a,16090,a)].">
      <j1 rule="hyper" parents="5276 16090"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,R(y,z,u))) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14058,a,b,16091,a)].">
      <j1 rule="hyper" parents="370 14058 16091"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10162,a(flip),b,16092,a)].">
      <j1 rule="hyper" parents="60 10162 16092"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13997,a,b,16093,a)].">
      <j1 rule="hyper" parents="60 13997 16093"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      L(T(x,R(y / T(1 / (1 / x),z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(5047(a,2),16093(a,2,2,1))].">
      <j1 rule="para" parents="5047 16093"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(15805(a,1),16094(a,1,2))].">
      <j1 rule="para" parents="15805 16094"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,T(z,y) * ((y * y) \ 1))
    ]]></literal>
    <justification jstring="[para(552(a,1),16062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="552 16062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,T(z,y) / (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15398,a(flip),b,16098,a),flip(a)].">
      <j1 rule="hyper" parents="370 15398 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,y * (y * (z * (1 / u))))
    ]]></literal>
    <justification jstring="[hyper(15471,a,15312,a)].">
      <j1 rule="hyper" parents="15471 15312"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,y * (y * (z * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(370,a,6163,a(flip),b,16100,a),flip(a)].">
      <j1 rule="hyper" parents="370 6163 16100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / u) = K(x,z * (u \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15435,a(flip),b,16101,a),flip(a)].">
      <j1 rule="hyper" parents="370 15435 16101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,T(x,z)) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5256(a,2),15524(a,1,3))].">
      <j1 rule="para" parents="5256 15524"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      L(T(x,x \ 1) \ y,x,x) = K(x,z) \ ((((z * x) / z) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(10152,a,16103,a)].">
      <j1 rule="hyper" parents="10152 16103"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(x * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(14375(a,1),15528(a,1,2))].">
      <j1 rule="para" parents="14375 15528"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * K(z,x \ ((1 / x) \ y)) = x \ ((K(y,z) / x) \ y)
    ]]></literal>
    <justification jstring="[para(15288(a,1),15315(a,2,2))].">
      <j1 rule="para" parents="15288 15315"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      T(x \ ((K(y,z) / x) \ y),z) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(16108(a,1),5280(a,1,1))].">
      <j1 rule="para" parents="16108 5280"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      T(x \ ((1 / x) \ y),y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(193(a,1),16109(a,1,1,2,1,1))].">
      <j1 rule="para" parents="193 16109"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(16110(a,1),8487(a,2,2,2))].">
      <j1 rule="para" parents="16110 8487"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a(K(x,y) / (K(x,y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(7546(a,1),15519(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7546 15519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,z \ y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(15517(a,1),15712(a,1,2,2))].">
      <j1 rule="para" parents="15517 15712"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),(y \ z) \ z,(y \ z) \ z),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),15708(a,2,2,2))].">
      <j1 rule="para" parents="74 15708"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(15629(a,1),15724(a,1))].">
      <j1 rule="para" parents="15629 15724"/>
    </justification>
  </clause>

  <clause id="16117">
    <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(15925(a,1),15972(a,2,1))].">
      <j1 rule="para" parents="15925 15972"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15887,a(flip),b,16117,a),flip(a)].">
      <j1 rule="hyper" parents="370 15887 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(93(a,1),16118(a,1,2,2))].">
      <j1 rule="para" parents="93 16118"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12487(a,2),16119(a,1,2,2))].">
      <j1 rule="para" parents="12487 16119"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * ((w \ v5) \ v5))))
    ]]></literal>
    <justification jstring="[para(74(a,1),15448(a,2,2,2,2,2))].">
      <j1 rule="para" parents="74 15448"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / (y / ((x \ (x * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(1259(a,1),15616(a,2,2))].">
      <j1 rule="para" parents="1259 15616"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) / (y / (1 / (x \ 1))) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),16124(a,2,2,2,1))].">
      <j1 rule="para" parents="4 16124"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      (1 / x) / (y / (1 / (x \ 1))) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1310(a,1),16125(a,1,1))].">
      <j1 rule="para" parents="1310 16125"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      (1 / x) / (y / x) = x / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(74(a,1),16128(a,1,2,2))].">
      <j1 rule="para" parents="74 16128"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      K(x,y \ (T(z,y \ (y \ 1)) * u)) = K(x,y * (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[para(75(a,1),15655(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 15655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,T(T(u,z) / z,z))
    ]]></literal>
    <justification jstring="[para(3(a,1),15675(a,2,3,2))].">
      <j1 rule="para" parents="3 15675"/>
    </justification>
  </clause>

  <clause id="16134">
    <literal><![CDATA[
      L(x,y,(z \ 1) * ((((z \ 1) \ 1) \ u) / (z \ 1))) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),16133(a,2,3))].">
      <j1 rule="para" parents="109 16133"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ T(u,z \ 1)) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(6970,a,16134,a)].">
      <j1 rule="hyper" parents="6970 16134"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      L(x,y,z \ T(u,z \ 1)) = L(x,y,z \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(3576,a,16135,a)].">
      <j1 rule="hyper" parents="3576 16135"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      K(x,L(y,T(1 / (z / u),z),(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(3376(a,1),15936(a,1,2))].">
      <j1 rule="para" parents="3376 15936"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      T(x,T(y,z * ((u \ 1) * w)) * (z * ((u \ 1) * w))) = T(x,(z * ((1 / u) * w)) * y)
    ]]></literal>
    <justification jstring="[para(4672(a,1),16050(a,1,2,1))].">
      <j1 rule="para" parents="4672 16050"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      T(x,(y * ((1 / z) * u)) * w) = T(x,(y * ((z \ 1) * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(12606,a,16138,a),flip(a)].">
      <j1 rule="hyper" parents="12606 16138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16140">
    <literal><![CDATA[
      x \ T(x,(y * ((z \ 1) * u)) * w) = K(x,(y * ((1 / z) * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(125,a,16139,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 16139 5256"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((z \ 1) * u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(16140(a,1),5290(a,1))].">
      <j1 rule="para" parents="16140 5290"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      R(K(x,y),z,L(L(z,u,w),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6,a(flip),b,15377,a),flip(a)].">
      <j1 rule="hyper" parents="370 6 15377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      R(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(15119(a,1),16142(a,1,3))].">
      <j1 rule="para" parents="15119 16142"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / (T(y,u) * (1 / u))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[para(14334(a,1),15412(a,1,2,1))].">
      <j1 rule="para" parents="14334 15412"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / (T(y,u) * (u \ 1))) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6175,a(flip),b,16146,a)].">
      <j1 rule="hyper" parents="60 6175 16146"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      L(x,L(K(y,z * u) * (u \ 1),z,y) \ w,v5) = L(x,((y * z) \ ((z * u) * y)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(15550(a,1),15632(a,1,2,1,1))].">
      <j1 rule="para" parents="15550 15632"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      T(x \ (y * z),K(z,y)) * L(u,x \ (z * y),K(y,z)) = K(y,z) * ((x \ (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(8700(a,1),15752(a,1,1))].">
      <j1 rule="para" parents="8700 15752"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(9372(a,1),15350(a,1,1,1,2))].">
      <j1 rule="para" parents="9372 15350"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5605(a,1),16150(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5605 16150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(4609(a,2),16151(a,1,2,2,1))].">
      <j1 rule="para" parents="4609 16151"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(77(a,1),16152(a,1,2,2))].">
      <j1 rule="para" parents="77 16152"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(12298(a,1),16153(a,1,2))].">
      <j1 rule="para" parents="12298 16153"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(221,a,16155,a(flip))].">
      <j1 rule="hyper" parents="221 16155"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      T(x * K((1 / y) * (y \ x),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(11783(a,1),15689(a,1,1,2))].">
      <j1 rule="para" parents="11783 15689"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z * K(z * u,z),u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(7846(a,1),15704(a,1,2,2,1))].">
      <j1 rule="para" parents="7846 15704"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      T(x * K(y \ (y \ x),x),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(15141(a,1),16157(a,1,1,2))].">
      <j1 rule="para" parents="15141 16157"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      T(x * K(x,y * y),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(15676(a,1),16159(a,1,1,2))].">
      <j1 rule="para" parents="15676 16159"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      T(T(x,y * y),y \ T(y \ 1,x * y)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[para(5256(a,2),16160(a,1,1))].">
      <j1 rule="para" parents="5256 16160"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      T(T(x,y * y),y \ T(y \ 1,x)) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14435,a(flip),b,16161,a)].">
      <j1 rule="hyper" parents="60 14435 16161"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      T(x,y * (y * (y \ T(y \ 1,x)))) = R(x,y \ T(y \ 1,x * y),x)
    ]]></literal>
    <justification jstring="[hyper(15569,a,16162,a)].">
      <j1 rule="hyper" parents="15569 16162"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      R(x,y \ T(y \ 1,x * y),x) = T(x,y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),16163(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      R(x,y \ T(y \ 1,x * y),x) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4760,a(flip),b,16164,a),flip(a)].">
      <j1 rule="hyper" parents="370 4760 16164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      (x \ T(x \ 1,y * x)) * y = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(16165(a,1),15690(a,1,2))].">
      <j1 rule="para" parents="16165 15690"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      T(1 / x,y * x) * (x \ y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10073,a(flip),b,16168,a)].">
      <j1 rule="hyper" parents="60 10073 16168"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z,T(u,z * u)))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(8797(a,1),16158(a,1,2,2,2))].">
      <j1 rule="para" parents="8797 16158"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      K(x,y * ((K(z,z * u) * (z \ w)) \ K(z,u))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(6702(a,1),16170(a,1,2,2,2))].">
      <j1 rule="para" parents="6702 16170"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ K(z * w,z)) * K(z,w))) = K(x,y / (R(z,w,z) \ u))
    ]]></literal>
    <justification jstring="[para(15267(a,1),16171(a,1,2,2))].">
      <j1 rule="para" parents="15267 16171"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x,x * y) \ L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(15438(a,1),15441(a,2,2,1))].">
      <j1 rule="para" parents="15438 15441"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      L(T(x,x \ y) \ L(T(x,x \ y),z,u),x,x) = T(x \ L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4205,a(flip),b,16173,a),flip(a)].">
      <j1 rule="hyper" parents="370 4205 16173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),x \ u),x,x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(4205(a,1),16174(a,1,1))].">
      <j1 rule="para" parents="4205 16174"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ u) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14689,a(flip),b,16175,a)].">
      <j1 rule="hyper" parents="60 14689 16175"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      (x * y) \ ((x \ L(x,z,u)) * (x * y)) = T(x \ L(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a(flip),b,16176,a)].">
      <j1 rule="hyper" parents="370 17 16176"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ L(x,z,u)) * y)) = T(x \ L(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[para(4118(a,1),16177(a,1,2))].">
      <j1 rule="para" parents="4118 16177"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),u,x) = T(x \ L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(1068,a,16179,a)].">
      <j1 rule="hyper" parents="1068 16179"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ u) = T(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14689,a(flip),b,16180,a),flip(a)].">
      <j1 rule="hyper" parents="60 14689 16180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = L(T(y \ L(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(16181(a,1),14864(a,2,1))].">
      <j1 rule="para" parents="16181 14864"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      x \ ((x / T(y,y \ x)) * L(T(y,y \ x),z,u)) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,12694,a(flip),b,16183,a),flip(a)].">
      <j1 rule="hyper" parents="370 12694 16183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      x \ ((y \ x) * L(T(y,y \ x),z,u)) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(308(a,1),16184(a,1,2,1))].">
      <j1 rule="para" parents="308 16184"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = y \ (L(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[para(273(a,1),16185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="273 16185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      (x \ y) \ (L(x,z,u) * (x \ (x \ y))) = y \ (L(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(404,a,16186,a),flip(a)].">
      <j1 rule="hyper" parents="404 16186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (L(x,y,z) * (x \ (L(x,y,z) \ u))) = (x * (L(x,y,z) \ u)) \ u
    ]]></literal>
    <justification jstring="[para(5(a,1),16186(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 16186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ u = (L(x,y,z) \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(2155(a,1),16188(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2155 16188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T(x,x * z))
    ]]></literal>
    <justification jstring="[para(15439(a,1),15445(a,2,2,2))].">
      <j1 rule="para" parents="15439 15445"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x,x * z) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7325(a,1),16191(a,2,2))].">
      <j1 rule="para" parents="7325 16191"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * K(y,(x \ 1) \ 1),x \ z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,10420,a(flip),b,16192,a),flip(a)].">
      <j1 rule="hyper" parents="370 10420 16192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      T((x \ 1) \ K(y,x),x \ z) = T(x * K(y,x),z * x)
    ]]></literal>
    <justification jstring="[para(5439(a,1),16193(a,1,1))].">
      <j1 rule="para" parents="5439 16193"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = T(x * K(y,x),y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,15702,a,b,16194,a)].">
      <j1 rule="hyper" parents="60 15702 16194"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      T((T(x,y) \ 1) \ K(x * y,T(x,y)),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(15274(a,1),16194(a,2,1))].">
      <j1 rule="para" parents="15274 16194"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      (x \ y) / ((((x \ y) \ y) \ y) / x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5498,a(flip),b,16195,a),flip(a)].">
      <j1 rule="hyper" parents="370 5498 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      (x / y) / ((y \ x) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,10182,a(flip),b,16197,a)].">
      <j1 rule="hyper" parents="60 10182 16197"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      L(x,y,x) * ((x \ y) / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(155,a,16198,a)].">
      <j1 rule="hyper" parents="155 16198"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      a(L((x \ y) / x,L(x,y,x),L(x,y,x)),z,u) = a(L(x,y,x) * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(16199(a,1),2956(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16199 2956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      a(L((x \ y) / x,x,x),z,u) = a(L(x,y,x) * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(14818(a,1),16200(a,1,1))].">
      <j1 rule="para" parents="14818 16200"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      a(L(x,y,x) * (y / x),z,u) = a(((x \ 1) * y) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1413(a,1),16202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1413 16202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      a(L(x,y,x) * (y / x),z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16016,a(flip),b,16204,a),flip(a)].">
      <j1 rule="hyper" parents="370 16016 16204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      a(x * (y / x),z,u) = a(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14072,a(flip),b,16206,a)].">
      <j1 rule="hyper" parents="60 14072 16206"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      a(K(x,y) * ((K(x * y,x) / z) / K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(15177(a,1),16207(a,2,1))].">
      <j1 rule="para" parents="15177 16207"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      a(K(x,y) * ((K(x * y,x) / z) * K(y,x)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6291(a,1),16209(a,1,1,2))].">
      <j1 rule="para" parents="6291 16209"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(4442(a,1),15525(a,1,2))].">
      <j1 rule="para" parents="4442 15525"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(4793(a,1),16211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4793 16211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,7687,a(flip),b,16213,a),flip(a)].">
      <j1 rule="hyper" parents="370 7687 16213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L(T(z,y \ 1) * y,u,w))
    ]]></literal>
    <justification jstring="[para(74(a,1),15628(a,2,2,1,2))].">
      <j1 rule="para" parents="74 15628"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ (z * ((y \ 1) \ 1))) / y,u,w)) = K(x,L((1 / y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15758,a(flip),b,16216,a),flip(a)].">
      <j1 rule="hyper" parents="370 15758 16216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      K(x,L(((1 / y) \ (z * y)) / y,u,w)) = K(x,L((1 / y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(7036(a,1),16218(a,1,2,1,1))].">
      <j1 rule="para" parents="7036 16218"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      T(T(x,K(y,(y \ 1) \ (y \ z))),y \ z) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[para(5(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="5 15652"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,(y \ 1) \ (y \ z))) = T(x,y \ (1 * T(1 \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(1146,a,16220,a)].">
      <j1 rule="hyper" parents="1146 16220"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      T(x,y \ (1 * T(1 \ z,y))) = T(x,T(y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(12690,a,16221,a),flip(a)].">
      <j1 rule="hyper" parents="12690 16221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      T(x,y \ (1 * T(1 \ z,y))) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8854,a(flip),b,16223,a),flip(a)].">
      <j1 rule="hyper" parents="370 8854 16223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      T(x,y \ (1 * T(z,y))) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(62(a,1),16224(a,1,2,2,2,1))].">
      <j1 rule="para" parents="62 16224"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(2(a,1),16225(a,1,2,2))].">
      <j1 rule="para" parents="2 16225"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      T(1 / x,y * x) = T(x \ 1,y / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7724,a(flip),b,16226,a)].">
      <j1 rule="hyper" parents="60 7724 16226"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(5749(a,2),16226(a,1,2))].">
      <j1 rule="para" parents="5749 16226"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      T((x * y) / x,z / (z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z \ x) \ ((z \ x) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(16226(a,1),15726(a,1))].">
      <j1 rule="para" parents="16226 15726"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      T(x,y / (z / y)) = T(x,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[para(109(a,1),16228(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 16228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K((T(x,y) \ y) \ T(z,y / x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (T(x,y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(16228(a,1),14562(a,1,1,2))].">
      <j1 rule="para" parents="16228 14562"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      T(1 / x,y * x) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8600,a(flip),b,16227,a),flip(a)].">
      <j1 rule="hyper" parents="370 8600 16227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      T(x,y / (z / y)) = T(x,y * (y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15715,a(flip),b,16230,a),flip(a)].">
      <j1 rule="hyper" parents="370 15715 16230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      T(x \ 1,x \ y) * (x \ y) = T((1 / x) * (y / x),y)
    ]]></literal>
    <justification jstring="[para(16232(a,1),16169(a,1,1))].">
      <j1 rule="para" parents="16232 16169"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(z \ x) \ ((z \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(16229,a,4664,a),flip(a)].">
      <j1 rule="hyper" parents="16229 4664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      T((1 / ((1 / x) \ x)) * y,(1 / x) \ x) = (x \ (1 / x)) * T(y,x * x)
    ]]></literal>
    <justification jstring="[para(407(a,1),15733(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="407 15733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      T((1 / ((1 / x) \ x)) * y,(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,1214,a(flip),b,16236,a),flip(a)].">
      <j1 rule="hyper" parents="370 1214 16236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      T((x \ (1 / x)) * y,(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[para(1224(a,1),16237(a,1,1,1))].">
      <j1 rule="para" parents="1224 16237"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),(1 / x) \ x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[para(1214(a,1),16238(a,1,1))].">
      <j1 rule="para" parents="1214 16238"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      T((x \ 1) * (x \ y),x * x) = (x \ 1) * (x \ T(y,x * x))
    ]]></literal>
    <justification jstring="[hyper(15474,a,16239,a)].">
      <j1 rule="hyper" parents="15474 16239"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T((T(x,y) \ 1) \ K(x * y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(7337(a,1),16196(a,1,1,2))].">
      <j1 rule="para" parents="7337 16196"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(((x \ 1) \ y) / (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,7993,a(flip),b,15217,a),flip(a)].">
      <j1 rule="hyper" parents="370 7993 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x \ 1) \ ((x \ 1) \ y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5674,a(flip),b,16242,a),flip(a)].">
      <j1 rule="hyper" parents="370 5674 16242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x \ 1) * ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,15700,a(flip),b,16243,a),flip(a)].">
      <j1 rule="hyper" parents="370 15700 16243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(x \ ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,15208,a(flip),b,16244,a),flip(a)].">
      <j1 rule="hyper" parents="370 15208 16244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K((x * x) \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(942(a,1),16245(a,2,1))].">
      <j1 rule="para" parents="942 16245"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(x \ 1) \ ((x \ 1) \ 1))),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,15130,a(flip),b,16246,a),flip(a)].">
      <j1 rule="hyper" parents="370 15130 16246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,(1 / x) \ x)),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(9034(a,1),16247(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9034 16247"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      K(x * ((x \ 1) \ T(y,x * x)),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(15251(a,1),16248(a,1,1,2,2))].">
      <j1 rule="para" parents="15251 16248"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      K(x * T(y / (1 / x),x),x \ 1) = K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(9989(a,1),16249(a,1,1,2))].">
      <j1 rule="para" parents="9989 16249"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      K((x / (1 / y)) * y,y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),16250(a,1,1))].">
      <j1 rule="para" parents="107 16250"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      K(x * ((1 / y) \ y),y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[para(1663(a,1),16251(a,1,1))].">
      <j1 rule="para" parents="1663 16251"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      K(x * ((y \ 1) \ y),y \ 1) = K(y \ (y \ x),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,6013,a(flip),b,16252,a)].">
      <j1 rule="hyper" parents="60 6013 16252"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x \ (x \ y),x \ 1) = K(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(311(a,1),16253(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="311 16253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,y \ (z * y)),u)
    ]]></literal>
    <justification jstring="[para(15161(a,1),15547(a,2,2))].">
      <j1 rule="para" parents="15161 15547"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,T(z,y)),u)
    ]]></literal>
    <justification jstring="[para(17(a,2),16255(a,2,2,2))].">
      <j1 rule="para" parents="17 16255"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * ((y \ 1) \ 1))) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(8596(a,1),16256(a,2,2))].">
      <j1 rule="para" parents="8596 16256"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      L(x,((1 / y) \ (z * y)) \ (z * ((y \ 1) \ 1)),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(7036(a,1),16257(a,1,2,1))].">
      <j1 rule="para" parents="7036 16257"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      L(x,((y \ 1) \ (z * y)) \ (z * y),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(16052(a,1),16258(a,1,2))].">
      <j1 rule="para" parents="16052 16258"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      L(x,(y \ (z * y)) \ (z * y),u) = L(x,T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3719,a(flip),b,16259,a)].">
      <j1 rule="hyper" parents="60 3719 16259"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      L(x,T(y \ 1,z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5821(a,2),16260(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5821 16260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      L(x,T(y,z),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(10139,a,16261,a),flip(a)].">
      <j1 rule="hyper" parents="10139 16261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(15447,a,16262,a)].">
      <j1 rule="hyper" parents="15447 16262"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(10160,a,16262,a)].">
      <j1 rule="hyper" parents="10160 16262"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(10169,a,16263,a)].">
      <j1 rule="hyper" parents="10169 16263"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x) = (1 / T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(790,a,16264,a),flip(a)].">
      <j1 rule="hyper" parents="790 16264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x) = (K(y,x) / x) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,5774,a(flip),b,16264,a),flip(a)].">
      <j1 rule="hyper" parents="60 5774 16264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(z,x,x) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(16264(a,1),4341(a,1,2))].">
      <j1 rule="para" parents="16264 4341"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,T(x,y),T(x,y))
    ]]></literal>
    <justification jstring="[para(16264(a,1),14912(a,2,2))].">
      <j1 rule="para" parents="16264 14912"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      K(x,y) \ ((((y * x) / y) \ 1) * z) = (1 / T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,16104,a(flip),b,16267,a)].">
      <j1 rule="hyper" parents="60 16104 16267"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,u),x) = (K(y,x) / x) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,16262,a,b,16268,a)].">
      <j1 rule="hyper" parents="60 16262 16268"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      ((x \ y) \ y) \ L(z,x,x) = (((x \ y) \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,16265,a(flip),b,2074,a)].">
      <j1 rule="hyper" parents="125 16265 2074"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      L(x,L(T(y \ z,y),y,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(16265(a,1),16114(a,1,2))].">
      <j1 rule="para" parents="16265 16114"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      x \ ((x * T(x,y)) * z) = (K(y,x) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(780,a,16273,a),flip(a)].">
      <j1 rule="hyper" parents="780 16273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(591(a,1),16277(a,1,2))].">
      <j1 rule="para" parents="591 16277"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      L(x,T((1 / y) * z,y),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14815,a,b,16279,a),flip(a)].">
      <j1 rule="hyper" parents="370 14815 16279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      L(x,y * ((y \ z) * y),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(4131,a,16281,a)].">
      <j1 rule="hyper" parents="4131 16281"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      L(x,y * (y * (z / y)),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12684,a(flip),b,16282,a)].">
      <j1 rule="hyper" parents="60 12684 16282"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      L(x,T(y * (T(y,z) * z),y),u) = L(x,L(z,T(y,z),T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9322,a,b,16283,a),flip(a)].">
      <j1 rule="hyper" parents="60 9322 16283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      ((x \ y) \ y) \ z != (((x \ y) \ y) \ 1) * u
    ]]></literal>
    <literal><![CDATA[
      L(u,x,x) = z
    ]]></literal>
    <justification jstring="[para(16276(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="16276 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      K(x,y) \ ((((y * x) / y) \ 1) * z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(308(a,1),16271(a,2,1))].">
      <j1 rule="para" parents="308 16271"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      K(x,y) * ((((x * y) / x) \ 1) * z) = (y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(7521,a,16287,a)].">
      <j1 rule="hyper" parents="7521 16287"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      K(x,L(((((y * z) / y) \ 1) * u) \ w,(((y * z) / y) \ 1) * u,K(y,z))) = K(x,((z \ 1) * u) \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(16288(a,1),11167(a,2,2,1))].">
      <j1 rule="para" parents="16288 11167"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      L(x,T(y * (T(y,z) * z),y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(16264(a,1),16284(a,2,2))].">
      <j1 rule="para" parents="16264 16284"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      L(x,(T(y,z) * z) * y,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14815,a(flip),b,16290,a)].">
      <j1 rule="hyper" parents="60 14815 16290"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      L(x,(y * z) * T(y,z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(6397(a,1),16291(a,1,2))].">
      <j1 rule="para" parents="6397 16291"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      L(x,R(y,z,z),u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9732,a(flip),b,16293,a)].">
      <j1 rule="hyper" parents="60 9732 16293"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      L(T(T(x,y),x \ 1) * z,T(T(x,y),x \ 1),T(T(x,y),x \ 1)) = T(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[para(16264(a,1),16270(a,2,2))].">
      <j1 rule="para" parents="16264 16270"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(K((x / (1 / y)) * ((x / (1 / y)) * z),x * y),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(15241(a,1),15453(a,1,1))].">
      <j1 rule="para" parents="15241 15453"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      K(K((x / (y \ 1)) * ((x / (1 / y)) * z),x * y),u) = K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u)
    ]]></literal>
    <justification jstring="[para(6019(a,1),16298(a,1,1))].">
      <j1 rule="para" parents="6019 16298"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      K(x,K(y * z,(y / (z \ 1)) * ((y / (1 / z)) * u))) = K((y / (z \ 1)) * (1 / T(y / (1 / z),u)),x)
    ]]></literal>
    <justification jstring="[hyper(6243,a,16299,a)].">
      <j1 rule="hyper" parents="6243 16299"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(3(a,1),15740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 15740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      ((K(x,y) * K(x,z)) \ 1) * ((K(x,y) * K(x,z)) * u) = L(u,K(x,y) * K(x,z),K(y,x) * K(z,x))
    ]]></literal>
    <justification jstring="[para(10843(a,1),16301(a,2,3))].">
      <j1 rule="para" parents="10843 16301"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * ((K(y,x) * K(y,z)) * u) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(10843(a,1),16302(a,1,1))].">
      <j1 rule="para" parents="10843 16302"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * (K(y,x) * (K(y,z) * u)) = L(u,K(y,x) * K(y,z),K(x,y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(10827(a,1),16303(a,1,2))].">
      <j1 rule="para" parents="10827 16303"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * (K(y,z) * (K(y,x) * u))) = L(u,K(y,z) * K(y,x),K(z,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10969,a(flip),b,16304,a)].">
      <j1 rule="hyper" parents="60 10969 16304"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = K(u,y) * (K(y,u) * x)
    ]]></literal>
    <justification jstring="[para(7500(a,1),16305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 16305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,7500,a(flip),b,16306,a),flip(a)].">
      <j1 rule="hyper" parents="370 7500 16306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      L(T(x,R(y / T((1 / x) \ 1,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(10428(a,1),16096(a,1,1))].">
      <j1 rule="para" parents="10428 16096"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      L(T(x,R(y / T(x,z),u,w)),y / T(1 / (1 / x),z),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w))
    ]]></literal>
    <justification jstring="[para(77(a,1),16310(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="77 16310"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      L(T(x,R(x \ y,z,u)),y / T(1 / (1 / x),w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u))
    ]]></literal>
    <justification jstring="[para(10915(a,1),16311(a,1,1))].">
      <j1 rule="para" parents="10915 16311"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      L(T(x,R(x \ y,z,u)),y / T((1 / x) \ 1,w),x) = T(x,R(((x \ 1) \ 1) * (y / T(x,w)),z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6900,a(flip),b,16312,a)].">
      <j1 rule="hyper" parents="60 6900 16312"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),y / T(x,z),x)
    ]]></literal>
    <justification jstring="[para(77(a,1),16313(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 16313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = L(T(x,R(x \ y,u,w)),x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,10165,a(flip),b,16315,a),flip(a)].">
      <j1 rule="hyper" parents="370 10165 16315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(x * (x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16093,a(flip),b,16316,a),flip(a)].">
      <j1 rule="hyper" parents="370 16093 16316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      T(x,R(((x \ 1) \ 1) * (y / T(x,z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16318(a,2,2,1))].">
      <j1 rule="para" parents="5 16318"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),16319(a,1,2,1))].">
      <j1 rule="para" parents="5047 16319"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (x \ 1)) \ ((z * (x \ 1)) \ (1 / x))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(4661(a,1),15727(a,1))].">
      <j1 rule="para" parents="4661 15727"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      T(T(x,(y / z) * T(z \ y,y \ z)),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(540(a,1),15684(a,1,1,2))].">
      <j1 rule="para" parents="540 15684"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) \ ((x \ 1) \ y),T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(7593(a,1),16012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7593 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) * ((x \ 1) * y),T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(16028(a,1),16324(a,2,2))].">
      <j1 rule="para" parents="16028 16324"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      T(T(x,(y \ z) * T(z / y,y / z)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(9817(a,1),16323(a,1,1,2))].">
      <j1 rule="para" parents="9817 16323"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      T(T(x,(y \ z) * T(z / y,z \ y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(4567(a,1),16326(a,1,1,2,2))].">
      <j1 rule="para" parents="4567 16326"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      T(T(x,(1 / (y \ z)) \ (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(13304(a,1),16327(a,1,1,2))].">
      <j1 rule="para" parents="13304 16327"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      T(T(x,(y \ z) * (z / y)),T(y \ z,z \ y) \ (T(y \ z,z \ y) \ u)) = T(T(x,(z / y) * (1 / (y \ z))),u)
    ]]></literal>
    <justification jstring="[para(15251(a,1),16328(a,1,1))].">
      <j1 rule="para" parents="15251 16328"/>
    </justification>
  </clause>

  <clause id="16330">
    <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(60,a,13723,a(flip),b,15032,a)].">
      <j1 rule="hyper" parents="60 13723 15032"/>
    </justification>
  </clause>

  <clause id="16331">
    <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(12008(a,1),16330(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12008 16330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(x * u,L(y,u,x)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),16331(a,2,2))].">
      <j1 rule="para" parents="8648 16331"/>
    </justification>
  </clause>

  <clause id="16334">
    <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(15588(a,1),16332(a,2,2))].">
      <j1 rule="para" parents="15588 16332"/>
    </justification>
  </clause>

  <clause id="16335">
    <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(8630(a,1),16334(a,2,2))].">
      <j1 rule="para" parents="8630 16334"/>
    </justification>
  </clause>

  <clause id="16336">
    <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(9640(a,1),16335(a,1,1))].">
      <j1 rule="para" parents="9640 16335"/>
    </justification>
  </clause>

  <clause id="16337">
    <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(60,a,12275,a,b,16336,a)].">
      <j1 rule="hyper" parents="60 12275 16336"/>
    </justification>
  </clause>

  <clause id="16338">
    <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(13454(a,1),16337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13454 16337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ ((x * T(y,K(z,u))) * K(z,K(u,x * y))) = v5
    ]]></literal>
    <justification jstring="[para(16338(a,1),721(a,1))].">
      <j1 rule="para" parents="16338 721"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x * (K(y,x) / T(x,z))) \ 1,x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(10898(a,1),16025(a,1,1))].">
      <j1 rule="para" parents="10898 16025"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),x * (K(y,x) / T(x,z))) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(16024(a,1),16340(a,1,2,2))].">
      <j1 rule="para" parents="16024 16340"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,(x \ K(x,y)) * T(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(10209(a,1),16341(a,1,2))].">
      <j1 rule="para" parents="10209 16341"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ L(u,K(x,y) * K(x,z),K(y,x) * K(z,x)) = ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u
    ]]></literal>
    <justification jstring="[para(9962(a,1),16342(a,1,2))].">
      <j1 rule="para" parents="9962 16342"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      ((((x * (K(y,x) / T(x,z))) \ 1) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(16307(a,1),16343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16307 16343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(16024(a,1),16344(a,1,1,1,1))].">
      <j1 rule="para" parents="16024 16344"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(10898(a,1),16345(a,1,1,1))].">
      <j1 rule="para" parents="10898 16345"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(16024(a,1),16346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16024 16346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,T(x,z) \ ((x \ 1) \ K(y,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(16347(a,1),9716(a,1,1))].">
      <j1 rule="para" parents="16347 9716"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,x * (K(y,x) / T(x,z)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(9384(a,1),16348(a,1,2))].">
      <j1 rule="para" parents="9384 16348"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,x * (T(x,y) \ K(z,x)),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,10768,a(flip),b,16349,a)].">
      <j1 rule="hyper" parents="60 10768 16349"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      L(((x \ K(x,y)) * T(x,z)) * u,K(y,x) * K(z,x),T(x,z)) = ((x \ 1) \ K(y,x)) \ (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(7932(a,1),16350(a,1,2))].">
      <j1 rule="para" parents="7932 16350"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(10978,a,16351,a),flip(a)].">
      <j1 rule="hyper" parents="10978 16351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ L(x \ (L(x,y,z) * L(x,y,z)),u,w) = x \ ((L(x,y,z) * L(x,y,z)) * L((L(x,y,z) \ x) / L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2156(a,1),10391(a,1,1))].">
      <j1 rule="para" parents="2156 10391"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ L(L(x,y,z) * (x \ L(x,y,z)),u,w) = x \ ((L(x,y,z) * L(x,y,z)) * L((L(x,y,z) \ x) / L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2156(a,1),16354(a,1,2,1))].">
      <j1 rule="para" parents="2156 16354"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ L(L(x,y,z) * (x \ L(x,y,z)),u,w) = x \ ((L(x,y,z) * L(x,y,z)) * L((L(x,y,z) * L(x,y,z)) \ x,u,w))
    ]]></literal>
    <justification jstring="[para(10390(a,1),16355(a,2,2,2,1))].">
      <j1 rule="para" parents="10390 16355"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ L(L(x,y,z) * (x \ L(x,y,z)),u,w) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(3806(a,1),16356(a,2,2))].">
      <j1 rule="para" parents="3806 16356"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      (((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z)) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(7062(a,1),11662(a,1,1,1))].">
      <j1 rule="para" parents="7062 11662"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      (((x \ K(x,y)) * T(x,x \ 1)) * z) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z) = T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(16352(a,1),16359(a,1,1))].">
      <j1 rule="para" parents="16352 16359"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(6041(a,1),16360(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6041 16360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((K(x,y) / x) * (x * z),x * z)
    ]]></literal>
    <justification jstring="[para(5574(a,1),16361(a,2,2))].">
      <j1 rule="para" parents="5574 16361"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K((x \ K(x,y)) * (x * z),x * z)
    ]]></literal>
    <justification jstring="[para(6864(a,1),16362(a,2,2))].">
      <j1 rule="para" parents="6864 16362"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(x \ (x * z),T(x * z,y))
    ]]></literal>
    <justification jstring="[para(11870(a,1),16363(a,2,2))].">
      <j1 rule="para" parents="11870 16363"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = (K(x,y) * z) * K(z,T(x * z,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),16364(a,2,2,1))].">
      <j1 rule="para" parents="4 16364"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = K(x,y) * T(z,T(x * z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6270,a(flip),b,16365,a),flip(a)].">
      <j1 rule="hyper" parents="370 6270 16365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      T(((x \ K(x,y)) \ 1) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9674,a(flip),b,16366,a),flip(a)].">
      <j1 rule="hyper" parents="370 9674 16366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      T(((x \ 1) \ K(y,x)) \ (T(x,x \ 1) * z),T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7062(a,1),16368(a,1,1,1))].">
      <j1 rule="para" parents="7062 16368"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      T(((x \ K(x,y)) * T(x,x \ 1)) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16352(a,1),16369(a,1,1))].">
      <j1 rule="para" parents="16352 16369"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6041(a,1),16370(a,1,1,1))].">
      <j1 rule="para" parents="6041 16370"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15571,a,16371,a)].">
      <j1 rule="hyper" parents="15571 16371"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5485(a,1),16372(a,2,1))].">
      <j1 rule="para" parents="5485 16372"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      T(K(x,x * (y \ L(y,z,u))) * w,x * w) = T(w,w * x) * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14946(a,1),16373(a,2,2))].">
      <j1 rule="para" parents="14946 16373"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,u * w) = T(w,w * u) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14946(a,1),16374(a,1,1,1))].">
      <j1 rule="para" parents="14946 16374"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * x,u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,16097,a(flip),b,16375,a),flip(a)].">
      <j1 rule="hyper" parents="370 16097 16375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(12070(a,1),16376(a,1,1))].">
      <j1 rule="para" parents="12070 16376"/>
    </justification>
  </clause>

  <clause id="16378">
    <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(2686(a,1),14863(a,2,1))].">
      <j1 rule="para" parents="2686 14863"/>
    </justification>
  </clause>

  <clause id="16379">
    <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(370,a,14269,a(flip),b,16378,a),flip(a)].">
      <j1 rule="hyper" parents="370 14269 16378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16381">
    <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(12042(a,1),16379(a,1,1))].">
      <j1 rule="para" parents="12042 16379"/>
    </justification>
  </clause>

  <clause id="16382">
    <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(60,a,12062,a(flip),b,16381,a)].">
      <j1 rule="hyper" parents="60 12062 16381"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,14975,a(flip),b,16382,a),flip(a)].">
      <j1 rule="hyper" parents="60 14975 16382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15818,a(flip),b,16383,a),flip(a)].">
      <j1 rule="hyper" parents="370 15818 16383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(16383(a,2),13023(a,1,1))].">
      <j1 rule="para" parents="16383 13023"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(16383(a,2),13409(a,1,1))].">
      <j1 rule="para" parents="16383 13409"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(16384(a,2),16377(a,1,1))].">
      <j1 rule="para" parents="16384 16377"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      T(T(x,y),a(z,u,y) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(1146,a,16385,a)].">
      <j1 rule="hyper" parents="1146 16385"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (1 / u))) \ x) = T(x,L(y * (z * (1 / u)),v5,w))
    ]]></literal>
    <justification jstring="[para(4674(a,1),16388(a,1,1))].">
      <j1 rule="para" parents="4674 16388"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(1146,a,16386,a)].">
      <j1 rule="hyper" parents="1146 16386"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(5622,a,16387,a)].">
      <j1 rule="hyper" parents="5622 16387"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16390,a(flip),b,16391,a),flip(a)].">
      <j1 rule="hyper" parents="60 16390 16391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      T(x,L((y / T(1 / (1 / x),z)) * x,u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16321,a(flip),b,16392,a),flip(a)].">
      <j1 rule="hyper" parents="60 16321 16392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(11970(a,1),16393(a,1,2,1))].">
      <j1 rule="para" parents="11970 16393"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ 1))),a(w,v5,y * (z * (u \ 1))) \ x) = T(x,L(y * (z * (1 / u)),v5,w))
    ]]></literal>
    <justification jstring="[para(5187(a,1),16389(a,1,2,1))].">
      <j1 rule="para" parents="5187 16389"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,16388,a(flip),b,16395,a),flip(a)].">
      <j1 rule="hyper" parents="60 16388 16395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      T(x,L(y * (x * (T(x,z) \ 1)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16394,a(flip),b,16396,a),flip(a)].">
      <j1 rule="hyper" parents="60 16394 16396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5719(a,2),16397(a,1,2,1,2))].">
      <j1 rule="para" parents="5719 16397"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(205(a,1),16398(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="205 16398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,16399,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 16399 17"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      x \ T(x,L(y,z,u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,16399,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 16399 5256"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5290,a,16402,a),flip(a)].">
      <j1 rule="hyper" parents="5290 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(16402(a,1),5290(a,1))].">
      <j1 rule="para" parents="16402 5290"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13965,a,b,16404,a)].">
      <j1 rule="hyper" parents="60 13965 16404"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13961,a,b,16404,a)].">
      <j1 rule="hyper" parents="60 13961 16404"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,L(x,y,z)) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,16404,a(flip),b,684,a)].">
      <j1 rule="hyper" parents="129 16404 684"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(349(a,1),16404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="349 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(908(a,1),16404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="908 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16413">
    <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(16404(a,1),10188(a,1,2))].">
      <j1 rule="para" parents="16404 10188"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12966,a,b,16407,a),flip(a)].">
      <j1 rule="hyper" parents="370 12966 16407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(16407(a,1),13975(a,1))].">
      <j1 rule="para" parents="16407 13975"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a,b,16408,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16144,a(flip),b,16408,a),flip(a)].">
      <j1 rule="hyper" parents="60 16144 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      K(x,L((y / z) / u,z \ y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12408,a(flip),b,16408,a),flip(a)].">
      <j1 rule="hyper" parents="60 12408 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      K((x * y) / (z * y),u) = K(x / z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9772,a(flip),b,16408,a)].">
      <j1 rule="hyper" parents="60 9772 16408"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(16408(a,1),103(a,1,1))].">
      <j1 rule="para" parents="16408 103"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[para(16408(a,1),430(a,1,1))].">
      <j1 rule="para" parents="16408 430"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(16408(a,1),12410(a,1,1))].">
      <j1 rule="para" parents="16408 12410"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * K(u,z) = K(x,L(y,z,u)) * (u * z)
    ]]></literal>
    <justification jstring="[para(16408(a,1),12388(a,2,1))].">
      <j1 rule="para" parents="16408 12388"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(104(a,1),16414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(L((x / y) / z,z,y),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(349(a,1),16414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="349 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      x * (K(L(y,z,u),x) * R(y,z,u)) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(16414(a,1),5303(a,1,2,1))].">
      <j1 rule="para" parents="16414 5303"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(16414(a,2),13036(a,1))].">
      <j1 rule="para" parents="16414 13036"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6920,a,16416,a),flip(a)].">
      <j1 rule="hyper" parents="6920 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9773,a(flip),b,16416,a),flip(a)].">
      <j1 rule="hyper" parents="60 9773 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(16416(a,1),103(a,1,1))].">
      <j1 rule="para" parents="16416 103"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      L(K(x,y),z,u) \ ((K(x,y) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(16416(a,1),210(a,1,1))].">
      <j1 rule="para" parents="16416 210"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(16416(a,2),13033(a,1))].">
      <j1 rule="para" parents="16416 13033"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16416(a,1),15753(a,1,1))].">
      <j1 rule="para" parents="16416 15753"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = 1 * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a,b,16417,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 16417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16437(a,2),130(a,1)),flip(b)].">
      <j1 rule="para" parents="16437 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),16405(a,1,2))].">
      <j1 rule="para" parents="104 16405"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      K(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(614(a,1),16439(a,1,2,3))].">
      <j1 rule="para" parents="614 16439"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2390(a,2),16439(a,1,2))].">
      <j1 rule="para" parents="2390 16439"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      K(x,L(y * z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2084(a,1),16444(a,1,2))].">
      <j1 rule="para" parents="2084 16444"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      L(K(x,y),z,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12922(a,2),16444(a,1))].">
      <j1 rule="para" parents="12922 16444"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(6918,a,16429,a),flip(a)].">
      <j1 rule="hyper" parents="6918 16429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      (x \ K(L(y,z,u) \ 1,w)) \ (x \ 1) = K(w,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(16452(a,1),15194(a,1,1,2))].">
      <j1 rule="para" parents="16452 15194"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      R(x,y,y) * T(z,x) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(15156(a,1),16401(a,1,2))].">
      <j1 rule="para" parents="15156 16401"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      R(x,y,y) * (x \ z) = (z / x) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),16454(a,1,2))].">
      <j1 rule="para" parents="109 16454"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[para(5233(a,1),16410(a,1,2,1,1))].">
      <j1 rule="para" parents="5233 16410"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(y,K(x,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),8638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16410 8638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(16410(a,1),11390(a,2,2))].">
      <j1 rule="para" parents="16410 11390"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(L(w,L(x,y,z),u),x))
    ]]></literal>
    <justification jstring="[hyper(370,a,12998,a(flip),b,16419,a),flip(a)].">
      <j1 rule="hyper" parents="370 12998 16419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(16420(a,1),41(a,1))].">
      <j1 rule="para" parents="16420 41"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = K(L(y,z,u),T(x,z * u))
    ]]></literal>
    <justification jstring="[para(16420(a,1),8017(a,1,1))].">
      <j1 rule="para" parents="16420 8017"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      (K(x,y * z) * z) * y = K(x,y * z) * (z * y)
    ]]></literal>
    <justification jstring="[para(15587(a,1),16420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15587 16420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <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="[para(16420(a,1),15809(a,1,1))].">
      <j1 rule="para" parents="16420 15809"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(9009,a,16425,a)].">
      <j1 rule="hyper" parents="9009 16425"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      K(L(x / y,y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(16425(a,2),8453(a,1))].">
      <j1 rule="para" parents="16425 8453"/>
    </justification>
  </clause>

  <clause id="16466">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16425(a,1),9009(a,1))].">
      <j1 rule="para" parents="16425 9009"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(L((x / y) / K(z,T(u,y)),K(z,T(u,y)),y),w) = K(x / (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(8758(a,1),16426(a,2,1,2))].">
      <j1 rule="para" parents="8758 16426"/>
    </justification>
  </clause>

  <clause id="16468">
    <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(8502,a,16430,a)].">
      <j1 rule="hyper" parents="8502 16430"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      ((K(x,y) * K(x,y)) * (z * u)) / u = L(K(x,y),K(x,y),z) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,114,a,b,16431,a)].">
      <j1 rule="hyper" parents="370 114 16431"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (K(x,u) * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(9645(a,1),16431(a,1,1))].">
      <j1 rule="para" parents="9645 16431"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,16462,a)].">
      <j1 rule="hyper" parents="625 16462"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = K(y,z * x) * (x * z)
    ]]></literal>
    <justification jstring="[para(12560(a,1),16462(a,1,1))].">
      <j1 rule="para" parents="12560 16462"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),16472(a,1,3,2))].">
      <j1 rule="para" parents="5 16472"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      L(x / y,y,K(z,x)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),16472(a,1,3,2))].">
      <j1 rule="para" parents="7 16472"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[para(12554(a,1),16472(a,1,3))].">
      <j1 rule="para" parents="12554 16472"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      L(x / y,y,K(x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5885,a,16475,a)].">
      <j1 rule="hyper" parents="5885 16475"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(14037,a,16477,a)].">
      <j1 rule="hyper" parents="14037 16477"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = (x * z) * K(y,z * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8114,a(flip),b,16473,a),flip(a)].">
      <j1 rule="hyper" parents="370 8114 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(665(a,1),16411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="665 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      K(x,L((y / z) / u,y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(15944,a,16418,a)].">
      <j1 rule="hyper" parents="15944 16418"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      K(x,L((y / z) * u,z \ y,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(15599,a,16418,a)].">
      <j1 rule="hyper" parents="15599 16418"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(74(a,1),16481(a,1,2,1,1))].">
      <j1 rule="para" parents="74 16481"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      K(x,L((y * z) / u,R(y,z,z),z \ 1)) = K(x,R(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(1112(a,1),16481(a,1,2,1,1))].">
      <j1 rule="para" parents="1112 16481"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      K(x,L((y / z) / (u \ w),y,z)) = K(x,y / ((u \ 1) * (u \ (((1 / u) \ w) * z))))
    ]]></literal>
    <justification jstring="[para(2102(a,2),16481(a,2,2,2))].">
      <j1 rule="para" parents="2102 16481"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y / u) * z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(16481(a,1),15599(a,1))].">
      <j1 rule="para" parents="16481 15599"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = ((z * z) \ (K(x,y) * (z * z))) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(16421(a,2),1447(a,1,1))].">
      <j1 rule="para" parents="16421 1447"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x,y \ (z * (u * (z \ y)))) * y = (K(x,T(u,z \ y)) * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(1032(a,1),16423(a,1,1,2))].">
      <j1 rule="para" parents="1032 16423"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      K(L(x,y,z),u) * R(x,y,z) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,16427,a),flip(a)].">
      <j1 rule="hyper" parents="31 274 16427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z)) = K(x,(y * z) / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16440,a,14646,a)].">
      <j1 rule="hyper" parents="16440 14646"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,T((x \ 1) \ y,x))) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(1278(a,1),16464(a,1,1,1))].">
      <j1 rule="para" parents="1278 16464"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,T(w,K(y,z))) = K((((x * y) \ u) * (x * y)) / (K(y,z) * (x * y)),w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),16464(a,1,1,1))].">
      <j1 rule="para" parents="6270 16464"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * T(u,z) = w
    ]]></literal>
    <justification jstring="[para(16424(a,1),6372(a,1))].">
      <j1 rule="para" parents="16424 6372"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      ((K(x,(y \ z) \ u) * (y \ z)) * y) \ ((y \ z) * y) = K(z \ (y * u),T(x,(y \ z) * y))
    ]]></literal>
    <justification jstring="[para(656(a,1),16461(a,2,1))].">
      <j1 rule="para" parents="656 16461"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(7864(a,1),16471(a,2,1))].">
      <j1 rule="para" parents="7864 16471"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(12343(a,1),16495(a,1,1))].">
      <j1 rule="para" parents="12343 16495"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x \ 1,x \ y) * ((x \ 1) * (x \ (y * z))) = (T(x \ 1,x \ y) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(1565(a,1),16496(a,1,2))].">
      <j1 rule="para" parents="1565 16496"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ u,z \ y,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(16448,a,16482,a)].">
      <j1 rule="hyper" parents="16448 16482"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      K(x,L(y / (z \ u),u,z)) = K(x,(y * z) / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15944,a,16490,a)].">
      <j1 rule="hyper" parents="15944 16490"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z \ u)) = K(x,(y * (z \ u)) / ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(108(a,1),16499(a,2,2,2))].">
      <j1 rule="para" parents="108 16499"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(15856(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="15856 16409"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6492,a,16501,a)].">
      <j1 rule="hyper" parents="6492 16501"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(12704,a,16502,a)].">
      <j1 rule="hyper" parents="12704 16502"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,16503,a)].">
      <j1 rule="hyper" parents="139 16503"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(16503(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="16503 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * ((z * u) * R(w,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(a(w,z,u),(z * u) * w,(z * u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(16503(a,1),3115(a,1,3,2))].">
      <j1 rule="para" parents="16503 3115"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(u,z,K(x,T(y,z))) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(8011(a,1),16503(a,1,1,1))].">
      <j1 rule="para" parents="8011 16503"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      a(x,y,y) * x = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(15853,a,16504,a)].">
      <j1 rule="hyper" parents="15853 16504"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(135,a,16504,a)].">
      <j1 rule="hyper" parents="135 16504"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      (x * (y \ 1)) / a(x / y,y,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(128,a,1109,a(flip),b,16504,a)].">
      <j1 rule="hyper" parents="128 1109 16504"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      R(x,y,y) / x = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,16504,a(flip),b,15848,a)].">
      <j1 rule="hyper" parents="128 16504 15848"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      x * (y \ R(y,z,z)) = x * a(y,z,z)
    ]]></literal>
    <justification jstring="[para(16504(a,1),173(a,1,2,2))].">
      <j1 rule="para" parents="16504 173"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      x \ R(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(16504(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="16504 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      (x \ 1) * a(x,y,y) = R(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(2962(a,1),16504(a,1,2))].">
      <j1 rule="para" parents="2962 16504"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) * z,u,u) = R(K(x,y) / z,u,u)
    ]]></literal>
    <justification jstring="[para(15171(a,1),16504(a,1,2))].">
      <j1 rule="para" parents="15171 16504"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) = K(x,L(y,R(z,u,u),z))
    ]]></literal>
    <justification jstring="[para(16504(a,1),15934(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16504 15934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      (1 / x) * R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,1783,a,b,16508,a)].">
      <j1 rule="hyper" parents="32 1783 16508"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = a(x,y,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(16508(a,1),92(a,1,1))].">
      <j1 rule="para" parents="16508 92"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      R(x / a(y,z,z),a(y,z,z),y) = (x * y) / R(y,z,z)
    ]]></literal>
    <justification jstring="[para(16508(a,1),104(a,2,2))].">
      <j1 rule="para" parents="16508 104"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      x \ R(x,L((y \ 1) \ z,u,w),L((y \ 1) \ z,u,w)) = a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3972,a(flip),b,16509,a),flip(a)].">
      <j1 rule="hyper" parents="370 3972 16509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      (x * y) \ (((z * x) * R((z * x) \ x,u,u)) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13791,a(flip),b,16509,a)].">
      <j1 rule="hyper" parents="60 13791 16509"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      L(x,y * R(y,z,z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(16509(a,1),3466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16509 3466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ R(1 / u,w,w)))) = K(x,y * (z * a(1 / u,w,w)))
    ]]></literal>
    <justification jstring="[para(16509(a,1),6162(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="16509 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K(x,((y \ 1) \ R(1 / y,z,z)) * u) = K(x,a(1 / y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(16509(a,1),15734(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16509 15734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      a(x,y,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(16511(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="16511 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * R(z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(16517(a,1),4672(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16517 4672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,u) = w
    ]]></literal>
    <justification jstring="[para(24(a,1),16513(a,1,2))].">
      <j1 rule="para" parents="24 16513"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      (x \ 1) \ L(R(x \ 1,x,x),y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(16514(a,1),3952(a,1,2,1))].">
      <j1 rule="para" parents="16514 3952"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) = K(x,L(y,L(z,u,u),z))
    ]]></literal>
    <justification jstring="[para(16294(a,1),16516(a,2,2))].">
      <j1 rule="para" parents="16294 16516"/>
    </justification>
  </clause>

  <clause id="16532">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16531(a,2),16445(a,1))].">
      <j1 rule="para" parents="16531 16445"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      T(x,y * (z * R(1 / z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(1863(a,1),16528(a,1,2,2))].">
      <j1 rule="para" parents="1863 16528"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16505,a,94,a(flip))].">
      <j1 rule="hyper" parents="16505 94"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(94(a,2),16505(a,1))].">
      <j1 rule="para" parents="94 16505"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      L(R(x \ R(x,y,z),u,w),x,y * z) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(16534(a,2),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16534 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y * z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(16534(a,2),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16534 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(16534(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="16534 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      L(a(x,y,z),u,w) != L(v5,x,y * z)
    ]]></literal>
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(16534(a,2),166(a,1,1))].">
      <j1 rule="para" parents="16534 166"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      (x \ 1) \ L(1 / x,y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2787(a,1),16530(a,1,2,1))].">
      <j1 rule="para" parents="2787 16530"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      (x \ 1) \ L(1 / x,y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3797,a(flip),b,16541,a),flip(a)].">
      <j1 rule="hyper" parents="370 3797 16541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      K(x,y * (z * (u * L(1 / u,w,v5)))) = K(x,y * (z * (u \ L(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(16542(a,1),6965(a,1,2,2,2))].">
      <j1 rule="para" parents="16542 6965"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(15195,a,16453,a),flip(a)].">
      <j1 rule="hyper" parents="15195 16453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T((u * z) / y,y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1096(a,1),16544(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1096 16544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      L(x \ R(x,y,y),z,u) = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(16529,a,7812,a),flip(a)].">
      <j1 rule="hyper" parents="16529 7812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(16509(a,1),16546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16509 16546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      a(L(x,y,z),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,14782,a(flip),b,16547,a),flip(a)].">
      <j1 rule="hyper" parents="370 14782 16547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (y * z) = z * (T(y,z) * a(x,u,u))
    ]]></literal>
    <justification jstring="[para(16547(a,2),15854(a,1,1))].">
      <j1 rule="para" parents="16547 15854"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(11142,a,16436,a)].">
      <j1 rule="hyper" parents="11142 16436"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(8630(a,1),16457(a,2,2))].">
      <j1 rule="para" parents="8630 16457"/>
    </justification>
  </clause>

  <clause id="16552">
    <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(15420(a,1),16458(a,1,2))].">
      <j1 rule="para" parents="15420 16458"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ u,y / z,z)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12533,a,b,16498,a)].">
      <j1 rule="hyper" parents="60 12533 16498"/>
    </justification>
  </clause>

  <clause id="16554">
    <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(60,a,11809,a,b,16550,a)].">
      <j1 rule="hyper" parents="60 11809 16550"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ 1) * z)) = K(x,(z * ((y / z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3409(a,1),16553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3409 16553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(w,L(x,L(x,y,z),u)))
    ]]></literal>
    <justification jstring="[para(12966(a,1),16459(a,2,3))].">
      <j1 rule="para" parents="12966 16459"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      K(L(x * K(y,x),y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ ((y * x) * z),u) = w
    ]]></literal>
    <justification jstring="[para(5233(a,1),16465(a,1,1,1))].">
      <j1 rule="para" parents="5233 16465"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      K(x,((y \ 1) \ R(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(2957(a,1),16525(a,2,2,1))].">
      <j1 rule="para" parents="2957 16525"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      K(x,(y * R(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),16559(a,1,2,1))].">
      <j1 rule="para" parents="5093 16559"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      K((L(x,y,z) * u) / (x * u),w) = a(z,y,K(w,x))
    ]]></literal>
    <justification jstring="[para(12934(a,1),16557(a,2,3))].">
      <j1 rule="para" parents="12934 16557"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      (K(x,T(y,z \ u)) * (u / z)) * z = u * K(x,(z * (y * (z \ u))) / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,8809,a(flip),b,16488,a),flip(a)].">
      <j1 rule="hyper" parents="60 8809 16488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <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(11048(a,1),16463(a,1,2,3))].">
      <j1 rule="para" parents="11048 16463"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(y,z,K(u,x)) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[para(15894(a,1),16564(a,1,2))].">
      <j1 rule="para" parents="15894 16564"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(16010,a,16566,a),flip(a)].">
      <j1 rule="hyper" parents="16010 16566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16460,a,16567,a)].">
      <j1 rule="hyper" parents="16460 16567"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * u)) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(15940(a,1),16567(a,1,1,1))].">
      <j1 rule="para" parents="15940 16567"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      K(x \ (y * z),L(u,x,y)) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,16568,a)].">
      <j1 rule="hyper" parents="60 15933 16568"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      K((x * y) \ z,L(u,y,x)) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12972,a(flip),b,16568,a)].">
      <j1 rule="hyper" parents="60 12972 16568"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),16568(a,1,2,1))].">
      <j1 rule="para" parents="344 16568"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      K(x,L(y \ (z * u),z \ y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(656(a,1),16568(a,1,2,1))].">
      <j1 rule="para" parents="656 16568"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,(x \ 1) \ y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(1264(a,1),16570(a,1,1))].">
      <j1 rule="para" parents="1264 16570"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      K(x \ ((y \ 1) * z),L(u,x,y)) = K(((y \ 1) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(1492(a,1),16570(a,1,2))].">
      <j1 rule="para" parents="1492 16570"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      K((x * y) \ ((z \ 1) \ u),L(w,y,x)) = K(y \ (x \ ((1 / z) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(6892,a,16571,a)].">
      <j1 rule="hyper" parents="6892 16571"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      K((x * (y / x)) \ z,L(u,x \ y,x)) = K((y / x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12533,a(flip),b,16571,a)].">
      <j1 rule="hyper" parents="60 12533 16571"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      K(((x * (y / x)) * x) \ z,L(u,T(x,x \ y),y)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5804(a,2),16571(a,1,1,1))].">
      <j1 rule="para" parents="5804 16571"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ u) = K(x,z \ (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15938,a(flip),b,16572,a)].">
      <j1 rule="hyper" parents="60 15938 16572"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      K(x,L(y \ z,u,y / u)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[para(7(a,1),16572(a,1,2,1,1))].">
      <j1 rule="para" parents="7 16572"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      K(x,L((y * z) \ u,T(y,z),z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16572(a,1,2,1,1))].">
      <j1 rule="para" parents="107 16572"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      K(x,L(a(y,y \ z,u),(y \ z) * u,y)) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(84(a,1),16572(a,1,2,1))].">
      <j1 rule="para" parents="84 16572"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ u,z \ 1,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(16572(a,2),15300(a,1))].">
      <j1 rule="para" parents="16572 15300"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      K(x,L(R(y,z,z) \ u,a(y,z,z),y)) = K(x,a(y,z,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(16504(a,1),16572(a,1,2,1,1))].">
      <j1 rule="para" parents="16504 16572"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      K(x,L(y * (y * z),u,w) \ v5) = K(x,L(z,u,w) \ (y \ (y \ v5)))
    ]]></literal>
    <justification jstring="[para(3905(a,2),16579(a,1,2,1))].">
      <j1 rule="para" parents="3905 16579"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(15944,a,16573,a)].">
      <j1 rule="hyper" parents="15944 16573"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,y \ (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(16439,a,16586,a),flip(a)].">
      <j1 rule="hyper" parents="16439 16586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = x * K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,16586,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 16586 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      K(x,(y \ (y \ z)) \ u) = K(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(656(a,1),16586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 16586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),y * (z \ 1),z)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[para(1217(a,2),16586(a,2,2,1))].">
      <j1 rule="para" parents="1217 16586"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      K(x,L((1 / y) \ (z * u),y,z)) = K(x,(z \ (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(3388(a,1),16586(a,1,2))].">
      <j1 rule="para" parents="3388 16586"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,R(u,z,z) \ (u * z))) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(13769(a,1),16586(a,1,2,1,2))].">
      <j1 rule="para" parents="13769 16586"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,16588,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 16588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(16588(a,2),5265(a,1))].">
      <j1 rule="para" parents="16588 5265"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ (y * u)) = T(x,(y \ z) \ ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2112(a,1),16593(a,1,2))].">
      <j1 rule="para" parents="2112 16593"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      T(x,L(T(y,z) \ (z * u),T(y,z),z)) = T(x,(T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5749(a,2),16593(a,2,2,1))].">
      <j1 rule="para" parents="5749 16593"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(2156(a,1),16587(a,2,2))].">
      <j1 rule="para" parents="2156 16587"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(15459,a,16597,a)].">
      <j1 rule="hyper" parents="15459 16597"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      x * K(x,L(y,z,u) * (y \ w)) = T(x,(L(y,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,16597,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 16597 5230"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ ((y * y) * w)) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[para(554(a,1),16597(a,2,2,2))].">
      <j1 rule="para" parents="554 16597"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) = K(x,a(z,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),16597(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1362 16597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = (w \ K(u,a(y,y,x) \ z)) \ (w \ 1)
    ]]></literal>
    <justification jstring="[para(16601(a,1),15194(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16601 15194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      x * K(x,L(y,z,u) * (y \ w)) = T(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(129,a,16598,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 16598 5230"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * ((y * y) * w)) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[para(554(a,1),16598(a,2,2,2))].">
      <j1 rule="para" parents="554 16598"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(16598(a,1),15462(a,1))].">
      <j1 rule="para" parents="16598 15462"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(16420(a,1),16569(a,1,1))].">
      <j1 rule="para" parents="16420 16569"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      (K(x,K(y,z * u)) * z) * u = T(z * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(32,a,8664,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="32 8664 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * u)) \ (K(x,y) * ((z * u) * u)) = a(K(x,y) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,16606,a(flip),b,82,a)].">
      <j1 rule="hyper" parents="125 16606 82"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      (T(K(x,y),(x \ R(x,y,x)) * z) * K(x * y,x)) * z = T((x \ R(x,y,x)) * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9336(a,1),16607(a,1,1))].">
      <j1 rule="para" parents="9336 16607"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12532,a(flip),b,16581,a)].">
      <j1 rule="hyper" parents="60 12532 16581"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      K(x,L((((y * z) / y) * (z \ y)) \ u,(y * z) / y,z \ y)) = K(x,((z \ y) \ T(y,z)) \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(2268(a,1),16611(a,2,2,1))].">
      <j1 rule="para" parents="2268 16611"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      K(x,L((y * L(1 / y,z,u)) \ w,y \ 1,L(y,z,u))) = K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(3797(a,1),16611(a,1,2,1,1))].">
      <j1 rule="para" parents="3797 16611"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      K(x,L((y * (z * (u * K(w,u)))) \ v5,y * (z * u),K(w,L(u,z,y)))) = K(x,T(y * (z * u),K(w,L(u,z,y))) \ (K(w,L(u,z,y)) \ v5))
    ]]></literal>
    <justification jstring="[para(13064(a,1),16611(a,1,2,1,1))].">
      <j1 rule="para" parents="13064 16611"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y * u)) = T(x,(y \ z) \ ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,4677,a(flip),b,16595,a)].">
      <j1 rule="hyper" parents="60 4677 16595"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      T(x,(y \ (y * z)) \ ((y \ 1) \ u)) = T(x,L(z,y,y) \ (y * u))
    ]]></literal>
    <justification jstring="[para(579(a,1),16595(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="579 16595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(5265,a,16599,a),flip(a)].">
      <j1 rule="hyper" parents="5265 16599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16599(a,1),5265(a,1))].">
      <j1 rule="para" parents="16599 5265"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16603(a,1),5265(a,1))].">
      <j1 rule="para" parents="16603 5265"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      K((x * (y / x)) \ z,L(u,y,x)) = K((y / x) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(15944,a,16577,a)].">
      <j1 rule="hyper" parents="15944 16577"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z * y) \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(663(a,1),16596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="663 16596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (z * u)) = T(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),16616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 16616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ u,z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(3401(a,1),16583(a,1,2))].">
      <j1 rule="para" parents="3401 16583"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(y,y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(16602(a,2),6378(a,1))].">
      <j1 rule="para" parents="16602 6378"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      K(x \ (y \ ((1 / z) \ u)),w) = K(x \ (y \ ((z \ 1) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16571,a(flip),b,16576,a),flip(a)].">
      <j1 rule="hyper" parents="60 16571 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      K((1 / x) \ (y \ ((z \ 1) \ u)),w) = K(x * (y \ ((1 / z) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(15493,a,16625,a),flip(a)].">
      <j1 rule="hyper" parents="15493 16625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      (x * y) / (K(z \ (u \ ((w \ 1) \ v5)),x) * y) = T(x,z \ (u \ ((1 / w) \ v5)))
    ]]></literal>
    <justification jstring="[para(16625(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="16625 7934"/>
    </justification>
  </clause>

  <clause id="16628">
    <literal><![CDATA[
      K(x * (y \ ((1 / z) \ u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ ((z \ 1) \ u)),w) = v5
    ]]></literal>
    <justification jstring="[para(16626(a,1),15493(a,1))].">
      <j1 rule="para" parents="16626 15493"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      K(x,L(y,z,u) * ((1 / y) \ w)) = K(x,(y * L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(1874(a,1),16604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1874 16604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      K(L((x / y) * K(z,T(u,y)),K(u,T(z,y)),y),w) = K(x / (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[para(8088(a,1),16467(a,1,1,1))].">
      <j1 rule="para" parents="8088 16467"/>
    </justification>
  </clause>

  <clause id="16631">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * (z * u))) / u = L(K(x,y),K(x,y),z) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10827(a,1),16470(a,1,1))].">
      <j1 rule="para" parents="10827 16470"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(((u * z) / y) \ 1,y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8030,a,b,16545,a),flip(a)].">
      <j1 rule="hyper" parents="370 8030 16545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      (x * x) \ ((K(y,z) * u) \ (K(y,z) * ((u * x) * x))) = a(K(y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(749,a,16608,a)].">
      <j1 rule="hyper" parents="749 16608"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * (z * u))) / u = K(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11393(a,1),16631(a,2,1))].">
      <j1 rule="para" parents="11393 16631"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) * u = K(x,y) * (K(x,y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(155,a,16634,a)].">
      <j1 rule="hyper" parents="155 16634"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = K(y,x) * (K(y,x) * (z * u))
    ]]></literal>
    <justification jstring="[para(9604(a,1),16635(a,1,1))].">
      <j1 rule="para" parents="9604 16635"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = x * (T(T(x,y),y) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9604,a(flip),b,16637,a),flip(a)].">
      <j1 rule="hyper" parents="370 9604 16637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9971,a(flip),b,16632,a),flip(a)].">
      <j1 rule="hyper" parents="370 9971 16632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(6501,a,16639,a),flip(a)].">
      <j1 rule="hyper" parents="6501 16639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,T(y / (z * (z \ u)),y / (z \ u))) = K(x,T(u,z) \ ((z \ u) * (y / (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,14573,a(flip),b,16640,a),flip(a)].">
      <j1 rule="hyper" parents="370 14573 16640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      K(x,T(y / ((z / (z * u)) * (z * u)),y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(6478(a,1),16640(a,2,2,1))].">
      <j1 rule="para" parents="6478 16640"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      L(a(x,y,y),x,K(z,u)) = a(K(z,u) * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3779,a(flip),b,16633,a)].">
      <j1 rule="hyper" parents="60 3779 16633"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ R(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(2957(a,1),16524(a,2,2,2,2))].">
      <j1 rule="para" parents="2957 16524"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      K(x,y * (z * (u * R(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(5093(a,1),16644(a,1,2,2,2))].">
      <j1 rule="para" parents="5093 16644"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,y))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15891,a,b,16582,a)].">
      <j1 rule="hyper" parents="60 15891 16582"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      T(x,y \ (z \ ((1 / u) \ w))) = T(x,y \ (z \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(7939,a,16627,a),flip(a)].">
      <j1 rule="hyper" parents="7939 16627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      T(x,y \ (z \ ((u \ 1) \ 1))) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(77(a,1),16647(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="77 16647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ ((1 / u) \ (w * (1 / u)))))
    ]]></literal>
    <justification jstring="[para(4694(a,2),16647(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4694 16647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ ((u \ 1) \ 1))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15165,a(flip),b,16648,a),flip(a)].">
      <j1 rule="hyper" parents="370 15165 16648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      T(x,y \ (z \ (1 / u))) = T(x,y \ (z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(77(a,1),16648(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 16648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(z * (x \ 1)) \ ((z * (x \ 1)) \ (x \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(16651(a,1),16322(a,1))].">
      <j1 rule="para" parents="16651 16322"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * (z \ ((u \ 1) \ 1))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(15475,a,16650,a)].">
      <j1 rule="hyper" parents="15475 16650"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(7327(a,1),16646(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7327 16646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15927,a(flip),b,16654,a),flip(a)].">
      <j1 rule="hyper" parents="370 15927 16654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16657">
    <literal><![CDATA[
      (x * y) \ (((z \ R(z,u,u)) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(2569(a,1),16521(a,1,2,1))].">
      <j1 rule="para" parents="2569 16521"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      (x * y) \ ((a(z,u,u) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(16509(a,1),16657(a,1,2,1,1))].">
      <j1 rule="para" parents="16509 16657"/>
    </justification>
  </clause>

  <clause id="16659">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(T(a(x,u,u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(1393,a,16658,a),flip(a)].">
      <j1 rule="hyper" parents="1393 16658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(15849(a,1),16659(a,2,1))].">
      <j1 rule="para" parents="15849 16659"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,x \ y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3392(a,1),16574(a,1,2))].">
      <j1 rule="para" parents="3392 16574"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      K((x \ y) \ ((1 / x) * z),L(u,y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(15944,a,16662,a)].">
      <j1 rule="hyper" parents="15944 16662"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      K((x \ y) \ ((x \ 1) * z),L(u,y,x)) = K((x \ ((x \ 1) \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6197,a(flip),b,16663,a)].">
      <j1 rule="hyper" parents="60 6197 16663"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) \ z,u) = K(y \ (x * ((x \ 1) * z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,16664,a),flip(a)].">
      <j1 rule="hyper" parents="60 15933 16664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) \ z,u) = K(y \ L(z,x,x),u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),16665(a,2,1,2))].">
      <j1 rule="para" parents="2074 16665"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) \ z,u) = K(y \ L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6673,a,b,16666,a)].">
      <j1 rule="hyper" parents="60 6673 16666"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      (T(x \ 1,x \ y) * (x \ y)) * z = T(x \ 1,x \ y) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(7900,a,16497,a),flip(a)].">
      <j1 rule="hyper" parents="7900 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      T(x \ 1,x \ y) * (x \ (y * z)) = T((1 / x) * (y / x),y) * z
    ]]></literal>
    <justification jstring="[para(16234(a,1),16668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16234 16668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16670">
    <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(13454(a,1),16554(a,1,1))].">
      <j1 rule="para" parents="13454 16554"/>
    </justification>
  </clause>

  <clause id="16671">
    <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(8700(a,1),16670(a,1,1,2))].">
      <j1 rule="para" parents="8700 16670"/>
    </justification>
  </clause>

  <clause id="16672">
    <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(16339,a,16671,a)].">
      <j1 rule="hyper" parents="16339 16671"/>
    </justification>
  </clause>

  <clause id="16673">
    <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(8930(a,2),16672(a,1,2,2))].">
      <j1 rule="para" parents="8930 16672"/>
    </justification>
  </clause>

  <clause id="16674">
    <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(11406(a,2),16673(a,1,2))].">
      <j1 rule="para" parents="11406 16673"/>
    </justification>
  </clause>

  <clause id="16675">
    <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(9193(a,2),16674(a,1,2,2,2))].">
      <j1 rule="para" parents="9193 16674"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z))))
    ]]></literal>
    <justification jstring="[para(5(a,1),16641(a,1,2,1,2))].">
      <j1 rule="para" parents="5 16641"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),y * z,z)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[para(3778(a,1),16590(a,1,2))].">
      <j1 rule="para" parents="3778 16590"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,1 / u)))
    ]]></literal>
    <justification jstring="[para(17(a,2),16649(a,2,2,2,2))].">
      <j1 rule="para" parents="17 16649"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u \ 1)))
    ]]></literal>
    <justification jstring="[para(4443(a,1),16678(a,2,2,2,2))].">
      <j1 rule="para" parents="4443 16678"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      (((x \ y) * K(z,u / (x \ y))) * x) \ ((x \ y) * x) = K(y \ (x * u),T(z,(x \ y) * x))
    ]]></literal>
    <justification jstring="[para(8809(a,1),16494(a,1,1,1))].">
      <j1 rule="para" parents="8809 16494"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (T(K(x,y),z) * K(x * y,x)) * z
    ]]></literal>
    <justification jstring="[para(14341(a,1),16610(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14341 16610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (T(x,K(y,z)) \ R(x,y,x)) * z
    ]]></literal>
    <justification jstring="[para(10009(a,1),16681(a,2,1))].">
      <j1 rule="para" parents="10009 16681"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = (x \ R(T(x,K(y,z)),y,x)) * z
    ]]></literal>
    <justification jstring="[para(9792(a,1),16682(a,2,1))].">
      <j1 rule="para" parents="9792 16682"/>
    </justification>
  </clause>

  <clause id="16685">
    <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(8017(a,2),16675(a,1,2,2))].">
      <j1 rule="para" parents="8017 16675"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,L(z,z,u * z))) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(4120(a,1),16592(a,1,2))].">
      <j1 rule="para" parents="4120 16592"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,((R(u,z,z) \ (u * z)) \ y) \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(15953,a,16686,a)].">
      <j1 rule="hyper" parents="15953 16686"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      K(x,((R(y,z,z) \ (y * z)) \ u) \ R(y,z,z)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16586,a(flip),b,16687,a),flip(a)].">
      <j1 rule="hyper" parents="60 16586 16687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = T(K(x,y),z * z) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),16487(a,2,1))].">
      <j1 rule="para" parents="17 16487"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,(y * z) / y,z \ y)) = K(x,((z \ y) \ T(y,z)) \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(2266(a,2),16612(a,1,2,1,1))].">
      <j1 rule="para" parents="2266 16612"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,y)) \ ((y \ z) \ u)) = K(x,L(T(z,y) \ u,T(y,z),y \ z))
    ]]></literal>
    <justification jstring="[para(8260(a,1),16690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8260 16690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,L((y * L(1 / y,z,u)) \ w,y,L(y,z,u))) = K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(3401(a,1),16613(a,1,2))].">
      <j1 rule="para" parents="3401 16613"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y * L(1 / y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(16439,a,16692,a),flip(a)].">
      <j1 rule="hyper" parents="16439 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y * L(y \ 1,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,6624,a(flip),b,16693,a),flip(a)].">
      <j1 rule="hyper" parents="370 6624 16693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      K(x,T(y \ 1,L(y,z,u)) \ (L(y,z,u) \ w)) = K(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(3816(a,1),16695(a,2,2,1))].">
      <j1 rule="para" parents="3816 16695"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,T(x * y,x))) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(15518(a,1),16491(a,1,2))].">
      <j1 rule="para" parents="15518 16491"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,T(u,y * x)) = K((((1 / x) \ z) * (1 / x)) / (T((x \ 1) \ y,x) * (1 / x)),u)
    ]]></literal>
    <justification jstring="[para(12567(a,1),16697(a,1,2))].">
      <j1 rule="para" parents="12567 16697"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(7(a,1),16642(a,1,2,1,2))].">
      <j1 rule="para" parents="7 16642"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(6713(a,2),16685(a,1,2))].">
      <j1 rule="para" parents="6713 16685"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,14520,a,b,16700,a),flip(a)].">
      <j1 rule="hyper" parents="370 14520 16700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z * u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,14518,a,b,16700,a),flip(a)].">
      <j1 rule="hyper" parents="370 14518 16700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(u * T((K(x,y) * z) / K(x,y),K(y,x)),K(y,x)) = T(u,T(K(x,y),z) * z)
    ]]></literal>
    <justification jstring="[para(5448(a,2),16700(a,2,2))].">
      <j1 rule="para" parents="5448 16700"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8700(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="8700 16700"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u \ 1)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(9455(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="9455 16700"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8700(a,1),16704(a,1,2))].">
      <j1 rule="para" parents="8700 16704"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(156,a,16706,a),flip(a)].">
      <j1 rule="hyper" parents="156 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16700,a(flip),b,16706,a)].">
      <j1 rule="hyper" parents="60 16700 16706"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14342,a,b,16708,a)].">
      <j1 rule="hyper" parents="370 14342 16708"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,z)) = y * T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,16708,a,b,16704,a),flip(a)].">
      <j1 rule="hyper" parents="129 16708 16704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,16708,a,b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 16708 5256"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      x / T(x,K(y,z) * u) = K(K(z,y) * u,x)
    ]]></literal>
    <justification jstring="[para(16708(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16708 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(7500(a,1),16708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7500 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16714">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7864(a,1),16708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7873(a,1),16708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7873 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(15370(a,1),16708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15370 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,15539,a,b,16713,a)].">
      <j1 rule="hyper" parents="60 15539 16713"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,15541,a(flip),b,16713,a),flip(a)].">
      <j1 rule="hyper" parents="37 15541 16713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      T(x,T(T(y,z),z) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(7565(a,1),16713(a,1,2))].">
      <j1 rule="para" parents="7565 16713"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9604(a,1),16713(a,1,2))].">
      <j1 rule="para" parents="9604 16713"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(16718(a,1),46(a,2))].">
      <j1 rule="para" parents="16718 46"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(15429(a,1),16721(a,1))].">
      <j1 rule="para" parents="15429 16721"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(15540(a,1),16721(a,1))].">
      <j1 rule="para" parents="15540 16721"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      T(x,y * (z \ (K(u,w) * K(u,w)))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15613,a(flip),b,16717,a)].">
      <j1 rule="hyper" parents="60 15613 16717"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * K(u,w)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(30(a,1),16717(a,1,2))].">
      <j1 rule="para" parents="30 16717"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),16720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 16720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(12635,a,16726,a),flip(a)].">
      <j1 rule="hyper" parents="12635 16726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      T(x,T(y \ z,z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14715,a(flip),b,16726,a)].">
      <j1 rule="hyper" parents="60 14715 16726"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      T(T(x,K(y,K(z,u))),K(u,z) * y) = T(x,y * K(z,z * u))
    ]]></literal>
    <justification jstring="[hyper(12634,a,16709,a),flip(a)].">
      <j1 rule="hyper" parents="12634 16709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5290,a,16711,a)].">
      <j1 rule="hyper" parents="5290 16711"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16711(a,1),5290(a,1))].">
      <j1 rule="para" parents="16711 5290"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14360,a,b,16730,a)].">
      <j1 rule="hyper" parents="370 14360 16730"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7506(a,2),16730(a,1,2))].">
      <j1 rule="para" parents="7506 16730"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7858(a,1),16730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 16730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7873(a,1),16730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7873 16730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(8143(a,1),16730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8143 16730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      K(x,K(y / (z \ u),z) * w) = K(x,K(z,(y * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(10653(a,2),16730(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10653 16730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ 1) \ u)) = K(x,u * T(u \ ((y \ 1) \ u),z))
    ]]></literal>
    <justification jstring="[para(5270(a,1),16733(a,2,2))].">
      <j1 rule="para" parents="5270 16733"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7506(a,2),16733(a,2,2))].">
      <j1 rule="para" parents="7506 16733"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      K(x,K(y,z) \ (y / u)) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(15370(a,1),16733(a,2,2))].">
      <j1 rule="para" parents="15370 16733"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(12922(a,2),16739(a,1,2,1))].">
      <j1 rule="para" parents="12922 16739"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(5734,a,16712,a)].">
      <j1 rule="hyper" parents="5734 16712"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(16712(a,1),5734(a,1))].">
      <j1 rule="para" parents="16712 5734"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      K(K(x,y) * (K(x,y) * z),u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(7500(a,1),16742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 16742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(7873(a,1),16742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 16742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(7565(a,1),16744(a,1,1))].">
      <j1 rule="para" parents="7565 16744"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      K(x * (T(T(x,y),y) \ z),u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9604(a,1),16744(a,1,1))].">
      <j1 rule="para" parents="9604 16744"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(262(a,1),16746(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="262 16746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),16747(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 16747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      K(T(x,x \ y) * z,u) = K((y / (y / x)) * z,u)
    ]]></literal>
    <justification jstring="[para(5839(a,1),16749(a,1,1,1,1))].">
      <j1 rule="para" parents="5839 16749"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      T(x,y * (K(z,y) * u)) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7967(a,1),16714(a,1,2))].">
      <j1 rule="para" parents="7967 16714"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      T(x,y \ (K(y,z) * u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7894(a,2),16715(a,1,2))].">
      <j1 rule="para" parents="7894 16715"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8209(a,2),16715(a,1,2))].">
      <j1 rule="para" parents="8209 16715"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(8210(a,1),16715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8210 16715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(8236(a,1),16715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8236 16715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      T(x,K(y,y * a(z,u,w)) * ((y * a(z,u,w)) / v5)) = T(x,(a(z,u,w) * y) / v5)
    ]]></literal>
    <justification jstring="[para(15090(a,1),16716(a,2,2,1))].">
      <j1 rule="para" parents="15090 16716"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      T(x,(y / (y / z)) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(77(a,1),16728(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 16728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7948(a,1),16734(a,1,2))].">
      <j1 rule="para" parents="7948 16734"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),16758(a,1,2,1,1))].">
      <j1 rule="para" parents="109 16758"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(262(a,1),16758(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="262 16758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(5548(a,1),16758(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5548 16758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14527,a,b,16745,a)].">
      <j1 rule="hyper" parents="60 14527 16745"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      K(((x * y) / x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(8209(a,2),16745(a,1,1))].">
      <j1 rule="para" parents="8209 16745"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      K(T(x * K(y,x),z) / z,u) = K(T(x,y) / T(z,T(x,y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,10218,a,b,16748,a)].">
      <j1 rule="hyper" parents="60 10218 16748"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      T(x,T(y,y \ z) * ((y \ z) \ u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[para(8210(a,1),16751(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8210 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(x,y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(7858(a,1),16752(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7858 16752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      T(x,T(T(y,z),z) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(263(a,1),16753(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="263 16753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      T(x,T(y,y \ z) \ u) = T(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(5835(a,1),16753(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5835 16753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      T(x,((y \ 1) * K((1 / y) \ z,1 / y)) * u) = T(x,T(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,5838,a(flip),b,16757,a)].">
      <j1 rule="hyper" parents="60 5838 16757"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5745(a,1),16759(a,1,2,1))].">
      <j1 rule="para" parents="5745 16759"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,y \ ((z * u) / z))) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[para(12522(a,2),16760(a,1,2))].">
      <j1 rule="para" parents="12522 16760"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K((x / y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16620,a(flip),b,16762,a),flip(a)].">
      <j1 rule="hyper" parents="60 16620 16762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      K(T(T(x,y),y) \ z,u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(263(a,1),16763(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="263 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(7500(a,1),16722(a,1,2,2))].">
      <j1 rule="para" parents="7500 16722"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(7858(a,1),16722(a,1,2,2))].">
      <j1 rule="para" parents="7858 16722"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(7908(a,1),16722(a,1,2,2))].">
      <j1 rule="para" parents="7908 16722"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y) / u) = w
    ]]></literal>
    <justification jstring="[para(15372(a,1),16722(a,1,2,2))].">
      <j1 rule="para" parents="15372 16722"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(9721(a,1),16723(a,1,2))].">
      <j1 rule="para" parents="9721 16723"/>
    </justification>
  </clause>

  <clause id="16780">
    <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(15613(a,1),16723(a,1))].">
      <j1 rule="para" parents="15613 16723"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16732(a,2),16731(a,1))].">
      <j1 rule="para" parents="16732 16731"/>
    </justification>
  </clause>

  <clause id="16782">
    <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(16706(a,2),16774(a,1))].">
      <j1 rule="para" parents="16706 16774"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z * y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16709(a,1),16774(a,1))].">
      <j1 rule="para" parents="16709 16774"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16709(a,2),16774(a,1))].">
      <j1 rule="para" parents="16709 16774"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),16779(a,1,2,2,1))].">
      <j1 rule="para" parents="109 16779"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      T(x,y * (z \ K(z,u))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7876(a,1),16724(a,1,2,2))].">
      <j1 rule="para" parents="7876 16724"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(30(a,1),16725(a,1,2,2))].">
      <j1 rule="para" parents="30 16725"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      T(x,y * (z \ T(T(u,w),w))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(9721(a,1),16725(a,1,2,2))].">
      <j1 rule="para" parents="9721 16725"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12611,a,16727,a),flip(a)].">
      <j1 rule="hyper" parents="12611 16727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      T(x,y * T(z \ u,z)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),16789(a,1,2,2,1))].">
      <j1 rule="para" parents="109 16789"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(262(a,1),16789(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="262 16789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      T(x,y * T(z,z \ u)) = T(x,y * (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(5839(a,1),16789(a,1,2,2,1))].">
      <j1 rule="para" parents="5839 16789"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      T(x,(y / z) * (y / z)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(5864(a,1),16790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5864 16790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(16791(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="16791 5701"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      K((x / (x / y)) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14396,a(flip),b,16750,a),flip(a)].">
      <j1 rule="hyper" parents="60 14396 16750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(T(x,u),y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15680,a,16766,a)].">
      <j1 rule="hyper" parents="15680 16766"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14555,a,16770,a)].">
      <j1 rule="hyper" parents="14555 16770"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      T(x,y * (z / (z / u))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14432,a(flip),b,16792,a),flip(a)].">
      <j1 rule="hyper" parents="60 14432 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      T(x,y * T(z \ u,u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(74(a,1),16798(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="74 16798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      T(x * K(y / z,x),z / y) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8225,a,b,16793,a)].">
      <j1 rule="hyper" parents="60 8225 16793"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,16794,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 16794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      K(x * T(y \ z,y),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),16801(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 16801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      K((x \ y) * ((z * ((x \ y) \ (x \ u))) / z),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(2225(a,1),16801(a,2,1))].">
      <j1 rule="para" parents="2225 16801"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14631,a(flip),b,16761,a),flip(a)].">
      <j1 rule="hyper" parents="60 14631 16761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16804(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 16804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      K(x,L((y / z) \ u,u,z)) = K(x,T(y,z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(13035,a,16806,a)].">
      <j1 rule="hyper" parents="13035 16806"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14573,a,b,16806,a)].">
      <j1 rule="hyper" parents="370 14573 16806"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14570,a(flip),b,16806,a),flip(a)].">
      <j1 rule="hyper" parents="370 14570 16806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y / z) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(12697(a,1),16806(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12697 16806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(16808(a,1),5865(a,1,1))].">
      <j1 rule="para" parents="16808 5865"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      K(x,(T(y,z) * z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(263(a,1),16809(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 16809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      K(x,(T(T(y,z * z),1 / z) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(1660(a,2),16812(a,2,2,1))].">
      <j1 rule="para" parents="1660 16812"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      T(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(7967(a,1),16776(a,1,2))].">
      <j1 rule="para" parents="7967 16776"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      T(x,y \ (T(z,u) \ u)) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(16785,a,14640,a),flip(a)].">
      <j1 rule="hyper" parents="16785 14640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      T(x,y \ (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(14640(a,1),16785(a,1))].">
      <j1 rule="para" parents="14640 16785"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(5749(a,1),16815(a,1,2,2))].">
      <j1 rule="para" parents="5749 16815"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),T(w,z),R(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(7317(a,1),16807(a,2,2,2))].">
      <j1 rule="para" parents="7317 16807"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      T(x * T(y,K(z,u) * x),K(u,z)) = y * T(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6233,a,16710,a)].">
      <j1 rule="hyper" parents="6233 16710"/>
    </justification>
  </clause>

  <clause id="16821">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(16796(a,2),15680(a,1))].">
      <j1 rule="para" parents="16796 15680"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      T(x * K(T(y \ z,z \ y) / 1,x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(3513(a,1),16800(a,1,2))].">
      <j1 rule="para" parents="3513 16800"/>
    </justification>
  </clause>

  <clause id="16823">
    <literal><![CDATA[
      T(x * K(L(y,z,y) * z,x),y / (y * (z * y))) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[para(5522(a,1),16800(a,1,1,2,1))].">
      <j1 rule="para" parents="5522 16800"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      K(x,T(y * (y * z),y) \ ((T(y,y * z) * z) * u)) = K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u))
    ]]></literal>
    <justification jstring="[para(5463(a,1),16810(a,1,2,2,1))].">
      <j1 rule="para" parents="5463 16810"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5871,a,16811,a),flip(a)].">
      <j1 rule="hyper" parents="5871 16811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16762,a(flip),b,16825,a),flip(a)].">
      <j1 rule="hyper" parents="370 16762 16825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      K((x * ((x * y) / x)) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),16825(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((1 / y) \ z) * (1 / y)) / (T((y \ 1) \ x,y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16698,a(flip),b,16826,a),flip(a)].">
      <j1 rule="hyper" parents="60 16698 16826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),16826(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      1 / (x \ K(T(y,z) \ u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z \ y) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(16826(a,1),5768(a,1,2,2))].">
      <j1 rule="para" parents="16826 5768"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) * a(w,v5,K((z * y) \ u,x)) = K(x,L(T(y * z,y) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(16829(a,1),12932(a,1,2,3))].">
      <j1 rule="para" parents="16829 12932"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(263(a,1),16827(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="263 16827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12633,a,16729,a),flip(a)].">
      <j1 rule="hyper" parents="12633 16729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      K(T(x,y) / T(z,T(x,y)),u) = K(z \ (x * K(y,x)),u)
    ]]></literal>
    <justification jstring="[hyper(14404,a,16764,a),flip(a)].">
      <j1 rule="hyper" parents="14404 16764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14428,a,16834,a),flip(a)].">
      <j1 rule="hyper" parents="14428 16834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5233(a,2),16835(a,1,1,2))].">
      <j1 rule="para" parents="5233 16835"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5254(a,1),16835(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5254 16835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      K(x \ T(y,y \ z),u) = K(x \ (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(5683(a,2),16835(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5683 16835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(16837(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16837 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      K(x \ (((y * y) * ((y \ 1) * (y \ z))) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(16240(a,1),16836(a,2,1,2))].">
      <j1 rule="para" parents="16240 16836"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,16839,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 16839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(16839(a,2),5870(a,1))].">
      <j1 rule="para" parents="16839 5870"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(262(a,1),16842(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="262 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5280(a,1),16842(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5280 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(5789(a,1),16842(a,1,2,2,1))].">
      <j1 rule="para" parents="5789 16842"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(11176,a,16845,a)].">
      <j1 rule="hyper" parents="11176 16845"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(4443(a,2),16847(a,2,2,2))].">
      <j1 rule="para" parents="4443 16847"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,u)))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7871(a,1),16787(a,1,2,2,2))].">
      <j1 rule="para" parents="7871 16787"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) = x \ T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(125,a,16850,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 16850 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      T(x,y * (z * T(T(u,w),w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5254(a,1),16850(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5254 16850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),16852(a,1,2,2))].">
      <j1 rule="para" parents="107 16852"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) = T(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(15260,a,16853,a)].">
      <j1 rule="hyper" parents="15260 16853"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z * u)) = T(x,(T(u,z) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(12620,a,16853,a),flip(a)].">
      <j1 rule="hyper" parents="12620 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = x * K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a(flip),b,16853,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      T(x,y * T(z * T(u,z),z)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14411,a,b,16853,a)].">
      <j1 rule="hyper" parents="60 14411 16853"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      T(x,T(y,z * (u * w)) * (z * (T(w,u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * (T(w,u) * u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(16853(a,1),12606(a,1,2,1))].">
      <j1 rule="para" parents="16853 12606"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (z * (T(w,u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (T(w,u) * u)) * y) = v5
    ]]></literal>
    <justification jstring="[para(16853(a,1),12637(a,1,2,1))].">
      <j1 rule="para" parents="16853 12637"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(16854(a,2),15260(a,1))].">
      <j1 rule="para" parents="16854 15260"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(15332,a,16856,a)].">
      <j1 rule="hyper" parents="15332 16856"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(5289,a,16856,a)].">
      <j1 rule="hyper" parents="5289 16856"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(16856(a,2),5265(a,1))].">
      <j1 rule="para" parents="16856 5265"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,y * (T(z \ u,w) * z)) = K(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(284(a,1),16862(a,1,2,2,1))].">
      <j1 rule="para" parents="284 16862"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (u * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[para(8418(a,1),16862(a,1,2,2))].">
      <j1 rule="para" parents="8418 16862"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(8855(a,1),16862(a,1,2,2,1))].">
      <j1 rule="para" parents="8855 16862"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (u * K(w,u)))) = K(x,y * (u * (z * K(w,u))))
    ]]></literal>
    <justification jstring="[para(8403(a,1),16862(a,1,2,2))].">
      <j1 rule="para" parents="8403 16862"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      K(x,y * (T(z,(u \ w) * (u \ w)) * (w / u))) = K(x,y * ((w / u) * (z * K(u / w,z))))
    ]]></literal>
    <justification jstring="[para(16800(a,1),16862(a,1,2,2,1))].">
      <j1 rule="para" parents="16800 16862"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      T(x,y * T(z * u,u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),16857(a,1,2,2,1))].">
      <j1 rule="para" parents="107 16857"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      T(x,y * (z * (u / z))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(256(a,1),16857(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="256 16857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16871">
    <literal><![CDATA[
      T(x,(y * z) * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(107(a,1),16869(a,1,2))].">
      <j1 rule="para" parents="107 16869"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = u / T(u,x * (z * y))
    ]]></literal>
    <justification jstring="[para(16869(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="16869 5701"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,16861,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 16861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(16861(a,2),15233(a,1))].">
      <j1 rule="para" parents="16861 15233"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w) / w) * (T(u,w) / w))) = K(x,y \ ((u / T(w,u)) * z))
    ]]></literal>
    <justification jstring="[para(5788(a,1),16873(a,2,2,2))].">
      <j1 rule="para" parents="5788 16873"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,16872,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 16872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      K(x * T(y * z,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(16872(a,2),5734(a,1))].">
      <j1 rule="para" parents="16872 5734"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16876(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      K(x * T(T(y,z),u \ y),w) = K(x * T((u \ y) * u,z),w)
    ]]></literal>
    <justification jstring="[para(4844(a,1),16878(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4844 16878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(16860,a,14452,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16860 14452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      T(x,y \ (a(z,u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * a(z,u,u))) = v5
    ]]></literal>
    <justification jstring="[para(15849(a,1),16860(a,1,2,2,1))].">
      <j1 rule="para" parents="15849 16860"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      T(x,y \ (z * (u / z))) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),16880(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      T(x,((y * y) \ z) * (u / z)) = T(x,(y * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[para(514(a,1),16882(a,1,2))].">
      <j1 rule="para" parents="514 16882"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      T(x,y * (T(z,u) * L(u,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (L(u,w,u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(7306(a,1),16863(a,1,2,2,1))].">
      <j1 rule="para" parents="7306 16863"/>
    </justification>
  </clause>

  <clause id="16885">
    <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(12600(a,1),16874(a,1,2,2,1))].">
      <j1 rule="para" parents="12600 16874"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * ((w \ u) * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((w \ u) * u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(14508(a,1),16874(a,1,2,2,1))].">
      <j1 rule="para" parents="14508 16874"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      T(x,(T(y,z) * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(16855(a,1),12606(a,1))].">
      <j1 rule="para" parents="16855 12606"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      T(x,((y * y) \ z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(16883(a,2),15248(a,1))].">
      <j1 rule="para" parents="16883 15248"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14417,a(flip),b,16846,a)].">
      <j1 rule="hyper" parents="60 14417 16846"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(5746(a,1),16889(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5746 16889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16890(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      K(x,y \ T((z * u) * (z \ 1),z \ 1)) = K(x,y \ (z * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(951(a,1),16891(a,2,2,2))].">
      <j1 rule="para" parents="951 16891"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,16851,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(16851(a,2),5290(a,1))].">
      <j1 rule="para" parents="16851 5290"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5254(a,1),16893(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5254 16893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,y * (z * (T(u,u * w) * w))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[para(5606(a,1),16895(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5606 16895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16701(a,1),16782(a,1))].">
      <j1 rule="para" parents="16701 16782"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16702(a,1),16782(a,1))].">
      <j1 rule="para" parents="16702 16782"/>
    </justification>
  </clause>

  <clause id="16900">
    <literal><![CDATA[
      T(x,K(y * z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(6557(a,2),16898(a,1,2,1))].">
      <j1 rule="para" parents="6557 16898"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      T(x,T(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z \ y) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5767(a,2),16830(a,1))].">
      <j1 rule="para" parents="5767 16830"/>
    </justification>
  </clause>

  <clause id="16902">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(5233(a,2),16894(a,1,2,2,2))].">
      <j1 rule="para" parents="5233 16894"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      K(x,y \ (z * ((u * w) / u))) = K(x,(y \ 1) * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(16902,a,15200,a),flip(a)].">
      <j1 rule="hyper" parents="16902 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) / u)) * (z * T(w,u))) = K(x,(z * ((u * w) / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(16902,a,12605,a)].">
      <j1 rule="hyper" parents="16902 12605"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,y \ (z * ((u * w) / u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,16903,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 16903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      K(x,y \ (z * ((T(u,w) * T(w,v5)) / T(u,w)))) = K(x,y \ (z * T(T(w,u),v5)))
    ]]></literal>
    <justification jstring="[para(5750(a,1),16906(a,2,2,2,2))].">
      <j1 rule="para" parents="5750 16906"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(9455(a,1),16705(a,1,2))].">
      <j1 rule="para" parents="9455 16705"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(16782,a,16908,a),flip(a)].">
      <j1 rule="hyper" parents="16782 16908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,16909,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 16909 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y \ 1))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(8711(a,1),16909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8711 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,16910,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 16910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16913">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(16731,a,16912,a)].">
      <j1 rule="hyper" parents="16731 16912"/>
    </justification>
  </clause>

  <clause id="16914">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,u * T(u \ (y \ u),z))
    ]]></literal>
    <justification jstring="[para(5412(a,1),16912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5412 16912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16915">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(16912(a,1),11793(a,1,1))].">
      <j1 rule="para" parents="16912 11793"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6463(a,1),16913(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6463 16913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16917">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(9460(a,1),16913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9460 16913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <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(16913(a,1),11794(a,1,1))].">
      <j1 rule="para" parents="16913 11794"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14420,a(flip),b,16916,a),flip(a)].">
      <j1 rule="hyper" parents="60 14420 16916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16735,a(flip),b,16919,a)].">
      <j1 rule="hyper" parents="60 16735 16919"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(8143(a,1),16919(a,1,2))].">
      <j1 rule="para" parents="8143 16919"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7873(a,1),16920(a,2,2))].">
      <j1 rule="para" parents="7873 16920"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      K(x,y * T(y \ (z \ y),u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16735,a(flip),b,16914,a),flip(a)].">
      <j1 rule="hyper" parents="60 16735 16914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z * K(y,z),u) * y)
    ]]></literal>
    <justification jstring="[para(5318(a,1),16914(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5318 16914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16925">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8711(a,1),16917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8711 16917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(16925(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16925 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,16926,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 16926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((z * (y \ x)) / z) * y,u) = w
    ]]></literal>
    <justification jstring="[para(16927(a,1),12617(a,1))].">
      <j1 rule="para" parents="16927 12617"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(y,z))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(9456(a,1),16911(a,1,2,2))].">
      <j1 rule="para" parents="9456 16911"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ 1) \ u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16923,a(flip),b,16738,a),flip(a)].">
      <j1 rule="hyper" parents="370 16923 16738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (u * (z * K(w,u))))
    ]]></literal>
    <justification jstring="[hyper(16894,a,16867,a)].">
      <j1 rule="hyper" parents="16894 16867"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) = K(x,y * (z * (u * K(z,w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,16865,a(flip),b,16932,a),flip(a)].">
      <j1 rule="hyper" parents="60 16865 16932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16736,a(flip),b,16921,a),flip(a)].">
      <j1 rule="hyper" parents="370 16736 16921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(11967(a,1),16934(a,1,2))].">
      <j1 rule="para" parents="11967 16934"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x,(y * K(y * z,z \ 1)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16699,a(flip),b,16935,a)].">
      <j1 rule="hyper" parents="60 16699 16935"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (((u \ 1) \ 1) \ z)))
    ]]></literal>
    <justification jstring="[para(6891(a,1),16935(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6891 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      T(x,y * (L(z,u,z) * w)) = T(x,y * (T(w,z) * z))
    ]]></literal>
    <justification jstring="[hyper(16884,a,14413,a)].">
      <j1 rule="hyper" parents="16884 14413"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      T(x,y * (L(z,u,z) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16853,a(flip),b,16938,a),flip(a)].">
      <j1 rule="hyper" parents="370 16853 16938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      T(x,y * L(z * u,z,z)) = T(x,y * (z * L(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1280(a,1),16939(a,1,2,2))].">
      <j1 rule="para" parents="1280 16939"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * T(u,w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16902,a,16866,a)].">
      <j1 rule="hyper" parents="16902 16866"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16862,a(flip),b,16941,a),flip(a)].">
      <j1 rule="hyper" parents="60 16862 16941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16942(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(263(a,1),16942(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="263 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(8202(a,1),16942(a,1,2,2))].">
      <j1 rule="para" parents="8202 16942"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x,(y \ z) * (T(T(y \ z,y),y) * u)) = K(x,T(y \ z,y) * ((z / y) * u))
    ]]></literal>
    <justification jstring="[para(8262(a,1),16943(a,1,2))].">
      <j1 rule="para" parents="8262 16943"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,(y \ 1) * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(15233,a,16945,a)].">
      <j1 rule="hyper" parents="15233 16945"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,16947,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 16947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(8203(a,1),16948(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8203 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(11674,a,16915,a),flip(a)].">
      <j1 rule="hyper" parents="11674 16915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6894(a,1),16951(a,1,2,1))].">
      <j1 rule="para" parents="6894 16951"/>
    </justification>
  </clause>

  <clause id="16953">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(11674,a,16918,a),flip(a)].">
      <j1 rule="hyper" parents="11674 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7633(a,1),16953(a,1,2,1))].">
      <j1 rule="para" parents="7633 16953"/>
    </justification>
  </clause>

  <clause id="16955">
    <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(8642(a,1),16954(a,2,2))].">
      <j1 rule="para" parents="8642 16954"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x \ (y * ((z * (y \ u)) / z)),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(2913(a,1),16803(a,1,1))].">
      <j1 rule="para" parents="2913 16803"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      K(x \ (y * T(y \ 1,z)),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(5245(a,1),16956(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5245 16956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      K(x \ K(y \ 1,z),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(5251(a,1),16957(a,1,1,2))].">
      <j1 rule="para" parents="5251 16957"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      (x \ K(y \ K(z,u \ 1),w)) \ (x \ 1) = K(w,y \ K(u \ 1,z))
    ]]></literal>
    <justification jstring="[para(16958(a,1),15194(a,1,1,2))].">
      <j1 rule="para" parents="16958 15194"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(15195,a,16959,a),flip(a)].">
      <j1 rule="hyper" parents="15195 16959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * (T(w,u) / u))) = K(x,y \ ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(14334(a,1),16875(a,1,2,2,1))].">
      <j1 rule="para" parents="14334 16875"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w)) * (z * T(u,w))) = K(x,(z * ((w * u) / w)) * y)
    ]]></literal>
    <justification jstring="[para(16791(a,1),16904(a,1,2,1))].">
      <j1 rule="para" parents="16791 16904"/>
    </justification>
  </clause>

  <clause id="16963">
    <literal><![CDATA[
      K(x,(y * ((z * u) / z)) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(12637,a,16962,a),flip(a)].">
      <j1 rule="hyper" parents="12637 16962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      K(x,(y * T(z \ u,z)) * w) = K(x,(y * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),16963(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 16963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(263(a,1),16963(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 16963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),16965(a,1,2,1))].">
      <j1 rule="para" parents="107 16965"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(T(u,z) * z) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12605,a,b,16966,a)].">
      <j1 rule="hyper" parents="370 12605 16966"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,(y * (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),16966(a,1,2,1,1))].">
      <j1 rule="para" parents="109 16966"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) = K(x,(z * (y * K(z,u))) * w)
    ]]></literal>
    <justification jstring="[para(8418(a,1),16966(a,1,2,1))].">
      <j1 rule="para" parents="8418 16966"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      K(x,(y * (z / y)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14490,a(flip),b,16968,a),flip(a)].">
      <j1 rule="hyper" parents="60 14490 16968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),16970(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6 16970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      K(x,((y \ z) * z) * u) = K(x,(z * (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14641,a(flip),b,16964,a)].">
      <j1 rule="hyper" parents="60 14641 16964"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(16967(a,1),12637(a,1))].">
      <j1 rule="para" parents="16967 12637"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      K(x,(T(y,z) * L(z,u,z)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(L(z,u,z) * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(7306(a,1),16973(a,1,2,1,1))].">
      <j1 rule="para" parents="7306 16973"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(T(u,y) * y) * w)
    ]]></literal>
    <justification jstring="[hyper(16974,a,14421,a)].">
      <j1 rule="hyper" parents="16974 14421"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,16966,a(flip),b,16975,a),flip(a)].">
      <j1 rule="hyper" parents="370 16966 16975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16977">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) * u) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(13607(a,1),16976(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13607 16976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      K(x,(T(y \ z,1) * z) * u) = K(x,((z \ y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14669,a(flip),b,16977,a),flip(a)].">
      <j1 rule="hyper" parents="60 14669 16977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,((z \ y) * y) * u)
    ]]></literal>
    <justification jstring="[para(222(a,1),16978(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="222 16978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,(y * (y / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16972,a(flip),b,16979,a),flip(a)].">
      <j1 rule="hyper" parents="370 16972 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      K(x,y \ (z * T((T(u,w) * w) / T(u,w),v5))) = K(x,y \ (z * T(T(w,u),v5)))
    ]]></literal>
    <justification jstring="[para(556(a,1),16907(a,1,2,2,2))].">
      <j1 rule="para" parents="556 16907"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      K(x,T(y \ z,y) * ((z / y) * u)) = K(x,(y \ z) * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16944,a(flip),b,16946,a),flip(a)].">
      <j1 rule="hyper" parents="60 16944 16946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      K(x,y \ (z * T(u * K(w,u),v5))) = K(x,y \ (z * T(T(u,w),v5)))
    ]]></literal>
    <justification jstring="[para(5672(a,1),16981(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5672 16981"/>
    </justification>
  </clause>

  <clause id="16985">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * ((y * a(w,z,u)) / v5)) = T(x,(a(w,z,u) * y) / v5)
    ]]></literal>
    <justification jstring="[para(15807(a,1),16756(a,1,2,1))].">
      <j1 rule="para" parents="15807 16756"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      K(x,(T(T(y,z * z),z \ 1) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(4443(a,1),16813(a,1,2,1,1))].">
      <j1 rule="para" parents="4443 16813"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      K(x,(y * K(y * z,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16952,a(flip),b,16936,a)].">
      <j1 rule="hyper" parents="60 16952 16936"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      K(x,(y * K(y,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14634,a(flip),b,16987,a)].">
      <j1 rule="hyper" parents="60 14634 16987"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(5256(a,2),16988(a,1,2,1))].">
      <j1 rule="para" parents="5256 16988"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * T(z,y)) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(5741(a,1),16989(a,1,2,1))].">
      <j1 rule="para" parents="5741 16989"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) * (z * z)) * (1 / z)) \ u) = K(x,T((z \ 1) * y,z * z) \ u)
    ]]></literal>
    <justification jstring="[para(15541(a,1),16986(a,1,2,1,1))].">
      <j1 rule="para" parents="15541 16986"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(107(a,1),16990(a,1,2,2,1))].">
      <j1 rule="para" parents="107 16990"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(107(a,1),16992(a,1,2,2,2,2))].">
      <j1 rule="para" parents="107 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(8851(a,1),16993(a,2,2))].">
      <j1 rule="para" parents="8851 16993"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16890,a(flip),b,16994,a)].">
      <j1 rule="hyper" parents="60 16890 16994"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      K(x,T(y * z,(y * z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(9308(a,1),16995(a,1,2,2,2))].">
      <j1 rule="para" parents="9308 16995"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y * y) \ u) = K(x,(T(z,y) * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(248(a,1),16991(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="248 16991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,y) * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(16998(a,2),6080(a,1))].">
      <j1 rule="para" parents="16998 6080"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      K(x,(y * z) \ u) * a(w,v5,K((y * z) \ u,x)) = K(x,L(T(z * y,z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(14570(a,1),16831(a,1,1))].">
      <j1 rule="para" parents="14570 16831"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(12988,a,17000,a),flip(a)].">
      <j1 rule="hyper" parents="12988 17000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      K(x,L(((1 / y) * (y * z)) \ u,w,v5)) = K(x,L(R(z,y,y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,14808,a(flip),b,17001,a),flip(a)].">
      <j1 rule="hyper" parents="60 14808 17001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      K(x,L(R(y,z,z) \ u,w,v5)) = K(x,L(L(y,z,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(579(a,1),17002(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="579 17002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      K(x,L(L(y,z,z) \ u,a(y,z,z),y)) = K(x,a(y,z,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16584,a(flip),b,17003,a),flip(a)].">
      <j1 rule="hyper" parents="60 16584 17003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,K(z,T(u,y)) * y)
    ]]></literal>
    <justification jstring="[para(8797(a,1),16924(a,2,2,1))].">
      <j1 rule="para" parents="8797 16924"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ ((z * K(y,z)) \ (y * z)),u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8758(a,1),17005(a,2,2))].">
      <j1 rule="para" parents="8758 17005"/>
    </justification>
  </clause>

  <clause id="17007">
    <literal><![CDATA[
      K(x,(y * z) * T((y * z) \ y,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(5318(a,1),17006(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5318 17006"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(5410(a,1),17007(a,1,2))].">
      <j1 rule="para" parents="5410 17007"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17008(a,1),5866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17008 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17010">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5866,a(flip),b,17009,a),flip(a)].">
      <j1 rule="hyper" parents="370 5866 17009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12594,a(flip),b,17010,a),flip(a)].">
      <j1 rule="hyper" parents="60 12594 17010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(16928,a,17011,a)].">
      <j1 rule="hyper" parents="16928 17011"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(13160,a,17012,a)].">
      <j1 rule="hyper" parents="13160 17012"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12804,a(flip),b,17013,a)].">
      <j1 rule="hyper" parents="370 12804 17013"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(4837(a,1),17014(a,1,1))].">
      <j1 rule="para" parents="4837 17014"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,x) / z,u) = w
    ]]></literal>
    <justification jstring="[para(17015(a,1),9020(a,1))].">
      <j1 rule="para" parents="17015 9020"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      K((x * K(y,x)) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) / z,u) = w
    ]]></literal>
    <justification jstring="[para(5233(a,1),17016(a,1,1,1))].">
      <j1 rule="para" parents="5233 17016"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(10240(a,1),16937(a,2,2))].">
      <j1 rule="para" parents="10240 16937"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,T(y / z,T((u \ z) / z,T(u,w)))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(8856(a,1),17018(a,1,2))].">
      <j1 rule="para" parents="8856 17018"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(10029(a,1),17019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10029 17019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9477,a(flip),b,17020,a),flip(a)].">
      <j1 rule="hyper" parents="370 9477 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16676,a(flip),b,17021,a)].">
      <j1 rule="hyper" parents="60 16676 17021"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      K(x,T(y,T(y,z) / z) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(5784(a,1),17023(a,1,2,2,1))].">
      <j1 rule="para" parents="5784 17023"/>
    </justification>
  </clause>

  <clause id="17025">
    <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(9228(a,1),16955(a,1,2,2,2))].">
      <j1 rule="para" parents="9228 16955"/>
    </justification>
  </clause>

  <clause id="17026">
    <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(8636(a,2),17025(a,1,2,2))].">
      <j1 rule="para" parents="8636 17025"/>
    </justification>
  </clause>

  <clause id="17028">
    <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(10495(a,1),17026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10495 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17029">
    <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(370,a,7526,a(flip),b,17028,a),flip(a)].">
      <j1 rule="hyper" parents="370 7526 17028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,14631,a(flip),b,17029,a)].">
      <j1 rule="hyper" parents="60 14631 17029"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(7548,a,17030,a),flip(a)].">
      <j1 rule="hyper" parents="7548 17030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16960,a,b,17031,a)].">
      <j1 rule="hyper" parents="60 16960 17031"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16848,a(flip),b,17035,a),flip(a)].">
      <j1 rule="hyper" parents="60 16848 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16847,a(flip),b,17036,a),flip(a)].">
      <j1 rule="hyper" parents="60 16847 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),17037(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="74 17037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,y \ T((z * u) * (z \ 1),z)) = K(x,y \ (z * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16892,a(flip),b,17038,a),flip(a)].">
      <j1 rule="hyper" parents="60 16892 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7347(a,1),17038(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7347 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(1131(a,1),17039(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1131 17039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      K(x,y \ R(z,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6166,a(flip),b,17041,a),flip(a)].">
      <j1 rule="hyper" parents="60 6166 17041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      K(x,T(y,R(z,u,u)) \ L(z,u,u)) = K(x,R(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(14575,a,17042,a),flip(a)].">
      <j1 rule="hyper" parents="14575 17042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      K(x,((R(y,z,z) \ (y * z)) \ u) \ L(y,z,z)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16688,a(flip),b,17042,a),flip(a)].">
      <j1 rule="hyper" parents="60 16688 17042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17045">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u)) \ L(z,u,u)) = K(x,R(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(16399(a,1),17043(a,1,2,1))].">
      <j1 rule="para" parents="16399 17043"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      K(x,R(y,z,z) / u) = K(x,L(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(14575,a,17045,a),flip(a)].">
      <j1 rule="hyper" parents="14575 17045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ L(z,y,y)) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[para(3730(a,1),17044(a,1,2,1,1))].">
      <j1 rule="para" parents="3730 17044"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / (T((y \ 1) \ x,y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(4459(a,1),16828(a,2,1,1))].">
      <j1 rule="para" parents="4459 16828"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      K(x \ ((((y \ 1) \ 1) * (y \ z)) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(946(a,1),16841(a,1,1,2,1))].">
      <j1 rule="para" parents="946 16841"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      K(x \ ((K(y,y \ 1) * z) / (y * y)),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(3554(a,1),17050(a,1,1,2,1))].">
      <j1 rule="para" parents="3554 17050"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * (z / (y * y))),u) = K(x \ ((y \ 1) * (y \ T(z,y * y))),u)
    ]]></literal>
    <justification jstring="[para(1098(a,1),17051(a,1,1,2))].">
      <j1 rule="para" parents="1098 17051"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K(x \ (z * (y \ (1 / y))),u)
    ]]></literal>
    <justification jstring="[para(7126(a,1),17052(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7126 17052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K((x \ z) * (y \ (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(1087(a,1),17053(a,2,1))].">
      <j1 rule="para" parents="1087 17053"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(11285(a,1),17024(a,1,2,1))].">
      <j1 rule="para" parents="11285 17024"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(5784(a,1),17055(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5784 17055"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16922,a(flip),b,17056,a)].">
      <j1 rule="hyper" parents="60 16922 17056"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[para(14334(a,1),17058(a,2,2))].">
      <j1 rule="para" parents="14334 17058"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16890,a(flip),b,17059,a)].">
      <j1 rule="hyper" parents="60 16890 17059"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / (T((y \ 1) \ x,y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6205,a(flip),b,17049,a),flip(a)].">
      <j1 rule="hyper" parents="370 6205 17049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),T(w,z),L(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(6572(a,1),16818(a,1,2))].">
      <j1 rule="para" parents="6572 16818"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      T(x * K(y * z,x),y / (y * (z * y))) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[para(14375(a,1),16823(a,1,1,2))].">
      <j1 rule="para" parents="14375 16823"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,((y * (z * y)) \ y) * ((y * (z * y)) \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,15639,a(flip),b,17063,a)].">
      <j1 rule="hyper" parents="60 15639 17063"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14443,a(flip),b,16997,a)].">
      <j1 rule="hyper" parents="60 14443 16997"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(16930(a,1),17067(a,1,2,2))].">
      <j1 rule="para" parents="16930 17067"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,y * z))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(5512(a,1),17068(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5512 17068"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(16833(a,1),17069(a,1,2,2))].">
      <j1 rule="para" parents="16833 17069"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,T(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(5256(a,2),17070(a,1,2,2,2))].">
      <j1 rule="para" parents="5256 17070"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,T(z * u,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(14555,a,17071,a),flip(a)].">
      <j1 rule="hyper" parents="14555 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16804,a(flip),b,17072,a),flip(a)].">
      <j1 rule="hyper" parents="370 16804 17072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9057(a,1),17073(a,1,2))].">
      <j1 rule="para" parents="9057 17073"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(9497,a,17074,a)].">
      <j1 rule="hyper" parents="9497 17074"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T((z * u) \ z,z * u)))
    ]]></literal>
    <justification jstring="[para(5411(a,1),17075(a,2,2,1))].">
      <j1 rule="para" parents="5411 17075"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T((K(y,z) * x) / K(y,z),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8707(a,1),16703(a,1,1))].">
      <j1 rule="para" parents="8707 16703"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T(T(x,K(z,y)),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(6225(a,1),17077(a,1,2,1,2,1))].">
      <j1 rule="para" parents="6225 17077"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8706(a,1),17078(a,1,2,1,2))].">
      <j1 rule="para" parents="8706 17078"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8700(a,1),17079(a,1,2))].">
      <j1 rule="para" parents="8700 17079"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,12600,a(flip),b,17080,a),flip(a)].">
      <j1 rule="hyper" parents="370 12600 17080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      T(x * K(T(y \ z,z \ y),x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),16822(a,1,1,2,1))].">
      <j1 rule="para" parents="72 16822"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      T(x * K(y \ z,x),(y \ z) \ 1) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(4908(a,1),17082(a,1,1,2))].">
      <j1 rule="para" parents="4908 17082"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(6462,a,17083,a)].">
      <j1 rule="hyper" parents="6462 17083"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      T(x,(T(y \ z,z \ y) \ 1) * (T(y \ z,z \ y) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6913,a(flip),b,17084,a),flip(a)].">
      <j1 rule="hyper" parents="60 6913 17084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      T(x,(1 / (y \ z)) * (T(y \ z,z \ y) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(3516(a,1),17085(a,1,2,1))].">
      <j1 rule="para" parents="3516 17085"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      T(x,(1 / (y \ z)) * (1 / (y \ z))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(3516(a,1),17086(a,1,2,2))].">
      <j1 rule="para" parents="3516 17086"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      T(x,(y \ z) \ (1 / (y \ z))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(15247,a,17087,a)].">
      <j1 rule="hyper" parents="15247 17087"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ 1)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,4658,a(flip),b,17088,a)].">
      <j1 rule="hyper" parents="60 4658 17088"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      T(T(x,y),(z \ u) * (z \ u)) = T(x,(u \ z) \ ((u \ z) \ y))
    ]]></literal>
    <justification jstring="[hyper(15680,a,17089,a),flip(a)].">
      <j1 rule="hyper" parents="15680 17089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ z) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16235,a,b,17089,a)].">
      <j1 rule="hyper" parents="60 16235 17089"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      T(x,y \ (z * ((z \ y) \ 1))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[para(1135(a,1),17089(a,1,2))].">
      <j1 rule="para" parents="1135 17089"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      T(x,((y * z) \ y) * ((y * z) \ y)) = T(x,(y * z) \ (y * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(4(a,1),17092(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 17092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(15579,a,17090,a),flip(a)].">
      <j1 rule="hyper" parents="15579 17090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(17090(a,1),15579(a,1))].">
      <j1 rule="para" parents="17090 15579"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,(z \ y) \ (K(z,z \ y) * u))
    ]]></literal>
    <justification jstring="[para(8382(a,1),17094(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8382 17094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      T(x,((y * z) \ y) * ((y * z) \ y)) = T(x,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(1113(a,1),17093(a,2,2))].">
      <j1 rule="para" parents="1113 17093"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,(z * y) \ ((z * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,17064,a,b,17097,a)].">
      <j1 rule="hyper" parents="60 17064 17097"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      T(x * K(y * z,x),z \ (y \ 1)) = T(x,y \ (z \ ((z * y) \ 1)))
    ]]></literal>
    <justification jstring="[para(1284(a,1),17098(a,2,2))].">
      <j1 rule="para" parents="1284 17098"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      T(x,(y \ (z \ 1)) * (y \ (z \ 1))) = T(x,z \ (y \ ((y * z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15224,a(flip),b,17101,a)].">
      <j1 rule="hyper" parents="60 15224 17101"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,T(z \ y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7890(a,1),17096(a,2,2))].">
      <j1 rule="para" parents="7890 17096"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * ((y / z) * u))) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16754,a(flip),b,17103,a),flip(a)].">
      <j1 rule="hyper" parents="370 16754 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((L(z,y,y) \ z) * ((L(z,y,y) / z) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),17104(a,1,2,1))].">
      <j1 rule="para" parents="1362 17104"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * ((L(z,y,y) / z) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),17105(a,1,2,2,1))].">
      <j1 rule="para" parents="1362 17105"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * ((z \ L(z,y,y)) * u))) = T(x,(L(z,y,y) / z) \ u)
    ]]></literal>
    <justification jstring="[para(3839(a,1),17106(a,1,2,2,2,1))].">
      <j1 rule="para" parents="3839 17106"/>
    </justification>
  </clause>

  <clause id="17108">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z / (z * u)))
    ]]></literal>
    <justification jstring="[para(8854(a,1),17076(a,2,2,2))].">
      <j1 rule="para" parents="8854 17076"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(9712(a,1),17108(a,2,2,2))].">
      <j1 rule="para" parents="9712 17108"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17040,a(flip),b,17109,a),flip(a)].">
      <j1 rule="hyper" parents="370 17040 17109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z * u,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16954,a(flip),b,17110,a),flip(a)].">
      <j1 rule="hyper" parents="370 16954 17110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14634,a(flip),b,17111,a),flip(a)].">
      <j1 rule="hyper" parents="370 14634 17111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(z,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(5256(a,2),17112(a,2,2,1))].">
      <j1 rule="para" parents="5256 17112"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17060,a(flip),b,17113,a),flip(a)].">
      <j1 rule="hyper" parents="370 17060 17113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),17114(a,1,2,1,2))].">
      <j1 rule="para" parents="5 17114"/>
    </justification>
  </clause>

  <clause id="17116">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7319(a,1),17115(a,1,2))].">
      <j1 rule="para" parents="7319 17115"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12567(a,1),17116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12567 17116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6(a,1),17117(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 17117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),17118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 17118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(9497,a,17119,a),flip(a)].">
      <j1 rule="hyper" parents="9497 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9492,a,17119,a)].">
      <j1 rule="hyper" parents="9492 17119"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      K(x,T(y,z * (z * u))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),17119(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      K(x,L(T(y,z * u),w,v5)) = K(x,T(L(y,w,v5),z \ u))
    ]]></literal>
    <justification jstring="[para(20(a,2),17119(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(227(a,1),17119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="227 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(17119(a,1),8649(a,1,2))].">
      <j1 rule="para" parents="17119 8649"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      K(x / (y * y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(8906,a,17124,a)].">
      <j1 rule="hyper" parents="8906 17124"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      K(x,L(T(y,z * z),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(8903,a,17124,a),flip(a)].">
      <j1 rule="hyper" parents="8903 17124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      T(K(x,y),z * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8021,a,17124,a)].">
      <j1 rule="hyper" parents="8021 17124"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,17124,a,b,8990,a),flip(a)].">
      <j1 rule="hyper" parents="124 17124 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      K(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(17124(a,1),8847(a,1))].">
      <j1 rule="para" parents="17124 8847"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      K(x,T(T(y,z * z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17124(a,1),8902(a,1))].">
      <j1 rule="para" parents="17124 8902"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(15252(a,1),17124(a,1,2))].">
      <j1 rule="para" parents="15252 17124"/>
    </justification>
  </clause>

  <clause id="17134">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,17130,a)].">
      <j1 rule="hyper" parents="53 17130"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      K(x,T(y * y,z)) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(11742,a,17134,a)].">
      <j1 rule="hyper" parents="11742 17134"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      K(x * x,T(y,z)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(9129,a,17134,a)].">
      <j1 rule="hyper" parents="9129 17134"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      T(x,T(y * y,z)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(8748,a,17134,a)].">
      <j1 rule="hyper" parents="8748 17134"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8603,a,17134,a)].">
      <j1 rule="hyper" parents="8603 17134"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      K(x * x,y) * (z * (x * x)) = z * T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(7595,a,17134,a)].">
      <j1 rule="hyper" parents="7595 17134"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      x * K(y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z * z) * x = u
    ]]></literal>
    <justification jstring="[para(17134(a,1),7503(a,1)),flip(a)].">
      <j1 rule="para" parents="17134 7503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      T(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(17134(a,1),8593(a,2))].">
      <j1 rule="para" parents="17134 8593"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      T(K(x,L(y,z * z,(z * z) \ u)) * u,z * z) = K(x,y) * T(u,z * z)
    ]]></literal>
    <justification jstring="[para(17129(a,1),16689(a,2,1))].">
      <j1 rule="para" parents="17129 16689"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      (((x \ 1) * (y * x)) / (x \ 1)) / T(1 / x,x * y) = y * (x * x)
    ]]></literal>
    <justification jstring="[para(17138(a,1),7678(a,1,2))].">
      <j1 rule="para" parents="17138 7678"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      T(x,T(y,z * (z * u))) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(15429(a,1),17138(a,1,2))].">
      <j1 rule="para" parents="15429 17138"/>
    </justification>
  </clause>

  <clause id="17145">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(17133(a,1),8847(a,1))].">
      <j1 rule="para" parents="17133 8847"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,y) * K(z * z,x)
    ]]></literal>
    <justification jstring="[para(17136(a,1),6103(a,2,2))].">
      <j1 rule="para" parents="17136 6103"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      L(x \ T(y,z * z),x,T(z * z,u)) = (T(z * z,u) * x) \ (y * T(z * z,u))
    ]]></literal>
    <justification jstring="[para(17137(a,1),653(a,1,1,2))].">
      <j1 rule="para" parents="17137 653"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      K(x,T(y,z * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15429(a,1),17131(a,1,2))].">
      <j1 rule="para" parents="15429 17131"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      K(x,T(y,z * (u * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15540(a,1),17131(a,1,2))].">
      <j1 rule="para" parents="15540 17131"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      T(x,T(y,z * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15429(a,1),17141(a,1,2))].">
      <j1 rule="para" parents="15429 17141"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17119,a(flip),b,17121,a)].">
      <j1 rule="hyper" parents="60 17119 17121"/>
    </justification>
  </clause>

  <clause id="17152">
    <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(17081(a,2),17121(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17081 17121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x * (x * y),T(z,y)) = K(x * (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(5980,a,17122,a),flip(a)].">
      <j1 rule="hyper" parents="5980 17122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) = K((y * y) \ (x / z),u)
    ]]></literal>
    <justification jstring="[para(524(a,1),17127(a,1,1))].">
      <j1 rule="para" parents="524 17127"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),17144(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 17144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),17151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 17151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y * x)) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(17151(a,1),8011(a,1,2))].">
      <j1 rule="para" parents="17151 8011"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      K(x,T(y * (z * u),z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(17151(a,1),12627(a,1))].">
      <j1 rule="para" parents="17151 12627"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      T(x / (x \ y),T(z,(y / x) * x)) = T(x / (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(14406,a,17155,a),flip(a)].">
      <j1 rule="hyper" parents="14406 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,y * (z * x))) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12543,a(flip),b,17155,a),flip(a)].">
      <j1 rule="hyper" parents="60 12543 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12686,a(flip),b,17156,a)].">
      <j1 rule="hyper" parents="60 12686 17156"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12626,a,17162,a),flip(a)].">
      <j1 rule="hyper" parents="12626 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,x)) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12588,a,17162,a),flip(a)].">
      <j1 rule="hyper" parents="12588 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) = K(T(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12579,a,17162,a),flip(a)].">
      <j1 rule="hyper" parents="12579 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      K(T(x,y) / z,T(u,x)) = K(z \ T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8461,a,17162,a),flip(a)].">
      <j1 rule="hyper" parents="8461 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      K(x * y,T(z,T(x,u))) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,12580,a(flip),b,17162,a),flip(a)].">
      <j1 rule="hyper" parents="370 12580 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8765,a(flip),b,17162,a),flip(a)].">
      <j1 rule="hyper" parents="370 8765 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a(flip),b,17162,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),17162(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17162(a,1),8758(a,1,1))].">
      <j1 rule="para" parents="17162 8758"/>
    </justification>
  </clause>

  <clause id="17176">
    <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(17162(a,1),8906(a,1))].">
      <j1 rule="para" parents="17162 8906"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x \ y,T(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = w
    ]]></literal>
    <justification jstring="[para(17162(a,2),8906(a,1))].">
      <j1 rule="para" parents="17162 8906"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(17162(a,1),12222(a,1,1))].">
      <j1 rule="para" parents="17162 12222"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17162(a,1),12579(a,1))].">
      <j1 rule="para" parents="17162 12579"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8021,a,17173,a)].">
      <j1 rule="hyper" parents="8021 17173"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17173(a,2),8122(a,1))].">
      <j1 rule="para" parents="17173 8122"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8747,a,17181,a)].">
      <j1 rule="hyper" parents="8747 17181"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17181,a,b,17181,a)].">
      <j1 rule="hyper" parents="370 17181 17181"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,17181,a(flip),b,8919,a),flip(a)].">
      <j1 rule="hyper" parents="126 17181 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      K(K(x,y),K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,17181,a(flip),b,8604,a),flip(a)].">
      <j1 rule="hyper" parents="126 17181 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,17190,a)].">
      <j1 rule="hyper" parents="53 17190"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12610,a,17196,a)].">
      <j1 rule="hyper" parents="12610 17196"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9561,a,17196,a),flip(a)].">
      <j1 rule="hyper" parents="9561 17196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9101,a,17196,a)].">
      <j1 rule="hyper" parents="9101 17196"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8719,a,17196,a)].">
      <j1 rule="hyper" parents="8719 17196"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8603,a,17196,a)].">
      <j1 rule="hyper" parents="8603 17196"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(51,a,17196,a)].">
      <j1 rule="hyper" parents="51 17196"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(17196(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="17196 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17196(a,1),328(a,1,2))].">
      <j1 rule="para" parents="17196 328"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(17196(a,1),7503(a,1)),flip(a)].">
      <j1 rule="para" parents="17196 7503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(17196(a,1),8593(a,2))].">
      <j1 rule="para" parents="17196 8593"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      T(x,K(y,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17196(a,1),9561(a,1))].">
      <j1 rule="para" parents="17196 9561"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17196(a,1),12611(a,1,1))].">
      <j1 rule="para" parents="17196 12611"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(17196(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="17196 16700"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8898,a,17185,a),flip(a)].">
      <j1 rule="hyper" parents="8898 17185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17213">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8303,a,17185,a),flip(a)].">
      <j1 rule="hyper" parents="8303 17185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * K(y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(6376,a,17185,a)].">
      <j1 rule="hyper" parents="6376 17185"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,17185,a(flip),b,7535,a),flip(a)].">
      <j1 rule="hyper" parents="129 17185 7535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,17185,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 17185 17"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,u)) = T(T(x,K(z,u)),y)
    ]]></literal>
    <justification jstring="[para(17185(a,1),7999(a,1,1))].">
      <j1 rule="para" parents="17185 7999"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      (x * K(y,z)) * K(x,u) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(17185(a,1),8480(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17185 8480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(17185(a,1),8835(a,1))].">
      <j1 rule="para" parents="17185 8835"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(17185(a,1),8898(a,1))].">
      <j1 rule="para" parents="17185 8898"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12626,a,17199,a),flip(a)].">
      <j1 rule="hyper" parents="12626 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12613,a,17199,a)].">
      <j1 rule="hyper" parents="12613 17199"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12588,a,17199,a),flip(a)].">
      <j1 rule="hyper" parents="12588 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(((x \ y) * x) / (K(z,u) * x),w) = K((x * K(z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16464,a(flip),b,17199,a)].">
      <j1 rule="hyper" parents="60 16464 17199"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17199(a,1),8848(a,1,1))].">
      <j1 rule="para" parents="17199 8848"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8936(a,1),17199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8936 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      x \ (K(y,z) * K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) \ K(y,z) = w
    ]]></literal>
    <justification jstring="[para(17199(a,1),8450(a,1,2,2))].">
      <j1 rule="para" parents="17199 8450"/>
    </justification>
  </clause>

  <clause id="17247">
    <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(17199(a,1),8902(a,1))].">
      <j1 rule="para" parents="17199 8902"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      L(K(x,y),x,z) = (x * K(u,w)) \ (T(x,y) * K(u,w))
    ]]></literal>
    <justification jstring="[para(17199(a,1),9894(a,1,1))].">
      <j1 rule="para" parents="17199 9894"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17199(a,1),12579(a,1))].">
      <j1 rule="para" parents="17199 12579"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(17199(a,1),12588(a,1))].">
      <j1 rule="para" parents="17199 12588"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(17199(a,1),12623(a,1))].">
      <j1 rule="para" parents="17199 12623"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17199(a,1),12626(a,1))].">
      <j1 rule="para" parents="17199 12626"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      K(x,y) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(17199(a,1),13411(a,1,1))].">
      <j1 rule="para" parents="17199 13411"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(7509(a,1),17201(a,1,2))].">
      <j1 rule="para" parents="7509 17201"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8587(a,1),17201(a,1,2))].">
      <j1 rule="para" parents="8587 17201"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8936(a,1),17212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8936 17212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8901,a,17203,a)].">
      <j1 rule="hyper" parents="8901 17203"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      x * R(K(y,K(z,u)),w,w \ x) = (K(y,K(z,u)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(17203(a,1),1047(a,1,2,1))].">
      <j1 rule="para" parents="17203 1047"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      T(x,T(y,z * u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(12545(a,1),17257(a,1,2))].">
      <j1 rule="para" parents="12545 17257"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(9094,a,17263,a)].">
      <j1 rule="hyper" parents="9094 17263"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8636,a(flip),b,17263,a),flip(a)].">
      <j1 rule="hyper" parents="370 8636 17263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(109(a,1),17263(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8024(a,2),17263(a,1,2))].">
      <j1 rule="para" parents="8024 17263"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(17263(a,2),8668(a,1))].">
      <j1 rule="para" parents="17263 8668"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ T(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(17263(a,1),9355(a,1,1))].">
      <j1 rule="para" parents="17263 9355"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y / T(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(17263(a,1),9364(a,1,1))].">
      <j1 rule="para" parents="17263 9364"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u) / y) = w
    ]]></literal>
    <justification jstring="[para(17263(a,1),9356(a,1,1))].">
      <j1 rule="para" parents="17263 9356"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(9385(a,1),17263(a,1,2))].">
      <j1 rule="para" parents="9385 17263"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((y \ u) \ u) / z) = K(x,z \ ((y \ u) \ u))
    ]]></literal>
    <justification jstring="[para(17263(a,1),9370(a,1,1))].">
      <j1 rule="para" parents="17263 9370"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12551(a,1),17263(a,1,2))].">
      <j1 rule="para" parents="12551 17263"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(8031(a,1),17269(a,1,2))].">
      <j1 rule="para" parents="8031 17269"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(17269(a,1),8117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17269 8117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17285">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17269(a,2),8678(a,1))].">
      <j1 rule="para" parents="17269 8678"/>
    </justification>
  </clause>

  <clause id="17286">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(17269(a,1),8667(a,1,2))].">
      <j1 rule="para" parents="17269 8667"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(y,u) / z) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(17269(a,1),9357(a,1,1))].">
      <j1 rule="para" parents="17269 9357"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x,K(y * z,u)) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[para(12551(a,1),17269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12551 17269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12557(a,2),17269(a,1,2))].">
      <j1 rule="para" parents="12557 17269"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17263,a,b,17272,a),flip(a)].">
      <j1 rule="hyper" parents="370 17263 17272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(7509(a,1),17207(a,1,2))].">
      <j1 rule="para" parents="7509 17207"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      T(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(9095(a,1),17207(a,1,2))].">
      <j1 rule="para" parents="9095 17207"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(9548(a,1),17207(a,1))].">
      <j1 rule="para" parents="9548 17207"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      T(x,K(y,y \ z) * (u * (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * (z / y)) = w
    ]]></literal>
    <justification jstring="[para(10332(a,2),17207(a,1,2))].">
      <j1 rule="para" parents="10332 17207"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15282(a,1),17207(a,1,2))].">
      <j1 rule="para" parents="15282 17207"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(6223(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="6223 17230"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K(x,T(y,L(K(z,u),w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(6591(a,1),17230(a,1,2,2))].">
      <j1 rule="para" parents="6591 17230"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(8936(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="8936 17230"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8701(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="8701 17230"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(8746(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="8746 17230"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(9095(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="9095 17230"/>
    </justification>
  </clause>

  <clause id="17307">
    <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(8845(a,2),17230(a,1))].">
      <j1 rule="para" parents="8845 17230"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(9070(a,1),17230(a,1))].">
      <j1 rule="para" parents="9070 17230"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      K((((x * y) \ z) * (x * y)) / (K(y,u) * (x * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * T(y,u)) \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(16492(a,1),17230(a,1))].">
      <j1 rule="para" parents="16492 17230"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(8936(a,1),17231(a,1,1))].">
      <j1 rule="para" parents="8936 17231"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      K((x \ y) * K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(8938(a,1),17231(a,1,1))].">
      <j1 rule="para" parents="8938 17231"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17171(a,1),8011(a,1,2))].">
      <j1 rule="para" parents="17171 8011"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      T(x,y) * K(x * z,u) = K(z * x,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17171(a,1),8758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17171 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17314">
    <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(370,a,16468,a,b,17174,a)].">
      <j1 rule="hyper" parents="370 16468 17174"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17119,a(flip),b,17174,a),flip(a)].">
      <j1 rule="hyper" parents="370 17119 17174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      K(x,T(y,z \ u)) * (u / z) = (u / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17174(a,1),8758(a,1,1))].">
      <j1 rule="para" parents="17174 8758"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),w,v5) = K(x,L(T(y,u / z),w,v5))
    ]]></literal>
    <justification jstring="[para(17174(a,1),12922(a,1,1))].">
      <j1 rule="para" parents="17174 12922"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,v5)) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(17186(a,1),10431(a,1,2))].">
      <j1 rule="para" parents="17186 10431"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      T(x,(y * z) * K(u,y)) = T(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(16776,a,17197,a),flip(a)].">
      <j1 rule="hyper" parents="16776 17197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(16775,a,17197,a),flip(a)].">
      <j1 rule="hyper" parents="16775 17197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16774,a,17197,a)].">
      <j1 rule="hyper" parents="16774 17197"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w \ (w \ 1)))) = T(x,u * ((w * w) \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(1012(a,1),17197(a,2,2))].">
      <j1 rule="para" parents="1012 17197"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(17197(a,1),16774(a,1))].">
      <j1 rule="para" parents="17197 16774"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u) \ z) = w
    ]]></literal>
    <justification jstring="[para(17197(a,1),16775(a,1))].">
      <j1 rule="para" parents="17197 16775"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9337,a,17200,a),flip(a)].">
      <j1 rule="hyper" parents="9337 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <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(370,a,14910,a(flip),b,17200,a),flip(a)].">
      <j1 rule="hyper" parents="370 14910 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,9520,a(flip),b,17200,a),flip(a)].">
      <j1 rule="hyper" parents="370 9520 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8654,a(flip),b,17200,a),flip(a)].">
      <j1 rule="hyper" parents="370 8654 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8609,a(flip),b,17200,a),flip(a)].">
      <j1 rule="hyper" parents="370 8609 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8630(a,1),17200(a,1,1))].">
      <j1 rule="para" parents="8630 17200"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8636(a,1),17200(a,1,1))].">
      <j1 rule="para" parents="8636 17200"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8647(a,2),17200(a,2,2))].">
      <j1 rule="para" parents="8647 17200"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(17200(a,1),9348(a,1,2))].">
      <j1 rule="para" parents="17200 9348"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      u * T(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(17200(a,2),8661(a,1))].">
      <j1 rule="para" parents="17200 8661"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) * z = w
    ]]></literal>
    <justification jstring="[para(17200(a,1),9337(a,1))].">
      <j1 rule="para" parents="17200 9337"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,16480,a,b,17213,a)].">
      <j1 rule="hyper" parents="370 16480 17213"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[para(17213(a,2),11561(a,2,2))].">
      <j1 rule="para" parents="17213 11561"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a,b,17217,a)].">
      <j1 rule="hyper" parents="370 7506 17217"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16731,a,17235,a)].">
      <j1 rule="hyper" parents="16731 17235"/>
    </justification>
  </clause>

  <clause id="17358">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,17008,a,b,17235,a)].">
      <j1 rule="hyper" parents="370 17008 17235"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16733,a,b,17235,a)].">
      <j1 rule="hyper" parents="60 16733 17235"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u)) = K(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16735,a(flip),b,17235,a),flip(a)].">
      <j1 rule="hyper" parents="60 16735 17235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(17235(a,1),16731(a,1))].">
      <j1 rule="para" parents="17235 16731"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(16743,a,17237,a)].">
      <j1 rule="hyper" parents="16743 17237"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      K(T(x \ y,x) * K(z,u),w) = K(K(z,u) * (y / x),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16802,a(flip),b,17237,a),flip(a)].">
      <j1 rule="hyper" parents="60 16802 17237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14525,a(flip),b,17237,a),flip(a)].">
      <j1 rule="hyper" parents="60 14525 17237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) = K(K(y,z) * (x / y),u)
    ]]></literal>
    <justification jstring="[para(6443(a,2),17237(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6443 17237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * (u * (z * y)),w) = K(u * (z * (y * K(x,y))),w)
    ]]></literal>
    <justification jstring="[para(13064(a,1),17237(a,2,1))].">
      <j1 rule="para" parents="13064 17237"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17237(a,1),16743(a,1))].">
      <j1 rule="para" parents="17237 16743"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * (y \ z))) = K(x,u * (z / y))
    ]]></literal>
    <justification jstring="[para(5631(a,1),17245(a,2,2))].">
      <j1 rule="para" parents="5631 17245"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / z)) = K(x,u / ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(6400(a,2),17245(a,2,2))].">
      <j1 rule="para" parents="6400 17245"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) \ (w * K(u,z)) = T(w * K(u,z),K(x,y))
    ]]></literal>
    <justification jstring="[para(17245(a,2),8614(a,1,1,2))].">
      <j1 rule="para" parents="17245 8614"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * z)) = K(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(12441(a,1),17245(a,2,2))].">
      <j1 rule="para" parents="12441 17245"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z * u),T(y,u * z)) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(17268(a,1),8967(a,1,2))].">
      <j1 rule="para" parents="17268 8967"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(15148(a,2),17273(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15148 17273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) = x * K(x,K(y,(w * u) \ z))
    ]]></literal>
    <justification jstring="[para(17273(a,1),16551(a,2,2))].">
      <j1 rule="para" parents="17273 16551"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,K(y,z * L(y,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12132,a,17282,a),flip(a)].">
      <j1 rule="hyper" parents="12132 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17282(a,1),8634(a,1))].">
      <j1 rule="para" parents="17282 8634"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u * z,y)) = w
    ]]></literal>
    <justification jstring="[para(17282(a,1),8678(a,1))].">
      <j1 rule="para" parents="17282 8678"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(17282(a,1),15633(a,1))].">
      <j1 rule="para" parents="17282 15633"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(17283(a,2),8678(a,1))].">
      <j1 rule="para" parents="17283 8678"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(12972(a,2),17283(a,1,2))].">
      <j1 rule="para" parents="12972 17283"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(17284(a,1),9356(a,1))].">
      <j1 rule="para" parents="17284 9356"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17288(a,1),8678(a,1))].">
      <j1 rule="para" parents="17288 8678"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(17288(a,2),8678(a,1))].">
      <j1 rule="para" parents="17288 8678"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u \ y) * u) / z) = K(x,z \ ((u \ y) * u))
    ]]></literal>
    <justification jstring="[para(17289(a,1),9357(a,1,1))].">
      <j1 rule="para" parents="17289 9357"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x * T(y,w),x) = K(x * T(y,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(17290(a,2),8736(a,1,1))].">
      <j1 rule="para" parents="17290 8736"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      T(x,K(y,z) * (u / y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[para(5855(a,1),17331(a,2,2))].">
      <j1 rule="para" parents="5855 17331"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6270(a,1),17331(a,2,2))].">
      <j1 rule="para" parents="6270 17331"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(17331(a,1),16820(a,1,1,2))].">
      <j1 rule="para" parents="17331 16820"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8673,a,17340,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8673 17340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(17342(a,2),6311(a,1))].">
      <j1 rule="para" parents="17342 6311"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12922(a,2),17350(a,1,1))].">
      <j1 rule="para" parents="12922 17350"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6270(a,1),17357(a,2,2))].">
      <j1 rule="para" parents="6270 17357"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ z)) = K(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(15179(a,1),17357(a,2,2))].">
      <j1 rule="para" parents="15179 17357"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(K(v5,w) * u,y,K(z,x)) = v6
    ]]></literal>
    <justification jstring="[para(17357(a,1),15902(a,1,3))].">
      <j1 rule="para" parents="17357 15902"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / z)) = K(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(5855(a,1),17359(a,2,2))].">
      <j1 rule="para" parents="5855 17359"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17237,a(flip),b,17362,a)].">
      <j1 rule="hyper" parents="60 17237 17362"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14372,a(flip),b,17362,a),flip(a)].">
      <j1 rule="hyper" parents="60 14372 17362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      (K(x,y) * z) * K(z * K(y,x),u) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,17362,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 17362 5230"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      K(K(x,y) * (z / x),u) = K(z / T(x,y),u)
    ]]></literal>
    <justification jstring="[para(5855(a,1),17362(a,2,1))].">
      <j1 rule="para" parents="5855 17362"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * (u * (z * y)),w) = K(u * (z * T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(6930(a,1),17362(a,2,1))].">
      <j1 rule="para" parents="6930 17362"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7506(a,2),17362(a,1,1))].">
      <j1 rule="para" parents="7506 17362"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      K(((x / y) \ z) * K(y \ x,y),u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(8383(a,1),17362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8383 17362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(12347(a,1),17362(a,2,1))].">
      <j1 rule="para" parents="12347 17362"/>
    </justification>
  </clause>

  <clause id="17415">
    <literal><![CDATA[
      K(K(x,x \ y) * (z * y),u) = K(z * ((x \ y) * x),u)
    ]]></literal>
    <justification jstring="[para(12380(a,1),17362(a,2,1))].">
      <j1 rule="para" parents="12380 17362"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      K(x,y) * (z * K(z * K(y,x),u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(17362(a,1),15219(a,1,2,2))].">
      <j1 rule="para" parents="17362 15219"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(w * K(u,K(y,x) * z),v5)
    ]]></literal>
    <justification jstring="[para(16730(a,1),17362(a,2,1,2))].">
      <j1 rule="para" parents="16730 17362"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      x * (K(y,z) * K(x * K(z,y),u)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(17407(a,1),15219(a,1,2,2))].">
      <j1 rule="para" parents="17407 15219"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * (u * (y \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * (u * y)) = w
    ]]></literal>
    <justification jstring="[para(2240(a,1),17145(a,1,2))].">
      <j1 rule="para" parents="2240 17145"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12545(a,1),17183(a,1,2))].">
      <j1 rule="para" parents="12545 17183"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8929(a,2),17275(a,1))].">
      <j1 rule="para" parents="8929 17275"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),17285(a,1,2,2))].">
      <j1 rule="para" parents="109 17285"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(92(a,1),17375(a,1,2,2))].">
      <j1 rule="para" parents="92 17375"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17162,a(flip),b,17120,a),flip(a)].">
      <j1 rule="hyper" parents="370 17162 17120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17120(a,2),17183(a,1))].">
      <j1 rule="para" parents="17120 17183"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (x * (y \ x)),u) = w
    ]]></literal>
    <justification jstring="[para(17426(a,1),8906(a,1))].">
      <j1 rule="para" parents="17426 8906"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((x / y) \ y),u) = w
    ]]></literal>
    <justification jstring="[para(17426(a,1),14409(a,1))].">
      <j1 rule="para" parents="17426 14409"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y \ 1),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[para(9975(a,1),17128(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9975 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17432">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x \ 1) * ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[para(17153(a,1),16325(a,2,2))].">
      <j1 rule="para" parents="17153 16325"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,y)) = K(x,(y \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[para(7860(a,1),17163(a,1,2,1))].">
      <j1 rule="para" parents="7860 17163"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      K(x * T(T(y,z),u),T(w,y)) = K(T(T(y,z),u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(17183,a,17165,a)].">
      <j1 rule="hyper" parents="17183 17165"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      K(x \ T(y,z),T(T(u,y),w)) = K(T(y,z) / x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(8902,a,17166,a),flip(a)].">
      <j1 rule="hyper" parents="8902 17166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      T(x,y) * K(z,x * u) = K(z,u * x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12551(a,1),17175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12551 17175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      T(T(x,y),z) * K(x * u,w) = K(u * x,w) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17171(a,1),17175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17171 17175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      K(x,y * z) * T(x,K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12595,a(flip),b,17227,a),flip(a)].">
      <j1 rule="hyper" parents="370 12595 17227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      K(K(x * (1 / y),y) * (z * (x * (1 / y))),u) = K(z * (y \ R(x,1 / y,y)),u)
    ]]></literal>
    <justification jstring="[para(736(a,2),17236(a,2,1,2))].">
      <j1 rule="para" parents="736 17236"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17331,a(flip),b,17256,a)].">
      <j1 rule="hyper" parents="60 17331 17256"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      T(x,K(y \ (y \ 1),(y \ 1) * z) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(7124(a,1),17256(a,2,2,2))].">
      <j1 rule="para" parents="7124 17256"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * (w / (y \ T(z,u)))) = T(x,w / T(y \ T(z,u),y))
    ]]></literal>
    <justification jstring="[para(13173(a,2),17256(a,1,2,1))].">
      <j1 rule="para" parents="13173 17256"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      T(x,y * (z * K(u,y))) = T(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(11028(a,1),17329(a,1,2))].">
      <j1 rule="para" parents="11028 17329"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u),w)) = K(x,w) * T(x * K(w,x),T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(17330(a,1),9813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17330 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8682,a,17338,a)].">
      <j1 rule="hyper" parents="8682 17338"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u * ((w \ 1) \ v5))) = K(x,T(y,u * ((1 / w) \ v5)) \ z)
    ]]></literal>
    <justification jstring="[para(4671(a,2),17360(a,2,2,1))].">
      <j1 rule="para" parents="4671 17360"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      K(x,(y \ z) * K(y,u * ((w \ 1) * v5))) = K(x,T(y,u * ((1 / w) * v5)) \ z)
    ]]></literal>
    <justification jstring="[para(4672(a,2),17360(a,2,2,1))].">
      <j1 rule="para" parents="4672 17360"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17235,a(flip),b,17404,a)].">
      <j1 rule="hyper" parents="60 17235 17404"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(11345(a,1),17425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11345 17425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17455">
    <literal><![CDATA[
      K(x,y * z) * T(x,K(y,z)) = K(x,z * y) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a(flip),b,17439,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6400(a,2),17444(a,1,2))].">
      <j1 rule="para" parents="6400 17444"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      T(x,T(y,z) * (u \ T(y,z))) = T(x,y * (u \ y))
    ]]></literal>
    <justification jstring="[para(15203(a,1),17447(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15203 17447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17459">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(263(a,1),17456(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="263 17456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = K(x,w) * T(x * K(w,x),y / T(u,z))
    ]]></literal>
    <justification jstring="[para(17456(a,1),9813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17456 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),w),1 / z)) = T(x,y / ((z \ T(u,w)) / (1 / z)))
    ]]></literal>
    <justification jstring="[para(15656(a,1),17456(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15656 17456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = x / K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,5698,a(flip),b,17459,a),flip(a)].">
      <j1 rule="hyper" parents="370 5698 17459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = w
    ]]></literal>
    <justification jstring="[para(17462(a,2),5709(a,1))].">
      <j1 rule="para" parents="17462 5709"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,u)) = K(x,(y * ((y \ 1) \ u)) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(17149,a,15556,a)].">
      <j1 rule="hyper" parents="17149 15556"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      T(x,T(y,y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7318(a,1),17150(a,1))].">
      <j1 rule="para" parents="7318 17150"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(8636(a,2),17205(a,1,1))].">
      <j1 rule="para" parents="8636 17205"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(8630(a,1),17206(a,1,2))].">
      <j1 rule="para" parents="8630 17206"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,y)) * x = w
    ]]></literal>
    <justification jstring="[para(8636(a,1),17206(a,1,2))].">
      <j1 rule="para" parents="8636 17206"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(u,z)) * x = w
    ]]></literal>
    <justification jstring="[para(8648(a,1),17206(a,1,2))].">
      <j1 rule="para" parents="8648 17206"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(16708(a,1),17210(a,1))].">
      <j1 rule="para" parents="16708 17210"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * y),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(8701(a,1),17247(a,1,2,1))].">
      <j1 rule="para" parents="8701 17247"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,y \ z) * (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(12441(a,1),17249(a,1,1))].">
      <j1 rule="para" parents="12441 17249"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(16742(a,1),17250(a,1))].">
      <j1 rule="para" parents="16742 17250"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(17362(a,1),17250(a,1))].">
      <j1 rule="para" parents="17362 17250"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(14419(a,2),17252(a,1))].">
      <j1 rule="para" parents="14419 17252"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(16730(a,1),17252(a,1))].">
      <j1 rule="para" parents="16730 17252"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17358(a,2),17252(a,1))].">
      <j1 rule="para" parents="17358 17252"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(17357(a,2),17302(a,1))].">
      <j1 rule="para" parents="17357 17302"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(17359(a,2),17302(a,1))].">
      <j1 rule="para" parents="17359 17302"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      K(K(x,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(17412(a,2),17310(a,1))].">
      <j1 rule="para" parents="17412 17310"/>
    </justification>
  </clause>

  <clause id="17489">
    <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(103(a,1),17385(a,1,2,2))].">
      <j1 rule="para" parents="103 17385"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * (z * y),z * u)) = w
    ]]></literal>
    <justification jstring="[para(12558(a,1),17421(a,1))].">
      <j1 rule="para" parents="12558 17421"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15405(a,2),17421(a,1,2))].">
      <j1 rule="para" parents="15405 17421"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17119(a,2),17421(a,1))].">
      <j1 rule="para" parents="17119 17421"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17121(a,2),17421(a,1))].">
      <j1 rule="para" parents="17121 17421"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      T(x,y / T(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),17464(a,1,2,2,1))].">
      <j1 rule="para" parents="109 17464"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      T(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(14346(a,1),17464(a,1))].">
      <j1 rule="para" parents="14346 17464"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      T(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5749(a,1),17497(a,1,2))].">
      <j1 rule="para" parents="5749 17497"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(16715(a,2),17497(a,1))].">
      <j1 rule="para" parents="16715 17497"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      T(x,y \ L(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(z,u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(20(a,2),17498(a,1,2,2))].">
      <j1 rule="para" parents="20 17498"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      T(x,T(y \ z,z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(y \ z,z)) = w
    ]]></literal>
    <justification jstring="[para(8874(a,1),17498(a,1,2,2))].">
      <j1 rule="para" parents="8874 17498"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      T(x,T(y * z,z) \ T(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(y * z,z)) = w
    ]]></literal>
    <justification jstring="[para(12545(a,1),17498(a,1,2,2))].">
      <j1 rule="para" parents="12545 17498"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      T(x,(y \ ((y \ 1) \ z)) \ T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (y \ ((y \ 1) \ z))) = w
    ]]></literal>
    <justification jstring="[para(15330(a,1),17498(a,1,2,2))].">
      <j1 rule="para" parents="15330 17498"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ T(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (y * (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(15398(a,1),17498(a,1,2,2))].">
      <j1 rule="para" parents="15398 17498"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ T(w,T(y,z * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w / T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(17155(a,1),17498(a,1,2,2))].">
      <j1 rule="para" parents="17155 17498"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K((x \ y) / z,L(u,z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,x * y)) = w
    ]]></literal>
    <justification jstring="[para(13007(a,1),17494(a,1))].">
      <j1 rule="para" parents="13007 17494"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17174(a,2),17494(a,1))].">
      <j1 rule="para" parents="17174 17494"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8887,a,17125,a),flip(a)].">
      <j1 rule="hyper" parents="8887 17125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17125(a,1),8887(a,1))].">
      <j1 rule="para" parents="17125 8887"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(17424,a,17508,a)].">
      <j1 rule="hyper" parents="17424 17508"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8892,a,17508,a),flip(a)].">
      <j1 rule="hyper" parents="8892 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8678,a,17508,a)].">
      <j1 rule="hyper" parents="8678 17508"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,17508,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 17508 5230"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(x,K(y,z * (z * u))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),17508(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      K(x,K(y,z \ (z \ u))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),17508(a,2,2,2))].">
      <j1 rule="para" parents="5 17508"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z \ u)) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(17508(a,1),9364(a,1,1))].">
      <j1 rule="para" parents="17508 9364"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(17508(a,1),17424(a,1))].">
      <j1 rule="para" parents="17508 17424"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(8678,a,17510,a)].">
      <j1 rule="hyper" parents="8678 17510"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,17512,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 17512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(u,y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16061,a,b,17512,a)].">
      <j1 rule="hyper" parents="60 16061 17512"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(17512(a,1),8678(a,1))].">
      <j1 rule="para" parents="17512 8678"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (u * z))) = K(y,(u * (u * z)) / x)
    ]]></literal>
    <justification jstring="[para(17514(a,1),9359(a,1,1))].">
      <j1 rule="para" parents="17514 9359"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,K(y,z * (u \ z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(14494(a,1),17514(a,1,2))].">
      <j1 rule="para" parents="14494 17514"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(u \ (u \ z)) \ x) = K(y,x / (u \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(17515(a,1),9360(a,1,1))].">
      <j1 rule="para" parents="17515 9360"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      T(x,K((y * y) \ z,u)) = K(x,K(u,z)) * x
    ]]></literal>
    <justification jstring="[para(17515(a,1),15382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17515 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      K(x,K(y / z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * z,u)) = w
    ]]></literal>
    <justification jstring="[para(17518(a,2),17378(a,1))].">
      <j1 rule="para" parents="17518 17378"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(5265,a,17513,a),flip(a)].">
      <j1 rule="hyper" parents="5265 17513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17513(a,1),5265(a,1))].">
      <j1 rule="para" parents="17513 5265"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9469,a,17528,a)].">
      <j1 rule="hyper" parents="9469 17528"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8728,a,17528,a)].">
      <j1 rule="hyper" parents="8728 17528"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      T(x,K(y,z * (z * u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),17528(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 17528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      T(T(x,y \ z),K(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(17528(a,1),8748(a,1))].">
      <j1 rule="para" parents="17528 8748"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(17528(a,1),9469(a,1))].">
      <j1 rule="para" parents="17528 9469"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(17528(a,1),9562(a,1,1))].">
      <j1 rule="para" parents="17528 9562"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      T(T(x,K(y,z * (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(17528(a,1),11101(a,1,1))].">
      <j1 rule="para" parents="17528 11101"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[para(17528(a,1),12595(a,1,1))].">
      <j1 rule="para" parents="17528 12595"/>
    </justification>
  </clause>

  <clause id="17538">
    <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(17528(a,1),12632(a,1,1))].">
      <j1 rule="para" parents="17528 12632"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(17528(a,1),14365(a,1,1))].">
      <j1 rule="para" parents="17528 14365"/>
    </justification>
  </clause>

  <clause id="17540">
    <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(17528(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="17528 16700"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17528,a(flip),b,17530,a)].">
      <j1 rule="hyper" parents="60 17528 17530"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      T(x,K(y,z * (z / u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),17530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 17530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ z)) = T(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(17530(a,1),9562(a,1,1))].">
      <j1 rule="para" parents="17530 9562"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u \ z) * y) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(17530(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="17530 12569"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ z)) = T(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[para(17530(a,1),12595(a,1,1))].">
      <j1 rule="para" parents="17530 12595"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      T(x,K(y,z * (u \ z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(14494(a,1),17532(a,1,2))].">
      <j1 rule="para" parents="14494 17532"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      T(x,K(y,z * (u * u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15425(a,2),17532(a,1,2))].">
      <j1 rule="para" parents="15425 17532"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      T(x,K(y * z,u)) = T(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(8728,a,17541,a)].">
      <j1 rule="hyper" parents="8728 17541"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / z)) \ y) = T(x,y / (u * (u / z)))
    ]]></literal>
    <justification jstring="[para(17542(a,1),9567(a,1,1))].">
      <j1 rule="para" parents="17542 9567"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) = T(x,(u * (z \ u)) \ y)
    ]]></literal>
    <justification jstring="[para(17546(a,1),9562(a,1,1))].">
      <j1 rule="para" parents="17546 9562"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17548(a,1),8728(a,1))].">
      <j1 rule="para" parents="17548 8728"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      T(x,K((y * y) \ z,u)) = T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8687,a(flip),b,17526,a),flip(a)].">
      <j1 rule="hyper" parents="370 8687 17526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      T(x,K(y \ (y \ z),u)) = T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(15130(a,1),17554(a,1,2))].">
      <j1 rule="para" parents="15130 17554"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K((w * w) \ z,u)) = T(y,K(u,(w * w) \ z) * x)
    ]]></literal>
    <justification jstring="[para(17554(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="17554 16700"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u \ y)) * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (u \ (u \ y))) = w
    ]]></literal>
    <justification jstring="[para(17556(a,1),12632(a,1,1))].">
      <j1 rule="para" parents="17556 12632"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17273(a,2),17509(a,1))].">
      <j1 rule="para" parents="17273 17509"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      K(x,T(y * y,z)) * (((x * T(y * y,z)) \ u) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,12090,a,b,17139,a)].">
      <j1 rule="hyper" parents="370 12090 17139"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      T(x,y) * K(z * z,x) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(15680,a,17146,a),flip(a)].">
      <j1 rule="hyper" parents="15680 17146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      L(x,T(y,z \ (z \ u)),w) = L(x,T(y,u),w)
    ]]></literal>
    <justification jstring="[para(17561(a,1),6957(a,1,2))].">
      <j1 rule="para" parents="17561 6957"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      L(x,T(y,z \ u),w) = L(x,T(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(4(a,1),17562(a,1,2,2,2))].">
      <j1 rule="para" parents="4 17562"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      L(x,T(y,z * u),z \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(12506,a,17563,a),flip(a)].">
      <j1 rule="hyper" parents="12506 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      L(x,T(y,z),(z / u) \ u) = L(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),17564(a,1,2,2))].">
      <j1 rule="para" parents="7 17564"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y \ (x / z)),u) = w
    ]]></literal>
    <justification jstring="[para(17154(a,2),15485(a,1))].">
      <j1 rule="para" parents="17154 15485"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      (x * y) * K(z,L(T(u,y * x),w,v5)) = K(z,L(u,w,v5)) * (x * y)
    ]]></literal>
    <justification jstring="[para(20(a,2),17157(a,1,2,2))].">
      <j1 rule="para" parents="20 17157"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      T(x * K(K(x * y,z),x),u) * K(x * y,z) = T(x,u) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5320,a,b,17312,a)].">
      <j1 rule="hyper" parents="370 5320 17312"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(K(((x \ 1) \ 1) * z,u),x,x) = K(z * ((x \ 1) \ 1),u) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16269,a,b,17313,a)].">
      <j1 rule="hyper" parents="60 16269 17313"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      x * K(y,(z * (u * (z \ x))) / x) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(17316(a,1),16563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17316 16563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8034,a,b,17339,a),flip(a)].">
      <j1 rule="hyper" parents="370 8034 17339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,T(y,z)) = K(x,y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8990(a,1),17343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8990 17343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      K(x / (y * K(z,y)),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17410,a(flip),b,17365,a),flip(a)].">
      <j1 rule="hyper" parents="370 17410 17365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15481,a,17573,a)].">
      <j1 rule="hyper" parents="15481 17573"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      K(x / T(y,y \ z),u) = K(x / (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(5683(a,2),17573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5683 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      K(x * (((y \ 1) * z) \ K((y \ 1) * z,y)),u) = K(x / ((y \ 1) * ((y \ z) * y)),u)
    ]]></literal>
    <justification jstring="[para(2875(a,2),17574(a,2,1,2))].">
      <j1 rule="para" parents="2875 17574"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) * a(w,v5,K(y / T(z,u),x)) = K(x,L(y * (z \ K(z,u)),v5,w))
    ]]></literal>
    <justification jstring="[para(17574(a,1),12932(a,1,2,3))].">
      <j1 rule="para" parents="17574 12932"/>
    </justification>
  </clause>

  <clause id="17578">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17406,a(flip),b,17369,a),flip(a)].">
      <j1 rule="hyper" parents="60 17406 17369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14576,a,b,17578,a)].">
      <j1 rule="hyper" parents="370 14576 17578"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      K(K(x,y * y) * T(z * x,y * y),u) = K(((y * y) \ z) * ((y * y) * x),u)
    ]]></literal>
    <justification jstring="[para(890(a,1),17414(a,1,1,2))].">
      <j1 rule="para" parents="890 17414"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * (y * (z / T(y,z))))
    ]]></literal>
    <justification jstring="[para(5789(a,1),17433(a,2,2,2))].">
      <j1 rule="para" parents="5789 17433"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17289,a(flip),b,17454,a),flip(a)].">
      <j1 rule="hyper" parents="60 17289 17454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(y,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(6273,a,17455,a)].">
      <j1 rule="hyper" parents="6273 17455"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(17473,a,17585,a)].">
      <j1 rule="hyper" parents="17473 17585"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * y) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(17472,a,17585,a)].">
      <j1 rule="hyper" parents="17472 17585"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      K(x,y * (z * (u * (1 / w)))) * K(x,K(y,z * (u * (w \ 1)))) = K(x,(z * (u * (1 / w))) * y)
    ]]></literal>
    <justification jstring="[para(5589(a,1),17585(a,1,2,2))].">
      <j1 rule="para" parents="5589 17585"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(8648(a,1),17585(a,1,2))].">
      <j1 rule="para" parents="8648 17585"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(17585(a,1),17399(a,1,2))].">
      <j1 rule="para" parents="17585 17399"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      K(x,(y / z) * u) * K(x,K(u,z * y)) = K(x,u * (y / z))
    ]]></literal>
    <justification jstring="[para(17518(a,1),17585(a,1,2))].">
      <j1 rule="para" parents="17518 17585"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x * y,z) * K(z,y * x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,17215,a,b,17587,a)].">
      <j1 rule="hyper" parents="32 17215 17587"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * T(y,u)) = K(z,T(y,u) * x)
    ]]></literal>
    <justification jstring="[para(17274(a,1),17587(a,1,1))].">
      <j1 rule="para" parents="17274 17587"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      K(x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) * K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(17587(a,1),17468(a,1))].">
      <j1 rule="para" parents="17587 17468"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      K(x,((y \ 1) * z) * u) * K(x,K(u,y \ z)) = K(x,u * ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(15200(a,1),17589(a,1,2,2))].">
      <j1 rule="para" parents="15200 17589"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ T(z,u)) * (x \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17091,a(flip),b,17458,a),flip(a)].">
      <j1 rule="hyper" parents="60 17091 17458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17508,a(flip),b,17511,a),flip(a)].">
      <j1 rule="hyper" parents="370 17508 17511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      L(x,y / z,(y / u) \ u) = L(x,z \ y,(y / u) \ u)
    ]]></literal>
    <justification jstring="[hyper(14836,a,17565,a),flip(a)].">
      <j1 rule="hyper" parents="14836 17565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(x,L(y,1 / (z / u),(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(17565(a,1),16137(a,1,2))].">
      <j1 rule="para" parents="17565 16137"/>
    </justification>
  </clause>

  <clause id="17600">
    <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(17571(a,2),40(a,1))].">
      <j1 rule="para" parents="17571 40"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      K(x,K(y * z,u * (y \ z))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8678,a,17597,a)].">
      <j1 rule="hyper" parents="8678 17597"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      K(x / T(y * y,z),u) = K(T(y * y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(17176,a,17124,a)].">
      <j1 rule="hyper" parents="17176 17124"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / T(x \ 1,y),u) = w
    ]]></literal>
    <justification jstring="[para(9477(a,1),17176(a,1))].">
      <j1 rule="para" parents="9477 17176"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      K(T(x * x,x) \ y,z) = K(y / ((1 / x) \ x),z)
    ]]></literal>
    <justification jstring="[para(582(a,1),17602(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="582 17602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      K(x / ((1 / y) \ y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16829,a(flip),b,17604,a),flip(a)].">
      <j1 rule="hyper" parents="60 16829 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      K(x / ((1 / y) \ y),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15130,a(flip),b,17605,a),flip(a)].">
      <j1 rule="hyper" parents="370 15130 17605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      K(x * (y \ (1 / y)),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(1662(a,1),17606(a,1,1))].">
      <j1 rule="para" parents="1662 17606"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ T(z,y * y))),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17054,a,b,17607,a)].">
      <j1 rule="hyper" parents="60 17054 17607"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(8770(a,1),17178(a,1,1))].">
      <j1 rule="para" parents="8770 17178"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      K(x * T(y * z,u),T(w,z * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(y * z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(17151(a,1),17179(a,1))].">
      <j1 rule="para" parents="17151 17179"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      T(K(x,y) / T(z,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,u) \ K(x,y) = w
    ]]></literal>
    <justification jstring="[para(5911(a,2),17246(a,1))].">
      <j1 rule="para" parents="5911 17246"/>
    </justification>
  </clause>

  <clause id="17613">
    <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(17197(a,2),17248(a,2,2,1))].">
      <j1 rule="para" parents="17197 17248"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(17296,a,13233,a)].">
      <j1 rule="hyper" parents="17296 13233"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      T(x * K(y,z),L(T(u,x),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20(a,2),17296(a,1,2))].">
      <j1 rule="para" parents="20 17296"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17331(a,1),17299(a,1))].">
      <j1 rule="para" parents="17331 17299"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      K(x,L(K(y,z) * (u * y),w,v5)) = K(L(x,w,v5),u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17303,a,12966,a),flip(a)].">
      <j1 rule="hyper" parents="17303 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(16730(a,1),17303(a,1))].">
      <j1 rule="para" parents="16730 17303"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16733(a,2),17303(a,1))].">
      <j1 rule="para" parents="16733 17303"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K((x \ y) * K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(17407(a,1),17311(a,1))].">
      <j1 rule="para" parents="17407 17311"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,v5 * K(u,w)) \ z) = v6
    ]]></literal>
    <justification jstring="[para(17235(a,2),17334(a,1,2,2))].">
      <j1 rule="para" parents="17235 17334"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17263(a,1),17382(a,1,2))].">
      <j1 rule="para" parents="17263 17382"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17357(a,1),17483(a,1))].">
      <j1 rule="para" parents="17357 17483"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(17284(a,1),17590(a,1))].">
      <j1 rule="para" parents="17284 17590"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,x * y) / T(x,z) = T(x,z) \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(17612,a,15693,a),flip(a)].">
      <j1 rule="hyper" parents="17612 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ y) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,10589,a(flip),b,17630,a),flip(a)].">
      <j1 rule="hyper" parents="60 10589 17630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ 1 = 1 / R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,14713,a(flip),b,17631,a)].">
      <j1 rule="hyper" parents="60 14713 17631"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ 1 = L(1 / y,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,11728,a,b,17632,a),flip(a)].">
      <j1 rule="hyper" parents="370 11728 17632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      (x / (T(x,y) / y)) \ L(z,y,y) = L(1 / y,x,y) * z
    ]]></literal>
    <justification jstring="[para(17633(a,1),14854(a,2,1))].">
      <j1 rule="para" parents="17633 14854"/>
    </justification>
  </clause>

  <clause id="17635">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * (v5 * w)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 * T(w,a(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(15496(a,2),17620(a,1,2,1))].">
      <j1 rule="para" parents="15496 17620"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      K((a(x,y,z) \ u) * a(x,y,K(z,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(T(a(x,y,z),w) \ u,v5) = v6
    ]]></literal>
    <justification jstring="[para(15496(a,2),17623(a,1,1,2))].">
      <j1 rule="para" parents="15496 17623"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,(y / z) * u) * K(x,K(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y / z)) = w
    ]]></literal>
    <justification jstring="[para(17518(a,1),17629(a,1,2))].">
      <j1 rule="para" parents="17518 17629"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,L(T(y,z \ u),w,v5)) = K(x,L(T(y,z * u),w,v5))
    ]]></literal>
    <justification jstring="[para(20(a,2),17123(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z \ u,z)) = K(x,u \ (z * (y * (z \ u))))
    ]]></literal>
    <justification jstring="[para(1149(a,1),17123(a,2,2))].">
      <j1 rule="para" parents="1149 17123"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      T(x / (x \ y),T(z,y)) = T(x / (x \ y),z)
    ]]></literal>
    <justification jstring="[para(7(a,1),17160(a,1,2,2))].">
      <j1 rule="para" parents="7 17160"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      T(x / (x \ y),z / y) = T(x / (x \ y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(9013,a,17640,a)].">
      <j1 rule="hyper" parents="9013 17640"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(17196(a,1),17211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17196 17211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a,b,17642,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 17642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(17642(a,2),389(a,1))].">
      <j1 rule="para" parents="17642 389"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(17475,a,17643,a)].">
      <j1 rule="hyper" parents="17475 17643"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(17294,a,17643,a)].">
      <j1 rule="hyper" parents="17294 17643"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(16774,a,17643,a)].">
      <j1 rule="hyper" parents="16774 17643"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17395,a(flip),b,17643,a)].">
      <j1 rule="hyper" parents="60 17395 17643"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(7506(a,2),17643(a,1,2))].">
      <j1 rule="para" parents="7506 17643"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(7873(a,1),17643(a,1,2))].">
      <j1 rule="para" parents="7873 17643"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      T(x,y * (K(z,K(u,w)) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),17643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(17643(a,1),16711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17643 16711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[para(17643(a,1),16712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17643 16712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6930(a,1),17646(a,1,2))].">
      <j1 rule="para" parents="6930 17646"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7992(a,1),17646(a,1,2))].">
      <j1 rule="para" parents="7992 17646"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8028(a,1),17646(a,1,2))].">
      <j1 rule="para" parents="8028 17646"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(9369(a,1),17646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9369 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(17335(a,1),17646(a,1,2))].">
      <j1 rule="para" parents="17335 17646"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(17648(a,1),16722(a,1))].">
      <j1 rule="para" parents="17648 16722"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8728,a,17656,a)].">
      <j1 rule="hyper" parents="8728 17656"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8720,a,17656,a),flip(a)].">
      <j1 rule="hyper" parents="8720 17656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(60,a,8592,a(flip),b,17656,a),flip(a)].">
      <j1 rule="hyper" parents="60 8592 17656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ 1)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8560(a,1),17657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8560 17657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(17657(a,1),9567(a,1,1))].">
      <j1 rule="para" parents="17657 9567"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      T(x,K(y / z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(109(a,1),17661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 17661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(8587(a,1),17647(a,1,2,2))].">
      <j1 rule="para" parents="8587 17647"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(9560(a,1),17647(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9560 17647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u * z)) = T(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12604,a,b,17649,a)].">
      <j1 rule="hyper" parents="60 12604 17649"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * z))) = T(x,y * (w * T(z,u)))
    ]]></literal>
    <justification jstring="[para(8701(a,1),17649(a,1,2,2))].">
      <j1 rule="para" parents="8701 17649"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      T(x,y * ((z \ u) * K(w,z))) = T(x,y * (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(8938(a,1),17649(a,1,2,2))].">
      <j1 rule="para" parents="8938 17649"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,17653,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 17653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(17653(a,2),5290(a,1))].">
      <j1 rule="para" parents="17653 5290"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17486,a,17676,a)].">
      <j1 rule="hyper" parents="17486 17676"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(17483,a,17676,a)].">
      <j1 rule="hyper" parents="17483 17676"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(17303,a,17676,a)].">
      <j1 rule="hyper" parents="17303 17676"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16735,a(flip),b,17676,a)].">
      <j1 rule="hyper" parents="60 16735 17676"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(6127(a,1),17676(a,1,2))].">
      <j1 rule="para" parents="6127 17676"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(9301(a,1),17676(a,1,2))].">
      <j1 rule="para" parents="9301 17676"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(17398(a,1),17676(a,1,2))].">
      <j1 rule="para" parents="17398 17676"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17571(a,1),17676(a,1,2))].">
      <j1 rule="para" parents="17571 17676"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(6770(a,1),17679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6770 17679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6930(a,1),17679(a,1,2))].">
      <j1 rule="para" parents="6930 17679"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,17654,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 17654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(17654(a,2),5734(a,1))].">
      <j1 rule="para" parents="17654 5734"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      K(x * T(y,K(z,u)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[hyper(17308,a,17689,a)].">
      <j1 rule="hyper" parents="17308 17689"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17250,a,17689,a)].">
      <j1 rule="hyper" parents="17250 17689"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,17414,a(flip),b,17689,a)].">
      <j1 rule="hyper" parents="60 17414 17689"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) = K(x / y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,17410,a(flip),b,17689,a)].">
      <j1 rule="hyper" parents="60 17410 17689"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(6127(a,1),17689(a,1,1))].">
      <j1 rule="para" parents="6127 17689"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(K(x,y) * u,w)
    ]]></literal>
    <justification jstring="[para(9301(a,1),17689(a,1,1))].">
      <j1 rule="para" parents="9301 17689"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z * K(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(12083(a,1),17689(a,1,1))].">
      <j1 rule="para" parents="12083 17689"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(17571(a,1),17689(a,1,1))].">
      <j1 rule="para" parents="17571 17689"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      K(x,y) * (x * K(z,K(u,w))) = T(x * K(z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(17692(a,1),5275(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17692 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17528,a(flip),b,17658,a),flip(a)].">
      <j1 rule="hyper" parents="370 17528 17658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(17658(a,1),8699(a,2,1))].">
      <j1 rule="para" parents="17658 8699"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u \ w)),K(w / u,z)) = T(y,K(z,u \ w) * x)
    ]]></literal>
    <justification jstring="[hyper(125,a,17667,a,b,16707,a(flip))].">
      <j1 rule="hyper" parents="125 17667 16707"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(8587(a,1),17680(a,1,2,2))].">
      <j1 rule="para" parents="8587 17680"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) \ w) = K(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(8587(a,1),17681(a,1,2,1))].">
      <j1 rule="para" parents="8587 17681"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = L(K(x,y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(17681(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17681 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <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(17681(a,1),14571(a,1))].">
      <j1 rule="para" parents="17681 14571"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) / w,v5,v6)) = L(K(x,y / w),v5,v6)
    ]]></literal>
    <justification jstring="[para(17682(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17682 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(9560(a,1),17685(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9560 17685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17709">
    <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(17685(a,1),14645(a,1))].">
      <j1 rule="para" parents="17685 14645"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      K(x * T(y,T(z,u)),w) = K(x * T(y,z),w)
    ]]></literal>
    <justification jstring="[para(8587(a,1),17691(a,1,1,2))].">
      <j1 rule="para" parents="8587 17691"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / T(y * x,K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16464,a,b,17694,a)].">
      <j1 rule="hyper" parents="370 16464 17694"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      K(T(x,y / z) / u,w) = K(T(x,z \ y) / u,w)
    ]]></literal>
    <justification jstring="[para(9560(a,1),17695(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9560 17695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      T(T(x,y / z),K(u,z * y)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8748,a,17700,a),flip(a)].">
      <j1 rule="hyper" parents="8748 17700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      T(T(x,y / z),K(u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(17700(a,1),8748(a,1))].">
      <j1 rule="para" parents="17700 8748"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(17700(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="17700 12569"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17700(a,1),12611(a,1,1))].">
      <j1 rule="para" parents="17700 12611"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(K(z,u) * y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12083(a,1),17644(a,1,2))].">
      <j1 rule="para" parents="12083 17644"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(17395(a,1),17644(a,1))].">
      <j1 rule="para" parents="17395 17644"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(6128(a,1),17660(a,1,2))].">
      <j1 rule="para" parents="6128 17660"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(9301(a,1),17660(a,1,2))].">
      <j1 rule="para" parents="9301 17660"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(u * K(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12083(a,1),17660(a,1,2))].">
      <j1 rule="para" parents="12083 17660"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      T(x,(T(y,K(z,u)) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(16495(a,1),17660(a,1,2))].">
      <j1 rule="para" parents="16495 17660"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(6218(a,2),17677(a,1,2,1))].">
      <j1 rule="para" parents="6218 17677"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(6130(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="6130 17677"/>
    </justification>
  </clause>

  <clause id="17725">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / w) = v5
    ]]></literal>
    <justification jstring="[para(6127(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="6127 17677"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(7864(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="7864 17677"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(8016(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="8016 17677"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(8683(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="8683 17677"/>
    </justification>
  </clause>

  <clause id="17729">
    <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(9669(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="9669 17677"/>
    </justification>
  </clause>

  <clause id="17730">
    <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(12094(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="12094 17677"/>
    </justification>
  </clause>

  <clause id="17731">
    <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(17571(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="17571 17677"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(8016(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="8016 17690"/>
    </justification>
  </clause>

  <clause id="17733">
    <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(12083(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="12083 17690"/>
    </justification>
  </clause>

  <clause id="17734">
    <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(12094(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="12094 17690"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      K(x / T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / y,w) = v5
    ]]></literal>
    <justification jstring="[para(17398(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="17398 17690"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(17571(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="17571 17690"/>
    </justification>
  </clause>

  <clause id="17737">
    <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(6770(a,1),17727(a,1,2))].">
      <j1 rule="para" parents="6770 17727"/>
    </justification>
  </clause>

  <clause id="17738">
    <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(6930(a,1),17727(a,1,2))].">
      <j1 rule="para" parents="6930 17727"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      K(x * (y * K(z,K(u,w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(9520(a,1),17732(a,1,1))].">
      <j1 rule="para" parents="9520 17732"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      T(x,y * (K(z,T(u,w)) * v5)) = T(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(9301(a,1),17652(a,1,2,2))].">
      <j1 rule="para" parents="9301 17652"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      T(x,y * (z * K(u,T(w,v5)))) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(17571(a,1),17652(a,1,2,2))].">
      <j1 rule="para" parents="17571 17652"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,16708,a,b,17659,a),flip(a)].">
      <j1 rule="hyper" parents="370 16708 17659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * (y \ w)) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,16715,a(flip),b,17659,a),flip(a)].">
      <j1 rule="hyper" parents="370 16715 17659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <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(17659(a,2),16774(a,1))].">
      <j1 rule="para" parents="17659 16774"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(1146,a,17663,a)].">
      <j1 rule="hyper" parents="1146 17663"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6242,a,b,17665,a)].">
      <j1 rule="hyper" parents="60 6242 17665"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14426,a,17669,a),flip(a)].">
      <j1 rule="hyper" parents="14426 17669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <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(17683(a,2),16731(a,1))].">
      <j1 rule="para" parents="17683 16731"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      K(x,y * K(z * u,w)) = K(x,y * K(u * z,w))
    ]]></literal>
    <justification jstring="[para(12578(a,1),17686(a,1,2,2))].">
      <j1 rule="para" parents="12578 17686"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(u * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17362,a(flip),b,17696,a),flip(a)].">
      <j1 rule="hyper" parents="370 17362 17696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17752">
    <literal><![CDATA[
      K(K(x,y / z) * u,w) = K(K(x,z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),17696(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 17696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * K(y,x),w) = v5
    ]]></literal>
    <justification jstring="[para(17696(a,2),17481(a,1))].">
      <j1 rule="para" parents="17696 17481"/>
    </justification>
  </clause>

  <clause id="17754">
    <literal><![CDATA[
      K(x * K(x \ y,x),z) * (x * T(x \ y,u)) = (x * T(x \ y,u)) * K(x,z)
    ]]></literal>
    <justification jstring="[para(17698(a,1),10392(a,1,1))].">
      <j1 rule="para" parents="17698 10392"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      K(x,L(y * T(z,T(u,w)),v5,v6)) = K(L(x,v5,v6),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13036,a,17703,a)].">
      <j1 rule="hyper" parents="13036 17703"/>
    </justification>
  </clause>

  <clause id="17757">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * T(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(17704(a,1),14571(a,1))].">
      <j1 rule="para" parents="17704 14571"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y,u) \ w)) = T(x,T(T(y,u),z) \ w)
    ]]></literal>
    <justification jstring="[para(7873(a,1),17742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7873 17742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      T(T(x,T(T(y,z),u)),w \ (w \ 1)) = T(T(x,K(y,z)),w \ (w \ T(y,u)))
    ]]></literal>
    <justification jstring="[para(17745(a,1),15661(a,1,1))].">
      <j1 rule="para" parents="17745 15661"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(u \ (u \ y),w)) = T(x,T(T(u \ (u \ y),z),w))
    ]]></literal>
    <justification jstring="[para(17556(a,1),17745(a,1,1))].">
      <j1 rule="para" parents="17556 17745"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      T(x,y * ((z \ u) * K(w,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8938(a,1),17718(a,1,2,2))].">
      <j1 rule="para" parents="8938 17718"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      T(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(16799(a,1),17718(a,1))].">
      <j1 rule="para" parents="16799 17718"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(8701(a,1),17719(a,1,2,2))].">
      <j1 rule="para" parents="8701 17719"/>
    </justification>
  </clause>

  <clause id="17764">
    <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(8701(a,1),17724(a,1,2,2))].">
      <j1 rule="para" parents="8701 17724"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8938(a,1),17724(a,1,2,2))].">
      <j1 rule="para" parents="8938 17724"/>
    </justification>
  </clause>

  <clause id="17766">
    <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(9095(a,1),17724(a,1,2,2))].">
      <j1 rule="para" parents="9095 17724"/>
    </justification>
  </clause>

  <clause id="17767">
    <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(7464(a,1),17725(a,1,2,1))].">
      <j1 rule="para" parents="7464 17725"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      K(x,(y * (z * K(y,u))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(9095(a,1),17726(a,1,2,1))].">
      <j1 rule="para" parents="9095 17726"/>
    </justification>
  </clause>

  <clause id="17769">
    <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(14442(a,1),17726(a,1))].">
      <j1 rule="para" parents="14442 17726"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,(v5 * L(K(y,z),u,w)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(11809(a,1),17728(a,1,2,1))].">
      <j1 rule="para" parents="11809 17728"/>
    </justification>
  </clause>

  <clause id="17771">
    <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(8936(a,1),17735(a,1,1,2))].">
      <j1 rule="para" parents="8936 17735"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      T(x,y * (z * (u * (w * K(u,v5))))) = T(x,y * (z * (T(u,v5) * w)))
    ]]></literal>
    <justification jstring="[para(9095(a,1),17655(a,1,2,2,2))].">
      <j1 rule="para" parents="9095 17655"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * K(y,T(x,z)) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8094(a,1),17662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8094 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      T(T(x,K(y,(z \ 1) * u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(7124(a,1),17666(a,1,2,1))].">
      <j1 rule="para" parents="7124 17666"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * (z * (z * u))) = T(x,(z * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(14333(a,1),17671(a,1,2,1))].">
      <j1 rule="para" parents="14333 17671"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(9560(a,1),17688(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9560 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K((K(x,y) * (z / y)) \ u,w) = K((z / T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(5855(a,1),17697(a,2,1,1))].">
      <j1 rule="para" parents="5855 17697"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      T(T(x,y / T(z * u,z)),K(w,(u * z) * y)) = T(x,T(y / T(z * u,z),w))
    ]]></literal>
    <justification jstring="[para(14487(a,1),17713(a,1,2))].">
      <j1 rule="para" parents="14487 17713"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,y * K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u * z,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(17750(a,1),17251(a,1))].">
      <j1 rule="para" parents="17750 17251"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,T(z,v5)) * u) = w
    ]]></literal>
    <justification jstring="[para(8763(a,1),17720(a,1,2,1))].">
      <j1 rule="para" parents="8763 17720"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) * w) = K(x,(u * T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(17729,a,14487,a)].">
      <j1 rule="hyper" parents="17729 14487"/>
    </justification>
  </clause>

  <clause id="17783">
    <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(12545(a,1),17729(a,1,2,1))].">
      <j1 rule="para" parents="12545 17729"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      K(x,y * K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u * z,w)) = v5
    ]]></literal>
    <justification jstring="[para(12578(a,1),17731(a,1,2,2))].">
      <j1 rule="para" parents="12578 17731"/>
    </justification>
  </clause>

  <clause id="17785">
    <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(109(a,1),17736(a,1,1,2,2))].">
      <j1 rule="para" parents="109 17736"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(x * (T(y,K(z,u)) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(6280(a,1),17739(a,1,1,2))].">
      <j1 rule="para" parents="6280 17739"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / T(u / z,w)) = K(x,T(u / z,w) \ y)
    ]]></literal>
    <justification jstring="[para(17510(a,1),17278(a,1,1))].">
      <j1 rule="para" parents="17510 17278"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,16844,a,b,17287,a)].">
      <j1 rule="hyper" parents="370 16844 17287"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14455,a,b,17287,a)].">
      <j1 rule="hyper" parents="370 14455 17287"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      K(x,L(T(y,z / u),w,v5)) = K(x,L(T(y,u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13033,a,17317,a),flip(a)].">
      <j1 rule="hyper" parents="13033 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5595,a(flip),b,17347,a),flip(a)].">
      <j1 rule="hyper" parents="370 5595 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(9166,a,17792,a)].">
      <j1 rule="hyper" parents="9166 17792"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(17621,a,17368,a)].">
      <j1 rule="hyper" parents="17621 17368"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) = K(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14633,a(flip),b,17371,a)].">
      <j1 rule="hyper" parents="60 14633 17371"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17621,a,17796,a),flip(a)].">
      <j1 rule="hyper" parents="17621 17796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17796(a,1),17621(a,1))].">
      <j1 rule="para" parents="17796 17621"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15830,a(flip),b,17401,a),flip(a)].">
      <j1 rule="hyper" parents="60 15830 17401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,z * K(z * K(y,x),u)),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(17416(a,1),12590(a,1,1,1))].">
      <j1 rule="para" parents="17416 12590"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((z / u) \ u)) = T(x,((z / u) \ u) \ y)
    ]]></literal>
    <justification jstring="[para(7(a,1),17535(a,1,1,2,2))].">
      <j1 rule="para" parents="7 17535"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((u \ z) \ u)) = T(x,((u \ z) \ u) \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17543(a,1,1,2,2))].">
      <j1 rule="para" parents="5 17543"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (z / u)) * y) = T(x,y * (u \ (z / u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),17544(a,1,1,2,2))].">
      <j1 rule="para" parents="7 17544"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17579(a,1),14580(a,1))].">
      <j1 rule="para" parents="17579 14580"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x * T(y,u * (w * u))) = K(z,T(y,(u * w) * u) * x)
    ]]></literal>
    <justification jstring="[para(14333(a,1),17593(a,1,2,2,2))].">
      <j1 rule="para" parents="14333 17593"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      T(x,y * (K(z / u,u) * (w * (z / u)))) = T(x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),17672(a,2,2,2,2))].">
      <j1 rule="para" parents="109 17672"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,y * (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(17295,a,17673,a)].">
      <j1 rule="hyper" parents="17295 17673"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      T(x,y * (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(17673(a,1),17295(a,1))].">
      <j1 rule="para" parents="17673 17295"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) * (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z \ y) \ w))
    ]]></literal>
    <justification jstring="[para(6446(a,1),17809(a,2,2,2,1))].">
      <j1 rule="para" parents="6446 17809"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y \ z) * (y \ (z * (z \ u))))
    ]]></literal>
    <justification jstring="[para(16669(a,2),17809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16669 17809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y * K(z / u,y)) \ w)) = T(x,T(y,(z \ u) * (z \ u)) * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(16800(a,1),17809(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16800 17809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7900,a,17699,a),flip(a)].">
      <j1 rule="hyper" parents="7900 17699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      T(K(x,y) * K(z,K(u,w)),v5) = K(x,T(y,v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(9150,a,17814,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9150 17814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * K(w,K(v5,v6)),v7) = K(x,L(T(y,v7),z,u)) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(8042(a,2),17814(a,2,1))].">
      <j1 rule="para" parents="8042 17814"/>
    </justification>
  </clause>

  <clause id="17817">
    <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(17814(a,2),8658(a,1,1))].">
      <j1 rule="para" parents="17814 8658"/>
    </justification>
  </clause>

  <clause id="17819">
    <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(17705(a,2),13033(a,1))].">
      <j1 rule="para" parents="17705 13033"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) / w,v5,v6)) = K(x,L(y / w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,17707,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 17707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17821">
    <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(17707(a,2),13033(a,1))].">
      <j1 rule="para" parents="17707 13033"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      T(x,y * (K(z,T(u,w)) * (u \ v5))) = T(x,y * (T(u,z) \ v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),17740(a,2,2,2))].">
      <j1 rule="para" parents="7873 17740"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      T(T(x,K(y,z * K(u,T(w,v5)))),(z * K(u,T(w,v5))) * y) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(12574,a,17741,a)].">
      <j1 rule="hyper" parents="12574 17741"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      T(x,K(y,z) * (T(z * y,u) \ w)) = T(x,T(T(z * y,u),z) \ w)
    ]]></literal>
    <justification jstring="[hyper(16898,a,17758,a)].">
      <j1 rule="hyper" parents="16898 17758"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      K((T(x,y) / y) \ z,u) = K((x / T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(7930(a,1),17778(a,1,1,1))].">
      <j1 rule="para" parents="7930 17778"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      K(x,L(T(y,z / u),w,v5)) = K(x,L(T(y,u * z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,17638,a(flip),b,17791,a),flip(a)].">
      <j1 rule="hyper" parents="370 17638 17791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) / w,v5,v6)) = K(x,L(T(y,z) / w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8587(a,1),17820(a,1,2,1,1))].">
      <j1 rule="para" parents="8587 17820"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      K(x,L(T(((y / z) \ 1) \ u,y * z),w,v5)) = K(x,L(u / ((y / z) \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13054,a,17826,a),flip(a)].">
      <j1 rule="hyper" parents="13054 17826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      K(x,L(T((y / z) \ u,z * y),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u / (y / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17826(a,1),13038(a,1))].">
      <j1 rule="para" parents="17826 13038"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17273,a,b,17280,a),flip(a)].">
      <j1 rule="hyper" parents="370 17273 17280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(17380,a,17381,a)].">
      <j1 rule="hyper" parents="17380 17381"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17709,a,15268,a)].">
      <j1 rule="hyper" parents="17709 15268"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,y / (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(129,a,17833,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 17833 5230"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y * ((z * u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(5630(a,1),17833(a,1,2,2))].">
      <j1 rule="para" parents="5630 17833"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(5855(a,1),17833(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5855 17833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),17833(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 17833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,17834,a),flip(a)].">
      <j1 rule="hyper" parents="5265 17834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(17834(a,1),5265(a,1))].">
      <j1 rule="para" parents="17834 5265"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,(y \ K(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(17721,a,15336,a)].">
      <j1 rule="hyper" parents="17721 15336"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      K(x * (T(T(y,K(z,u)),w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x * (T(y,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(18(a,1),17786(a,1,1,2,1))].">
      <j1 rule="para" parents="18 17786"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      K(x,K(y,(z * (u * w)) / (z * w))) = K(x,K(y,L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),17830(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <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(17(a,2),17831(a,1,2,1,1))].">
      <j1 rule="para" parents="17 17831"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K((y * K(z,u)) \ (y * x),w)
    ]]></literal>
    <justification jstring="[para(4(a,1),17241(a,1,1,1,1))].">
      <j1 rule="para" parents="4 17241"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      x / T(x,K(K(y,z) * u,w) * v5) = K(v5 * K(w,K(z,y) * u),x)
    ]]></literal>
    <justification jstring="[hyper(5728,a,17417,a)].">
      <j1 rule="hyper" parents="5728 17417"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) != v5 / v6
    ]]></literal>
    <literal><![CDATA[
      T(v5,w * K(u,K(y,x) * z)) = v6
    ]]></literal>
    <justification jstring="[para(17417(a,2),5733(a,1))].">
      <j1 rule="para" parents="17417 5733"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      T(T(x,x \ 1),y) * K(x * z,u) = (T(x,y) \ K(u,z * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,15558,a(flip),b,17438,a),flip(a)].">
      <j1 rule="hyper" parents="370 15558 17438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z \ u)) = K(x,T(u / z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14445,a,b,17516,a),flip(a)].">
      <j1 rule="hyper" parents="370 14445 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / y)) \ z) = T(x,z / (u * (u / y)))
    ]]></literal>
    <justification jstring="[para(8700(a,1),17551(a,1,1))].">
      <j1 rule="para" parents="8700 17551"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      K(x,L(K(y,z) * (u * y),w,v5)) = K(x,L(u * T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,12966,a(flip),b,17619,a),flip(a)].">
      <j1 rule="hyper" parents="370 12966 17619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(y,(1 / z) \ (x / z)))
    ]]></literal>
    <justification jstring="[para(1582(a,1),17747(a,1,1))].">
      <j1 rule="para" parents="1582 17747"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x,L(y * T(z,T(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * T(z,u),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17755(a,2),13036(a,1))].">
      <j1 rule="para" parents="17755 13036"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (y / u)) * z) = T(x,z * (u \ (y / u)))
    ]]></literal>
    <justification jstring="[para(8700(a,1),17803(a,1,1))].">
      <j1 rule="para" parents="8700 17803"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      T(K(x,y) * K(z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,w)) * K(x,T(y,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17815(a,2),17206(a,1))].">
      <j1 rule="para" parents="17815 17206"/>
    </justification>
  </clause>

  <clause id="17859">
    <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(17335(a,1),17817(a,1,1,1))].">
      <j1 rule="para" parents="17335 17817"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w)) \ v5)) = T(x,y * (T(z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(8097(a,1),17822(a,1,2,2))].">
      <j1 rule="para" parents="8097 17822"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      T(x,y * (T(z,u * w) \ v5)) = T(x,y * (T(z,w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(12545(a,1),17860(a,1,2,2,1))].">
      <j1 rule="para" parents="12545 17860"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      T(T(x,K(y,K(z,z \ (y / z)) * u)),((y / z) / z) * u) = T(x,(K(z,z \ (y / z)) * u) * (z \ (y / z)))
    ]]></literal>
    <justification jstring="[para(8203(a,1),17857(a,1,2))].">
      <j1 rule="para" parents="8203 17857"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      x * R(K(y,K(z,u)),w,w \ x) = (K(u,K(y,z)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(8636(a,1),17264(a,2,1,1))].">
      <j1 rule="para" parents="8636 17264"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      T(x,K(y,L((z / u) / w,w,u))) != x * v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(w * u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(17374(a,2),40(a,1))].">
      <j1 rule="para" parents="17374 40"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      K(K(x,x \ y) * (z * y),u) = K(z * T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(17480,a,16878,a)].">
      <j1 rule="hyper" parents="17480 16878"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      K(x * ((y \ z) * y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17415,a(flip),b,17866,a)].">
      <j1 rule="hyper" parents="60 17415 17866"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      K(x * T((y \ z) * y,u),w) = K(x * T(T(z,u),y),w)
    ]]></literal>
    <justification jstring="[para(4803(a,2),17867(a,1,1,2))].">
      <j1 rule="para" parents="4803 17867"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      K(x,T(y * ((z \ u) * z),w)) = ((w * x) / w) / ((w * (x * K(y * T(u,z),x))) / w)
    ]]></literal>
    <justification jstring="[para(17867(a,1),9748(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17867 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      K(x,y \ (z * (u * (z \ y)))) = K(x,L(T(u,z * y),y,z))
    ]]></literal>
    <justification jstring="[hyper(15944,a,17639,a),flip(a)].">
      <j1 rule="hyper" parents="15944 17639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      T(T(x,K(y,z)),((u * u) / z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((u * u) / z)) = w
    ]]></literal>
    <justification jstring="[para(17547(a,1),17716(a,1,1))].">
      <j1 rule="para" parents="17547 17716"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x,K(y,z) * T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u * y) * (u * T(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(17403(a,1),17764(a,1))].">
      <j1 rule="para" parents="17403 17764"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) = K(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(17766,a,16933,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17766 16933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) * u)) = v5
    ]]></literal>
    <justification jstring="[para(16933(a,2),17766(a,1))].">
      <j1 rule="para" parents="16933 17766"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w / z))) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[para(5855(a,1),17873(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5855 17873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,u) * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(16969(a,2),17768(a,1))].">
      <j1 rule="para" parents="16969 17768"/>
    </justification>
  </clause>

  <clause id="17877">
    <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(8587(a,1),17819(a,1,2,1,1))].">
      <j1 rule="para" parents="8587 17819"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      x * K(y,K(z,R(u,w,w \ x))) = (K(z,K(u,y)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(10732(a,1),17863(a,1,2))].">
      <j1 rule="para" parents="10732 17863"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13674(a,1),17879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13674 17879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8632,a(flip),b,17880,a),flip(a)].">
      <j1 rule="hyper" parents="370 8632 17880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8636(a,2),17881(a,1,1,1))].">
      <j1 rule="para" parents="8636 17881"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(128,a,8019,a,b,17882,a)].">
      <j1 rule="hyper" parents="128 8019 17882"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(77(a,1),17883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="77 17883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(8680,a,17884,a)].">
      <j1 rule="hyper" parents="8680 17884"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(x,K(y,z)) = T(K(x,y) / u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17885(a,1),7464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17885 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      (T(x,K(y,z)) / (K(y,z) \ 1)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(7561(a,1),17143(a,1,1,1))].">
      <j1 rule="para" parents="7561 17143"/>
    </justification>
  </clause>

  <clause id="17889">
    <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(7506(a,1),17152(a,2,2,2))].">
      <j1 rule="para" parents="7506 17152"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      K(x,y) * ((K(x * y,z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),17253(a,1,2,1,1,1))].">
      <j1 rule="para" parents="107 17253"/>
    </justification>
  </clause>

  <clause id="17892">
    <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(17890(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17890 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,K(z,y)) * K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(15597(a,1),17281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15597 17281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w \ (w \ 1)))) = T(x,u * (w \ (w \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(15185(a,1),17332(a,2,2,2))].">
      <j1 rule="para" parents="15185 17332"/>
    </justification>
  </clause>

  <clause id="17896">
    <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(17336(a,1),9162(a,1))].">
      <j1 rule="para" parents="17336 9162"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(31,a,17790,a(flip),b,17387,a),flip(a)].">
      <j1 rule="hyper" parents="31 17790 17387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(4(a,1),17897(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 17897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = (w * K(u,(y * x) / z)) \ w
    ]]></literal>
    <justification jstring="[para(17898(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17898 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,17899,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 17899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K((x * y) / z,T(u,x * y)) = K(z \ T(y * x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12573,a,17900,a),flip(a)].">
      <j1 rule="hyper" parents="12573 17900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),17900(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 17900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(16466,a,17902,a)].">
      <j1 rule="hyper" parents="16466 17902"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(8461,a,17901,a),flip(a)].">
      <j1 rule="hyper" parents="8461 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),17904(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,L(((y \ 1) \ z) / y,u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(15721,a,17431,a)].">
      <j1 rule="hyper" parents="15721 17431"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,L((y \ z) * y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17908(a,1),16116(a,1))].">
      <j1 rule="para" parents="17908 16116"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) \ z)) / (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / ((y \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(17465(a,1),8911(a,1))].">
      <j1 rule="para" parents="17465 8911"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,T(u,x * z)) = w
    ]]></literal>
    <justification jstring="[para(12970(a,1),17506(a,1))].">
      <j1 rule="para" parents="12970 17506"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x \ (u * (u * y))) = K(z,(u * (u * y)) / x)
    ]]></literal>
    <justification jstring="[para(8648(a,1),17523(a,1,1))].">
      <j1 rule="para" parents="8648 17523"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,(u \ (u \ x)) \ y) = K(z,y / (u \ (u \ x)))
    ]]></literal>
    <justification jstring="[para(8636(a,1),17525(a,1,1))].">
      <j1 rule="para" parents="8636 17525"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(14514,a,17539,a)].">
      <j1 rule="hyper" parents="14514 17539"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(17538,a,17914,a),flip(a)].">
      <j1 rule="hyper" parents="17538 17914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(17914(a,1),17538(a,1))].">
      <j1 rule="para" parents="17914 17538"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      T(x,((y \ z) / y) * u) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),17915(a,1,2,1,1))].">
      <j1 rule="para" parents="109 17915"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      (x * y) * K(z,L(T(u,y * x),x,y)) = (K(z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,16420,a(flip),b,17567,a),flip(a)].">
      <j1 rule="hyper" parents="370 16420 17567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(275,a,17919,a(flip),b,12940,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="275 17919 12940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) = T(z,u) * K(x,y * y)
    ]]></literal>
    <justification jstring="[para(17135(a,1),17920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17135 17920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) = K(x,y * y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(17140,a,17923,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17140 17923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      x * T(K(y,z * z) * T(u,x),w) = T(u,w) * (x * K(y,z * z))
    ]]></literal>
    <justification jstring="[para(17923(a,2),11840(a,1,2))].">
      <j1 rule="para" parents="17923 11840"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      T(x,(y \ T(z,u)) * (y \ T(z,u))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17091,a(flip),b,17596,a),flip(a)].">
      <j1 rule="hyper" parents="60 17091 17596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      T((x * y) / x,z * (x \ z)) = T(y,(x \ T((z \ 1) \ 1,u)) * (x \ T((z \ 1) \ 1,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16653,a(flip),b,17596,a)].">
      <j1 rule="hyper" parents="60 16653 17596"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      K(x \ T((y \ 1) * (y \ z),y * y),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(16240(a,2),17608(a,1,1,2))].">
      <j1 rule="para" parents="16240 17608"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9378,a(flip),b,17701,a),flip(a)].">
      <j1 rule="hyper" parents="370 9378 17701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8728,a,17929,a)].">
      <j1 rule="hyper" parents="8728 17929"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6463(a,1),17930(a,1,2))].">
      <j1 rule="para" parents="6463 17930"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K((x * L(K(z,u),w,v5)) \ y,v8)
    ]]></literal>
    <justification jstring="[hyper(17301,a,17711,a),flip(a)].">
      <j1 rule="hyper" parents="17301 17711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      T(x,(y / z) * (u * (z \ y))) = T(x,(z \ y) * (u * (y / z)))
    ]]></literal>
    <justification jstring="[para(7867(a,1),17808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7867 17808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y * z,u) \ w)) = T(x,T(T(y * z,u),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(16774,a,17824,a)].">
      <j1 rule="hyper" parents="16774 17824"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      (T(x,y) \ K(z,y * x)) \ 1 = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16106,a(flip),b,17849,a),flip(a)].">
      <j1 rule="hyper" parents="60 16106 17849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(x,K(y,z)) = T(K(x,y) / u,K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8605(a,2),17886(a,2,2))].">
      <j1 rule="para" parents="8605 17886"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(17728,a,17889,a)].">
      <j1 rule="hyper" parents="17728 17889"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(9024,a,17939,a)].">
      <j1 rule="hyper" parents="9024 17939"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(17725,a,17940,a),flip(a)].">
      <j1 rule="hyper" parents="17725 17940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8788,a(flip),b,17942,a),flip(a)].">
      <j1 rule="hyper" parents="370 8788 17942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(17942(a,2),8860(a,1))].">
      <j1 rule="para" parents="17942 8860"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17427,a,17945,a),flip(a)].">
      <j1 rule="hyper" parents="17427 17945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17421,a,17945,a)].">
      <j1 rule="hyper" parents="17421 17945"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8021,a,17945,a)].">
      <j1 rule="hyper" parents="8021 17945"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6130(a,1),17945(a,1,2,2))].">
      <j1 rule="para" parents="6130 17945"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * (K(x,y) * z) = v5
    ]]></literal>
    <justification jstring="[para(17945(a,1),8012(a,1,2))].">
      <j1 rule="para" parents="17945 8012"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,T(y,w)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(17945(a,1),8923(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17945 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      K(x,T(y,z * (K(u,w) * v5))) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(10354(a,1),17945(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10354 17945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * (x \ K(y,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(17947(a,1),12588(a,1))].">
      <j1 rule="para" parents="17947 12588"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17947(a,1),17316(a,1,1))].">
      <j1 rule="para" parents="17947 17316"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) = K((y * K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(12579,a,17948,a),flip(a)].">
      <j1 rule="hyper" parents="12579 17948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6442(a,1),17948(a,1,2,2))].">
      <j1 rule="para" parents="6442 17948"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17948(a,1),8758(a,1,1))].">
      <j1 rule="para" parents="17948 8758"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      K(L(x * K(y,x),y,K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y * K(z,u)) \ ((y * x) * K(z,u)),w) = v5
    ]]></literal>
    <justification jstring="[para(17948(a,1),16558(a,1))].">
      <j1 rule="para" parents="17948 16558"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (x \ R(x,y,x))) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(11731,a,17949,a)].">
      <j1 rule="hyper" parents="11731 17949"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,T(y,z * L(T(u,w),v5,v6))) = K(x,T(y,z * L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(20(a,2),17951(a,1,2,2,2))].">
      <j1 rule="para" parents="20 17951"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(17951(a,2),17421(a,1))].">
      <j1 rule="para" parents="17951 17421"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(7506(a,2),17946(a,1,2,2))].">
      <j1 rule="para" parents="7506 17946"/>
    </justification>
  </clause>

  <clause id="17976">
    <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(7864(a,1),17946(a,1,2,2))].">
      <j1 rule="para" parents="7864 17946"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,8923,a(flip),b,17953,a),flip(a)].">
      <j1 rule="hyper" parents="370 8923 17953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17385,a,17979,a)].">
      <j1 rule="hyper" parents="17385 17979"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(6130(a,1),17979(a,1,2,2))].">
      <j1 rule="para" parents="6130 17979"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * w)) = K(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(7864(a,1),17979(a,1,2,2))].">
      <j1 rule="para" parents="7864 17979"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(8330(a,1),17979(a,1,2,2))].">
      <j1 rule="para" parents="8330 17979"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(9075(a,1),17979(a,1,2,2))].">
      <j1 rule="para" parents="9075 17979"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      K(x,K(y,z * (K(u,w) * v5))) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(10354(a,1),17979(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10354 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(K(u,w) * z) * y) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(17979(a,1),17586(a,1,1))].">
      <j1 rule="para" parents="17979 17586"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(17517,a,17980,a)].">
      <j1 rule="hyper" parents="17517 17980"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,17980,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 17980 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      K(x,K(y,z * (u / w))) = K(x,K(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5631(a,1),17980(a,1,2,2))].">
      <j1 rule="para" parents="5631 17980"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6400(a,2),17980(a,1,2,2))].">
      <j1 rule="para" parents="6400 17980"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6442(a,1),17980(a,1,2,2))].">
      <j1 rule="para" parents="6442 17980"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6444(a,2),17980(a,1,2,2))].">
      <j1 rule="para" parents="6444 17980"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7081(a,1),17980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7081 17980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(12258(a,1),17980(a,1,2,2))].">
      <j1 rule="para" parents="12258 17980"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,17992,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 17992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18002">
    <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(9573,a,18000,a)].">
      <j1 rule="hyper" parents="9573 18000"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(9466,a,18000,a),flip(a)].">
      <j1 rule="hyper" parents="9466 18000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8678,a,18000,a)].">
      <j1 rule="hyper" parents="8678 18000"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(18000(a,1),9466(a,1))].">
      <j1 rule="para" parents="18000 9466"/>
    </justification>
  </clause>

  <clause id="18006">
    <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(9526,a,18003,a)].">
      <j1 rule="hyper" parents="9526 18003"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(2217(a,1),18003(a,1,2,1))].">
      <j1 rule="para" parents="2217 18003"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,18003,a,b,18004,a),flip(a)].">
      <j1 rule="hyper" parents="370 18003 18004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17282,a,b,17984,a),flip(a)].">
      <j1 rule="hyper" parents="370 17282 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z * T(u,w))) = K(x,(z * T(u,w)) \ y)
    ]]></literal>
    <justification jstring="[para(17984(a,1),9364(a,1,1))].">
      <j1 rule="para" parents="17984 9364"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y / (z * ((u \ w) \ w))) = K(x,(z * ((u \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(17984(a,1),14439(a,1,1))].">
      <j1 rule="para" parents="17984 14439"/>
    </justification>
  </clause>

  <clause id="18013">
    <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(17984(a,2),17385(a,1))].">
      <j1 rule="para" parents="17984 17385"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y \ (T(z,w) * u)) = K(x,(T(z,w) * u) / y)
    ]]></literal>
    <justification jstring="[para(17985(a,1),9355(a,1,1))].">
      <j1 rule="para" parents="17985 9355"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ w)) = v5
    ]]></literal>
    <justification jstring="[para(17985(a,2),17521(a,1))].">
      <j1 rule="para" parents="17985 17521"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * w) * K(x,K(w,z * y)) = K(x,w * (y / T(z,u)))
    ]]></literal>
    <justification jstring="[para(17985(a,1),17591(a,1,2))].">
      <j1 rule="para" parents="17985 17591"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,17993,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 17993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(17553,a,18018,a)].">
      <j1 rule="hyper" parents="17553 18018"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(17534,a,18018,a)].">
      <j1 rule="hyper" parents="17534 18018"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      T(x,K(y,z * T(u,w))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(2219(a,1),18018(a,1,2,2))].">
      <j1 rule="para" parents="2219 18018"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(5859(a,1),18018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5859 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      T(x,K(y,((z \ u) \ u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(6391(a,2),18018(a,1,2,2))].">
      <j1 rule="para" parents="6391 18018"/>
    </justification>
  </clause>

  <clause id="18024">
    <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(18018(a,1),16700(a,1,2,1,2))].">
      <j1 rule="para" parents="18018 16700"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z \ K(u,w))) = T(x,(z \ K(u,w)) * y)
    ]]></literal>
    <justification jstring="[para(18018(a,1),17537(a,1,1))].">
      <j1 rule="para" parents="18018 17537"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      T(T(x,K(y,z)),(K(u,w) / z) * y) = T(x,y * (K(u,w) / z))
    ]]></literal>
    <justification jstring="[para(18018(a,1),17715(a,1,1))].">
      <j1 rule="para" parents="18018 17715"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      T(T(x,K(y,z)),(K(u,w) * z) / y) = T(x,y \ (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(18019(a,1),9563(a,1,1))].">
      <j1 rule="para" parents="18019 9563"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = K(y,K(w,x)) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,8614,a,b,18020,a),flip(a)].">
      <j1 rule="hyper" parents="370 8614 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17845,a(flip),b,18007,a),flip(a)].">
      <j1 rule="hyper" parents="60 17845 18007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) = K(x,K(y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),18010(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 18010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,T(z,v5) * u)) = w
    ]]></literal>
    <justification jstring="[para(18010(a,1),17385(a,1))].">
      <j1 rule="para" parents="18010 17385"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      T(T(x,y \ T(z,u)),K(w,y * z)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(17533,a,18021,a),flip(a)].">
      <j1 rule="hyper" parents="17533 18021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ T(z,w))) = T(x,(u \ T(z,w)) \ y)
    ]]></literal>
    <justification jstring="[para(18022(a,1),17543(a,1,1))].">
      <j1 rule="para" parents="18022 17543"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      T(x,K(y,K(z,u) \ w)) = K(w,K(y,x)) \ x
    ]]></literal>
    <justification jstring="[para(8630(a,1),18028(a,2,1))].">
      <j1 rule="para" parents="8630 18028"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8730,a,18034,a)].">
      <j1 rule="hyper" parents="8730 18034"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * K(u,w)) = T(x * K(u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(18035(a,1),17370(a,1,1))].">
      <j1 rule="para" parents="18035 17370"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,T(y,z * ((u / w) \ v5))) = K(x,T(y,z * ((w \ u) \ v5)))
    ]]></literal>
    <justification jstring="[para(8210(a,1),17956(a,1,2,2,2))].">
      <j1 rule="para" parents="8210 17956"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8927,a,17962,a)].">
      <j1 rule="hyper" parents="8927 17962"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,(1 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(17379,a,17989,a)].">
      <j1 rule="hyper" parents="17379 17989"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,K(y,z * (K(u,w) * v5))) = K(x,K(y,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17282,a,b,17989,a),flip(a)].">
      <j1 rule="hyper" parents="370 17282 17989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,x / (z * (w / u))) = K(y,(z * (w / u)) \ x)
    ]]></literal>
    <justification jstring="[para(17994(a,1),9363(a,1,1))].">
      <j1 rule="para" parents="17994 9363"/>
    </justification>
  </clause>

  <clause id="18049">
    <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(17996(a,2),9519(a,1,1))].">
      <j1 rule="para" parents="17996 9519"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(8564(a,1),17998(a,1,2,2,1))].">
      <j1 rule="para" parents="8564 17998"/>
    </justification>
  </clause>

  <clause id="18052">
    <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(17998(a,2),17385(a,1))].">
      <j1 rule="para" parents="17998 17385"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(9472,a,17999,a)].">
      <j1 rule="hyper" parents="9472 17999"/>
    </justification>
  </clause>

  <clause id="18054">
    <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(60,a,11390,a(flip),b,18009,a),flip(a)].">
      <j1 rule="hyper" parents="60 11390 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ ((z \ w) \ w))) = T(x,(u \ ((z \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[para(18023(a,1),17543(a,1,1))].">
      <j1 rule="para" parents="18023 17543"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ v5))) = K(x,K(z / y,(v5 / w) * u))
    ]]></literal>
    <justification jstring="[para(8215(a,1),18030(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8215 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(15605(a,1),18044(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15605 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      K(x,K(y,z * (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * v5)) = v6
    ]]></literal>
    <justification jstring="[para(18044(a,2),17385(a,1))].">
      <j1 rule="para" parents="18044 17385"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9429,a,b,18053,a)].">
      <j1 rule="hyper" parents="370 9429 18053"/>
    </justification>
  </clause>

  <clause id="18060">
    <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(18053(a,1),9472(a,1))].">
      <j1 rule="para" parents="18053 9472"/>
    </justification>
  </clause>

  <clause id="18061">
    <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(18053(a,2),9472(a,1))].">
      <j1 rule="para" parents="18053 9472"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17844,a(flip),b,18059,a),flip(a)].">
      <j1 rule="hyper" parents="370 17844 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <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(1400(a,1),18059(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1400 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w / (u * z))) = v5
    ]]></literal>
    <justification jstring="[para(18059(a,1),9472(a,1))].">
      <j1 rule="para" parents="18059 9472"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,T(y,z)) / (z * K(u,w)) = (K(w,u) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15467,a,17959,a)].">
      <j1 rule="hyper" parents="15467 17959"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15466,a,17959,a)].">
      <j1 rule="hyper" parents="15466 17959"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15522,a,b,18066,a)].">
      <j1 rule="hyper" parents="60 15522 18066"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5434(a,1),17965(a,1,1))].">
      <j1 rule="para" parents="5434 17965"/>
    </justification>
  </clause>

  <clause id="18069">
    <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(370,a,9524,a,b,18002,a),flip(a)].">
      <j1 rule="hyper" parents="370 9524 18002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[para(7997(a,1),18006(a,1,2,2,1))].">
      <j1 rule="para" parents="7997 18006"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8686,a,18036,a),flip(a)].">
      <j1 rule="hyper" parents="8686 18036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6996,a,18072,a),flip(a)].">
      <j1 rule="hyper" parents="6996 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,17373,a(flip),b,18043,a),flip(a)].">
      <j1 rule="hyper" parents="370 17373 18043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(9472,a,18082,a)].">
      <j1 rule="hyper" parents="9472 18082"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(6130(a,1),18082(a,1,2,2,1))].">
      <j1 rule="para" parents="6130 18082"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(8801(a,1),18083(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8801 18083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(9765(a,1),18083(a,1,2,2,2))].">
      <j1 rule="para" parents="9765 18083"/>
    </justification>
  </clause>

  <clause id="18089">
    <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(18086(a,1),17571(a,1,1))].">
      <j1 rule="para" parents="18086 17571"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18053,a(flip),b,18085,a)].">
      <j1 rule="hyper" parents="60 18053 18085"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(109(a,1),18090(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 18090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K(x * y,T(x,z)) / ((z * (x \ R(x,y,x))) / K(x * y,x)) = ((z * (x \ R(x,y,x))) / (K(x,y) * z)) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(17969(a,1),11732(a,1,1))].">
      <j1 rule="para" parents="17969 11732"/>
    </justification>
  </clause>

  <clause id="18094">
    <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(60,a,16119,a(flip),b,18029,a)].">
      <j1 rule="hyper" parents="60 16119 18029"/>
    </justification>
  </clause>

  <clause id="18095">
    <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(8723(a,1),18029(a,1,2,1))].">
      <j1 rule="para" parents="8723 18029"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,K(y,(z / T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * (z / u))) = v6
    ]]></literal>
    <justification jstring="[para(5855(a,1),18052(a,1,2,2,1))].">
      <j1 rule="para" parents="5855 18052"/>
    </justification>
  </clause>

  <clause id="18097">
    <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(5232(a,1),18058(a,1,2,2,2))].">
      <j1 rule="para" parents="5232 18058"/>
    </justification>
  </clause>

  <clause id="18098">
    <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(7481(a,1),18058(a,1,2,2,2))].">
      <j1 rule="para" parents="7481 18058"/>
    </justification>
  </clause>

  <clause id="18100">
    <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(7867(a,1),18058(a,1,2,2))].">
      <j1 rule="para" parents="7867 18058"/>
    </justification>
  </clause>

  <clause id="18101">
    <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(12078(a,1),18058(a,1,2,2))].">
      <j1 rule="para" parents="12078 18058"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(y \ K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(8700(a,1),18025(a,1,1))].">
      <j1 rule="para" parents="8700 18025"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (K(u,w) / y)) = T(x,(K(u,w) / y) * z)
    ]]></literal>
    <justification jstring="[para(6224(a,1),18026(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6224 18026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z \ T(u,w)) = T(x,T(z \ T(u,w),y))
    ]]></literal>
    <justification jstring="[hyper(1146,a,18032,a)].">
      <j1 rule="hyper" parents="1146 18032"/>
    </justification>
  </clause>

  <clause id="18106">
    <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(1245(a,1),18051(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1245 18051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[para(77(a,1),18057(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 18057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(15619,a,18068,a),flip(a)].">
      <j1 rule="hyper" parents="15619 18068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,18067,a(flip),b,18108,a),flip(a)].">
      <j1 rule="hyper" parents="60 18067 18108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18110">
    <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(18109(a,2),11914(a,2,2))].">
      <j1 rule="para" parents="18109 11914"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(370,a,9429,a,b,18087,a),flip(a)].">
      <j1 rule="hyper" parents="370 9429 18087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(y * K(w,u)) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,17840,a,b,18102,a),flip(a)].">
      <j1 rule="hyper" parents="370 17840 18102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,(K(u,w) / y) * z)
    ]]></literal>
    <justification jstring="[hyper(17762,a,18103,a)].">
      <j1 rule="hyper" parents="17762 18103"/>
    </justification>
  </clause>

  <clause id="18114">
    <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(17541(a,1),18104(a,1,1))].">
      <j1 rule="para" parents="17541 18104"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,((v6 / (v6 / z)) / u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18107(a,1),17385(a,1))].">
      <j1 rule="para" parents="18107 17385"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(18060,a,18111,a)].">
      <j1 rule="hyper" parents="18060 18111"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / (y * K(u,w))) = T(x,(y * K(u,w)) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17838,a,b,18112,a)].">
      <j1 rule="hyper" parents="60 17838 18112"/>
    </justification>
  </clause>

  <clause id="18118">
    <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(8706(a,1),18114(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8706 18114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(18116(a,2),18060(a,1))].">
      <j1 rule="para" parents="18116 18060"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(37,a,9563,a,b,18117,a)].">
      <j1 rule="hyper" parents="37 9563 18117"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(y,w)),w * (y \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(18117(a,1),17839(a,1))].">
      <j1 rule="para" parents="18117 17839"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y * K(u,w))) = T(x,(y * K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(18120(a,1),12569(a,1,1))].">
      <j1 rule="para" parents="18120 12569"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,x \ (u * (u * y))) = K(z,y / (u \ (u \ x)))
    ]]></literal>
    <justification jstring="[para(16589(a,1),17913(a,1,2))].">
      <j1 rule="para" parents="16589 17913"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      x * T(T(K(y,z * z) * u,x),w) = T(u,w) * (x * K(y,z * z))
    ]]></literal>
    <justification jstring="[para(17924(a,2),17925(a,1,2,1))].">
      <j1 rule="para" parents="17924 17925"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y * z,y) \ u)) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16767,a(flip),b,17935,a),flip(a)].">
      <j1 rule="hyper" parents="370 16767 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,(y * (y * z)) / u) = K(x,z / (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17912,a(flip),b,18123,a)].">
      <j1 rule="hyper" parents="60 17912 18123"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x,(y * (y * z)) / (y * u)) = K(x,z / (y \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),18127(a,2,2,2,2))].">
      <j1 rule="para" parents="4 18127"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ u)) = K(x,(y * z) / (y * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),18128(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      K(x,K(y * z,y * u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9355,a,b,18129,a)].">
      <j1 rule="hyper" parents="370 9355 18129"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,(y \ ((1 / y) * z)) / (y \ u)) = K(x,((y \ 1) * (y * z)) / (y * u))
    ]]></literal>
    <justification jstring="[para(951(a,2),18129(a,2,2,1))].">
      <j1 rule="para" parents="951 18129"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      T(K(x,y * y) * z,u) * w = T(z,u) * (w * K(x,y * y))
    ]]></literal>
    <justification jstring="[hyper(488,a,18124,a)].">
      <j1 rule="hyper" parents="488 18124"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      K(x * (y * (z * K(u,z))),w) = K(x * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,17411,a(flip),b,17366,a),flip(a)].">
      <j1 rule="hyper" parents="60 17411 17366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,z))),w) = K((x \ 1) * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(15221,a,18133,a)].">
      <j1 rule="hyper" parents="15221 18133"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      K(x \ (y * (z * K(u,z))),w) = K(x \ (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,15208,a(flip),b,18134,a),flip(a)].">
      <j1 rule="hyper" parents="370 15208 18134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      K(x \ (y * T(z,z \ u)),w) = K(x \ (y * (u / (u / z))),w)
    ]]></literal>
    <justification jstring="[para(5683(a,2),18135(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5683 18135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      K(x * (y * z),T(u,y * z)) = K(T(z * y,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(17610,a,16876,a),flip(a)].">
      <j1 rule="hyper" parents="17610 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      K(T(x * y,y) * z,u) = K((y * x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(12579,a,18138,a),flip(a)].">
      <j1 rule="hyper" parents="12579 18138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) * a(w,v5,K((z * y) * u,x)) = K(x,L(T(y * z,z) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(18139(a,1),12932(a,1,2,3))].">
      <j1 rule="para" parents="18139 12932"/>
    </justification>
  </clause>

  <clause id="18142">
    <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(10521(a,1),17616(a,1))].">
      <j1 rule="para" parents="10521 17616"/>
    </justification>
  </clause>

  <clause id="18143">
    <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(12987(a,1),18142(a,1))].">
      <j1 rule="para" parents="12987 18142"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * (u * (z \ y))) = T(x,y * ((u * u) / z))
    ]]></literal>
    <justification jstring="[hyper(17871,a,15648,a),flip(a)].">
      <j1 rule="hyper" parents="17871 15648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(16102(a,1),17910(a,1))].">
      <j1 rule="para" parents="16102 17910"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,y / ((1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(15591(a,1),18146(a,1))].">
      <j1 rule="para" parents="15591 18146"/>
    </justification>
  </clause>

  <clause id="18148">
    <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(6291(a,1),17307(a,1,1,1))].">
      <j1 rule="para" parents="6291 17307"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,u) \ z,w)) = v5
    ]]></literal>
    <justification jstring="[para(17448(a,2),9814(a,1))].">
      <j1 rule="para" parents="17448 9814"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9813,a(flip),b,17460,a),flip(a)].">
      <j1 rule="hyper" parents="370 9813 17460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) = K(z,K(u,y / x))
    ]]></literal>
    <justification jstring="[hyper(370,a,13676,a(flip),b,17520,a),flip(a)].">
      <j1 rule="hyper" parents="370 13676 17520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K((x / (y \ 1)) * T((x / (1 / y)) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(u,x * y)) = w
    ]]></literal>
    <justification jstring="[para(18152(a,2),17559(a,1))].">
      <j1 rule="para" parents="18152 17559"/>
    </justification>
  </clause>

  <clause id="18154">
    <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(17528(a,1),17540(a,1,2))].">
      <j1 rule="para" parents="17528 17540"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) * K(x * y,z) = T(x,u) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9106(a,1),17568(a,1,1,1))].">
      <j1 rule="para" parents="9106 17568"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      T(x,T(y,z)) * K(x * y,z) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(8588(a,1),18155(a,1,1))].">
      <j1 rule="para" parents="8588 18155"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      T(K(x * y,z) * y,T(x,y)) = T(y,T(x,z)) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,13230,a,b,18156,a)].">
      <j1 rule="hyper" parents="370 13230 18156"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      K(x,T(y,z)) * (x * K(x * y,z)) = T(K(y * x,z) * x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,7864,a,b,18157,a)].">
      <j1 rule="hyper" parents="370 7864 18157"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y * x,z) * x) = T(K(y * x,z) * x,T(y,x))
    ]]></literal>
    <justification jstring="[para(12586(a,2),18158(a,1,2))].">
      <j1 rule="para" parents="12586 18158"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,12585,a,b,18159,a)].">
      <j1 rule="hyper" parents="32 12585 18159"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      K(x,((y \ 1) * z) * u) * K(x,K(u,y * z)) = K(x,u * ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[para(17508(a,1),17595(a,1,2))].">
      <j1 rule="para" parents="17508 17595"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      K(x,L(y,z / u,(z / u) \ u)) = K(x,L(y,u,(1 / (z / u)) \ u))
    ]]></literal>
    <justification jstring="[para(3388(a,1),17599(a,1,2))].">
      <j1 rule="para" parents="3388 17599"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      K(x,L(y,z \ u,(u / z) \ z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(17598(a,1),18162(a,1,2))].">
      <j1 rule="para" parents="17598 18162"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(w / u,z)) = T(y,K(z,u \ w) * x)
    ]]></literal>
    <justification jstring="[para(17528(a,1),17702(a,1,2,1,2))].">
      <j1 rule="para" parents="17528 17702"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      T(T(x,K(y,z)),u \ (u \ T(y,w))) = T(x,u \ (u \ T(T(y,z),w)))
    ]]></literal>
    <justification jstring="[hyper(15680,a,17759,a),flip(a)].">
      <j1 rule="hyper" parents="15680 17759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(31,a,17850,a,b,17788,a),flip(a)].">
      <j1 rule="hyper" parents="31 17850 17788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      K(x,L(y / T(z / u,z),w,v5)) = K(L(x,w,v5),y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,18166,a)].">
      <j1 rule="hyper" parents="13036 18166"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,y / ((z \ u) \ u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),18166(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="74 18166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,y / T(z,u * z)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5821(a,2),18168(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5821 18168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(x,L(y / T(z / u,z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18167(a,2),13036(a,1))].">
      <j1 rule="para" parents="18167 13036"/>
    </justification>
  </clause>

  <clause id="18171">
    <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(6304,a,17859,a),flip(a)].">
      <j1 rule="hyper" parents="6304 17859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x,(y / L(T(z,u),z,z)) * w) * K(x,K(w,T(z,u) * y)) = K(x,w * (y / T(T(z,u),z \ 1)))
    ]]></literal>
    <justification jstring="[para(1335(a,1),18017(a,1,1,2,1,2))].">
      <j1 rule="para" parents="1335 18017"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x * (K(y,(z / T(u,w)) * v5) * K(y,K(v5,u * z))),v6) = K(K(v5 * (z / T(u,w)),y) * x,v6)
    ]]></literal>
    <justification jstring="[para(18017(a,2),17362(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="18017 17362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18174">
    <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(370,a,18069,a(flip),b,18054,a),flip(a)].">
      <j1 rule="hyper" parents="370 18069 18054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9637,a(flip),b,18174,a),flip(a)].">
      <j1 rule="hyper" parents="370 9637 18174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18005,a,18176,a)].">
      <j1 rule="hyper" parents="18005 18176"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(17600,a,18089,a),flip(a)].">
      <j1 rule="hyper" parents="17600 18089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(5855(a,1),18179(a,1,2,2,1))].">
      <j1 rule="para" parents="5855 18179"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(9711,a,18180,a)].">
      <j1 rule="hyper" parents="9711 18180"/>
    </justification>
  </clause>

  <clause id="18182">
    <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(370,a,11067,a(flip),b,18181,a),flip(a)].">
      <j1 rule="hyper" parents="370 11067 18181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(109(a,1),18181(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 18181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18184">
    <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(18181(a,1),5371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18181 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      K(x,((y \ 1) * (y \ z)) / (y \ u)) = K(x,((y \ 1) * (y * z)) / (y * u))
    ]]></literal>
    <justification jstring="[para(2073(a,1),18131(a,1,2,1))].">
      <j1 rule="para" parents="2073 18131"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K((x * K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(18148,a,xx),flip(a)].">
      <j1 rule="hyper" parents="18148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16782,a,18154,a),flip(a)].">
      <j1 rule="hyper" parents="16782 18154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18188">
    <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(18154(a,1),16782(a,1))].">
      <j1 rule="para" parents="18154 16782"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(K(x,y),((z \ 1) * u) * w) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8605,a(flip),b,18161,a),flip(a)].">
      <j1 rule="hyper" parents="370 8605 18161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18190">
    <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(8019(a,2),18171(a,1,2))].">
      <j1 rule="para" parents="8019 18171"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,(y \ 1) * (y \ (z / (y \ u))))
    ]]></literal>
    <justification jstring="[para(1789(a,1),18185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1789 18185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <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(8090,a,18190,a),flip(a)].">
      <j1 rule="hyper" parents="8090 18190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,T(z / ((1 / y) \ u),y * y))
    ]]></literal>
    <justification jstring="[para(15321(a,2),18191(a,2,2))].">
      <j1 rule="para" parents="15321 18191"/>
    </justification>
  </clause>

  <clause id="18194">
    <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(10412,a,18192,a)].">
      <j1 rule="hyper" parents="10412 18192"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,z / ((1 / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17124,a(flip),b,18193,a),flip(a)].">
      <j1 rule="hyper" parents="370 17124 18193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) / (y * u)) = K(x,z / ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,6173,a(flip),b,18195,a),flip(a)].">
      <j1 rule="hyper" parents="370 6173 18195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / (y * u)) = K(x,z / ((y \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(951(a,1),18197(a,1,2,1))].">
      <j1 rule="para" parents="951 18197"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      K(x,L(y,z,z) / (z * u)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9947,a(flip),b,18198,a)].">
      <j1 rule="hyper" parents="60 9947 18198"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      T(K(x,y) * z,u * u) = K(x,y) * T(z,u * u)
    ]]></literal>
    <justification jstring="[para(614(a,1),17142(a,1,1,1,2))].">
      <j1 rule="para" parents="614 17142"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(L(K(x,y) \ 1,z,u),w * w)
    ]]></literal>
    <justification jstring="[para(3853(a,2),18200(a,1,1))].">
      <j1 rule="para" parents="3853 18200"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      T(K(x,y) * T(z,u),w * w) = K(x,y) * T(z,w * (w * u))
    ]]></literal>
    <justification jstring="[para(15429(a,1),18200(a,2,2))].">
      <j1 rule="para" parents="15429 18200"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),w * w) = K(z,u) * T(K(x,y),w * w)
    ]]></literal>
    <justification jstring="[para(17218(a,1),18200(a,1,1))].">
      <j1 rule="para" parents="17218 18200"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      (((x * x) * y) / (x * x)) / (((x * x) * (y * K(K(z,u) * T(w,v5),y))) / (x * x)) = K(y,K(z,u) * T(w,x * (x * v5)))
    ]]></literal>
    <justification jstring="[para(18203(a,1),9748(a,2,2))].">
      <j1 rule="para" parents="18203 9748"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),w * w) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17129(a,1),18204(a,2,2))].">
      <j1 rule="para" parents="17129 18204"/>
    </justification>
  </clause>

  <clause id="18209">
    <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(17742(a,1),17613(a,2,2,1))].">
      <j1 rule="para" parents="17742 17613"/>
    </justification>
  </clause>

  <clause id="18210">
    <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(370,a,7935,a(flip),b,17892,a),flip(a)].">
      <j1 rule="hyper" parents="370 7935 17892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) = T(K(y * x,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(8243,a,18210,a),flip(a)].">
      <j1 rule="hyper" parents="8243 18210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) = K(y * x,z) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,17244,a(flip),b,18211,a),flip(a)].">
      <j1 rule="hyper" parents="60 17244 18211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) \ T(y,T(x,z)) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(18213(a,2),12818(a,1,1))].">
      <j1 rule="para" parents="18213 12818"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      T(x * K(x * y,z),y) \ T(x,T(y,z)) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(12586(a,1),18214(a,1,1,1))].">
      <j1 rule="para" parents="12586 18214"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      T(x * K(x * ((y * z) \ z),y),(y * z) \ z) \ T(x,T((y * z) \ z,T(y,u))) = K(y,x * ((y * z) \ z))
    ]]></literal>
    <justification jstring="[para(6893(a,2),18215(a,1,2,2))].">
      <j1 rule="para" parents="6893 18215"/>
    </justification>
  </clause>

  <clause id="18218">
    <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(17896,a,14658,a)].">
      <j1 rule="hyper" parents="17896 14658"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x * T(y,z),x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(31,a,17391,a,b,18218,a)].">
      <j1 rule="hyper" parents="31 17391 18218"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(18219(a,1),5767(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18219 5767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8086,a,18220,a)].">
      <j1 rule="hyper" parents="8086 18220"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12577,a,18222,a)].">
      <j1 rule="hyper" parents="12577 18222"/>
    </justification>
  </clause>

  <clause id="18224">
    <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(9277(a,1),17328(a,1,2))].">
      <j1 rule="para" parents="9277 17328"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      T(x,K(y \ z,y) * (u / (y \ T(z,w)))) = T(x,u / T(y \ T(z,w),y))
    ]]></literal>
    <justification jstring="[hyper(17744,a,17446,a)].">
      <j1 rule="hyper" parents="17744 17446"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ T(y,w)))) = T(x,u / T(z \ T(y,w),z))
    ]]></literal>
    <justification jstring="[hyper(16897,a,18225,a)].">
      <j1 rule="hyper" parents="16897 18225"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ T(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (T(y,w) / z)) = v5
    ]]></literal>
    <justification jstring="[para(18226(a,2),17495(a,1))].">
      <j1 rule="para" parents="18226 17495"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * w) = w \ T(x * T(w,K(u,y)),K(u,y))
    ]]></literal>
    <justification jstring="[para(17554(a,1),17557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17554 17557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,16700,a(flip),b,18229,a),flip(a)].">
      <j1 rule="hyper" parents="370 16700 18229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6468(a,1),18230(a,1,2,1))].">
      <j1 rule="para" parents="6468 18230"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[para(15131(a,1),18230(a,1,2,1))].">
      <j1 rule="para" parents="15131 18230"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      T(x,K(y * z,y \ 1) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14433,a(flip),b,18232,a),flip(a)].">
      <j1 rule="hyper" parents="370 14433 18232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(4(a,1),18233(a,1,2,1,2,2))].">
      <j1 rule="para" parents="4 18233"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,K(z,z) * u)
    ]]></literal>
    <justification jstring="[para(15668(a,1),18233(a,1,2,1))].">
      <j1 rule="para" parents="15668 18233"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,1 * u)
    ]]></literal>
    <justification jstring="[para(193(a,1),18236(a,2,2,1))].">
      <j1 rule="para" parents="193 18236"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(2(a,1),18237(a,2,2))].">
      <j1 rule="para" parents="2 18237"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      T(x,y * (z / (u * u))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(17298,a,18238,a)].">
      <j1 rule="hyper" parents="17298 18238"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      T(x,T(y,z * z) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(16777,a,18238,a)].">
      <j1 rule="hyper" parents="16777 18238"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(16776,a,18238,a)].">
      <j1 rule="hyper" parents="16776 18238"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17395,a(flip),b,18238,a)].">
      <j1 rule="hyper" parents="60 17395 18238"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      T(x,y * (K(z * z,u) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(12016(a,1),18238(a,1,2))].">
      <j1 rule="para" parents="12016 18238"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(18238(a,1),16722(a,1))].">
      <j1 rule="para" parents="18238 16722"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      T(x,T(y * (z * z),z)) = T(x,(z * y) * z)
    ]]></literal>
    <justification jstring="[hyper(15415,a,18242,a)].">
      <j1 rule="hyper" parents="15415 18242"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[para(1452(a,1),18242(a,1,2))].">
      <j1 rule="para" parents="1452 18242"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * w) = T(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(15540(a,1),18242(a,1,2,1))].">
      <j1 rule="para" parents="15540 18242"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      T(x,y * T(z,u * (u * w))) = T(x,y * T(z,w))
    ]]></literal>
    <justification jstring="[para(15429(a,1),18243(a,1,2,2))].">
      <j1 rule="para" parents="15429 18243"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      T(x,y * K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(8758(a,1),18245(a,1,2))].">
      <j1 rule="para" parents="8758 18245"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      T(x,K(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(15766(a,1),18245(a,1,2,1))].">
      <j1 rule="para" parents="15766 18245"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(16714(a,1),18245(a,1))].">
      <j1 rule="para" parents="16714 18245"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(17395(a,1),18245(a,1))].">
      <j1 rule="para" parents="17395 18245"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,17822,a(flip),b,18244,a)].">
      <j1 rule="hyper" parents="60 17822 18244"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      T(x,y * (z * K(u,w * w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8801(a,1),18244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8801 18244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      T(x,T(y * (z * z),z)) = T(x,z * (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14333,a(flip),b,18246,a),flip(a)].">
      <j1 rule="hyper" parents="370 14333 18246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      T(x,y * (z * T(u,w * w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(2219(a,1),18256(a,1,2,2))].">
      <j1 rule="para" parents="2219 18256"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,v5 * v5)))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(6930(a,1),18256(a,1,2,2))].">
      <j1 rule="para" parents="6930 18256"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      T(x,T(1 / y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = w
    ]]></literal>
    <justification jstring="[para(550(a,1),18252(a,1,2,1))].">
      <j1 rule="para" parents="550 18252"/>
    </justification>
  </clause>

  <clause id="18261">
    <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(15540(a,1),18252(a,1,2,1))].">
      <j1 rule="para" parents="15540 18252"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      T(x,y * ((z * z) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ (z * z))) = w
    ]]></literal>
    <justification jstring="[para(16799(a,1),18254(a,1))].">
      <j1 rule="para" parents="16799 18254"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,w * K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17197,a(flip),b,18235,a),flip(a)].">
      <j1 rule="hyper" parents="370 17197 18235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      x / T(x,K(y,z * u) * w) = K(K(y,z \ u) * w,x)
    ]]></literal>
    <justification jstring="[para(18235(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18235 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18265">
    <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(18235(a,2),17210(a,1))].">
      <j1 rule="para" parents="18235 17210"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      T(x,y * (z * (u \ (u \ 1)))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[para(603(a,2),18240(a,1,2,2))].">
      <j1 rule="para" parents="603 18240"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u / y))) = T(x,z \ (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(16888,a,18247,a),flip(a)].">
      <j1 rule="hyper" parents="16888 18247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(15567,a,18247,a)].">
      <j1 rule="hyper" parents="15567 18247"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      T(x,T(y,z \ u) * w) = T(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(15538(a,1),18248(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15538 18248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      T(x,y * T(z,u \ w)) = T(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18249(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(67(a,1),18249(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="67 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      T(x,y * (T(z,u \ (u \ 1)) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(15252(a,1),18255(a,1,2,2,1))].">
      <j1 rule="para" parents="15252 18255"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      T(x,y * T(z * ((u * u) \ w),u * u)) = T(x,y * (((u * u) \ z) * w))
    ]]></literal>
    <justification jstring="[para(1447(a,2),18258(a,1,2,2))].">
      <j1 rule="para" parents="1447 18258"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(17210,a,18263,a)].">
      <j1 rule="hyper" parents="17210 18263"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u * w)) = T(x,T(y,u \ w) \ z)
    ]]></literal>
    <justification jstring="[hyper(16775,a,18263,a),flip(a)].">
      <j1 rule="hyper" parents="16775 18263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,15695,a,b,18268,a)].">
      <j1 rule="hyper" parents="60 15695 18268"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(18268(a,1),15672(a,1,1))].">
      <j1 rule="para" parents="18268 15672"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      T(x,(y \ 1) * T(z,u * w)) = T(x,y \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18270,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      x \ T(x,y * T(z,u * w)) = K(x,y * T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(125,a,18270,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 18270 5256"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      x \ T(x,y * K(z,u * w)) = K(x,y * K(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(125,a,18274,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 18274 5256"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      T(x,(y * (z * u)) * K(L(u,z,y),w * v5)) = T(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(6930(a,1),18274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6930 18274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z * K(u,w * v5)) = T(x,T(z * K(u,w \ v5),y))
    ]]></literal>
    <justification jstring="[para(18274(a,1),9813(a,1,2))].">
      <j1 rule="para" parents="18274 9813"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      K(K(x,y \ z) * u,w) = K(K(x,y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(5734,a,18264,a),flip(a)].">
      <j1 rule="hyper" parents="5734 18264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      K(K(x,y \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y * z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(18264(a,1),5734(a,1))].">
      <j1 rule="para" parents="18264 5734"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      K(K(x,y * z) * u,w) = K(u * K(y \ z,x),w)
    ]]></literal>
    <justification jstring="[hyper(17481,a,18283,a),flip(a)].">
      <j1 rule="hyper" parents="17481 18283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      K(K(x,y * (y * z)) * u,w) = K(K(x,z) * u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),18283(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 18283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      K(x * K(y \ z,u),w) = K(x * K(y * z,u),w)
    ]]></literal>
    <justification jstring="[hyper(17481,a,18285,a),flip(a)].">
      <j1 rule="hyper" parents="17481 18285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18288">
    <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(18285(a,1),17481(a,1))].">
      <j1 rule="para" parents="18285 17481"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      K(K(x,y * (z * z)) * u,w) = K(K(x,y) * u,w)
    ]]></literal>
    <justification jstring="[para(15425(a,2),18286(a,1,1,1))].">
      <j1 rule="para" parents="15425 18286"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      (x * K(y,z * K(u * w,v5))) \ x = K(z * K(u \ w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a,b,18287,a)].">
      <j1 rule="hyper" parents="370 6294 18287"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      K(((x / y) \ z) * K(y * x,y),u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17413,a(flip),b,18287,a),flip(a)].">
      <j1 rule="hyper" parents="60 17413 18287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = T(x,y \ (y \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(15720,a,18267,a)].">
      <j1 rule="hyper" parents="15720 18267"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      T(x,y \ (y \ T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(18267(a,1),15720(a,1))].">
      <j1 rule="para" parents="18267 15720"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      T(T(x,K(y,z)),u \ (u \ T(y,w))) = T(x,T(u \ (u \ T(y,z)),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,18165,a,b,18292,a)].">
      <j1 rule="hyper" parents="370 18165 18292"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) \ ((u * u) \ w))) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(1564(a,1),18272(a,1,2,2))].">
      <j1 rule="para" parents="1564 18272"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      T(x,T(y,z \ u) \ w) = T(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(17334,a,18275,a),flip(a)].">
      <j1 rule="hyper" parents="17334 18275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      T(x,T(y,z * u) \ T(w,T(y,z * u))) = T(x,w / T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(17505,a,18296,a),flip(a)].">
      <j1 rule="hyper" parents="17505 18296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      T(x,T(y,y * z) \ u) = T(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16768,a(flip),b,18296,a),flip(a)].">
      <j1 rule="hyper" parents="60 16768 18296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      T(x,T(y,z \ 1) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3(a,1),18296(a,2,2,1,2))].">
      <j1 rule="para" parents="3 18296"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) * (T(z,u \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,u \ w) \ v5) * y) = v6
    ]]></literal>
    <justification jstring="[para(18296(a,1),12637(a,1,2,1))].">
      <j1 rule="para" parents="18296 12637"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14370,a(flip),b,18298,a),flip(a)].">
      <j1 rule="hyper" parents="60 14370 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      T(x,T(y \ z,z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(74(a,1),18301(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="74 18301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      T(x,(y / z) \ T(u,y / z)) = T(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(17501,a,18302,a),flip(a)].">
      <j1 rule="hyper" parents="17501 18302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      T(x,y * (z * (u \ (1 / u)))) = T(x,y * (z * (u \ (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(370,a,18266,a,b,18276,a),flip(a)].">
      <j1 rule="hyper" parents="370 18266 18276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18278,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      T(x,(y \ z) \ T(u,y * z)) = T(x,u / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(17498,a,18305,a),flip(a)].">
      <j1 rule="hyper" parents="17498 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      x / T(x,y \ T(z,u * w)) = K(y \ T(z,u \ w),x)
    ]]></literal>
    <justification jstring="[para(18305(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18305 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16779,a,18306,a),flip(a)].">
      <j1 rule="hyper" parents="16779 18306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      T(x,T(y,(z / u) * z) / u) = T(x,((z / u) \ z) \ y)
    ]]></literal>
    <justification jstring="[para(77(a,1),18308(a,1,2,2))].">
      <j1 rule="para" parents="77 18308"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      T(x,T(y,z * T(u,z \ 1)) / (u * ((z \ u) / u))) = T(x,(z \ T(u,z \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(6149(a,1),18308(a,1,2,2))].">
      <j1 rule="para" parents="6149 18308"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(5290,a,18279,a),flip(a)].">
      <j1 rule="hyper" parents="5290 18279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      K(L(x,y,z),u * T(w,v5 * v6)) = K(x,L(u * T(w,v5 \ v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,18311,a),flip(a)].">
      <j1 rule="hyper" parents="13036 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      K(x,((y * z) \ (y * y)) * T(u,z * y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16113,a(flip),b,18311,a),flip(a)].">
      <j1 rule="hyper" parents="60 16113 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18314">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),18311(a,2,2,2,2))].">
      <j1 rule="para" parents="3 18311"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      K(x,y * T(z,u * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(227(a,1),18311(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="227 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),18311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      (x * K(y,z * T(u,w * v5))) \ x = K(z * T(u,w \ v5),y)
    ]]></literal>
    <justification jstring="[para(18311(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18311 6294"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      K(x,y * (z / (u * u))) = K(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17795,a(flip),b,18315,a)].">
      <j1 rule="hyper" parents="60 17795 18315"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      K(x,y * ((z * z) * u)) = K(x,y * (u * (z * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14423,a(flip),b,18315,a),flip(a)].">
      <j1 rule="hyper" parents="60 14423 18315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17795,a(flip),b,18314,a),flip(a)].">
      <j1 rule="hyper" parents="60 17795 18314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      K(x,y * ((z * z) * (u \ 1))) = K(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(519(a,1),18319(a,2,2,2))].">
      <j1 rule="para" parents="519 18319"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(5290,a,18280,a),flip(a)].">
      <j1 rule="hyper" parents="5290 18280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17626,a,18322,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17626 18322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      K(x,y * K(z * u,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(5690(a,1),18323(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5690 18323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      K(K(x,y) * ((y / x) \ z),u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17408,a(flip),b,18291,a)].">
      <j1 rule="hyper" parents="60 17408 18291"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      T(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(18303(a,1),17498(a,1))].">
      <j1 rule="para" parents="18303 17498"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      K(x \ T(y,z \ u),w) = K(x \ T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(5734,a,18307,a),flip(a)].">
      <j1 rule="hyper" parents="5734 18307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16838,a(flip),b,18327,a),flip(a)].">
      <j1 rule="hyper" parents="60 16838 18327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18329">
    <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(60,a,16571,a(flip),b,18327,a),flip(a)].">
      <j1 rule="hyper" parents="60 16571 18327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(227(a,1),18327(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="227 18327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) = K(T(y,x) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14378,a,b,18330,a),flip(a)].">
      <j1 rule="hyper" parents="370 14378 18330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(x \ T((y \ 1) * z,u * u),w) = K(x \ ((1 / y) * z),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,6197,a,b,18330,a),flip(a)].">
      <j1 rule="hyper" parents="370 6197 18330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K(x \ ((y \ 1) * (y \ z)),u) = K(y \ (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17928,a(flip),b,18330,a),flip(a)].">
      <j1 rule="hyper" parents="60 17928 18330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      K(x \ T(y,z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,u) = w
    ]]></literal>
    <justification jstring="[para(18331(a,2),14404(a,1))].">
      <j1 rule="para" parents="18331 14404"/>
    </justification>
  </clause>

  <clause id="18335">
    <literal><![CDATA[
      K(x \ (y / (y / z)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14397,a(flip),b,18328,a),flip(a)].">
      <j1 rule="hyper" parents="60 14397 18328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      K((x \ y) \ T(z,u),L(w,y,x)) = K(y \ (x * (u / (u / z))),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,18335,a),flip(a)].">
      <j1 rule="hyper" parents="60 15933 18335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      K(x \ T(y \ z,z),u) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[para(74(a,1),18335(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 18335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      T(x,T(y,z * (u \ z)) / u) = T(x,((z / u) \ z) \ y)
    ]]></literal>
    <justification jstring="[para(14500(a,1),18309(a,1,2,1))].">
      <j1 rule="para" parents="14500 18309"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) = K(x,(y \ 1) * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,18320,a)].">
      <j1 rule="hyper" parents="15233 18320"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      K(x,y / (z * (u / (w * w)))) = K(x,y * ((z * u) \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(15487,a,18321,a)].">
      <j1 rule="hyper" parents="15487 18321"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K(((x \ 1) \ y) \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16575,a(flip),b,18333,a),flip(a)].">
      <j1 rule="hyper" parents="60 16575 18333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K((x * y) \ ((1 / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13008,a(flip),b,18333,a),flip(a)].">
      <j1 rule="hyper" parents="60 13008 18333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      K(x \ (x \ (y \ (x * z))),u) = K(y \ ((x \ 1) * z),u)
    ]]></literal>
    <justification jstring="[para(4(a,1),18333(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 18333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      T(x,T(y,z * (u \ z)) / u) = T(x,u \ y)
    ]]></literal>
    <justification jstring="[para(77(a,1),18338(a,2,2,1))].">
      <j1 rule="para" parents="77 18338"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z / u)) = T(x,(z / u) \ y)
    ]]></literal>
    <justification jstring="[para(77(a,1),18345(a,1,2,1,2,2))].">
      <j1 rule="para" parents="77 18345"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * (u * (z \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ (u * u))) = w
    ]]></literal>
    <justification jstring="[para(18145(a,2),18262(a,1))].">
      <j1 rule="para" parents="18145 18262"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      K(K(x,y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x,z * y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(17752(a,2),18284(a,1))].">
      <j1 rule="para" parents="17752 18284"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      K(K(x,y * z) * (u * (x * (z / y))),w) = K(u * ((z / y) * x),w)
    ]]></literal>
    <justification jstring="[hyper(18348,a,17414,a)].">
      <j1 rule="hyper" parents="18348 17414"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (w * (u * u))))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(953(a,2),18259(a,1,2,2,2))].">
      <j1 rule="para" parents="953 18259"/>
    </justification>
  </clause>

  <clause id="18351">
    <literal><![CDATA[
      x * K(x,y * K(z * u,w)) = T(x,y * K(z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,5699,a(flip),b,18290,a),flip(a)].">
      <j1 rule="hyper" parents="36 5699 18290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,18351,a)].">
      <j1 rule="hyper" parents="31 5256 18351"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17235,a,b,18352,a)].">
      <j1 rule="hyper" parents="370 17235 18352"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(17(a,2),18352(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      K(x,y * K((z * (u * u)) \ w,v5)) = K(x,y * K(z * ((u * u) * w),v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),18352(a,2,2,2,1))].">
      <j1 rule="para" parents="29 18352"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      K(x,y * K((z / u) * z,w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[para(77(a,1),18352(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      K(x,y * K((z * u) * (z * ((z \ 1) \ w)),v5)) = K(x,y * K(((z \ 1) * u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(1512(a,1),18352(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1512 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18358">
    <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(12941(a,1),18352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12941 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17235,a,b,18353,a)].">
      <j1 rule="hyper" parents="370 17235 18353"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z * u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18353(a,1),17252(a,1))].">
      <j1 rule="para" parents="18353 17252"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(18353(a,2),17361(a,1))].">
      <j1 rule="para" parents="18353 17361"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      K(x,y * K(z * (z / u),w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(17784,a,18356,a)].">
      <j1 rule="hyper" parents="17784 18356"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      (x * K(y,K(z * u,w) * v5)) \ x = K(K(z \ u,w) * v5,y)
    ]]></literal>
    <justification jstring="[para(18359(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18359 6294"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      K(x,K(y \ z,T(u,z)) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(12578(a,1),18359(a,2,2,1))].">
      <j1 rule="para" parents="12578 18359"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(u,T(w,z)))
    ]]></literal>
    <justification jstring="[para(8024(a,1),18354(a,2,2,2))].">
      <j1 rule="para" parents="8024 18354"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[para(8765(a,1),18364(a,1,2,1))].">
      <j1 rule="para" parents="8765 18364"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z) * w) = K(x,K(z,(y * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16737,a(flip),b,18367,a),flip(a)].">
      <j1 rule="hyper" parents="60 16737 18367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,y * K(z * (u * z),w)) = K(x,y * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17686,a(flip),b,18366,a),flip(a)].">
      <j1 rule="hyper" parents="370 17686 18366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * u))) = K(x,(y \ z) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17453,a(flip),b,18369,a)].">
      <j1 rule="hyper" parents="60 17453 18369"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * u))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17453,a(flip),b,18371,a),flip(a)].">
      <j1 rule="hyper" parents="370 17453 18371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      K(x,y \ T(z,(u \ w) * w)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),18372(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5 18372"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u / w))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[para(14508(a,1),18373(a,1,2,2))].">
      <j1 rule="para" parents="14508 18373"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(18361,a,16730,a)].">
      <j1 rule="hyper" parents="18361 16730"/>
    </justification>
  </clause>

  <clause id="18376">
    <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(16730(a,1),18361(a,1))].">
      <j1 rule="para" parents="16730 18361"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      K(x,K(y,y \ (z \ u)) * w) = K(x,K(y,(z * y) * u) * w)
    ]]></literal>
    <justification jstring="[para(12334(a,1),18375(a,1,2,1))].">
      <j1 rule="para" parents="12334 18375"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * u) * w) = K(x,K(y,u / z) * w)
    ]]></literal>
    <justification jstring="[para(14574(a,1),18375(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14574 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * u,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(18375(a,2),16731(a,1))].">
      <j1 rule="para" parents="18375 16731"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(12605(a,1),18378(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12605 18378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <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(16730(a,1),18379(a,1))].">
      <j1 rule="para" parents="16730 18379"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * (w * (v5 \ (v5 \ 1)))) = T(x,w * (v5 \ (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(17660,a,18304,a),flip(a)].">
      <j1 rule="hyper" parents="17660 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      K(x * T(y,z \ u),w) = K(x * T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(6305,a,18317,a),flip(a)].">
      <j1 rule="hyper" parents="6305 18317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <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(18317(a,1),6305(a,1))].">
      <j1 rule="para" parents="18317 6305"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      K(x * T(y,z * z),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(227(a,1),18383(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="227 18383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      K(x * T((y \ z) * y,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * T(T(z,u),y * z),w) = v5
    ]]></literal>
    <justification jstring="[para(16879(a,1),18384(a,1))].">
      <j1 rule="para" parents="16879 18384"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      K(x \ ((1 / y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((y \ 1) * z),u) = w
    ]]></literal>
    <justification jstring="[para(18332(a,1),18334(a,1))].">
      <j1 rule="para" parents="18332 18334"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      K(x,y \ T((z \ 1) \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(18339(a,2),15233(a,1))].">
      <j1 rule="para" parents="18339 15233"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(K(x * y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(6305,a,18363,a),flip(a)].">
      <j1 rule="hyper" parents="6305 18363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(18363(a,1),6305(a,1))].">
      <j1 rule="para" parents="18363 6305"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(u * K(z,x * y),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17362,a(flip),b,18389,a),flip(a)].">
      <j1 rule="hyper" parents="370 17362 18389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K(x * K(y,z \ u),w) = K(x * K(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(17481,a,18391,a)].">
      <j1 rule="hyper" parents="17481 18391"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      K(x * K(y,z / u),w) = K(x * K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(17785,a,18392,a)].">
      <j1 rule="hyper" parents="17785 18392"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      K(x,K(y,(z * y) * u) * w) = K(x,K(y,z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(16781,a,18377,a),flip(a)].">
      <j1 rule="hyper" parents="16781 18377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      K(x,K(y,(z * y) * u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,18375,a(flip),b,18394,a),flip(a)].">
      <j1 rule="hyper" parents="370 18375 18394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      K(x,K(y,(z * y) / u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18380,a,b,18395,a)].">
      <j1 rule="hyper" parents="60 18380 18395"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z) * w) = K(x,K(z,y * u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18368,a,b,18396,a)].">
      <j1 rule="hyper" parents="60 18368 18396"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      K(x,y * K(z,u * (z \ w))) = K(x,K(z,u * w) * y)
    ]]></literal>
    <justification jstring="[hyper(17484,a,18397,a)].">
      <j1 rule="hyper" parents="17484 18397"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      K(x \ (y * (z / (z / u))),w) = K(x \ (y * T(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,18336,a),flip(a)].">
      <j1 rule="hyper" parents="60 15933 18336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18400">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K((x * y) \ ((x \ 1) * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6197,a(flip),b,18343,a),flip(a)].">
      <j1 rule="hyper" parents="370 6197 18343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / (z \ 1))) = w
    ]]></literal>
    <justification jstring="[para(14462(a,1),18388(a,1))].">
      <j1 rule="para" parents="14462 18388"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(u \ (u \ y),w)) = T(x,T(u \ (u \ T(y,z)),w))
    ]]></literal>
    <justification jstring="[hyper(18293,a,18294,a)].">
      <j1 rule="hyper" parents="18293 18294"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      T(x,y / T(z,u \ w)) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(17498,a,18297,a),flip(a)].">
      <j1 rule="hyper" parents="17498 18297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      T(x,(1 / y) / T(z * y,y * 1)) = T(x,y \ (((y \ 1) \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15610,a,18403,a),flip(a)].">
      <j1 rule="hyper" parents="15610 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17670,a,b,18403,a)].">
      <j1 rule="hyper" parents="60 17670 18403"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      K(x,L(y * T(z,u \ w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * T(z,u * w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18312(a,1),13036(a,1))].">
      <j1 rule="para" parents="18312 13036"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * (1 / y))),u) = K(z * ((1 / y) * x),u)
    ]]></literal>
    <justification jstring="[para(3(a,1),18349(a,1,1,1,2))].">
      <j1 rule="para" parents="3 18349"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      T(x,y * L(z * (u * u),u,u)) = T(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(2074(a,1),18350(a,1,2,2))].">
      <j1 rule="para" parents="2074 18350"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      T(x,T(y,L(z * (u * u),u,u)) * (u * (u * z))) = T(x,L(z * (u * u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12606,a,18408,a),flip(a)].">
      <j1 rule="hyper" parents="12606 18408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      ((x * L(y * (z * z),z,z)) * T(u,w)) / ((x * L(y * (z * z),z,z)) * u) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(18408(a,1),8981(a,2,2))].">
      <j1 rule="para" parents="18408 8981"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      T(x,y * (z \ (z \ K(u,K(w,v5))))) = T(x,y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17895,a(flip),b,18382,a)].">
      <j1 rule="hyper" parents="60 17895 18382"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      T(x,y * (z \ (z \ K(u,K(w,v5))))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15694,a(flip),b,18411,a),flip(a)].">
      <j1 rule="hyper" parents="370 15694 18411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      T(x,y * (z \ (z \ 1))) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[para(193(a,1),18412(a,1,2,2,2,2))].">
      <j1 rule="para" parents="193 18412"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[para(603(a,1),18413(a,1,2))].">
      <j1 rule="para" parents="603 18413"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,y \ (y \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16099,a,b,18414,a)].">
      <j1 rule="hyper" parents="60 16099 18414"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * z) \ z)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[para(1099(a,1),18414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1099 18414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      T(x,(1 / y) * (((y * y) \ z) * y)) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,16817,a(flip),b,18415,a),flip(a)].">
      <j1 rule="hyper" parents="370 16817 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      T(x,T(T(y \ (y \ z),u),w)) = T(x,T(y \ (y \ T(z,u)),w))
    ]]></literal>
    <justification jstring="[hyper(60,a,17760,a(flip),b,18402,a)].">
      <j1 rule="hyper" parents="60 17760 18402"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,(1 / y) / T(z * y,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),18404(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3 18404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      K(x \ (y \ T(z,u \ w)),v5) = K(x \ (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,16571,a(flip),b,18329,a),flip(a)].">
      <j1 rule="hyper" parents="60 16571 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(12941(a,1),18358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12941 18358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(3(a,1),18421(a,2,2,2,2,1))].">
      <j1 rule="para" parents="3 18421"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * (z * K(1,w)))
    ]]></literal>
    <justification jstring="[para(63(a,1),18421(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="63 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(w * v5,u))) = K(x,y * (z / T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(5855(a,1),18421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5855 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w \ v5)) * K(w * v5,u))) = K(x,y * (K(w \ v5,u) * z))
    ]]></literal>
    <justification jstring="[para(6226(a,1),18421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6226 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      (x * K(y,z * (u * K(w * v5,v6)))) \ x = K(z * (u * K(w \ v5,v6)),y)
    ]]></literal>
    <justification jstring="[para(18421(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18421 6294"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w * v5,z))) = K(x,y * (z * (u * K(w \ v5,z))))
    ]]></literal>
    <justification jstring="[para(11028(a,1),18421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11028 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      K(x,y * ((z \ 1) * K(u * w,v5))) = K(x,y * (z \ K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[para(15133(a,1),18421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15133 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,7154,a,b,18422,a)].">
      <j1 rule="hyper" parents="60 7154 18422"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * (z * 1))
    ]]></literal>
    <justification jstring="[para(228(a,1),18423(a,2,2,2,2))].">
      <j1 rule="para" parents="228 18423"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x,y * (z * K(u * u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3(a,1),18430(a,2,2,2))].">
      <j1 rule="para" parents="3 18430"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,y * (K(z * z,u) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(17737,a,18431,a)].">
      <j1 rule="hyper" parents="17737 18431"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      K(x,y * (T(z,u * u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(5859(a,1),18431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5859 18431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      K(x,K(y,z * z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8105(a,1),18431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8105 18431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      K(x,y * K(z * z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(17484,a,18435,a)].">
      <j1 rule="hyper" parents="17484 18435"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      K(x,T(y,z * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16735,a(flip),b,18435,a)].">
      <j1 rule="hyper" parents="60 16735 18435"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,T(y,z * z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14457,a(flip),b,18435,a)].">
      <j1 rule="hyper" parents="60 14457 18435"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6128(a,1),18435(a,1,2))].">
      <j1 rule="para" parents="6128 18435"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      K(x,y / T(z,u * u)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5855(a,1),18436(a,1,2))].">
      <j1 rule="para" parents="5855 18436"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ 1)) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(16999,a,18437,a)].">
      <j1 rule="hyper" parents="16999 18437"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z,y)) \ u) = K(x,(z * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[para(6496(a,1),18437(a,1,2,1))].">
      <j1 rule="para" parents="6496 18437"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) \ w) = K(x,T(y,u) \ w)
    ]]></literal>
    <justification jstring="[para(15429(a,1),18437(a,1,2,1))].">
      <j1 rule="para" parents="15429 18437"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(15429(a,1),18438(a,1,2,1))].">
      <j1 rule="para" parents="15429 18438"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,y \ (((z * z) \ u) * w)) = K(x,y \ (u * (w / (z * z))))
    ]]></literal>
    <justification jstring="[para(1445(a,1),18439(a,1,2,2))].">
      <j1 rule="para" parents="1445 18439"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u * w))) = K(x,y \ T(z,w))
    ]]></literal>
    <justification jstring="[para(15429(a,1),18439(a,1,2,2))].">
      <j1 rule="para" parents="15429 18439"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(18439(a,1),16843(a,1))].">
      <j1 rule="para" parents="18439 16843"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      K(x,y / ((1 / z) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(1337(a,1),18440(a,1,2,2))].">
      <j1 rule="para" parents="1337 18440"/>
    </justification>
  </clause>

  <clause id="18449">
    <literal><![CDATA[
      K(x,y / T(z,u * (u * w))) = K(x,y / T(z,w))
    ]]></literal>
    <justification jstring="[para(15429(a,1),18440(a,1,2,2))].">
      <j1 rule="para" parents="15429 18440"/>
    </justification>
  </clause>

  <clause id="18450">
    <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(15429(a,1),18447(a,1,2,2))].">
      <j1 rule="para" parents="15429 18447"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w * K(u / z,w)))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16868,a(flip),b,18434,a)].">
      <j1 rule="hyper" parents="60 16868 18434"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(5(a,1),18443(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17783,a,18444,a)].">
      <j1 rule="hyper" parents="17783 18444"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),18444(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      K(x,T(y,(z * z) * u) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(15166(a,2),18444(a,1,2,1))].">
      <j1 rule="para" parents="15166 18444"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18446(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(x,y / T(z,u \ w)) = K(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18449(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      K(x,y / T(z,(u / w) * u)) = K(x,y / T(z,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),18449(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 18449"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) \ v6) = K(x,L(T(u,w \ v5) \ v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,18452,a),flip(a)].">
      <j1 rule="hyper" parents="13036 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,T(y,(z * (u * u)) \ w) \ v5) = K(x,T(y,z * ((u * u) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),18452(a,2,2,1,2))].">
      <j1 rule="para" parents="29 18452"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * u) \ w) = K(x,T(y,u / z) \ w)
    ]]></literal>
    <justification jstring="[para(16228(a,1),18452(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16228 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) = K(w,K(y,x)) * K(x,w * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17593,a,b,18453,a),flip(a)].">
      <j1 rule="hyper" parents="370 17593 18453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      K(x,T(y,z * (u * z)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(14333(a,1),18453(a,1,2,1))].">
      <j1 rule="para" parents="14333 18453"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) * v6) = K(x,L(T(u,w \ v5) * v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,18454,a),flip(a)].">
      <j1 rule="hyper" parents="13036 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,18454,a),flip(a)].">
      <j1 rule="hyper" parents="12637 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) \ ((z * z) * w)) * v5) = K(x,T(y,(z * T(u,z * z)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1418(a,1),18454(a,2,2,1,2))].">
      <j1 rule="para" parents="1418 18454"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(18454(a,1),12637(a,1))].">
      <j1 rule="para" parents="18454 12637"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) \ u) * w) * v5) = K(x,T(y,(z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(946(a,1),18455(a,1,2,1,2))].">
      <j1 rule="para" parents="946 18455"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,T(y,T(z,u \ w)) \ T(z,u * w)) = K(x,T(z,u \ w) / y)
    ]]></literal>
    <justification jstring="[hyper(14575,a,18456,a),flip(a)].">
      <j1 rule="hyper" parents="14575 18456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      L(K(x,y \ T(z,u * w)),v5,v6) = K(x,L(y \ T(z,u \ w),v5,v6))
    ]]></literal>
    <justification jstring="[para(18456(a,1),12922(a,1,1))].">
      <j1 rule="para" parents="18456 12922"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17708,a,b,18457,a)].">
      <j1 rule="hyper" parents="60 17708 18457"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      (x * K(y,z / T(u,w * v5))) \ x = K(z / T(u,w \ v5),y)
    ]]></literal>
    <justification jstring="[para(18457(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18457 6294"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * w) = x * K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(129,a,18463,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 18463 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(7(a,1),18463(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,T(y,(z * z) * u) * (z \ ((1 / z) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[para(553(a,1),18465(a,1,2,1,2))].">
      <j1 rule="para" parents="553 18465"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      K(x,y / T((z / u) * w,u * z)) = K(x,y / (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(14645,a,18471,a),flip(a)].">
      <j1 rule="hyper" parents="14645 18471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * ((z / y) \ 1)) \ u) = K(x,(((z / y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5753(a,1),18441(a,1,2,1,1))].">
      <j1 rule="para" parents="5753 18441"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(18442(a,2),6080(a,1))].">
      <j1 rule="para" parents="18442 6080"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18147,a,18448,a)].">
      <j1 rule="hyper" parents="18147 18448"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,T(y,z / u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[para(12600(a,1),18461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12600 18461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      T(x,T(y,z * (u * z)) * w) = T(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,18473,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 18473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      T(x,T(y,z) * (u * (u * z))) = T(x,(u * (u * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,17776,a(flip),b,18481,a),flip(a)].">
      <j1 rule="hyper" parents="60 17776 18481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      T(x,T(y,z / u) * w) = T(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(7(a,1),18481(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(18371(a,1),18450(a,1))].">
      <j1 rule="para" parents="18371 18450"/>
    </justification>
  </clause>

  <clause id="18486">
    <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(14505(a,1),18467(a,1,2,1))].">
      <j1 rule="para" parents="14505 18467"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z \ T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ T(u,w \ v5)) * y) = v6
    ]]></literal>
    <justification jstring="[para(18270(a,1),18467(a,1,2,1))].">
      <j1 rule="para" parents="18270 18467"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5256(a,2),18429(a,2,2,2))].">
      <j1 rule="para" parents="5256 18429"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15472,a,18488,a)].">
      <j1 rule="hyper" parents="15472 18488"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17805,a,18489,a)].">
      <j1 rule="hyper" parents="17805 18489"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(15469,a,18490,a),flip(a)].">
      <j1 rule="hyper" parents="15469 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14504,a,18491,a)].">
      <j1 rule="hyper" parents="14504 18491"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = K(x,z * y) * x
    ]]></literal>
    <justification jstring="[para(18492(a,1),5275(a,2,1))].">
      <j1 rule="para" parents="18492 5275"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,18493,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 18493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18495">
    <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(60,a,16704,a,b,18494,a)].">
      <j1 rule="hyper" parents="60 16704 18494"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      K(x / T(y,z \ u),w) = K(x / T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(6305,a,18472,a),flip(a)].">
      <j1 rule="hyper" parents="6305 18472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <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(18472(a,1),6305(a,1))].">
      <j1 rule="para" parents="18472 6305"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      K(x / L(T(y,z \ u),w,v5),v6) = K(x / T(L(y,w,v5),z * u),v6)
    ]]></literal>
    <justification jstring="[para(20(a,2),18496(a,1,1,2))].">
      <j1 rule="para" parents="20 18496"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      K(x / T(y,z * z),u) = K(x / y,u)
    ]]></literal>
    <justification jstring="[para(227(a,1),18496(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="227 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      K(x / T(y,y * z),u) = K(x / ((y \ z) \ z),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),18496(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="108 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      K(x / ((y * y) * z),u) = K(x / (z * (y * y)),u)
    ]]></literal>
    <justification jstring="[hyper(14652,a,18499,a),flip(a)].">
      <j1 rule="hyper" parents="14652 18499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      K(x / ((y \ 1) * T(z,y)),u) = K(x / (z * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(6496(a,1),18499(a,1,1,2))].">
      <j1 rule="para" parents="6496 18499"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      K(x / (y * (z * z)),u) = K(z \ (z \ (x / y)),u)
    ]]></literal>
    <justification jstring="[hyper(17566,a,18501,a),flip(a)].">
      <j1 rule="hyper" parents="17566 18501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K(x / ((y \ 1) * T(z,y)),u) = K(x / (z * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6205,a(flip),b,18502,a),flip(a)].">
      <j1 rule="hyper" parents="370 6205 18502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      K(x / (y / (y / z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / T(z,z * y),u) = w
    ]]></literal>
    <justification jstring="[para(17575(a,1),18497(a,1))].">
      <j1 rule="para" parents="17575 18497"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * (z / (z / u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,18458,a(flip),b,18476,a)].">
      <j1 rule="hyper" parents="60 18458 18476"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(6289(a,2),18478(a,1,2,1))].">
      <j1 rule="para" parents="6289 18478"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),18508(a,1,2,1,1,1))].">
      <j1 rule="para" parents="109 18508"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,y * (z / T(u,w \ v5))) = K(x,y * (z / T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(5855(a,1),18424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5855 18424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      K(x,y * (z / T(u,u * w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(108(a,1),18510(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 18510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,v5))) = K(x,y * (z \ K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(15133(a,1),18428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15133 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(w,u / z))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16894,a,18451,a)].">
      <j1 rule="hyper" parents="16894 18451"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18459(a,1),13036(a,1))].">
      <j1 rule="para" parents="18459 13036"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) * w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18464(a,1),13036(a,1))].">
      <j1 rule="para" parents="18464 13036"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) * v5) = K(x,T(y,(u \ w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(17783,a,18468,a)].">
      <j1 rule="hyper" parents="17783 18468"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w)) \ T(z,u * w)) = K(x,T(z,u \ w) / y)
    ]]></literal>
    <justification jstring="[para(17155(a,1),18469(a,1,2,1))].">
      <j1 rule="para" parents="17155 18469"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ w),v5,v6)) = K(x,L(y \ T(z,u * w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(13033,a,18470,a),flip(a)].">
      <j1 rule="hyper" parents="13033 18470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      K(x / L(T(y,z \ u),w,v5),v6) = K(x / L(T(y,z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(20(a,2),18498(a,2,1,2))].">
      <j1 rule="para" parents="20 18498"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * (u * K(u \ z,u))))
    ]]></literal>
    <justification jstring="[para(5683(a,1),18507(a,2,2,2,2))].">
      <j1 rule="para" parents="5683 18507"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      K(x,T(y,z \ u) / w) = K(x,T(y,z * u) / w)
    ]]></literal>
    <justification jstring="[hyper(14575,a,18519,a),flip(a)].">
      <j1 rule="hyper" parents="14575 18519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18524">
    <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(18519(a,1),14575(a,1))].">
      <j1 rule="para" parents="18519 14575"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * v5) / v6) = K(x,L(T(u,w \ v5) / v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,18523,a),flip(a)].">
      <j1 rule="hyper" parents="13036 18523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      (x * K(y,T(z,u * w) / v5)) \ x = K(T(z,u \ w) / v5,y)
    ]]></literal>
    <justification jstring="[para(18523(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18523 6294"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      K(T(x,y \ z) / u,w) = K(T(x,y * z) / u,w)
    ]]></literal>
    <justification jstring="[hyper(6305,a,18526,a),flip(a)].">
      <j1 rule="hyper" parents="6305 18526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      K(T(x,y \ z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y * z) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(18526(a,1),6305(a,1))].">
      <j1 rule="para" parents="18526 6305"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      K(T(x,(y / z) * y) / u,w) = K(T(x,z) / u,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),18527(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 18527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18530">
    <literal><![CDATA[
      K(T(x,y * (z \ y)) / u,w) = K(T(x,z) / u,w)
    ]]></literal>
    <justification jstring="[para(14500(a,1),18529(a,1,1,1))].">
      <j1 rule="para" parents="14500 18529"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      K(T(x,y) / (z * (y \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * (y \ z)) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(18530(a,1),14404(a,1))].">
      <j1 rule="para" parents="18530 14404"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      K(T(x,y / z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z * y) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(17712(a,2),18528(a,1))].">
      <j1 rule="para" parents="17712 18528"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      K((x * (y \ x)) \ T(z,y),u) = K(z / (x * (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(18531,a,16746,a)].">
      <j1 rule="hyper" parents="18531 16746"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K((x \ y) \ (y \ T(z,x)),L(u,x \ y,y)) = K(z / (y * (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(13037,a,18533,a)].">
      <j1 rule="hyper" parents="13037 18533"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y * 1),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,17431,a(flip),b,18520,a),flip(a)].">
      <j1 rule="hyper" parents="60 17431 18520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      K(x,L(T(y,z \ u) / w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * u) / w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18525(a,1),13036(a,1))].">
      <j1 rule="para" parents="18525 13036"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      K(x,L(y \ T(y * z,y),u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[para(3(a,1),18535(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3 18535"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      K(x,L((y * z) / y,u,w)) = K(x,L((y \ z) * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(14581,a,18537,a)].">
      <j1 rule="hyper" parents="14581 18537"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,L((y \ z) * y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,9124,a(flip),b,18538,a),flip(a)].">
      <j1 rule="hyper" parents="60 9124 18538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(x,L(((1 / y) \ z) / y,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(17909,a,18539,a)].">
      <j1 rule="hyper" parents="17909 18539"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      K(x,L(T(y * z,z),u,w)) = K(x,L((1 / z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16219,a(flip),b,18540,a),flip(a)].">
      <j1 rule="hyper" parents="60 16219 18540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18542">
    <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(18541(a,1),13039(a,1))].">
      <j1 rule="para" parents="18541 13039"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      K(x,L((K(y,z) * u) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L((u \ K(z,y)) * w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(15262(a,1),18542(a,1,2,1,1))].">
      <j1 rule="para" parents="15262 18542"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,(y \ (1 / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * (y * u),z,y)) = w
    ]]></literal>
    <justification jstring="[para(16591(a,1),18542(a,1))].">
      <j1 rule="para" parents="16591 18542"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,L(y * (z * u),y,z)) = K(x,(z \ (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18544,a,6165,a)].">
      <j1 rule="hyper" parents="18544 6165"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ (y \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (L(y,z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18545(a,1),16439(a,1))].">
      <j1 rule="para" parents="18545 16439"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x * T(T(y,z),u * y),w) = K(x * T(T(y,z),u),w)
    ]]></literal>
    <justification jstring="[hyper(18386,a,17868,a)].">
      <j1 rule="hyper" parents="18386 17868"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,((y \ z) \ 1) * y)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(18509,a,14576,a)].">
      <j1 rule="hyper" parents="18509 14576"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ u) = K(x,(y * ((z / y) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18509,a,xx),flip(a)].">
      <j1 rule="hyper" parents="18509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y * ((z / y) \ 1))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14576,a(flip),b,18549,a),flip(a)].">
      <j1 rule="hyper" parents="370 14576 18549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      T(x,y * (((z * z) \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * ((z * z) \ w))) = v5
    ]]></literal>
    <justification jstring="[para(18273(a,1),18254(a,1))].">
      <j1 rule="para" parents="18273 18254"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      T(x,(1 / y) * (z * ((y * y) \ y))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(18551,a,18417,a)].">
      <j1 rule="hyper" parents="18551 18417"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      T(x,(1 / y) * (z * (1 / y))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(313(a,1),18552(a,1,2,2,2))].">
      <j1 rule="para" parents="313 18552"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(4481(a,1),18553(a,1,2))].">
      <j1 rule="para" parents="4481 18553"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      T(x,y \ (z * (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18554,a)].">
      <j1 rule="hyper" parents="15260 18554"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      K(x,y * K((z * z) \ (u \ w),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[para(517(a,1),18355(a,1,2,2,1))].">
      <j1 rule="para" parents="517 18355"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x * (y * K(z \ u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * K(z * u,w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(18426(a,1),6305(a,1))].">
      <j1 rule="para" parents="18426 6305"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w * v5,z))) = K(x,y * (T(z,w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17873,a(flip),b,18427,a),flip(a)].">
      <j1 rule="hyper" parents="370 17873 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w * v5,z)))) = K(x,y * (T(z,w \ v5) * u))
    ]]></literal>
    <justification jstring="[para(11028(a,1),18558(a,1,2,2))].">
      <j1 rule="para" parents="11028 18558"/>
    </justification>
  </clause>

  <clause id="18560">
    <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(18559(a,1),17874(a,1))].">
      <j1 rule="para" parents="18559 17874"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      K(x,T(y,(z * z) \ (u \ w)) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(517(a,1),18460(a,1,2,1,2))].">
      <j1 rule="para" parents="517 18460"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      K(x,(((y / z) \ 1) * z) \ u) = K(x,(z * ((z \ y) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(8529(a,1),18477(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8529 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      K(x,y * K(z \ (z \ (u \ w)),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[para(15130(a,1),18556(a,1,2,2))].">
      <j1 rule="para" parents="15130 18556"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ (u \ w))) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(15162(a,1),18561(a,1,2,1))].">
      <j1 rule="para" parents="15162 18561"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x,y * K(z * (z \ (u \ w)),v5)) = K(x,y * K(u * ((z * z) * w),v5))
    ]]></literal>
    <justification jstring="[hyper(18360,a,18563,a)].">
      <j1 rule="hyper" parents="18360 18563"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      K(x,T(y,z * (z \ (u \ w))) \ v5) = K(x,T(y,u * ((z * z) * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18452,a(flip),b,18564,a)].">
      <j1 rule="hyper" parents="60 18452 18564"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      K(x,y * K(z * ((u * u) * w),v5)) = K(x,y * K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(5(a,1),18565(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      K(x,y * K(z * ((u * u) * w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z * w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18567(a,2),18360(a,1))].">
      <j1 rule="para" parents="18567 18360"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      K(x,T(y,z * ((u * u) * w)) \ v5) = K(x,T(y,z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(5(a,1),18566(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(x,T(y,z * ((u * u) * w)) \ v5) = K(x,T(y,z * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,18452,a(flip),b,18570,a),flip(a)].">
      <j1 rule="hyper" parents="370 18452 18570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) \ v5) = K(x,T(y,z * (u \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(936(a,1),18571(a,1,2,1,2,2))].">
      <j1 rule="para" parents="936 18571"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(6930(a,1),18281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6930 18281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w \ v5)) * T(u,w * v5))) = T(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16863,a,18574,a),flip(a)].">
      <j1 rule="hyper" parents="16863 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * T(u,w * v5))) = T(x,y \ (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18574,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w \ v5)) * (z * T(u,w * v5))) = T(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(12606,a,18574,a),flip(a)].">
      <j1 rule="hyper" parents="12606 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      x \ T(x,y * (z * T(u,w * v5))) = K(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(125,a,18574,a(flip),b,5256,a(flip))].">
      <j1 rule="hyper" parents="125 18574 5256"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      T(x,y * ((z \ u) * T(w,z * u))) = T(x,y * (w * (z \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),18574(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      x / T(x,y * (z * T(u,w * v5))) = K(y * (z * T(u,w \ v5)),x)
    ]]></literal>
    <justification jstring="[para(18574(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18574 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      T(x,y \ (z * T(u,w \ v5))) = T(x,y \ (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18576,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      T(x,y \ (z * T(u,w * w))) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(227(a,1),18581(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="227 18581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15620,a(flip),b,18582,a),flip(a)].">
      <j1 rule="hyper" parents="60 15620 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(549(a,1),18582(a,1,2,2,2))].">
      <j1 rule="para" parents="549 18582"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      T(x,(y \ (z * z)) * u) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15331,a(flip),b,18583,a)].">
      <j1 rule="hyper" parents="60 15331 18583"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      T(x,y * (y * ((y * z) \ u))) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4682,a(flip),b,18583,a),flip(a)].">
      <j1 rule="hyper" parents="60 4682 18583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ ((u * z) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14436,a,b,18584,a)].">
      <j1 rule="hyper" parents="60 14436 18584"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(5290,a,18578,a),flip(a)].">
      <j1 rule="hyper" parents="5290 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(18578(a,1),5290(a,1))].">
      <j1 rule="para" parents="18578 5290"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      K(x,(y \ 1) * (z * T(u,w * v5))) = K(x,y \ (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,18589,a),flip(a)].">
      <j1 rule="hyper" parents="15233 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w \ v5)) * (z * T(u,w * v5))) = K(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,18589,a),flip(a)].">
      <j1 rule="hyper" parents="12637 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,(y * (z * T(u,w \ v5))) * (1 / (z * T(u,w \ v5))))
    ]]></literal>
    <justification jstring="[para(1288(a,1),18589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1288 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u \ w)) * (1 / (y * T(z,u \ w))))
    ]]></literal>
    <justification jstring="[para(4452(a,1),18589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4452 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(u,w * v5))) = K(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(6269(a,1),18589(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6269 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x * (y * T(z,u \ w)),v5) = K(x * (y * T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(5734,a,18580,a),flip(a)].">
      <j1 rule="hyper" parents="5734 18580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      K((x \ 1) * (y * T(z,u * w)),v5) = K(x \ (y * T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(15221,a,18596,a),flip(a)].">
      <j1 rule="hyper" parents="15221 18596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w \ v5))) = K(x,y \ (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,18591,a),flip(a)].">
      <j1 rule="hyper" parents="15233 18591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(18591(a,1),15233(a,1))].">
      <j1 rule="para" parents="18591 15233"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * (w * v5)))) = K(x,y \ (z * T(u,v5)))
    ]]></literal>
    <justification jstring="[para(4(a,1),18598(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 18598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * w))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(227(a,1),18598(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="227 18598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      K(x,y \ (z * (u / (w * w)))) = K(x,y \ (z * ((w * w) \ u)))
    ]]></literal>
    <justification jstring="[para(109(a,1),18601(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="109 18601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,y \ (((z * z) \ u) * w)) = K(x,y \ (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18445,a,b,18602,a)].">
      <j1 rule="hyper" parents="60 18445 18602"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(6269(a,1),18595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6269 18595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (v5 * K(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(17737,a,18604,a)].">
      <j1 rule="hyper" parents="17737 18604"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(z,u * w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(18605(a,2),17737(a,1))].">
      <j1 rule="para" parents="18605 17737"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      K(x \ (y * T(z,u \ w)),v5) = K(x \ (y * T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(15221,a,18597,a),flip(a)].">
      <j1 rule="hyper" parents="15221 18597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18608">
    <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(18597(a,1),15221(a,1))].">
      <j1 rule="para" parents="18597 15221"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      K(x \ ((y \ z) * T(u,y * z)),w) = K(x \ (u * (y \ z)),w)
    ]]></literal>
    <justification jstring="[para(107(a,1),18607(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18610">
    <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(17777(a,2),18590(a,1))].">
      <j1 rule="para" parents="17777 18590"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      K(x \ (y * (z / (z / u))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y * T(u,u * z)),w) = v5
    ]]></literal>
    <justification jstring="[para(18137(a,1),18608(a,1))].">
      <j1 rule="para" parents="18137 18608"/>
    </justification>
  </clause>

  <clause id="18612">
    <literal><![CDATA[
      K(x,y * ((z / u) * T(w,z * u))) = K(x,y * (w * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(18610,a,18513,a)].">
      <j1 rule="hyper" parents="18610 18513"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * T(z * u,1 * u)))
    ]]></literal>
    <justification jstring="[para(4552(a,2),18612(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4552 18612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      K(x \ (y * T(z,z * u)),w) = K(x \ (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(18611,a,18399,a)].">
      <j1 rule="hyper" parents="18611 18399"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      K(x \ (y * T(z,z * T((u \ w) \ 1,v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(9904(a,1),18614(a,2,1,2,2))].">
      <j1 rule="para" parents="9904 18614"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      T(x,y \ T((z * u) * (1 / z),z * u)) = T(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(1111(a,1),18588(a,2,2,2))].">
      <j1 rule="para" parents="1111 18588"/>
    </justification>
  </clause>

  <clause id="18617">
    <literal><![CDATA[
      T(x,y \ ((1 / z) * (z * u))) = T(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14414,a(flip),b,18616,a)].">
      <j1 rule="hyper" parents="60 14414 18616"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      T(x,y \ R(z,u,u)) = T(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[para(579(a,1),18617(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="579 18617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      K(x,L(T(y,z * 1) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[hyper(18515,a,12725,a)].">
      <j1 rule="hyper" parents="18515 12725"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z)) = K(x,(y * (z \ 1)) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(3(a,1),18619(a,1,2,1,1,2))].">
      <j1 rule="para" parents="3 18619"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((1 / z) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12534,a(flip),b,18620,a),flip(a)].">
      <j1 rule="hyper" parents="60 12534 18620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(15803,a,18621,a)].">
      <j1 rule="hyper" parents="15803 18621"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) \ u,y,z \ 1)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12534,a,b,18622,a)].">
      <j1 rule="hyper" parents="60 12534 18622"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      K(x,L(T(y,(z / y) \ 1) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(12697(a,1),18623(a,2,2))].">
      <j1 rule="para" parents="12697 18623"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      K(x,L(T(y,z \ (y * 1)) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11094(a,1),18624(a,1,2,1,1))].">
      <j1 rule="para" parents="11094 18624"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,(z / y) \ 1)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(3(a,1),18625(a,1,2,1,1,2,2))].">
      <j1 rule="para" parents="3 18625"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,z / y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(1492(a,1),18626(a,1,2))].">
      <j1 rule="para" parents="1492 18626"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(K(x,y * y) * (z * x),u) = K(((y * y) \ z) * ((y * y) * x),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18385,a(flip),b,17582,a)].">
      <j1 rule="hyper" parents="60 18385 17582"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(((x * x) \ y) * ((x * x) * z),u) = K(y * T(z,x * x),u)
    ]]></literal>
    <justification jstring="[hyper(17308,a,18628,a),flip(a)].">
      <j1 rule="hyper" parents="17308 18628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      K(T(x,y * y) * z,u) = K(x * T(z,y * y),u)
    ]]></literal>
    <justification jstring="[para(997(a,1),18629(a,1,1))].">
      <j1 rule="para" parents="997 18629"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      K(T(x,y * y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18385,a(flip),b,18631,a),flip(a)].">
      <j1 rule="hyper" parents="370 18385 18631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(((x * x) \ y) * z,u) = K(y * ((x * x) \ z),u)
    ]]></literal>
    <justification jstring="[para(1452(a,1),18632(a,1,1))].">
      <j1 rule="para" parents="1452 18632"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      K(x \ (x \ (y * z)),u) = K(y * ((x * x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(15573,a,18634,a)].">
      <j1 rule="hyper" parents="15573 18634"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      K(x,T(y,x \ z)) * (x * T(x \ z,u)) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8797(a,1),17754(a,1,1))].">
      <j1 rule="para" parents="8797 17754"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      K(x,T(y,z)) * (x * T(x \ z,u)) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8120(a,1),18636(a,1,1))].">
      <j1 rule="para" parents="8120 18636"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      T(x,T(y,z)) * T(x \ z,u) = (x * T(x \ z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7900,a,18638,a)].">
      <j1 rule="hyper" parents="7900 18638"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      (x * T(x \ y,z)) * K(x,T(y,u)) = T(x,T(y,u)) * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(203(a,1),18639(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="203 18639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(z * u) * y)) = T(x,T(y / T(u * z,u),w))
    ]]></literal>
    <justification jstring="[para(14650(a,1),17779(a,1,1))].">
      <j1 rule="para" parents="14650 17779"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      T(x,T(y / T(z * u,z),w)) = T(x,T(y / (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(17714,a,18641,a),flip(a)].">
      <j1 rule="hyper" parents="17714 18641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * u))) = K(x,y * T(z,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,18462,a(flip),b,17807,a),flip(a)].">
      <j1 rule="hyper" parents="31 18462 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18646">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) = K(x,L(u / ((y / z) \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,16019,a(flip),b,17828,a)].">
      <j1 rule="hyper" parents="60 16019 17828"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u * (y / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18646(a,2),15599(a,1))].">
      <j1 rule="para" parents="18646 15599"/>
    </justification>
  </clause>

  <clause id="18648">
    <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(18018(a,1),18024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18018 18024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,16700,a(flip),b,18648,a),flip(a)].">
      <j1 rule="hyper" parents="370 16700 18648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18651">
    <literal><![CDATA[
      T(x,y * K(z * K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(17210,a,18649,a)].">
      <j1 rule="hyper" parents="17210 18649"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7996(a,1),18649(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7996 18649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K(x * K(y,K(z,u) * w),v5) = v5 / T(v5,K(w,y) * x)
    ]]></literal>
    <justification jstring="[para(18653(a,1),17847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18653 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      K(x * K(y,K(z,u) * w),v5) = K(K(w,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,18654,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 18654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K(K(u,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(17482,a,18655,a)].">
      <j1 rule="hyper" parents="17482 18655"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(K(z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17367,a,18655,a)].">
      <j1 rule="hyper" parents="17367 18655"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(K(x,K(y,z) * u) * w,v5) = K(K(u,x) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17249,a,18655,a)].">
      <j1 rule="hyper" parents="17249 18655"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = K(w * K(u,z),v5)
    ]]></literal>
    <justification jstring="[para(7500(a,1),18655(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7500 18655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(K(x,y) * ((K(z,u) * x) * w),v5) = K(T(K(z,u) * x,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(7864(a,1),18658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 18658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(K((x / y) * z,u) * w,v5) = K(K((y \ x) * z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(8364(a,1),18658(a,1,1,1,1))].">
      <j1 rule="para" parents="8364 18658"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(K(T(x * (y / z),K(y,z)),u) * w,v5) = K(K(x * (z \ y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(10332(a,1),18658(a,1,1,1,1))].">
      <j1 rule="para" parents="10332 18658"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(K(K(x,y) * z,u) * w,v5) = v5 / T(v5,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a(flip),b,18660,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 18660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,y * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(17848,a,18665,a)].">
      <j1 rule="hyper" parents="17848 18665"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ v5) = T(x,(y \ v5) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17624,a,18666,a)].">
      <j1 rule="hyper" parents="17624 18666"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(18667(a,2),17334(a,1))].">
      <j1 rule="para" parents="18667 17334"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(5256(a,2),18668(a,1,2,1,2))].">
      <j1 rule="para" parents="5256 18668"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(K(x * (y / z),u) * w,v5) = K(K(x * (z \ y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(17212(a,1),18664(a,1,1,1))].">
      <j1 rule="para" parents="17212 18664"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x / (u * (u / z))) = K(y,(u * (u / z)) \ x)
    ]]></literal>
    <justification jstring="[para(17524(a,1),18048(a,1,1))].">
      <j1 rule="para" parents="17524 18048"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / (u * (u / x))) = K(z,(u * (u / x)) \ y)
    ]]></literal>
    <justification jstring="[para(8636(a,1),18672(a,1,1))].">
      <j1 rule="para" parents="8636 18672"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,z / (w * (w / x))),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[para(18673(a,1),18286(a,2,1))].">
      <j1 rule="para" parents="18673 18286"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = w
    ]]></literal>
    <justification jstring="[para(18130(a,1),9356(a,1))].">
      <j1 rule="para" parents="18130 9356"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      K(x,K(y \ z,y * u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[para(17519(a,2),18130(a,1,1))].">
      <j1 rule="para" parents="17519 18130"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      T(x,T(y * K(z,u \ w),v5)) = T(x,T(y * K(z,u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(9814,a,18282,a),flip(a)].">
      <j1 rule="hyper" parents="9814 18282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      T(x,T((y \ z) * K(y,u * w),v5)) = T(x,T(T(y,u \ w) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(18149,a,18677,a),flip(a)].">
      <j1 rule="hyper" parents="18149 18677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      T(x,T(T(y,z \ u) \ w,v5)) = T(x,T(T(y,z * u) \ w,v5))
    ]]></literal>
    <justification jstring="[hyper(18149,a,18678,a),flip(a)].">
      <j1 rule="hyper" parents="18149 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w * v5)) * K(w * v5,u))) = K(x,y * (K(w \ v5,u) * z))
    ]]></literal>
    <justification jstring="[para(17528(a,1),18425(a,1,2,2,1))].">
      <j1 rule="para" parents="17528 18425"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * (z \ ((1 / z) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[para(15166(a,1),18475(a,1,2,1))].">
      <j1 rule="para" parents="15166 18475"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w * v5)) * T(u,w * v5))) = T(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[para(17155(a,1),18575(a,1,2,2,1))].">
      <j1 rule="para" parents="17155 18575"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      K(x,K(y \ z,y \ u)) * K(x,(y * z) \ (y * u)) = K(x,(y \ u) / (y \ z))
    ]]></literal>
    <justification jstring="[para(17508(a,2),18676(a,1,1))].">
      <j1 rule="para" parents="17508 18676"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * v5)) = K(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[para(6226(a,1),18681(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6226 18681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      K(x,y * (K(z * u,w) * (w \ v5))) = K(x,y * (T(w,z \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),18685(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 18685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * ((K(u,z \ 1) / z) \ w))
    ]]></literal>
    <justification jstring="[para(8306(a,1),18685(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8306 18685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) \ v5)) = K(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),18686(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 18686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * (z \ ((z \ 1) \ u))) = K(x,(z \ ((1 / z) \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,6661,a(flip),b,18682,a)].">
      <j1 rule="hyper" parents="60 6661 18682"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16863,a,18683,a),flip(a)].">
      <j1 rule="hyper" parents="16863 18683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) * v5)) = T(x,y \ (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18690,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18692">
    <literal><![CDATA[
      x * K(x,y \ (T(z,u * w) * v5)) = T(x,y \ (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15333,a,18691,a)].">
      <j1 rule="hyper" parents="15333 18691"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) * v5)) = T(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15260,a,18691,a),flip(a)].">
      <j1 rule="hyper" parents="15260 18691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18694">
    <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(18691(a,1),15260(a,1))].">
      <j1 rule="para" parents="18691 15260"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      T(x,y \ (T(z,T(u,w) * w) * v5)) = T(x,y \ (T(z,w / u) * v5))
    ]]></literal>
    <justification jstring="[para(16228(a,1),18693(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="16228 18693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * v5)) = K(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(31,a,5256,a(flip),b,18692,a)].">
      <j1 rule="hyper" parents="31 5256 18692"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      K(x,y \ (T(z,y * (y \ 1)) * u)) = K(x,y * (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16131,a(flip),b,18696,a),flip(a)].">
      <j1 rule="hyper" parents="60 16131 18696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      T(x,y \ (T(z,u / w) * v5)) = T(x,y \ (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[para(12600(a,1),18695(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12600 18695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      K(x,y * (z * ((y * y) \ u))) = K(x,y \ (T(z,1) * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),18697(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(x,y * (z * ((y * y) \ u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(222(a,1),18699(a,2,2,2,1))].">
      <j1 rule="para" parents="222 18699"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(1470(a,1),18701(a,1,2,2))].">
      <j1 rule="para" parents="1470 18701"/>
    </justification>
  </clause>

  <clause id="18703">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z \ (y \ 1)) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(15313,a,18702,a)].">
      <j1 rule="hyper" parents="15313 18702"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      K(x,(y \ z) \ (y \ u)) = K(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(9358,a,18684,a)].">
      <j1 rule="hyper" parents="9358 18684"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(x,L((y \ (y * z)) \ (y * u),u,y)) = K(x,(y \ z) \ (y \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15937,a,b,18704,a)].">
      <j1 rule="hyper" parents="370 15937 18704"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      K(x,L((y \ (y * z)) \ (y * u),u,y)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),18705(a,2,2,2))].">
      <j1 rule="para" parents="4 18705"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),18706(a,1,2,1,1))].">
      <j1 rule="para" parents="4 18706"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / u)) = K(x,((z / u) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),18707(a,1,2,1,2))].">
      <j1 rule="para" parents="7 18707"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ ((u \ 1) \ z))) = K(x,(u \ ((1 / u) \ z)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,18444,a(flip),b,18689,a)].">
      <j1 rule="hyper" parents="60 18444 18689"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      K(x,(y \ ((1 / y) \ z)) * u) = K(x,(y \ ((y \ 1) \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(15357,a,18709,a),flip(a)].">
      <j1 rule="hyper" parents="15357 18709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      K(x,T((y \ ((1 / (y \ 1)) \ z)) * u,y \ (y \ 1))) = K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y)))
    ]]></literal>
    <justification jstring="[para(1761(a,2),18710(a,1,2))].">
      <j1 rule="para" parents="1761 18710"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(370,a,18000,a(flip),b,17348,a),flip(a)].">
      <j1 rule="hyper" parents="370 18000 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(17380,a,18713,a)].">
      <j1 rule="hyper" parents="17380 18713"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16413,a(flip),b,18714,a),flip(a)].">
      <j1 rule="hyper" parents="60 16413 18714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(8678,a,18716,a)].">
      <j1 rule="hyper" parents="8678 18716"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17584,a(flip),b,18717,a),flip(a)].">
      <j1 rule="hyper" parents="60 17584 18717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(77(a,1),18718(a,1,2,2,1,2))].">
      <j1 rule="para" parents="77 18718"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13680,a(flip),b,18719,a),flip(a)].">
      <j1 rule="hyper" parents="60 13680 18719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17997,a(flip),b,18720,a),flip(a)].">
      <j1 rule="hyper" parents="60 17997 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(8634,a,18721,a)].">
      <j1 rule="hyper" parents="8634 18721"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(370,a,8630,a,b,18722,a),flip(a)].">
      <j1 rule="hyper" parents="370 8630 18722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(K(x \ y,x) * (z * (y * (1 / x))),u) = K(z * (x \ R(y,1 / x,x)),u)
    ]]></literal>
    <justification jstring="[para(6840(a,1),17441(a,1,1,1))].">
      <j1 rule="para" parents="6840 17441"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * (1 / y))),u) = K(z * (y \ R(x,1 / y,y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14525,a(flip),b,18724,a)].">
      <j1 rule="hyper" parents="60 14525 18724"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x * (y \ R(z,1 / y,y)),u) = K(x * ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18407,a(flip),b,18725,a),flip(a)].">
      <j1 rule="hyper" parents="60 18407 18725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x * T(y * (1 / z),z),u) = K(x * ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(736(a,1),18726(a,1,1,2))].">
      <j1 rule="para" parents="736 18726"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * T((y * z) * (1 / y),y),u)
    ]]></literal>
    <justification jstring="[para(8527(a,2),18727(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8527 18727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * ((z * y) * (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(3281(a,1),18728(a,2,1,2))].">
      <j1 rule="para" parents="3281 18728"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * ((z * y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6014,a(flip),b,18729,a),flip(a)].">
      <j1 rule="hyper" parents="370 6014 18729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x * ((y \ 1) * (T(y,y \ 1) * z)),u) = K(x * R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(1111(a,1),18730(a,2,1,2))].">
      <j1 rule="para" parents="1111 18730"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x * ((1 / y) * (y * z)),u) = K(x * R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(8527(a,1),18731(a,1,1,2))].">
      <j1 rule="para" parents="8527 18731"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x * R(y,z,z),u) = K(x * L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(579(a,1),18732(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="579 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18734">
    <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(18649(a,1),18209(a,2,2,1))].">
      <j1 rule="para" parents="18649 18209"/>
    </justification>
  </clause>

  <clause id="18735">
    <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(8004(a,1),17314(a,1,2,2))].">
      <j1 rule="para" parents="8004 17314"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),w),1 / z)) = T(x,y / T((z \ u) / (1 / z),w))
    ]]></literal>
    <justification jstring="[para(4834(a,1),17461(a,2,2,2))].">
      <j1 rule="para" parents="4834 17461"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      K(x * (((y \ 1) * z) \ K(y \ z,y)),u) = K(x / ((y \ 1) * ((y \ z) * y)),u)
    ]]></literal>
    <justification jstring="[para(7732(a,1),17576(a,1,1,2,2))].">
      <j1 rule="para" parents="7732 17576"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      T(T(x,K(y,z)),(z * K(u,T(w,v5))) * y) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(18018(a,1),17823(a,1,1))].">
      <j1 rule="para" parents="18018 17823"/>
    </justification>
  </clause>

  <clause id="18740">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,17931,a(flip),b,17854,a),flip(a)].">
      <j1 rule="hyper" parents="370 17931 17854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6201(a,1),18740(a,1,2))].">
      <j1 rule="para" parents="6201 18740"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6304,a,18741,a)].">
      <j1 rule="hyper" parents="6304 18741"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8340(a,1),18742(a,1,2))].">
      <j1 rule="para" parents="8340 18742"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      (K(x,T(y,z)) / u) * K(z,(K(x,y) / u) / (u \ 1)) = T(K(x,y) / u,K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8019(a,2),18743(a,1,1,1))].">
      <j1 rule="para" parents="8019 18743"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,T(y * ((z \ u) * z),w)) = K(x,T(y * T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9748,a(flip),b,17869,a),flip(a)].">
      <j1 rule="hyper" parents="370 9748 17869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x,T(y * T(z * u,z),w)) = K(x,T(y * (u * z),w))
    ]]></literal>
    <justification jstring="[para(4(a,1),18745(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 18745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),w)) = K(x,T((y \ 1) * (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(15596,a,18746,a)].">
      <j1 rule="hyper" parents="15596 18746"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (u * z),w)) = v5
    ]]></literal>
    <justification jstring="[para(18747(a,2),15596(a,1))].">
      <j1 rule="para" parents="18747 15596"/>
    </justification>
  </clause>

  <clause id="18750">
    <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(7463(a,1),18194(a,1,2,1))].">
      <j1 rule="para" parents="7463 18194"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      T(x,T(y,z * T(u,z)) / (u * ((z \ u) / u))) = T(x,(z \ T(u,z \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(18271(a,1),18310(a,1,2,1))].">
      <j1 rule="para" parents="18271 18310"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      T(x,T(y,z * u) / (z * ((u \ z) / z))) = T(x,(u \ T(z,u \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),18751(a,1,2,1,2))].">
      <j1 rule="para" parents="107 18751"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      K(x,y * K((z * u) * (z * ((z \ 1) \ w)),v5)) = K(x,y * K(((z \ 1) * u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,18352,a(flip),b,18357,a),flip(a)].">
      <j1 rule="hyper" parents="370 18352 18357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      T(x,T(y,L(z * (u * u),u,u)) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(3900(a,1),18409(a,2,2))].">
      <j1 rule="para" parents="3900 18409"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,(y \ z) \ y)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(15252(a,1),18548(a,1,2,2))].">
      <j1 rule="para" parents="15252 18548"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,y * (y / z))) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(15715(a,1),18755(a,1,2,2))].">
      <j1 rule="para" parents="15715 18755"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,z)) = K(x,u / (((y \ z) \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,18374,a(flip),b,18756,a)].">
      <j1 rule="hyper" parents="60 18374 18756"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y / (z / y))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[para(15398(a,1),18550(a,1,2,2))].">
      <j1 rule="para" parents="15398 18550"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,y * (y / z))) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[para(16233(a,1),18759(a,1,2,2))].">
      <j1 rule="para" parents="16233 18759"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * y) \ T(u,z)) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18374,a(flip),b,18760,a)].">
      <j1 rule="hyper" parents="60 18374 18760"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      K(x,(y * ((z / y) \ 1)) \ T(u,z)) = K(x,u / (y * ((z / y) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18509,a,18761,a)].">
      <j1 rule="hyper" parents="18509 18761"/>
    </justification>
  </clause>

  <clause id="18764">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ 1) * z)) = K(x,y / (z * ((u / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18757,a(flip),b,18762,a)].">
      <j1 rule="hyper" parents="60 18757 18762"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      K(x,y / (z * ((u / z) \ 1))) = K(x,(z * ((y / z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16556,a(flip),b,18764,a),flip(a)].">
      <j1 rule="hyper" parents="60 16556 18764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w * v5)) * (z * T(u,w * v5))) = T(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[para(18270(a,1),18577(a,1,2,1))].">
      <j1 rule="para" parents="18270 18577"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z * T(u,w * v5))) = K(x,(z * T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[para(18270(a,1),18592(a,1,2,1))].">
      <j1 rule="para" parents="18270 18592"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      K(x \ (y * T(z,T(z * ((u \ w) \ 1),v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(18223(a,2),18615(a,1,1,2,2))].">
      <j1 rule="para" parents="18223 18615"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6797(a,1),18735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6797 18735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a(flip),b,18769,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 18769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(8227,a,18770,a),flip(a)].">
      <j1 rule="hyper" parents="8227 18770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,T(u,z / x)) = w
    ]]></literal>
    <justification jstring="[para(18770(a,1),8227(a,1))].">
      <j1 rule="para" parents="18770 8227"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(31,a,17938,a,b,18744,a),flip(a)].">
      <j1 rule="hyper" parents="31 17938 18744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,12641,a(flip),b,18774,a)].">
      <j1 rule="hyper" parents="60 12641 18774"/>
    </justification>
  </clause>

  <clause id="18777">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,18775,a(flip),b,9900,a)].">
      <j1 rule="hyper" parents="129 18775 9900"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(x,y)) = u \ K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17206,a,18777,a)].">
      <j1 rule="hyper" parents="17206 18777"/>
    </justification>
  </clause>

  <clause id="18779">
    <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(17571(a,1),18750(a,1,2,1))].">
      <j1 rule="para" parents="17571 18750"/>
    </justification>
  </clause>

  <clause id="18780">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,x) * T(z * K(x,T(y,w)),u)
    ]]></literal>
    <justification jstring="[hyper(7521,a,18779,a),flip(a)].">
      <j1 rule="hyper" parents="7521 18779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18781">
    <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(60,a,18224,a(flip),b,18780,a)].">
      <j1 rule="hyper" parents="60 18224 18780"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,y * K((z * u) * ((z * z) * w),v5)) = K(x,y * K(((z \ 1) * u) * w,v5))
    ]]></literal>
    <justification jstring="[para(12706(a,1),18753(a,1,2,2))].">
      <j1 rule="para" parents="12706 18753"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) * u) * w,v5)) = K(x,y * K((z * u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(18569,a,18782,a),flip(a)].">
      <j1 rule="hyper" parents="18569 18782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,K(y * ((z \ 1) * u),w) * v5) = K(x,v5 * K((z * u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(17780,a,18783,a)].">
      <j1 rule="hyper" parents="17780 18783"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,K(((y \ 1) * z) * u,w) * v5) = K(x,v5 * K((y * z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(17251,a,18783,a)].">
      <j1 rule="hyper" parents="17251 18783"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      K(x,y * K(z,u * ((w \ 1) * v5))) = K(x,y * K((w * v5) * u,z))
    ]]></literal>
    <justification jstring="[hyper(17484,a,18785,a)].">
      <j1 rule="hyper" parents="17484 18785"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) * w)) \ v5) = K(x,(y \ v5) * K((u * w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17452,a(flip),b,18787,a)].">
      <j1 rule="hyper" parents="60 17452 18787"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,T(y / T(z,(u * w) * v5),z)) = K(x,T(z,v5 * ((1 / u) * w)) \ y)
    ]]></literal>
    <justification jstring="[para(9096(a,2),18788(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9096 18788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) * w)) \ v5) = K(x,T(y,(u * w) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(17304,a,18789,a),flip(a)].">
      <j1 rule="hyper" parents="17304 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) * w)) \ v5) = K(x,T(y,(u * w) * z) \ v5)
    ]]></literal>
    <justification jstring="[para(4672(a,1),18790(a,1,2,1))].">
      <j1 rule="para" parents="4672 18790"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(15156(a,1),18754(a,1,2,1))].">
      <j1 rule="para" parents="15156 18754"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      T(x,T(y,z) * (u * (u * z))) = T(x,L(z,u,u) * ((u * u) * y))
    ]]></literal>
    <justification jstring="[hyper(18261,a,18792,a)].">
      <j1 rule="hyper" parents="18261 18792"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      T(x,L(y,z,z) * ((z * z) * u)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18482,a(flip),b,18793,a),flip(a)].">
      <j1 rule="hyper" parents="60 18482 18793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      T(x,(y * T(z,u \ w)) * v5) = T(x,(y * T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(12606,a,18766,a),flip(a)].">
      <j1 rule="hyper" parents="12606 18766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18798">
    <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(18766(a,1),12606(a,1))].">
      <j1 rule="para" parents="18766 12606"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      T(x,(y * T(z,u * u)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(227(a,1),18797(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="227 18797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18800">
    <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(18767(a,1),12637(a,1))].">
      <j1 rule="para" parents="18767 12637"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      K(x \ (y * T(z,T((u \ w) \ z,v5))),v6) = K(x \ (y * T(z,T(w \ u,v5))),v6)
    ]]></literal>
    <justification jstring="[para(9664(a,1),18768(a,1,1,2,2))].">
      <j1 rule="para" parents="9664 18768"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(y,z)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(6319(a,1),17887(a,1,1))].">
      <j1 rule="para" parents="6319 17887"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) / T(1 / K(y,z),K(y,z) * x) = x * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(10054(a,2),18803(a,1,1))].">
      <j1 rule="para" parents="10054 18803"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) / T(1 / K(x,z),K(x,z) * (x * y)) = (x * y) * (K(x,z) * K(x,z))
    ]]></literal>
    <justification jstring="[para(7273(a,1),18804(a,1,1,1))].">
      <j1 rule="para" parents="7273 18804"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      T(x,(y \ T((z \ 1) \ 1,u)) * (y \ T((z \ 1) \ 1,u))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17091,a(flip),b,17927,a),flip(a)].">
      <j1 rule="hyper" parents="60 17091 17927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,(y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17926,a(flip),b,18806,a)].">
      <j1 rule="hyper" parents="60 17926 18806"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ ((z * (y \ 1)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17102,a(flip),b,18807,a)].">
      <j1 rule="hyper" parents="60 17102 18807"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      T(x,y * (z \ ((z * (y \ 1)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(15396,a,18808,a)].">
      <j1 rule="hyper" parents="15396 18808"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,((z \ 1) \ 1) * (y \ ((y * (1 / z)) \ 1)))
    ]]></literal>
    <justification jstring="[para(1307(a,1),18809(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1307 18809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18811">
    <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(370,a,15844,a,b,18063,a),flip(a)].">
      <j1 rule="hyper" parents="370 15844 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      K(x,(y * z) * u) * a(w,v5,K((y * z) * u,x)) = K(x,L(T(z * y,y) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(16971(a,1),18140(a,1,1))].">
      <j1 rule="para" parents="16971 18140"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      K(x,L(T(y * z,z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((z * y) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18812(a,1),12988(a,1))].">
      <j1 rule="para" parents="18812 12988"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) * u) * w)) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(8605(a,1),18189(a,1,1))].">
      <j1 rule="para" parents="8605 18189"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(L(K(y,x),z,u),w * w)
    ]]></literal>
    <justification jstring="[para(5865(a,1),18202(a,2,2,1,1))].">
      <j1 rule="para" parents="5865 18202"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * T(K(y,L(x,z,u)),w * w)
    ]]></literal>
    <justification jstring="[para(12922(a,1),18815(a,2,2,1))].">
      <j1 rule="para" parents="12922 18815"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      T((1 / K(x,y)) * L(K(x,y),z,u),w * w) = K(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(17129(a,1),18816(a,2,2))].">
      <j1 rule="para" parents="17129 18816"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      T(K(x,y) * L(K(y,x),z,u),w * w) = K(y,x) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5866(a,1),18817(a,1,1,1))].">
      <j1 rule="para" parents="5866 18817"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      T(K(x,y) * K(y,L(x,z,u)),w * w) = K(y,x) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12922(a,1),18818(a,1,1,2))].">
      <j1 rule="para" parents="12922 18818"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = K(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18206,a(flip),b,18820,a)].">
      <j1 rule="hyper" parents="60 18206 18820"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      x * (K(x,y) * K(y,L(x,z,u))) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,18821,a(flip),b,7857,a)].">
      <j1 rule="hyper" parents="129 18821 7857"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = T(x,y) * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(7877,a,18822,a),flip(a)].">
      <j1 rule="hyper" parents="7877 18822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,L(y,z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,8404,a,b,18823,a)].">
      <j1 rule="hyper" parents="370 8404 18823"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) * K(x,1 / x) = T(K(x,L(1 / x,y,z)) / x,x)
    ]]></literal>
    <justification jstring="[para(6279(a,1),18824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6279 18824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) * K(x,x \ 1) = T(K(x,L(1 / x,y,z)) / x,x)
    ]]></literal>
    <justification jstring="[para(1706(a,1),18825(a,1,2))].">
      <j1 rule="para" parents="1706 18825"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      T(K(x,L(1 / x,y,z)) / x,x) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4719,a(flip),b,18826,a),flip(a)].">
      <j1 rule="hyper" parents="60 4719 18826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      T(K(x,L(x \ 1,y,z)) / x,x) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5440(a,1),18827(a,1,1,1))].">
      <j1 rule="para" parents="5440 18827"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z)) = T(K(x,x \ 1) / x,x)
    ]]></literal>
    <justification jstring="[para(6739(a,1),18828(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6739 18828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,6133,a(flip),b,18829,a),flip(a)].">
      <j1 rule="hyper" parents="370 6133 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18833">
    <literal><![CDATA[
      (L(x,y,z) \ T((x \ 1) * L(x,y,z),u)) \ (1 / x) = K(u,(x \ 1) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(18830(a,1),15301(a,1,2))].">
      <j1 rule="para" parents="18830 15301"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      K(x,(1 / y) \ (L(y,z,u) \ w)) = K(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(18830(a,1),16696(a,1,2,1))].">
      <j1 rule="para" parents="18830 16696"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(15228,a,18834,a),flip(a)].">
      <j1 rule="hyper" parents="15228 18834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      x * K(x,y * (L(y,z,u) \ w)) = T(x,(y \ L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,18835,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 18835 5230"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) \ w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(5265,a,18837,a),flip(a)].">
      <j1 rule="hyper" parents="5265 18837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      T(x,(y * (L(y,z,u) \ 1)) * w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,15761,a,b,18838,a)].">
      <j1 rule="hyper" parents="60 15761 18838"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) * w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(2162(a,1),18839(a,1,2,1))].">
      <j1 rule="para" parents="2162 18839"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) = T(x,(L(y,z,u) \ y) / w)
    ]]></literal>
    <justification jstring="[hyper(15531,a,18840,a),flip(a)].">
      <j1 rule="hyper" parents="15531 18840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      T(T(x,y * (L(y,z,u) \ w)),(L(y,z,u) \ y) \ (y \ L(y,z,u))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[para(18840(a,1),15685(a,1,1))].">
      <j1 rule="para" parents="18840 15685"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = (1 / x) * K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(36,a,15290,a,b,18833,a),flip(a)].">
      <j1 rule="hyper" parents="36 15290 18833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = (1 / x) * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(12999(a,1),18843(a,2,2))].">
      <j1 rule="para" parents="12999 18843"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      K(x,T(y,z * (z * (((z \ 1) * u) \ w))) * v5) = K(x,T(y,(z * T(u,z * z)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(18583(a,1),18466(a,1,2,1))].">
      <j1 rule="para" parents="18583 18466"/>
    </justification>
  </clause>

  <clause id="18846">
    <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(18(a,1),18495(a,1,2,1,2))].">
      <j1 rule="para" parents="18 18495"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,(w * (w / x)) * z),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18393,a(flip),b,18674,a)].">
      <j1 rule="hyper" parents="60 18393 18674"/>
    </justification>
  </clause>

  <clause id="18848">
    <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(17283(a,1),18811(a,2,3))].">
      <j1 rule="para" parents="17283 18811"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      K(x,T(y,(z * T(u,z * z)) * w) * v5) = K(x,T(y,((z \ 1) * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18444,a(flip),b,18845,a),flip(a)].">
      <j1 rule="hyper" parents="60 18444 18845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      K(x,T(y,(z * T(u,z * z)) * w) * v5) = K(x,T(y,((z \ 1) * u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,18454,a(flip),b,18849,a),flip(a)].">
      <j1 rule="hyper" parents="370 18454 18849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18852">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,(z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(18799(a,1),18851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18799 18851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,w * (z * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17783,a,18852,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17783 18852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w * (z * u)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18852(a,2),17783(a,1))].">
      <j1 rule="para" parents="18852 17783"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18853(a,2),17783(a,1))].">
      <j1 rule="para" parents="18853 17783"/>
    </justification>
  </clause>

  <clause id="18857">
    <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(8700(a,1),18846(a,1,2))].">
      <j1 rule="para" parents="8700 18846"/>
    </justification>
  </clause>

  <clause id="18858">
    <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(60,a,17988,a(flip),b,18848,a)].">
      <j1 rule="hyper" parents="60 17988 18848"/>
    </justification>
  </clause>

  <clause id="18860">
    <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(17397(a,1),18857(a,1,2))].">
      <j1 rule="para" parents="17397 18857"/>
    </justification>
  </clause>

  <clause id="18861">
    <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(60,a,10873,a(flip),b,18860,a)].">
      <j1 rule="hyper" parents="60 10873 18860"/>
    </justification>
  </clause>

  <clause id="18862">
    <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(18074(a,2),18861(a,1,2))].">
      <j1 rule="para" parents="18074 18861"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u * K(K(y,z) * u,x),K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(12587(a,1),18862(a,1,2,1))].">
      <j1 rule="para" parents="12587 18862"/>
    </justification>
  </clause>

  <clause id="18864">
    <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(15220(a,1),18863(a,1,2))].">
      <j1 rule="para" parents="15220 18863"/>
    </justification>
  </clause>

  <clause id="18865">
    <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(7506(a,1),18864(a,1,2))].">
      <j1 rule="para" parents="7506 18864"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(9302,a,18865,a)].">
      <j1 rule="hyper" parents="9302 18865"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,18781,a(flip),b,18866,a)].">
      <j1 rule="hyper" parents="60 18781 18866"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7518,a,18867,a),flip(a)].">
      <j1 rule="hyper" parents="7518 18867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(18868(a,2),15754(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18868 15754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15637,a,18869,a)].">
      <j1 rule="hyper" parents="15637 18869"/>
    </justification>
  </clause>

  <clause id="18871">
    <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(4(a,1),18106(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 18106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18872">
    <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(17489,a,18871,a)].">
      <j1 rule="hyper" parents="17489 18871"/>
    </justification>
  </clause>

  <clause id="18874">
    <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(24(a,1),18872(a,1,2,2,2))].">
      <j1 rule="para" parents="24 18872"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) * (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(18300,a,18688,a),flip(a)].">
      <j1 rule="hyper" parents="18300 18688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x,(T(y,z \ u) \ w) * v5) = K(x,(T(y,z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(12637,a,18875,a),flip(a)].">
      <j1 rule="hyper" parents="12637 18875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      K(x,(T(y,z * z) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(227(a,1),18876(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="227 18876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      (x * K(y,(T(z,u * w) \ v5) * v6)) \ x = K((T(z,u \ w) \ v5) * v6,y)
    ]]></literal>
    <justification jstring="[para(18876(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="18876 6294"/>
    </justification>
  </clause>

  <clause id="18880">
    <literal><![CDATA[
      K((T(x,y \ z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y * z) \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(18879(a,1),6305(a,1))].">
      <j1 rule="para" parents="18879 6305"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * T(z * u,u)))
    ]]></literal>
    <justification jstring="[para(2(a,1),18613(a,2,2,2,2,2))].">
      <j1 rule="para" parents="2 18613"/>
    </justification>
  </clause>

  <clause id="18882">
    <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(370,a,17613,a,b,18734,a),flip(a)].">
      <j1 rule="hyper" parents="370 17613 18734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18883">
    <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(370,a,16476,a(flip),b,18882,a),flip(a)].">
      <j1 rule="hyper" parents="370 16476 18882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      L(K(x,y * K(z,u * K(w,v5))),x,v6) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(106(a,1),18883(a,1,1,2,2,2))].">
      <j1 rule="para" parents="106 18883"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(16449,a,18884,a)].">
      <j1 rule="hyper" parents="16449 18884"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17251,a,18885,a)].">
      <j1 rule="hyper" parents="17251 18885"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      K(K(x,y * K(z,u)) * w,v5) = (v6 * K(v5,w * K(y,x))) \ v6
    ]]></literal>
    <justification jstring="[para(18886(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18886 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      K(K(x,y * K(z,u)) * w,v5) = K(w * K(y,x),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a(flip),b,18887,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 18887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      K((x * K(y,z)) * K(x,u),w) = K(x * K(y,z),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(9010,a,18888,a),flip(a)].">
      <j1 rule="hyper" parents="9010 18888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      K(T(x,y) * K(z,u),w) = K(x * K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(17229(a,1),18889(a,1,1))].">
      <j1 rule="para" parents="17229 18889"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(K(z,u) * (y / x),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,17363,a(flip),b,18890,a),flip(a)].">
      <j1 rule="hyper" parents="60 17363 18890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      T(x,K(y \ (y \ 1),y \ z) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(15200(a,1),17445(a,1,2,1))].">
      <j1 rule="para" parents="15200 17445"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      T(x,K(y \ z,y * y) * (u / ((y \ 1) * z))) = T(x,u / (y * (z * (y \ (1 / y)))))
    ]]></literal>
    <justification jstring="[para(15711(a,1),18892(a,1,2,1))].">
      <j1 rule="para" parents="15711 18892"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      T(x,y / (z * (u * (z \ (1 / z))))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(18893(a,1),18251(a,1))].">
      <j1 rule="para" parents="18893 18251"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      K(x,y * (z * (u * (w \ 1)))) * K(x,K(y,z * (u * (w \ 1)))) = K(x,(z * (u * (1 / w))) * y)
    ]]></literal>
    <justification jstring="[para(6163(a,1),17588(a,1,1))].">
      <j1 rule="para" parents="6163 17588"/>
    </justification>
  </clause>

  <clause id="18896">
    <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(9635(a,1),18110(a,1,1))].">
      <j1 rule="para" parents="9635 18110"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      K(x * (K(y,(z / T(u,w)) * v5) * K(y,K(v5,u * z))),v6) = K(K(v5 * (T(u,w) \ z),y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,18670,a(flip),b,18173,a),flip(a)].">
      <j1 rule="hyper" parents="370 18670 18173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) \ 1)) * (y \ ((z \ 1) \ 1))) = T(x,z * (y \ ((y * (1 / z)) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,4653,a(flip),b,18810,a),flip(a)].">
      <j1 rule="hyper" parents="370 4653 18810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      T(x,y * (z \ ((z * (1 / y)) \ 1))) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,18807,a(flip),b,18898,a),flip(a)].">
      <j1 rule="hyper" parents="60 18807 18898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      K(x,(y * (z * (1 / u))) * w) = K(x,(y * (z * (u \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(17629,a,18895,a),flip(a)].">
      <j1 rule="hyper" parents="17629 18895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * ((u * z) * (z \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,14563,a,b,18900,a)].">
      <j1 rule="hyper" parents="60 14563 18900"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      K(x,(y * T((z * u) * (1 / z),z * u)) * w) = K(x,(y * R(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(1111(a,1),18901(a,2,2,1,2))].">
      <j1 rule="para" parents="1111 18901"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      K(K(x * (T(y,z) \ u),w) * v5,v6) = K(v5 * K(w,(u / T(y,z)) * x),v6)
    ]]></literal>
    <justification jstring="[hyper(17739,a,18897,a),flip(a)].">
      <j1 rule="hyper" parents="17739 18897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      (T(x,y) \ 1) \ L(K(x * z,u),x,x) = K(z * ((x \ 1) \ 1),u) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(6003(a,1),17569(a,1,2,1))].">
      <j1 rule="para" parents="6003 17569"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) * T((y \ 1) \ 1,u) = (T(y,u) \ 1) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(15117(a,1),18904(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15117 18904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      K(x * y,z) * T((y \ 1) \ 1,u) = (T(y,u) \ 1) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(5998(a,1),18905(a,1,1))].">
      <j1 rule="para" parents="5998 18905"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      (T(x,y) \ K(z,u * x)) \ 1 = (T(x,y) \ 1) \ K(x * u,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15559,a(flip),b,18906,a)].">
      <j1 rule="hyper" parents="60 15559 18906"/>
    </justification>
  </clause>

  <clause id="18909">
    <literal><![CDATA[
      (T(x,y) \ 1) \ K(x * y,z) = y \ T(T(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17936,a(flip),b,18908,a),flip(a)].">
      <j1 rule="hyper" parents="60 17936 18908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      T(x \ T(T(y,y \ 1) * x,y),T(y,x) \ z) = T(x \ T(y * x,T(y,x)),z * T(y,x))
    ]]></literal>
    <justification jstring="[para(18909(a,1),16241(a,1,1))].">
      <j1 rule="para" parents="18909 16241"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = T(x \ (y * ((y \ x) * y)),T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(2118(a,1),18910(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2118 18910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      T(L(x,x \ y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(93(a,1),18911(a,2,1)),flip(a)].">
      <j1 rule="para" parents="93 18911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      T(L(x,x * y,x),T(x,y) \ z) = T(y \ T(x * y,T(x,y)),z * T(x,y))
    ]]></literal>
    <justification jstring="[para(14596(a,1),18912(a,1,1))].">
      <j1 rule="para" parents="14596 18912"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = L(T(y,T(y,x) \ z),y * x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20,a,b,18913,a),flip(a)].">
      <j1 rule="hyper" parents="60 20 18913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      T(x \ T(y * x,T(y,x)),z * T(y,x)) = L(T(y,y \ z),y * x,y)
    ]]></literal>
    <justification jstring="[para(9174(a,1),18914(a,2,1))].">
      <j1 rule="para" parents="9174 18914"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      T(x \ T(y * x,y),z * T(y,x)) = L(T(y,y \ z),y * x,y)
    ]]></literal>
    <justification jstring="[para(5474(a,1),18915(a,1,1,2))].">
      <j1 rule="para" parents="5474 18915"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      T(R(x,y,x),z * T(x,y)) = L(T(x,x \ z),x * y,x)
    ]]></literal>
    <justification jstring="[para(5536(a,1),18916(a,1,1))].">
      <j1 rule="para" parents="5536 18916"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),z,x) = L(T(x,x \ y),x * z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,22,a,b,18918,a)].">
      <j1 rule="hyper" parents="60 22 18918"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      L(T(x,x \ y),x * z,x) = R(T(x,x * y),z,x)
    ]]></literal>
    <justification jstring="[para(7369(a,1),18919(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7369 18919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(11981(a,1),17609(a,1,1))].">
      <j1 rule="para" parents="11981 17609"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(y \ x,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6410(a,1),18922(a,1,2))].">
      <j1 rule="para" parents="6410 18922"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(17172(a,1),18923(a,1,2))].">
      <j1 rule="para" parents="17172 18923"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14137,a(flip),b,18924,a),flip(a)].">
      <j1 rule="hyper" parents="60 14137 18924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18926">
    <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(18925(a,1),14897(a,1,1))].">
      <j1 rule="para" parents="18925 14897"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(15200(a,1),17774(a,1,1,2))].">
      <j1 rule="para" parents="15200 17774"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * (u * (z \ (1 / z)))) \ y) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(17528(a,1),18927(a,1,1))].">
      <j1 rule="para" parents="17528 18927"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z * ((z \ 1) \ ((z * u) \ y))) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[para(3342(a,1),18928(a,1,2))].">
      <j1 rule="para" parents="3342 18928"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z * (z * ((z * u) \ y))) = T(x,y / T((z \ 1) * u,z \ (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15488,a,18929,a)].">
      <j1 rule="hyper" parents="15488 18929"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      T(x,y / T((z \ 1) * u,z \ (z \ 1))) = T(x,y * ((z * u) \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(18347,a,18930,a),flip(a)].">
      <j1 rule="hyper" parents="18347 18930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      T(x,y / (z * (u * (z \ (1 / z))))) = T(x,y * ((z * u) \ (z * z)))
    ]]></literal>
    <justification jstring="[para(7124(a,1),18931(a,1,2,2))].">
      <j1 rule="para" parents="7124 18931"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      T(x,y * ((z * u) \ (z * z))) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(18894,a,18932,a),flip(a)].">
      <j1 rule="hyper" parents="18894 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      T(T(x,K(y,(z * u) \ (z * z))),((z * u) \ (z * z)) * y) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(12574,a,18933,a)].">
      <j1 rule="hyper" parents="12574 18933"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      T(x,y * (((z * (u / z)) \ w) \ (K(z \ u,z) * K(z \ u,z)))) = T(x,y / ((K(z \ u,z) \ 1) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(12097(a,1),18933(a,1,2,2,1))].">
      <j1 rule="para" parents="12097 18933"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),((u * z) \ (u * u)) * y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(15125(a,1),18934(a,1,1,2))].">
      <j1 rule="para" parents="15125 18934"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u * z) \ (u * u)) * y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(17528(a,1),18936(a,1,1))].">
      <j1 rule="para" parents="17528 18936"/>
    </justification>
  </clause>

  <clause id="18938">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u * (u * ((u * z) \ y))) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18586,a(flip),b,18937,a)].">
      <j1 rule="hyper" parents="60 18586 18937"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u \ 1) * z) \ y) = T(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18587,a(flip),b,18938,a)].">
      <j1 rule="hyper" parents="60 18587 18938"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      T(T(x,K(y * K(z \ 1,u),u * z)),((z \ 1) * u) \ (y * K(z \ 1,u))) = T(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(12385(a,1),18939(a,2,2))].">
      <j1 rule="para" parents="12385 18939"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      (T(x,y) * z) / T(1 / K(x,y),K(x,y) * (x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(9128(a,1),18805(a,1,1))].">
      <j1 rule="para" parents="9128 18805"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      (T(x,y) * z) / T(K(y,x),K(x,y) * (x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(5866(a,1),18941(a,1,2,1))].">
      <j1 rule="para" parents="5866 18941"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      (T(x,y) * z) / K(y,T(x,x * z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(17949(a,1),18942(a,1,2))].">
      <j1 rule="para" parents="17949 18942"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      (T(x,y) * z) / K(y,T(x,z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(7325(a,1),18943(a,1,2))].">
      <j1 rule="para" parents="7325 18943"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,T(y,z)) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8090,a,18944,a)].">
      <j1 rule="hyper" parents="8090 18944"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      T(x,y) * (z * K(x,T(y,z))) = (x * z) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7418,a,18946,a)].">
      <j1 rule="hyper" parents="7418 18946"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(8047,a,18947,a),flip(a)].">
      <j1 rule="hyper" parents="8047 18947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = K(x,z) * (T(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7906,a,b,18948,a),flip(a)].">
      <j1 rule="hyper" parents="370 7906 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      (x * y) * (K(x,z) * K(x,z)) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,7924,a(flip),b,18949,a),flip(a)].">
      <j1 rule="hyper" parents="370 7924 18949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(1188,a,18950,a)].">
      <j1 rule="hyper" parents="1188 18950"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      T(x,y * (T(T(z,u),u) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(18950(a,1),16725(a,1,2,2))].">
      <j1 rule="para" parents="18950 16725"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      T(T(x,y * (L(y,z,u) \ w)),L(y,z,u) * (y \ (y \ L(y,z,u)))) = T(T(x,(L(y,z,u) \ y) \ w),1)
    ]]></literal>
    <justification jstring="[hyper(16618,a,18842,a)].">
      <j1 rule="hyper" parents="16618 18842"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),((u \ 1) * z) \ (y * K(u \ 1,z))) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(18120(a,1),18940(a,1,1))].">
      <j1 rule="para" parents="18120 18940"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T((z * (u \ 1)) \ y,K(u \ 1,z))) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(12645(a,2),18954(a,1,2))].">
      <j1 rule="para" parents="12645 18954"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * (u \ 1)) \ y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(17207,a,18955,a)].">
      <j1 rule="hyper" parents="17207 18955"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y \ z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5(a,1),17812(a,2,2,2,2))].">
      <j1 rule="para" parents="5 17812"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y \ 1,y * z) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,18269,a(flip),b,18959,a),flip(a)].">
      <j1 rule="hyper" parents="370 18269 18959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) = T(x,(K(u,u \ (y / u)) * z) * (u \ (y / u)))
    ]]></literal>
    <justification jstring="[para(18019(a,1),17862(a,1,1))].">
      <j1 rule="para" parents="18019 17862"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) = T(x,K(u,u \ (y / u)) * (z * (u \ (y / u))))
    ]]></literal>
    <justification jstring="[para(7456(a,1),18961(a,2,2))].">
      <j1 rule="para" parents="7456 18961"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      T(T(x,K(y,z)),((y / u) / u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * ((y / u) / u)) = w
    ]]></literal>
    <justification jstring="[para(18962(a,2),17298(a,1))].">
      <j1 rule="para" parents="18962 17298"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      ((x * L(y,z,z)) * ((z * z) * T(u,w))) / ((x * L(y * (z * z),z,z)) * u) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(3903(a,1),18410(a,1,1))].">
      <j1 rule="para" parents="3903 18410"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y))) = K(x,T((y \ (y \ z)) * u,y \ (y \ 1)))
    ]]></literal>
    <justification jstring="[para(74(a,1),18712(a,1,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      K(x,((y \ 1) \ (((y \ 1) \ 1) \ z)) * (u / (y * y))) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17133,a(flip),b,18966,a),flip(a)].">
      <j1 rule="hyper" parents="370 17133 18966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * (u / (y * y))) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[para(1015(a,1),18968(a,1,2,1))].">
      <j1 rule="para" parents="1015 18968"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * ((y * y) \ u)) = K(x,(y \ (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18318,a(flip),b,18970,a)].">
      <j1 rule="hyper" parents="60 18318 18970"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      T(x,y / ((K(z \ u,z) \ 1) * (u \ w))) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(16780,a,18935,a),flip(a)].">
      <j1 rule="hyper" parents="16780 18935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      T(x,y / (K(z,z \ u) * (u \ w))) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[para(5865(a,1),18972(a,1,2,2,1))].">
      <j1 rule="para" parents="5865 18972"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      T(x,y / (((z \ u) * z) \ w)) = T(x,y / ((z * (u / z)) \ w))
    ]]></literal>
    <justification jstring="[para(12088(a,1),18974(a,1,2,2))].">
      <j1 rule="para" parents="12088 18974"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      ((x * L(y,z,z)) * ((z * z) * T(u,w))) / ((x * L(y,z,z)) * ((z * z) * u)) = K(u,T(w,x * (z * (z * y))))
    ]]></literal>
    <justification jstring="[para(3903(a,1),18965(a,1,2))].">
      <j1 rule="para" parents="3903 18965"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(x \ ((x \ 1) * y),x \ 1)
    ]]></literal>
    <justification jstring="[para(6644(a,1),17432(a,2,2))].">
      <j1 rule="para" parents="6644 17432"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K((x * x) \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(942(a,1),18977(a,2,2,1))].">
      <j1 rule="para" parents="942 18977"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(x \ (x \ y),x \ 1)
    ]]></literal>
    <justification jstring="[para(15130(a,1),18978(a,2,2))].">
      <j1 rule="para" parents="15130 18978"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = (y / (1 / x)) * K(y * (x * x),x \ 1)
    ]]></literal>
    <justification jstring="[para(16254(a,1),18979(a,2,2))].">
      <j1 rule="para" parents="16254 18979"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(1 / x,T(y * (x * x),x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8147,a(flip),b,18980,a),flip(a)].">
      <j1 rule="hyper" parents="370 8147 18980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(1 / x,x * (y * x))
    ]]></literal>
    <justification jstring="[para(18257(a,1),18981(a,2,2))].">
      <j1 rule="para" parents="18257 18981"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,x \ (y * x))
    ]]></literal>
    <justification jstring="[para(7721(a,1),18982(a,2,2))].">
      <j1 rule="para" parents="7721 18982"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(17(a,2),18983(a,2,2,2))].">
      <j1 rule="para" parents="17 18983"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      (T(x \ 1,x \ y) \ (y / (1 / x))) * T(x \ 1,x \ y) = y / T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8596(a,1),18984(a,2,2))].">
      <j1 rule="para" parents="8596 18984"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y * K(z / u,y)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,18242,a(flip),b,17813,a),flip(a)].">
      <j1 rule="hyper" parents="370 18242 17813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,T(y,z / u)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(8857(a,1),18986(a,1,2,2,1))].">
      <j1 rule="para" parents="8857 18986"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      T(x,(y * K(z / u,y)) * (T(u / z,y) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,17860,a(flip),b,18988,a)].">
      <j1 rule="hyper" parents="60 17860 18988"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      T(x,y * (K(z / u,y) * (T(u / z,y) \ w))) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(7845(a,1),18989(a,1,2))].">
      <j1 rule="para" parents="7845 18989"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      T(x,T(y,z / u) * (T(u / z,y) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(16814,a,18991,a)].">
      <j1 rule="hyper" parents="16814 18991"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      T(x,T(y,z * u) * (T(z / u,y) \ w)) = T(x,y * ((z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18483,a(flip),b,18992,a)].">
      <j1 rule="hyper" parents="60 18483 18992"/>
    </justification>
  </clause>

  <clause id="18994">
    <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(4(a,1),18926(a,1,1,1))].">
      <j1 rule="para" parents="4 18926"/>
    </justification>
  </clause>

  <clause id="18995">
    <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(4(a,1),18994(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4 18994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18996">
    <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(6465(a,1),18995(a,2,2))].">
      <j1 rule="para" parents="6465 18995"/>
    </justification>
  </clause>

  <clause id="18997">
    <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(4(a,1),18996(a,2,2,2))].">
      <j1 rule="para" parents="4 18996"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5667(a,1),18997(a,2,2))].">
      <j1 rule="para" parents="5667 18997"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,11468,a(flip),b,18998,a),flip(a)].">
      <j1 rule="hyper" parents="370 11468 18998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6503,a,18999,a)].">
      <j1 rule="hyper" parents="6503 18999"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),19000(a,1,2))].">
      <j1 rule="para" parents="4 19000"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6734,a,19001,a)].">
      <j1 rule="hyper" parents="6734 19001"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(15457,a,19002,a)].">
      <j1 rule="hyper" parents="15457 19002"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),19003(a,2,1))].">
      <j1 rule="para" parents="5 19003"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12195,a(flip),b,19004,a),flip(a)].">
      <j1 rule="hyper" parents="60 12195 19004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(6726,a,19005,a)].">
      <j1 rule="hyper" parents="6726 19005"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7156,a(flip),b,19006,a)].">
      <j1 rule="hyper" parents="60 7156 19006"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11200,a,b,19008,a)].">
      <j1 rule="hyper" parents="60 11200 19008"/>
    </justification>
  </clause>

  <clause id="19011">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),19008(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      T(x * K(y \ x,y),(y * z) \ z) \ T(x,T((y * z) \ z,T(y,u))) = K(y,x * ((y * z) \ z))
    ]]></literal>
    <justification jstring="[para(19010(a,1),18216(a,1,1,1,2))].">
      <j1 rule="para" parents="19010 18216"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8555,a,b,19011,a),flip(a)].">
      <j1 rule="hyper" parents="370 8555 19011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,19014,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="129 19014 88"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9330,a,b,19015,a)].">
      <j1 rule="hyper" parents="60 9330 19015"/>
    </justification>
  </clause>

  <clause id="19017">
    <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(19016(a,1),18771(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="19016 18771"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      T((x \ y) * x,(x * z) \ z) \ T(y,T((x * z) \ z,T(x,u))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(353(a,1),19013(a,1,1,1))].">
      <j1 rule="para" parents="353 19013"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T((x * z) \ z,T(x,u))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(9057(a,1),19018(a,1,1))].">
      <j1 rule="para" parents="9057 19018"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T((x * z) \ z,x)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),19020(a,1,2,2,2))].">
      <j1 rule="para" parents="106 19020"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,T(z \ (x \ z),x)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(9912(a,1),19021(a,1,2))].">
      <j1 rule="para" parents="9912 19021"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      T((x \ y) * x,z \ (x \ z)) \ T(y,z \ (x \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[para(4475(a,1),19022(a,1,2))].">
      <j1 rule="para" parents="4475 19022"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      K(x,T(x \ y,z \ (x \ z))) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,13176,a(flip),b,19023,a)].">
      <j1 rule="hyper" parents="60 13176 19023"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      K(x,T(x \ y,z \ z)) = K(x,y * ((x * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,11650,a(flip),b,19024,a)].">
      <j1 rule="hyper" parents="60 11650 19024"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      K(x,y * ((x * z) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(227(a,1),19025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="227 19025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      K(x,R(x \ 1,x,y) * z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10373,a,b,19026,a)].">
      <j1 rule="hyper" parents="60 10373 19026"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x,y * (z / (x * z))) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(10119,a,19027,a)].">
      <j1 rule="hyper" parents="10119 19027"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,11348,a(flip),b,19029,a),flip(a)].">
      <j1 rule="hyper" parents="60 11348 19029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,19031,a(flip),b,5765,a)].">
      <j1 rule="hyper" parents="129 19031 5765"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,7610,a,b,19033,a)].">
      <j1 rule="hyper" parents="60 7610 19033"/>
    </justification>
  </clause>

  <clause id="19035">
    <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(19034(a,1),19017(a,1,1,1))].">
      <j1 rule="para" parents="19034 19017"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(18773,a,19035,a),flip(a)].">
      <j1 rule="hyper" parents="18773 19035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17962,a,b,19036,a),flip(a)].">
      <j1 rule="hyper" parents="370 17962 19036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18183,a,b,19037,a)].">
      <j1 rule="hyper" parents="60 18183 19037"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(17492,a,19038,a),flip(a)].">
      <j1 rule="hyper" parents="17492 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19040">
    <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(19039(a,1),18184(a,2,1))].">
      <j1 rule="para" parents="19039 18184"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5371,a(flip),b,19040,a),flip(a)].">
      <j1 rule="hyper" parents="370 5371 19040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19042">
    <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(19041(a,1),6898(a,1,1))].">
      <j1 rule="para" parents="19041 6898"/>
    </justification>
  </clause>

  <clause id="19043">
    <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(60,a,6898,a(flip),b,19042,a),flip(a)].">
      <j1 rule="hyper" parents="60 6898 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      K(x,y * y) * (((x * T(y * y,z)) \ u) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(17135(a,1),17560(a,1,1))].">
      <j1 rule="para" parents="17135 17560"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,y * y) * ((T(y * y,z) \ (x \ u)) * T(y * y,z)) = K(y * y,z) * (((T(y * y,z) * x) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(3597(a,1),19044(a,1,2,1))].">
      <j1 rule="para" parents="3597 19044"/>
    </justification>
  </clause>

  <clause id="19047">
    <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(17423,a,18095,a),flip(a)].">
      <j1 rule="hyper" parents="17423 18095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <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(16407(a,1),19047(a,2,2))].">
      <j1 rule="para" parents="16407 19047"/>
    </justification>
  </clause>

  <clause id="19050">
    <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(370,a,18177,a(flip),b,19049,a),flip(a)].">
      <j1 rule="hyper" parents="370 18177 19049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19051">
    <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(18119,a,19050,a)].">
      <j1 rule="hyper" parents="18119 19050"/>
    </justification>
  </clause>

  <clause id="19053">
    <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(60,a,18062,a(flip),b,19051,a)].">
      <j1 rule="hyper" parents="60 18062 19051"/>
    </justification>
  </clause>

  <clause id="19054">
    <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(60,a,18071,a(flip),b,19053,a),flip(a)].">
      <j1 rule="hyper" parents="60 18071 19053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19055">
    <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(12984,a,19054,a)].">
      <j1 rule="hyper" parents="12984 19054"/>
    </justification>
  </clause>

  <clause id="19057">
    <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(15121(a,1),19054(a,1,2,2,2))].">
      <j1 rule="para" parents="15121 19054"/>
    </justification>
  </clause>

  <clause id="19058">
    <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(370,a,15887,a,b,19055,a),flip(a)].">
      <j1 rule="hyper" parents="370 15887 19055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19059">
    <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(370,a,9528,a(flip),b,19057,a),flip(a)].">
      <j1 rule="hyper" parents="370 9528 19057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19060">
    <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(19059(a,1),18896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19059 18896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19061">
    <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(15888,a,19058,a)].">
      <j1 rule="hyper" parents="15888 19058"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5232(a,1),19061(a,1,2))].">
      <j1 rule="para" parents="5232 19061"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(7466(a,1),19061(a,1,2))].">
      <j1 rule="para" parents="7466 19061"/>
    </justification>
  </clause>

  <clause id="19064">
    <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(60,a,13684,a(flip),b,19063,a),flip(a)].">
      <j1 rule="hyper" parents="60 13684 19063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19065">
    <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(8636(a,2),19064(a,2,3))].">
      <j1 rule="para" parents="8636 19064"/>
    </justification>
  </clause>

  <clause id="19066">
    <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(13680(a,1),19065(a,2,3))].">
      <j1 rule="para" parents="13680 19065"/>
    </justification>
  </clause>

  <clause id="19067">
    <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(5(a,1),19066(a,1,3,2,2))].">
      <j1 rule="para" parents="5 19066"/>
    </justification>
  </clause>

  <clause id="19068">
    <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(8636(a,1),19067(a,1,3))].">
      <j1 rule="para" parents="8636 19067"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,z)))
    ]]></literal>
    <justification jstring="[para(5(a,1),19068(a,2,3,2,2))].">
      <j1 rule="para" parents="5 19068"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,1),19069(a,2,3))].">
      <j1 rule="para" parents="8636 19069"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(77(a,1),19070(a,1,2,2))].">
      <j1 rule="para" parents="77 19070"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),19071(a,1,3))].">
      <j1 rule="para" parents="8636 19071"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),19072(a,2,3))].">
      <j1 rule="para" parents="8636 19072"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(15950,a,19073,a)].">
      <j1 rule="hyper" parents="15950 19073"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),19074(a,2,3))].">
      <j1 rule="para" parents="8648 19074"/>
    </justification>
  </clause>

  <clause id="19076">
    <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(8647(a,1),19060(a,2,2))].">
      <j1 rule="para" parents="8647 19060"/>
    </justification>
  </clause>

  <clause id="19078">
    <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(370,a,13357,a(flip),b,19076,a),flip(a)].">
      <j1 rule="hyper" parents="370 13357 19076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19079">
    <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(11914(a,1),19078(a,2,1))].">
      <j1 rule="para" parents="11914 19078"/>
    </justification>
  </clause>

  <clause id="19080">
    <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(370,a,15976,a(flip),b,19079,a),flip(a)].">
      <j1 rule="hyper" parents="370 15976 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19081">
    <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(18109(a,1),19080(a,1,2))].">
      <j1 rule="para" parents="18109 19080"/>
    </justification>
  </clause>

  <clause id="19082">
    <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(8647(a,1),19081(a,1,3))].">
      <j1 rule="para" parents="8647 19081"/>
    </justification>
  </clause>

  <clause id="19083">
    <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(13041,a,19082,a)].">
      <j1 rule="hyper" parents="13041 19082"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(193(a,1),19083(a,1,2,1))].">
      <j1 rule="para" parents="193 19083"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19075,a(flip),b,19084,a)].">
      <j1 rule="hyper" parents="60 19075 19084"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,K(x,w))) = v5
    ]]></literal>
    <justification jstring="[para(19085(a,2),15918(a,1))].">
      <j1 rule="para" parents="19085 15918"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,(y * (z * T(u,w \ v5))) / (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15237,a(flip),b,18593,a),flip(a)].">
      <j1 rule="hyper" parents="370 15237 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(x,(y * ((z * T(u,w \ v5)) \ 1)) * (z * T(u,w * v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),19087(a,2,2))].">
      <j1 rule="para" parents="6 19087"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) * (1 / (y * T(z,u \ w))))
    ]]></literal>
    <justification jstring="[para(18270(a,1),18594(a,2,2,1))].">
      <j1 rule="para" parents="18270 18594"/>
    </justification>
  </clause>

  <clause id="19090">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) / (y * T(z,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15237,a(flip),b,19089,a),flip(a)].">
      <j1 rule="hyper" parents="370 15237 19089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19091">
    <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(4590(a,1),7213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4590 7213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <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(9333(a,1),19091(a,2,2,2))].">
      <j1 rule="para" parents="9333 19091"/>
    </justification>
  </clause>

  <clause id="19094">
    <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(16214(a,1),19093(a,2,2))].">
      <j1 rule="para" parents="16214 19093"/>
    </justification>
  </clause>

  <clause id="19095">
    <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(370,a,7506,a(flip),b,19094,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 19094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19096">
    <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(370,a,6684,a(flip),b,19095,a),flip(a)].">
      <j1 rule="hyper" parents="370 6684 19095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19097">
    <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(4590(a,1),19096(a,1,2,2,2))].">
      <j1 rule="para" parents="4590 19096"/>
    </justification>
  </clause>

  <clause id="19099">
    <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(7506(a,1),19097(a,1,2,2))].">
      <j1 rule="para" parents="7506 19097"/>
    </justification>
  </clause>

  <clause id="19100">
    <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(7247(a,1),19099(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7247 19099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19101">
    <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(370,a,9741,a(flip),b,19100,a),flip(a)].">
      <j1 rule="hyper" parents="370 9741 19100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19102">
    <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(222(a,1),19101(a,2,2))].">
      <j1 rule="para" parents="222 19101"/>
    </justification>
  </clause>

  <clause id="19103">
    <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(19043(a,1),19102(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19043 19102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19104">
    <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(370,a,19102,a(flip),b,19103,a),flip(a)].">
      <j1 rule="hyper" parents="370 19102 19103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19105">
    <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(370,a,8024,a(flip),b,19104,a),flip(a)].">
      <j1 rule="hyper" parents="370 8024 19104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19106">
    <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(8181,a,19105,a)].">
      <j1 rule="hyper" parents="8181 19105"/>
    </justification>
  </clause>

  <clause id="19107">
    <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(60,a,18181,a(flip),b,19106,a)].">
      <j1 rule="hyper" parents="60 18181 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <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(60,a,18182,a(flip),b,19107,a),flip(a)].">
      <j1 rule="hyper" parents="60 18182 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19109">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,11067,a(flip),b,19108,a)].">
      <j1 rule="hyper" parents="60 11067 19108"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(106(a,1),19109(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 19109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17962,a(flip),b,19110,a)].">
      <j1 rule="hyper" parents="60 17962 19110"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8621,a,b,19112,a)].">
      <j1 rule="hyper" parents="370 8621 19112"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(31,a,18041,a,b,19113,a)].">
      <j1 rule="hyper" parents="31 18041 19113"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(9472,a,19114,a)].">
      <j1 rule="hyper" parents="9472 19114"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17997,a(flip),b,19114,a),flip(a)].">
      <j1 rule="hyper" parents="60 17997 19114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17995,a(flip),b,19114,a),flip(a)].">
      <j1 rule="hyper" parents="60 17995 19114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19118">
    <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(19114(a,1),18049(a,1,1))].">
      <j1 rule="para" parents="19114 18049"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(17385,a,19117,a)].">
      <j1 rule="hyper" parents="17385 19117"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),19119(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 19119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19121">
    <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(9580,a,19118,a),flip(a)].">
      <j1 rule="hyper" parents="9580 19118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19122">
    <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(60,a,18094,a(flip),b,19121,a),flip(a)].">
      <j1 rule="hyper" parents="60 18094 19121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19123">
    <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(77(a,1),19121(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="77 19121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19124">
    <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(17386,a,19123,a)].">
      <j1 rule="hyper" parents="17386 19123"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),19122(a,2,2,2,2))].">
      <j1 rule="para" parents="5 19122"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,18059,a,b,19125,a),flip(a)].">
      <j1 rule="hyper" parents="370 18059 19125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(19125(a,2),18061(a,1))].">
      <j1 rule="para" parents="19125 18061"/>
    </justification>
  </clause>

  <clause id="19128">
    <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(60,a,19124,a(flip),b,19126,a)].">
      <j1 rule="hyper" parents="60 19124 19126"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(15418(a,1),19126(a,1,2))].">
      <j1 rule="para" parents="15418 19126"/>
    </justification>
  </clause>

  <clause id="19130">
    <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(19126(a,2),18061(a,1))].">
      <j1 rule="para" parents="19126 18061"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19129,a(flip),b,19128,a),flip(a)].">
      <j1 rule="hyper" parents="60 19129 19128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19133">
    <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(6150(a,2),19128(a,2,2,2,1))].">
      <j1 rule="para" parents="6150 19128"/>
    </justification>
  </clause>

  <clause id="19134">
    <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(15420(a,1),19133(a,1,2))].">
      <j1 rule="para" parents="15420 19133"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(19127,a,19134,a),flip(a)].">
      <j1 rule="hyper" parents="19127 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19115,a(flip),b,19135,a)].">
      <j1 rule="hyper" parents="60 19115 19135"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(18096,a,19136,a)].">
      <j1 rule="hyper" parents="18096 19136"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18057,a,b,19137,a)].">
      <j1 rule="hyper" parents="60 18057 19137"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18107,a(flip),b,19137,a),flip(a)].">
      <j1 rule="hyper" parents="60 18107 19137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(18115,a,19138,a)].">
      <j1 rule="hyper" parents="18115 19138"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(18064,a,19139,a)].">
      <j1 rule="hyper" parents="18064 19139"/>
    </justification>
  </clause>

  <clause id="19142">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19132,a,b,19139,a)].">
      <j1 rule="hyper" parents="60 19132 19139"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16552,a,b,19141,a)].">
      <j1 rule="hyper" parents="60 16552 19141"/>
    </justification>
  </clause>

  <clause id="19144">
    <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(10396(a,1),19141(a,1,2))].">
      <j1 rule="para" parents="10396 19141"/>
    </justification>
  </clause>

  <clause id="19145">
    <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(16156(a,1),19141(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="16156 19141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(18064,a,19142,a)].">
      <j1 rule="hyper" parents="18064 19142"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16120,a(flip),b,19143,a)].">
      <j1 rule="hyper" parents="60 16120 19143"/>
    </justification>
  </clause>

  <clause id="19148">
    <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(17793(a,1),19144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17793 19144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19149">
    <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(370,a,19146,a(flip),b,19145,a),flip(a)].">
      <j1 rule="hyper" parents="370 19146 19145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19151">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19140,a(flip),b,19149,a)].">
      <j1 rule="hyper" parents="60 19140 19149"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(18061,a,19151,a)].">
      <j1 rule="hyper" parents="18061 19151"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18091,a(flip),b,19151,a)].">
      <j1 rule="hyper" parents="60 18091 19151"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(9472,a,19154,a)].">
      <j1 rule="hyper" parents="9472 19154"/>
    </justification>
  </clause>

  <clause id="19156">
    <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(60,a,18858,a(flip),b,19155,a),flip(a)].">
      <j1 rule="hyper" parents="60 18858 19155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <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(17377,a,19156,a)].">
      <j1 rule="hyper" parents="17377 19156"/>
    </justification>
  </clause>

  <clause id="19158">
    <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(370,a,15931,a,b,19156,a),flip(a)].">
      <j1 rule="hyper" parents="370 15931 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,((y / w) / (u * y)) * (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(19156(a,1),8634(a,1))].">
      <j1 rule="para" parents="19156 8634"/>
    </justification>
  </clause>

  <clause id="19160">
    <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(7(a,1),19157(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 19157"/>
    </justification>
  </clause>

  <clause id="19161">
    <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(7(a,1),19158(a,2,2))].">
      <j1 rule="para" parents="7 19158"/>
    </justification>
  </clause>

  <clause id="19162">
    <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(370,a,9428,a(flip),b,19148,a),flip(a)].">
      <j1 rule="hyper" parents="370 9428 19148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,19119,a(flip),b,19162,a),flip(a)].">
      <j1 rule="hyper" parents="60 19119 19162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19165">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19115,a(flip),b,19163,a),flip(a)].">
      <j1 rule="hyper" parents="370 19115 19163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(302(a,1),19165(a,1,2,2,2))].">
      <j1 rule="para" parents="302 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17986,a(flip),b,19166,a),flip(a)].">
      <j1 rule="hyper" parents="370 17986 19166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19169">
    <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(60,a,18874,a(flip),b,19167,a),flip(a)].">
      <j1 rule="hyper" parents="60 18874 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(103(a,1),19169(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="103 19169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19172">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(18101,a,19171,a)].">
      <j1 rule="hyper" parents="18101 19171"/>
    </justification>
  </clause>

  <clause id="19173">
    <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(18013,a,19172,a),flip(a)].">
      <j1 rule="hyper" parents="18013 19172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(15633,a,19172,a)].">
      <j1 rule="hyper" parents="15633 19172"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(18013,a,19173,a),flip(a)].">
      <j1 rule="hyper" parents="18013 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(18098,a,19175,a)].">
      <j1 rule="hyper" parents="18098 19175"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,13678,a(flip),b,19174,a),flip(a)].">
      <j1 rule="hyper" parents="370 13678 19174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,19152,a(flip),b,19177,a),flip(a)].">
      <j1 rule="hyper" parents="370 19152 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(9472,a,19178,a)].">
      <j1 rule="hyper" parents="9472 19178"/>
    </justification>
  </clause>

  <clause id="19180">
    <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(15097(a,1),19179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15097 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19181">
    <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(370,a,15886,a,b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="370 15886 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <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(370,a,19084,a(flip),b,19181,a),flip(a)].">
      <j1 rule="hyper" parents="370 19084 19181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19183">
    <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(8636(a,1),19182(a,2,3))].">
      <j1 rule="para" parents="8636 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <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(6102(a,1),19183(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6102 19183"/>
    </justification>
  </clause>

  <clause id="19185">
    <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(7219(a,1),19184(a,1,2))].">
      <j1 rule="para" parents="7219 19184"/>
    </justification>
  </clause>

  <clause id="19186">
    <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(15348(a,1),19185(a,1,2))].">
      <j1 rule="para" parents="15348 19185"/>
    </justification>
  </clause>

  <clause id="19187">
    <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(6443(a,1),19186(a,1,2,2,1))].">
      <j1 rule="para" parents="6443 19186"/>
    </justification>
  </clause>

  <clause id="19188">
    <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(60,a,19176,a(flip),b,19187,a)].">
      <j1 rule="hyper" parents="60 19176 19187"/>
    </justification>
  </clause>

  <clause id="19189">
    <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(18052,a,19188,a)].">
      <j1 rule="hyper" parents="18052 19188"/>
    </justification>
  </clause>

  <clause id="19190">
    <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(8351(a,1),19189(a,2,3,2))].">
      <j1 rule="para" parents="8351 19189"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17980(a,1),19190(a,2,3))].">
      <j1 rule="para" parents="17980 19190"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19160,a(flip),b,19191,a)].">
      <j1 rule="hyper" parents="60 19160 19191"/>
    </justification>
  </clause>

  <clause id="19194">
    <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(74(a,1),19192(a,1,3,2,1))].">
      <j1 rule="para" parents="74 19192"/>
    </justification>
  </clause>

  <clause id="19195">
    <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(19120(a,1),19194(a,1,3))].">
      <j1 rule="para" parents="19120 19194"/>
    </justification>
  </clause>

  <clause id="19196">
    <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(8630(a,1),19195(a,1,3))].">
      <j1 rule="para" parents="8630 19195"/>
    </justification>
  </clause>

  <clause id="19197">
    <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(18723(a,1),19196(a,1,3))].">
      <j1 rule="para" parents="18723 19196"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15925,a(flip),b,19197,a),flip(a)].">
      <j1 rule="hyper" parents="60 15925 19197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),19198(a,1,3))].">
      <j1 rule="para" parents="8648 19198"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19062,a,b,19199,a)].">
      <j1 rule="hyper" parents="60 19062 19199"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(19086,a,19200,a),flip(a)].">
      <j1 rule="hyper" parents="19086 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(8630(a,1),19201(a,2,3))].">
      <j1 rule="para" parents="8630 19201"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(19159,a,19202,a)].">
      <j1 rule="hyper" parents="19159 19202"/>
    </justification>
  </clause>

  <clause id="19204">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(8636(a,2),19203(a,2,3))].">
      <j1 rule="para" parents="8636 19203"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19161,a(flip),b,19204,a)].">
      <j1 rule="hyper" parents="60 19161 19204"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(9429(a,1),19205(a,1,3))].">
      <j1 rule="para" parents="9429 19205"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(8648(a,1),19206(a,2,3))].">
      <j1 rule="para" parents="8648 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19202,a(flip),b,19207,a),flip(a)].">
      <j1 rule="hyper" parents="60 19202 19207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19209">
    <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(19208(a,1),15883(a,1,1))].">
      <j1 rule="para" parents="19208 15883"/>
    </justification>
  </clause>

  <clause id="19210">
    <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(8630(a,1),19209(a,1,2))].">
      <j1 rule="para" parents="8630 19209"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(16042,a,19210,a),flip(a)].">
      <j1 rule="hyper" parents="16042 19210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(9574,a,19211,a)].">
      <j1 rule="hyper" parents="9574 19211"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,19147,a(flip),b,19212,a),flip(a)].">
      <j1 rule="hyper" parents="370 19147 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <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(1036(a,1),19212(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1036 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19215">
    <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(10137(a,1),19212(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10137 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(19130,a,19213,a)].">
      <j1 rule="hyper" parents="19130 19213"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(19215(a,2),9444(a,1))].">
      <j1 rule="para" parents="19215 9444"/>
    </justification>
  </clause>

  <clause id="19218">
    <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(370,a,17273,a,b,19214,a),flip(a)].">
      <j1 rule="hyper" parents="370 17273 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19219">
    <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(370,a,19216,a(flip),b,19218,a),flip(a)].">
      <j1 rule="hyper" parents="370 19216 19218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19220">
    <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(370,a,19116,a(flip),b,19219,a),flip(a)].">
      <j1 rule="hyper" parents="370 19116 19219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19223">
    <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(8849(a,1),19220(a,2,2))].">
      <j1 rule="para" parents="8849 19220"/>
    </justification>
  </clause>

  <clause id="19224">
    <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(370,a,17263,a(flip),b,19223,a),flip(a)].">
      <j1 rule="hyper" parents="370 17263 19223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19227">
    <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(60,a,16120,a(flip),b,19224,a)].">
      <j1 rule="hyper" parents="60 16120 19224"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19217,a,19227,a),flip(a)].">
      <j1 rule="hyper" parents="19217 19227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(11055(a,1),19228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11055 19228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,9428,a(flip),b,19230,a),flip(a)].">
      <j1 rule="hyper" parents="370 9428 19230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12956,a,19233,a)].">
      <j1 rule="hyper" parents="12956 19233"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(9527,a,19233,a)].">
      <j1 rule="hyper" parents="9527 19233"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,19233,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 19233 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      K(x,K(y,(z \ u) \ w)) = K(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(656(a,1),19233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="656 19233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      T(x / T(K(y,L(z,u,w)),v5),K(K(y,L(z,u,w)),v5)) = K(v5,K(y,z)) * (x / K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(19233(a,1),7509(a,2,1))].">
      <j1 rule="para" parents="19233 7509"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(19233(a,1),9520(a,1,2))].">
      <j1 rule="para" parents="19233 9520"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(11013(a,1),19233(a,1,2))].">
      <j1 rule="para" parents="11013 19233"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16404(a,2),19233(a,1,2))].">
      <j1 rule="para" parents="16404 19233"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19233(a,1),17337(a,1,1))].">
      <j1 rule="para" parents="19233 17337"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,19237,a,b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="126 19237 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,19237,a(flip),b,15873,a),flip(a)].">
      <j1 rule="hyper" parents="126 19237 15873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      a(x,y,K(K(z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,19237,a(flip),b,15922,a),flip(a)].">
      <j1 rule="hyper" parents="124 19237 15922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19257">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(19237(a,1),16431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19237 16431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,15805,a,b,19253,a)].">
      <j1 rule="hyper" parents="60 15805 19253"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,19255,a)].">
      <j1 rule="hyper" parents="49 19255"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      K(a(x,y,K(z,u)),w) = 1
    ]]></literal>
    <justification jstring="[hyper(15509,a,19256,a)].">
      <j1 rule="hyper" parents="15509 19256"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,19260,a)].">
      <j1 rule="hyper" parents="49 19260"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(53,a,19266,a)].">
      <j1 rule="hyper" parents="53 19266"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10144,a,19271,a)].">
      <j1 rule="hyper" parents="10144 19271"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(1079,a,19271,a)].">
      <j1 rule="hyper" parents="1079 19271"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(19271(a,1),47(a,2))].">
      <j1 rule="para" parents="19271 47"/>
    </justification>
  </clause>

  <clause id="19278">
    <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(19271(a,1),620(a,1,2,2,1))].">
      <j1 rule="para" parents="19271 620"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(13047,a,19265,a)].">
      <j1 rule="hyper" parents="13047 19265"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13033,a,19265,a)].">
      <j1 rule="hyper" parents="13033 19265"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(w,u) * z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,13052,a(flip),b,19265,a),flip(a)].">
      <j1 rule="hyper" parents="60 13052 19265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,12943,a(flip),b,19265,a),flip(a)].">
      <j1 rule="hyper" parents="60 12943 19265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7528,a(flip),b,19265,a),flip(a)].">
      <j1 rule="hyper" parents="60 7528 19265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,19265,a(flip),b,14810,a(flip))].">
      <j1 rule="hyper" parents="129 19265 14810"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      L(L(K(x,y),z,u),w,K(v5,v6)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(19265(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19265 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6591(a,1),19265(a,1,3))].">
      <j1 rule="para" parents="6591 19265"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u * K(x,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(17968,a,19279,a)].">
      <j1 rule="hyper" parents="17968 19279"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(w,L(u,z,y))) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,16614,a(flip),b,19280,a)].">
      <j1 rule="hyper" parents="60 16614 19280"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(7522(a,1),19280(a,1,2))].">
      <j1 rule="para" parents="7522 19280"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10145(a,1),19280(a,1,2))].">
      <j1 rule="para" parents="10145 19280"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14466,a,19275,a),flip(a)].">
      <j1 rule="hyper" parents="14466 19275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      L(x,y,T(z,T(u,w))) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8587(a,1),19275(a,1,3))].">
      <j1 rule="para" parents="8587 19275"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      L(x,y,z * (u * K(z,w))) = L(x,y,T(z,w) * u)
    ]]></literal>
    <justification jstring="[para(9095(a,1),19275(a,1,3))].">
      <j1 rule="para" parents="9095 19275"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * ((v5 / T(y,L(x,z,u))) / (v5 / y))
    ]]></literal>
    <justification jstring="[para(19238(a,1),13467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19238 13467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,9829,a,b,19249,a)].">
      <j1 rule="hyper" parents="60 9829 19249"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      T(K(x,y),R(z,u,w)) = K(x,y) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(19250(a,1),8610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19250 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (K(z,K(x,y)) * K(x,y)) = a(w,u,K(x,y))
    ]]></literal>
    <justification jstring="[para(19303(a,1),12105(a,1,2,1))].">
      <j1 rule="para" parents="19303 12105"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,19274,a)].">
      <j1 rule="hyper" parents="51 19274"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,19274,a(flip),b,17642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 19274 17642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,w)) * x = v5
    ]]></literal>
    <justification jstring="[para(19274(a,1),328(a,1,2))].">
      <j1 rule="para" parents="19274 328"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(15109(a,1),19315(a,1,2))].">
      <j1 rule="para" parents="15109 19315"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      T(x,a(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(15111(a,2),19315(a,1,2))].">
      <j1 rule="para" parents="15111 19315"/>
    </justification>
  </clause>

  <clause id="19323">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(15496(a,1),19315(a,1,2))].">
      <j1 rule="para" parents="15496 19315"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12610,a,19321,a)].">
      <j1 rule="hyper" parents="12610 19321"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      T(x,a(y,z,u) / w) = T(x,w \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9561,a,19321,a),flip(a)].">
      <j1 rule="hyper" parents="9561 19321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9101,a,19321,a)].">
      <j1 rule="hyper" parents="9101 19321"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8748,a,19321,a)].">
      <j1 rule="hyper" parents="8748 19321"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(19321(a,1),8593(a,2))].">
      <j1 rule="para" parents="19321 8593"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      T(x,y / a(z,u,w)) = T(x,a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(19321(a,1),9562(a,1,1))].">
      <j1 rule="para" parents="19321 9562"/>
    </justification>
  </clause>

  <clause id="19340">
    <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(19321(a,1),12610(a,1))].">
      <j1 rule="para" parents="19321 12610"/>
    </justification>
  </clause>

  <clause id="19341">
    <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(19321(a,1),12611(a,1,1))].">
      <j1 rule="para" parents="19321 12611"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14959(a,2),19321(a,1,2))].">
      <j1 rule="para" parents="14959 19321"/>
    </justification>
  </clause>

  <clause id="19343">
    <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(19321(a,1),16704(a,1,2,1,2))].">
      <j1 rule="para" parents="19321 16704"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      (a(K(x,y),z,u) \ w) * a(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[hyper(3282,a,19322,a)].">
      <j1 rule="hyper" parents="3282 19322"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      K(a(x,y,z),u) * (w \ 1) = w \ a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15631,a,19323,a)].">
      <j1 rule="hyper" parents="15631 19323"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      K(x,a(y,z,u) / w) = K(x,w \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8911,a,19328,a)].">
      <j1 rule="hyper" parents="8911 19328"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      K(x,y) * a(z,u,w) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(19328(a,1),8011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19328 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19355">
    <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(19328(a,1),8453(a,1))].">
      <j1 rule="para" parents="19328 8453"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(19328(a,1),8847(a,1))].">
      <j1 rule="para" parents="19328 8847"/>
    </justification>
  </clause>

  <clause id="19357">
    <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(19328(a,1),12588(a,1))].">
      <j1 rule="para" parents="19328 12588"/>
    </justification>
  </clause>

  <clause id="19358">
    <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(19328(a,1),12623(a,1))].">
      <j1 rule="para" parents="19328 12623"/>
    </justification>
  </clause>

  <clause id="19359">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ 1) = a(z,u,w) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(19328(a,1),15644(a,1,1))].">
      <j1 rule="para" parents="19328 15644"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(9469,a,19342,a)].">
      <j1 rule="hyper" parents="9469 19342"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (L(y,z,u) \ y)) = v5
    ]]></literal>
    <justification jstring="[para(19342(a,1),9561(a,1))].">
      <j1 rule="para" parents="19342 9561"/>
    </justification>
  </clause>

  <clause id="19362">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9561,a,19360,a),flip(a)].">
      <j1 rule="hyper" parents="9561 19360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (y \ L(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(19360(a,1),9561(a,1))].">
      <j1 rule="para" parents="19360 9561"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ L(z,u,w)) * y) = v5
    ]]></literal>
    <justification jstring="[para(19360(a,1),12610(a,1))].">
      <j1 rule="para" parents="19360 12610"/>
    </justification>
  </clause>

  <clause id="19365">
    <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(60,a,12943,a(flip),b,19288,a),flip(a)].">
      <j1 rule="hyper" parents="60 12943 19288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19366">
    <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="[hyper(129,a,19288,a(flip),b,14810,a(flip))].">
      <j1 rule="hyper" parents="129 19288 14810"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,L(w,z,x)) = K(z \ (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16571,a(flip),b,19296,a),flip(a)].">
      <j1 rule="hyper" parents="60 16571 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K((T(x,y) \ z) \ u,L(w,z,x)) = K(z \ (T(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,19296,a),flip(a)].">
      <j1 rule="hyper" parents="60 15933 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x / y,x)) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15428,a(flip),b,19296,a),flip(a)].">
      <j1 rule="hyper" parents="60 15428 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(109(a,1),19296(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="109 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      K(x,L(y,1 / z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3388(a,1),19296(a,2,2))].">
      <j1 rule="para" parents="3388 19296"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      L(x,y,T(T(z,u) / w,z)) = L(x,y,w \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14469,a,19298,a),flip(a)].">
      <j1 rule="hyper" parents="14469 19298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19373">
    <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(8787(a,1),19356(a,1))].">
      <j1 rule="para" parents="8787 19356"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,19243,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 19243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19243(a,2),5265(a,1))].">
      <j1 rule="para" parents="19243 5265"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      T(x,K(y,L(z / u,w,v5))) = x * K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(17273(a,1),19243(a,2,2))].">
      <j1 rule="para" parents="17273 19243"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9640,a,b,19374,a)].">
      <j1 rule="hyper" parents="60 9640 19374"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = ((x * (y * K(z,u))) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,13120,a(flip),b,19374,a),flip(a)].">
      <j1 rule="hyper" parents="60 13120 19374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(656(a,1),19374(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="656 19374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      T(x / L(K(y,z),u,w),K(y,z)) = L(K(y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,19379,a),flip(a)].">
      <j1 rule="hyper" parents="494 19379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(u,z)) * (K(z,u) * L(K(y,z),w,v5)) = x * ((x * L(K(y,z),w,v5)) / x)
    ]]></literal>
    <justification jstring="[para(19379(a,1),11871(a,1,1,1))].">
      <j1 rule="para" parents="19379 11871"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (L(u,K(y,z),x) * w)) = L(w,L(u,K(y,z),x),K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,620,a,b,19297,a)].">
      <j1 rule="hyper" parents="370 620 19297"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      L(x,y,K(z,u * u) * (w * v5)) = L(x,y,w * (v5 * K(z,u * u)))
    ]]></literal>
    <justification jstring="[para(11340(a,1),19297(a,2,3))].">
      <j1 rule="para" parents="11340 19297"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,15825,a,b,19316,a)].">
      <j1 rule="hyper" parents="370 15825 19316"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = w * a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,15826,a,b,19316,a)].">
      <j1 rule="hyper" parents="60 15826 19316"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      (1 / x) * a(y,z,K(u,w)) = a(y,z,K(u,w)) / x
    ]]></literal>
    <justification jstring="[hyper(60,a,15617,a(flip),b,19316,a),flip(a)].">
      <j1 rule="hyper" parents="60 15617 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15816(a,1),19316(a,1,1))].">
      <j1 rule="para" parents="15816 19316"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) / x = K(x,w / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,19338,a(flip),b,5275,a(flip))].">
      <j1 rule="hyper" parents="128 19338 5275"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) \ x = K(w / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(19338(a,1),5699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="19338 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (w * a(u,z,K(y,x))) = w
    ]]></literal>
    <justification jstring="[hyper(15880,a,19345,a)].">
      <j1 rule="hyper" parents="15880 19345"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      a(K(x,y),z,u) \ w = w * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(13842,a,19345,a),flip(a)].">
      <j1 rule="hyper" parents="13842 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) \ y = K(y,x) * (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(19353(a,2),15529(a,1,1))].">
      <j1 rule="para" parents="19353 15529"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      K(x,L(y,1 / z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19296,a(flip),b,19371,a)].">
      <j1 rule="hyper" parents="60 19296 19371"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      K(x,L(y,z \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(74(a,1),19400(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      T(x,K(y,(z * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ (z \ w))) = v5
    ]]></literal>
    <justification jstring="[para(344(a,1),19375(a,1,2,2))].">
      <j1 rule="para" parents="344 19375"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      x / (x * a(y,z,K(u,w))) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(376,a,19388,a)].">
      <j1 rule="hyper" parents="376 19388"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[hyper(155,a,19388,a)].">
      <j1 rule="hyper" parents="155 19388"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = T(x,a(w,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,19392,a(flip),b,7857,a)].">
      <j1 rule="hyper" parents="129 19392 7857"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = v5 / (v5 * a(w,z,K(u,y / x)))
    ]]></literal>
    <justification jstring="[para(8767(a,1),19403(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="8767 19403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19409">
    <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(19286(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="19286 617"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      T(K(x,y),R(z,u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8610,a(flip),b,19309,a),flip(a)].">
      <j1 rule="hyper" parents="370 8610 19309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      T(K(x,y),L(z,u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16399,a(flip),b,19410,a)].">
      <j1 rule="hyper" parents="60 16399 19410"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8122,a,19411,a)].">
      <j1 rule="hyper" parents="8122 19411"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,19412,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 19412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,19413,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 19413 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(344(a,1),19413(a,1,2,2))].">
      <j1 rule="para" parents="344 19413"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      L(x,y,z) * K(u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(19413(a,1),8012(a,1,2))].">
      <j1 rule="para" parents="19413 8012"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x * L(y,z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(y,z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(19413(a,1),12579(a,1))].">
      <j1 rule="para" parents="19413 12579"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      K(x,T(y,R(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(16399(a,2),19413(a,1,2))].">
      <j1 rule="para" parents="16399 19413"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K(x * R(y,z,u),T(w,y)) = K(R(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(12579,a,19421,a),flip(a)].">
      <j1 rule="hyper" parents="12579 19421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x * R(y,z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(y,z,u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(19421(a,1),12579(a,1))].">
      <j1 rule="para" parents="19421 12579"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19416(a,2),5265(a,1))].">
      <j1 rule="para" parents="19416 5265"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      K(x,K(y,z \ (u * w))) = K(x,K(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(17509,a,19244,a),flip(a)].">
      <j1 rule="hyper" parents="17509 19244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(17471,a,19248,a)].">
      <j1 rule="hyper" parents="17471 19248"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(17200(a,2),19251(a,2,2))].">
      <j1 rule="para" parents="17200 19251"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(19248(a,1),19251(a,2,2))].">
      <j1 rule="para" parents="19248 19251"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19251,a(flip),b,19257,a),flip(a)].">
      <j1 rule="hyper" parents="370 19251 19257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,K(y,z)) * ((x \ u) * w) = (T(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(8683(a,1),19257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8683 19257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(17200(a,1),19257(a,1,1))].">
      <j1 rule="para" parents="17200 19257"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(8679(a,2),19276(a,2,2))].">
      <j1 rule="para" parents="8679 19276"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(7506(a,2),19282(a,2,2,2))].">
      <j1 rule="para" parents="7506 19282"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(17733,a,19283,a)].">
      <j1 rule="hyper" parents="17733 19283"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K((x / y) \ (K(z,x) * u),w) = K((T(x,z) / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(15370(a,1),19283(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15370 19283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,8045,a(flip),b,19285,a),flip(a)].">
      <j1 rule="hyper" parents="370 8045 19285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(x,y)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(8758(a,1),19285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8758 19285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) = (K(x,y) / z) * K(u,w)
    ]]></literal>
    <justification jstring="[para(15121(a,1),19285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15121 19285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(17706,a,19295,a)].">
      <j1 rule="hyper" parents="17706 19295"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      L(x,y,z * (K(u,z) * w)) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15742,a,b,19299,a)].">
      <j1 rule="hyper" parents="60 15742 19299"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ 1) = w \ a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15496(a,2),19348(a,1,1))].">
      <j1 rule="para" parents="15496 19348"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      L(x,y,z \ T(u,z \ 1)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,14020,a(flip),b,19372,a),flip(a)].">
      <j1 rule="hyper" parents="60 14020 19372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      L(x,y,z \ T(u,z)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16136,a(flip),b,19451,a)].">
      <j1 rule="hyper" parents="60 16136 19451"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      L(x,y,T(z,u) \ u) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5749(a,2),19452(a,1,3))].">
      <j1 rule="para" parents="5749 19452"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      L(x,y,z / (u / z)) = L(x,y,(z \ u) \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),19453(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="109 19453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      L(x,y,(z / y) \ y) = L(x,y,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(14486,a,19454,a)].">
      <j1 rule="hyper" parents="14486 19454"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      L(x,y \ z,(z / y) \ y) = L(x,y \ z,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12703,a(flip),b,19454,a)].">
      <j1 rule="hyper" parents="60 12703 19454"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(17529,a,19381,a),flip(a)].">
      <j1 rule="hyper" parents="17529 19381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      K(x,(L(1 / y,z,1 / y) * a(u,w,K(v5,v6))) * v7) = K(x,(a(u,w,K(v5,v6)) / y) * v7)
    ]]></literal>
    <justification jstring="[para(19391(a,1),16976(a,2,2,1))].">
      <j1 rule="para" parents="19391 16976"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(15808(a,1),19406(a,1,2,2))].">
      <j1 rule="para" parents="15808 19406"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(17494,a,19417,a),flip(a)].">
      <j1 rule="hyper" parents="17494 19417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(K(x,R(y,z,u)) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8797,a(flip),b,19422,a),flip(a)].">
      <j1 rule="hyper" parents="370 8797 19422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K((x \ y) * R(x,z,z),T(u,x)) = K((y / x) * R(x,z,z),u)
    ]]></literal>
    <justification jstring="[para(16455(a,1),19422(a,2,1))].">
      <j1 rule="para" parents="16455 19422"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * w)) = K(x,K(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(17509,a,19426,a),flip(a)].">
      <j1 rule="hyper" parents="17509 19426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) != u * v5
    ]]></literal>
    <literal><![CDATA[
      w * K(y,K(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(19428(a,2),40(a,1))].">
      <j1 rule="para" parents="19428 40"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(19431(a,1),17676(a,1,2))].">
      <j1 rule="para" parents="19431 17676"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(19431(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="19431 17677"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(9669(a,1),19468(a,1,2,2))].">
      <j1 rule="para" parents="9669 19468"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(17398(a,1),19468(a,1,2,2))].">
      <j1 rule="para" parents="17398 19468"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,19431,a(flip),b,19438,a),flip(a)].">
      <j1 rule="hyper" parents="370 19431 19438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,(y \ z) \ (K(u,y) \ w)) = K(x,(T(y,u) \ z) \ w)
    ]]></literal>
    <justification jstring="[para(7853(a,1),19440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7853 19440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K(x \ (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18186,a,b,19441,a)].">
      <j1 rule="hyper" parents="60 18186 19441"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K((x * y) / (K(z,u) * y),w) = K(y \ (K(u,z) * (y * x)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,17846,a,b,19441,a)].">
      <j1 rule="hyper" parents="60 17846 19441"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (L(K(u,y),w,v5) * v6),v7)
    ]]></literal>
    <justification jstring="[para(10895(a,2),19441(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10895 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z \ u,z) * w)) = K(x,(y * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[para(5631(a,1),19448(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5631 19448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (K(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(7506(a,2),19448(a,2,2,2))].">
      <j1 rule="para" parents="7506 19448"/>
    </justification>
  </clause>

  <clause id="19481">
    <literal><![CDATA[
      L(x,y,((z * u) / z) * w) = L(x,y,T(u,z) * w)
    ]]></literal>
    <justification jstring="[para(8202(a,2),19449(a,1,3))].">
      <j1 rule="para" parents="8202 19449"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      T(x,K(y,(z \ u) * w)) = T(x,K(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(17529,a,19457,a),flip(a)].">
      <j1 rule="hyper" parents="17529 19457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19484">
    <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(19461(a,1),17494(a,1))].">
      <j1 rule="para" parents="19461 17494"/>
    </justification>
  </clause>

  <clause id="19485">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(18100,a,19465,a)].">
      <j1 rule="hyper" parents="18100 19465"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(8587(a,1),19472(a,1,2,2,2))].">
      <j1 rule="para" parents="8587 19472"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,19473,a)].">
      <j1 rule="hyper" parents="625 19473"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ ((x * K(y,K(z,u))) * (w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,w,x * K(y,K(z,u))) = v6
    ]]></literal>
    <justification jstring="[para(19473(a,1),629(a,1,1))].">
      <j1 rule="para" parents="19473 629"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(K(z,u),y) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7539,a(flip),b,19488,a)].">
      <j1 rule="hyper" parents="60 7539 19488"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) * w) = L(x,y,T(u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,14533,a(flip),b,19481,a)].">
      <j1 rule="hyper" parents="60 14533 19481"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      L(x,y,(((((z * z) \ u) * w) / u) * (z * z)) * v5) = L(x,y,T(w,(z * z) \ u) * v5)
    ]]></literal>
    <justification jstring="[para(1082(a,1),19481(a,1,3,1))].">
      <j1 rule="para" parents="1082 19481"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) / z) * v5) = L(x,y,T(K(z,u) * w,z) * v5)
    ]]></literal>
    <justification jstring="[para(7839(a,1),19481(a,1,3,1,1))].">
      <j1 rule="para" parents="7839 19481"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      T(T(x,y),K(y,z * (u * w))) = T(x,T(y,T(z / u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(14459,a,19482,a),flip(a)].">
      <j1 rule="hyper" parents="14459 19482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      T(x,K(y,z * ((u \ z) * w))) = T(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18023,a(flip),b,19482,a),flip(a)].">
      <j1 rule="hyper" parents="60 18023 19482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      T(T(x,K(y,z * (u * w))),y \ ((u \ z) * w)) = T(x,((u \ z) * w) / y)
    ]]></literal>
    <justification jstring="[para(19482(a,1),9566(a,1,1))].">
      <j1 rule="para" parents="19482 9566"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ v5))) = K(x,K(z / y,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18056,a,b,19485,a)].">
      <j1 rule="hyper" parents="60 18056 19485"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      K(x,K(y * z,y * ((z \ 1) * ((y / (1 / z)) * u)))) = K((y / (z \ 1)) * (1 / T(y / (1 / z),u)),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,16300,a(flip),b,19485,a),flip(a)].">
      <j1 rule="hyper" parents="60 16300 19485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) * w))) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(74(a,1),19485(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="74 19485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(8647(a,1),19490(a,2,1))].">
      <j1 rule="para" parents="8647 19490"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      T(x,K(y,(z / u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(77(a,1),19495(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[para(17200(a,2),19500(a,1,1))].">
      <j1 rule="para" parents="17200 19500"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      T(T(x,y / (z / u)),K(w,z * (u * y))) = T(x,T(y / (z / u),w))
    ]]></literal>
    <justification jstring="[hyper(17714,a,19501,a),flip(a)].">
      <j1 rule="hyper" parents="17714 19501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[hyper(799,a,19502,a),flip(a)].">
      <j1 rule="hyper" parents="799 19502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u \ (y * w)),K(x,K(y,z)) \ u,K(x,K(y,z))) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[para(19502(a,1),10378(a,1,1))].">
      <j1 rule="para" parents="19502 10378"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19439,a(flip),b,19504,a),flip(a)].">
      <j1 rule="hyper" parents="60 19439 19504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(19504(a,2),17678(a,1,2))].">
      <j1 rule="para" parents="19504 17678"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) * v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,19282,a(flip),b,19507,a)].">
      <j1 rule="hyper" parents="60 19282 19507"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(17449(a,1),19507(a,1,2,1))].">
      <j1 rule="para" parents="17449 19507"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(6130(a,1),19508(a,1,2,2))].">
      <j1 rule="para" parents="6130 19508"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) \ v5)) = K(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(7858(a,1),19508(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7858 19508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      T(x,y \ (K(z,K(u,w)) \ v5)) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(19506(a,1),17650(a,1,2))].">
      <j1 rule="para" parents="19506 17650"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      T(x,y \ (T(z,K(u,w)) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(7853(a,1),19512(a,1,2,2))].">
      <j1 rule="para" parents="7853 19512"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,(y * T(z,T(u,w))) \ v5) = K(x,(y * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(8587(a,1),19509(a,1,2,1,2))].">
      <j1 rule="para" parents="8587 19509"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      K(x,y \ (z * T(u,T(w,v5)))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(8587(a,1),19510(a,1,2,2,2))].">
      <j1 rule="para" parents="8587 19510"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) * (w \ 1)) \ v5)) = T(x,y \ ((w \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(15196(a,1),19513(a,1,2,2,1))].">
      <j1 rule="para" parents="15196 19513"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17864,a,19376,a)].">
      <j1 rule="hyper" parents="17864 19376"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,(z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(17509,a,19518,a),flip(a)].">
      <j1 rule="hyper" parents="17509 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17509,a,19519,a),flip(a)].">
      <j1 rule="hyper" parents="17509 19519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17994,a(flip),b,19521,a),flip(a)].">
      <j1 rule="hyper" parents="370 17994 19521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <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(19521(a,2),18097(a,1))].">
      <j1 rule="para" parents="19521 18097"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      K(x,K(y,T(z * u,w) * v5)) = K(x,K(y,z * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18031,a,19522,a)].">
      <j1 rule="hyper" parents="18031 19522"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,R(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(19522(a,1),9361(a,1,1))].">
      <j1 rule="para" parents="19522 9361"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) * (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(19522(a,1),18814(a,1,1))].">
      <j1 rule="para" parents="19522 18814"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * v5)) = v6
    ]]></literal>
    <justification jstring="[para(7864(a,1),19469(a,1,2,2))].">
      <j1 rule="para" parents="7864 19469"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(8683(a,1),19469(a,1,2,2))].">
      <j1 rule="para" parents="8683 19469"/>
    </justification>
  </clause>

  <clause id="19531">
    <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(18778(a,1),19469(a,1,2,2))].">
      <j1 rule="para" parents="18778 19469"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) \ (w \ 1)) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(15568,a,19362,a)].">
      <j1 rule="hyper" parents="15568 19362"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      T(x * K(L(y,z,u),w),K(w,y)) = L(K(w,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(12946(a,1),19382(a,1,1))].">
      <j1 rule="para" parents="12946 19382"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * z = (x \ u) * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(17344,a,19437,a),flip(a)].">
      <j1 rule="hyper" parents="17344 19437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      (x \ R(T(x,K(y,z)),u,x)) * z = (x \ R(x,u,x)) * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9792(a,1),19534(a,1,1))].">
      <j1 rule="para" parents="9792 19534"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(17952,a,19444,a)].">
      <j1 rule="hyper" parents="17952 19444"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (x * w)) = K(z,u) * (T(x,y) * w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),19536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (y \ w)) = K(z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(7873(a,1),19536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7873 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = (x * K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17965,a(flip),b,19445,a)].">
      <j1 rule="hyper" parents="60 17965 19445"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(6302,a,19547,a)].">
      <j1 rule="hyper" parents="6302 19547"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) \ (x * K(u,w)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(19547(a,1),6294(a,1,1))].">
      <j1 rule="para" parents="19547 6294"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,w)) \ (x * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = v5
    ]]></literal>
    <justification jstring="[para(19547(a,1),6305(a,1,1))].">
      <j1 rule="para" parents="19547 6305"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      x * K(y,z) != u * K(w,v5)
    ]]></literal>
    <literal><![CDATA[
      (u * K(z,y)) * K(w,v5) = x
    ]]></literal>
    <justification jstring="[para(19549(a,1),41(a,2)),flip(b)].">
      <j1 rule="para" parents="19549 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * w) = (K(x,y) / w) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(15619,a,19447,a)].">
      <j1 rule="hyper" parents="15619 19447"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a((K(x,y) / z) * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(19556(a,1),16112(a,2,1))].">
      <j1 rule="para" parents="19556 16112"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      K(x,L(y,z \ u,(z \ u) \ z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(19456(a,1),18163(a,1,2))].">
      <j1 rule="para" parents="19456 18163"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      K(x,y * (T(z,u) / T(w,z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14516,a(flip),b,19487,a),flip(a)].">
      <j1 rule="hyper" parents="60 14516 19487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),u \ v5))) = K(x,y * (z / T((u \ v5) \ v5,w)))
    ]]></literal>
    <justification jstring="[para(5757(a,1),19487(a,1,2,2,2))].">
      <j1 rule="para" parents="5757 19487"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * T(u,y)) \ w) = K(x,(u * (T(y,z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(18478,a,19514,a),flip(a)].">
      <j1 rule="hyper" parents="18478 19514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      K(x,K(y,T(z * u,w) * v5)) = K(x,y) * K(y,T(x,z * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8649,a,b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="370 8649 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = (w * K(L(x,z,u),y)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,19533,a(flip),b,7505,a)].">
      <j1 rule="hyper" parents="125 19533 7505"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * x)) \ (K(z,u) * (T(x,y) * w)) = L(L(w,x,K(z,u)),K(z,u) * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(19545(a,1),621(a,1,2))].">
      <j1 rule="para" parents="19545 621"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      K(x,y * z) * ((z * y) \ u) = K(y,z) * (T(y * z,x) \ u)
    ]]></literal>
    <justification jstring="[para(12083(a,1),19546(a,1,2))].">
      <j1 rule="para" parents="12083 19546"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / T(w,z)) * (w \ T(z,u))) = K(x,(T(z,u) / T(w,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,19560,a),flip(a)].">
      <j1 rule="hyper" parents="12637 19560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K((x * y) \ z,L(u,x,y)) = K(x \ (T(y,x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16832,a(flip),b,19367,a)].">
      <j1 rule="hyper" parents="60 16832 19367"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(19402,a,17528,a)].">
      <j1 rule="hyper" parents="19402 17528"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * (z \ w))) = v5
    ]]></literal>
    <justification jstring="[para(19571(a,1),17529(a,1))].">
      <j1 rule="para" parents="19571 17529"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * v5)) = K(x,y * ((w \ K(z,u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(19527,a,14481,a)].">
      <j1 rule="hyper" parents="19527 14481"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * K(z,u)) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(7501(a,1),19527(a,1,2,2,1))].">
      <j1 rule="para" parents="7501 19527"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(19323(a,1),19343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19323 19343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(19578(a,2),389(a,1))].">
      <j1 rule="para" parents="19578 389"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(15109(a,2),19579(a,1,2,1))].">
      <j1 rule="para" parents="15109 19579"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      T(x,y / T(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = v6
    ]]></literal>
    <justification jstring="[para(17394(a,1),19579(a,1))].">
      <j1 rule="para" parents="17394 19579"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      T(x,y * T(a(z,u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(17395(a,1),19579(a,1))].">
      <j1 rule="para" parents="17395 19579"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(19581,a,19324,a),flip(a)].">
      <j1 rule="hyper" parents="19581 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) / v5) = T(x,(w * a(y,z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(19581,a,16985,a),flip(a)].">
      <j1 rule="hyper" parents="19581 16985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(19581,a,xx),flip(a)].">
      <j1 rule="hyper" parents="19581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      K((T(x,y) \ (y * a(z,u,K(w,v5)))) \ 1,v6) = K(((y * a(z,u,K(w,v5))) / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(19584(a,1),14680(a,1,1,1,1))].">
      <j1 rule="para" parents="19584 14680"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),T(y,a(u,w,K(v5,v6)) * z)) = K(x,z * a(u,w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(19584(a,1),17372(a,1,2,1))].">
      <j1 rule="para" parents="19584 17372"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(L(v5,w,u),u * w,K(x,K(y,z))) = v6
    ]]></literal>
    <justification jstring="[para(19434(a,1),1199(a,1,2))].">
      <j1 rule="para" parents="19434 1199"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      K((x \ y) * L(x,z,z),T(u,x)) = K((y / x) * R(x,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18733,a(flip),b,19464,a)].">
      <j1 rule="hyper" parents="60 18733 19464"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      T(x,T(y,T(z / u,z) * w)) = T(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(8603,a,19494,a),flip(a)].">
      <j1 rule="hyper" parents="8603 19494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      T(x,T(y,(z \ u) * w)) = T(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(14507(a,1),19592(a,1,2))].">
      <j1 rule="para" parents="14507 19592"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      T(x,T(y \ z,z * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(19593(a,1),17466(a,1))].">
      <j1 rule="para" parents="19593 17466"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      T(x / (y / z),T(z \ y,x)) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19594,a,17161,a)].">
      <j1 rule="hyper" parents="19594 17161"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (w \ 1))) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(16618,a,19532,a)].">
      <j1 rule="hyper" parents="16618 19532"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      K(x,y) * (T(x * y,z) \ u) = T(y * x,T(z,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,12559,a(flip),b,19568,a),flip(a)].">
      <j1 rule="hyper" parents="60 12559 19568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      T(x,T(y * z,T(z,y)) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(19597(a,1),18125(a,1,2))].">
      <j1 rule="para" parents="19597 18125"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(18669,a,19598,a)].">
      <j1 rule="hyper" parents="18669 19598"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      T(x,(y * z) \ T(u,y * z)) = T(x,u / T(z * y,y))
    ]]></literal>
    <justification jstring="[hyper(17502,a,19599,a),flip(a)].">
      <j1 rule="hyper" parents="17502 19599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),z) \ u) = T(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18299,a(flip),b,19599,a)].">
      <j1 rule="hyper" parents="60 18299 19599"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      T(x,y / T(z * u,u)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17498,a,19600,a),flip(a)].">
      <j1 rule="hyper" parents="17498 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,(1 / y) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18419,a,b,19602,a)].">
      <j1 rule="hyper" parents="60 18419 19602"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      T(x,y / (z * (u / z))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),19602(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 19602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      T(x,T(y,z * u) / T(u \ z,z)) = T(x,(u \ T(z,u \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,18752,a(flip),b,19604,a),flip(a)].">
      <j1 rule="hyper" parents="60 18752 19604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = K(x,w) * T(x * K(w,x),((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(19601(a,1),9813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19601 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) \ z) \ 1)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,15402,a(flip),b,19603,a),flip(a)].">
      <j1 rule="hyper" parents="370 15402 19603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      T(x,(y \ 1) / ((y \ 1) \ z)) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15534,a,19607,a)].">
      <j1 rule="hyper" parents="15534 19607"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      T(x,(y \ 1) * (z \ (y \ 1))) = T(x,y \ ((y * z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15576,a,19608,a)].">
      <j1 rule="hyper" parents="15576 19608"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      T(x,y \ ((y * z) \ 1)) = T(x,y \ (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15260,a,19609,a),flip(a)].">
      <j1 rule="hyper" parents="15260 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      T(x,(y * z) \ ((y * z) \ z)) = T(x,y \ (z \ (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18416,a,b,19610,a)].">
      <j1 rule="hyper" parents="60 18416 19610"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      T((x * y) / x,z \ (x \ (z \ 1))) = T(y,(z * x) \ ((z * x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(15664,a,19611,a),flip(a)].">
      <j1 rule="hyper" parents="15664 19611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ ((x \ 1) \ (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1)) = u
    ]]></literal>
    <justification jstring="[para(19611(a,1),16652(a,1))].">
      <j1 rule="para" parents="19611 16652"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(w \ K(z,u),v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(16504(a,1),19575(a,2,2,2))].">
      <j1 rule="para" parents="16504 19575"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K((z / x) * R(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(19420,a,19591,a)].">
      <j1 rule="hyper" parents="19420 19591"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K((z / x) * L(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18733,a(flip),b,19615,a),flip(a)].">
      <j1 rule="hyper" parents="370 18733 19615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (L(y,z,u) \ y)) = v5
    ]]></literal>
    <justification jstring="[para(18841(a,2),19361(a,1))].">
      <j1 rule="para" parents="18841 19361"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[para(16404(a,1),19463(a,1,1,1))].">
      <j1 rule="para" parents="16404 19463"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(w,v5)))) = K(x,y * ((z / u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(19531,a,17836,a),flip(a)].">
      <j1 rule="hyper" parents="19531 17836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(w,v5)))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17836,a(flip),b,19619,a),flip(a)].">
      <j1 rule="hyper" parents="370 17836 19619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(u,w) \ z) / (K(w,u) * y))
    ]]></literal>
    <justification jstring="[para(7506(a,2),19281(a,2,2,1))].">
      <j1 rule="para" parents="7506 19281"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(370,a,8797,a(flip),b,19291,a),flip(a)].">
      <j1 rule="hyper" parents="370 8797 19291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(19624(a,2),8847(a,1))].">
      <j1 rule="para" parents="19624 8847"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ T(K(x,y),z) = a(w,u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8676(a,1),19314(a,1,2))].">
      <j1 rule="para" parents="8676 19314"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * a(w,u,K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(156,a,19627,a)].">
      <j1 rule="hyper" parents="156 19627"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) * a(w,u,K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8019(a,2),19629(a,1,1,1))].">
      <j1 rule="para" parents="8019 19629"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) * a(w,u,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8019,a,b,19630,a),flip(a)].">
      <j1 rule="hyper" parents="370 8019 19630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11917,a,19631,a)].">
      <j1 rule="hyper" parents="11917 19631"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      a(x * (y / x),z,K(u,w)) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(15917,a,19632,a)].">
      <j1 rule="hyper" parents="15917 19632"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15808,a,b,19632,a),flip(a)].">
      <j1 rule="hyper" parents="370 15808 19632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(109(a,1),19632(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="109 19632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),z)) = a(x,y,K(z * (w \ u),z))
    ]]></literal>
    <justification jstring="[para(14585(a,1),19632(a,1,3))].">
      <j1 rule="para" parents="14585 19632"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = w * a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[para(19632(a,1),15507(a,2,2))].">
      <j1 rule="para" parents="19632 15507"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y \ (w \ v5),y)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(19632(a,1),15879(a,1,2))].">
      <j1 rule="para" parents="19632 15879"/>
    </justification>
  </clause>

  <clause id="19639">
    <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(19634(a,2),15867(a,1))].">
      <j1 rule="para" parents="19634 15867"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(19634(a,1),16507(a,1,2))].">
      <j1 rule="para" parents="19634 16507"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),19633(a,1,1,2))].">
      <j1 rule="para" parents="6 19633"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,19635,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 19635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15857,a(flip),b,19641,a),flip(a)].">
      <j1 rule="hyper" parents="370 15857 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19644">
    <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(19641(a,1),15902(a,1))].">
      <j1 rule="para" parents="19641 15902"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15902,a,19643,a)].">
      <j1 rule="hyper" parents="15902 19643"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(19643(a,1),15910(a,1,2))].">
      <j1 rule="para" parents="19643 15910"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      a(x,y,K(z,u \ (x * w))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,15977,a(flip),b,19645,a),flip(a)].">
      <j1 rule="hyper" parents="60 15977 19645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = v5 / (v5 * a(w,z,K(u,x * y)))
    ]]></literal>
    <justification jstring="[para(19642(a,1),19408(a,2,2,2))].">
      <j1 rule="para" parents="19642 19408"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u / z,w)) = v5
    ]]></literal>
    <justification jstring="[para(8031(a,1),19639(a,1,3))].">
      <j1 rule="para" parents="8031 19639"/>
    </justification>
  </clause>

  <clause id="19651">
    <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(15862(a,2),19639(a,1))].">
      <j1 rule="para" parents="15862 19639"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      a(x,y,K(z,u * (x * w))) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,15958,a(flip),b,19647,a)].">
      <j1 rule="hyper" parents="60 15958 19647"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      a(x,y,K(z,(x \ u) * w)) = a(z,y,K(u * w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,15967,a,b,19654,a)].">
      <j1 rule="hyper" parents="60 15967 19654"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      a(x,y,K(T(z * K(u * w,z),v5) * w,u)) = a(u,y,K(x,(u * w) * T(z,v5)))
    ]]></literal>
    <justification jstring="[para(5320(a,1),19654(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5320 19654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,z,K(u,y * x)) = v5
    ]]></literal>
    <justification jstring="[para(15894(a,1),19644(a,1))].">
      <j1 rule="para" parents="15894 19644"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      T(a(x,y,z),x * u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15503,a,19646,a),flip(a)].">
      <j1 rule="hyper" parents="15503 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16063,a,b,19658,a)].">
      <j1 rule="hyper" parents="60 16063 19658"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = T(a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,15956,a(flip),b,19659,a),flip(a)].">
      <j1 rule="hyper" parents="370 15956 19659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15508,a(flip),b,19660,a)].">
      <j1 rule="hyper" parents="370 15508 19660"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,w))) / (x * (y * K(z,T(u,w)))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19639,a,19661,a),flip(a)].">
      <j1 rule="hyper" parents="19639 19661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2022,a,b,19661,a),flip(a)].">
      <j1 rule="hyper" parents="370 2022 19661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      a(x,y,z) = R(R(x,y,z) / x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,715,a,b,19661,a),flip(a)].">
      <j1 rule="hyper" parents="370 715 19661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(155,a,19661,a(flip))].">
      <j1 rule="hyper" parents="155 19661"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) = a(z,z \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),19661(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 19661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      R((1 / x) * R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(19663(a,2),592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19663 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      R(R(x,y,T(z,y)) / x,x,z * y) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),19664(a,2,3)),flip(a)].">
      <j1 rule="para" parents="107 19664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      a(x,x \ y,z) \ (y * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,171,a(flip),b,19665,a)].">
      <j1 rule="hyper" parents="125 171 19665"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,19665,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="128 19665 92"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      a(x,y / z,z) * (x * y) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(7(a,1),19665(a,1,2,2))].">
      <j1 rule="para" parents="7 19665"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(19665(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19665 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      a(x,y,z) * (x * ((y \ 1) * z)) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3050(a,1),19665(a,1,1))].">
      <j1 rule="para" parents="3050 19665"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      K(x,((y * z) * y) \ u) = K(x,(y * (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(19665(a,1),14629(a,1,2,1))].">
      <j1 rule="para" parents="19665 14629"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      (x * (y \ x)) / (y * ((y \ x) * (y \ x))) = y \ R(y,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,16509,a,b,19667,a),flip(a)].">
      <j1 rule="hyper" parents="370 16509 19667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2022(a,2),19674(a,1))].">
      <j1 rule="para" parents="2022 19674"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = w
    ]]></literal>
    <justification jstring="[para(19677(a,1),13050(a,1))].">
      <j1 rule="para" parents="19677 13050"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(2012(a,1),19669(a,1,1))].">
      <j1 rule="para" parents="2012 19669"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19679,a,19682,a),flip(a)].">
      <j1 rule="hyper" parents="19679 19682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      (x \ 1) * a(x,y,z) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,19683,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 19683 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,19683,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="125 19683 579"/>
    </justification>
  </clause>

  <clause id="19686">
    <literal><![CDATA[
      (a(x,y,z) \ a(x,y,z)) * (a(x,y,z) \ 1) = L(a(x,y,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(19683(a,1),3832(a,1,1,2))].">
      <j1 rule="para" parents="19683 3832"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      (x * x) \ a(x,y,z) = x \ (x \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,19684,a(flip),b,944,a),flip(a)].">
      <j1 rule="hyper" parents="125 19684 944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      R(x / (y \ 1),y \ 1,a(y,z,u)) = (x * a(y,z,u)) / (y \ a(y,z,u))
    ]]></literal>
    <justification jstring="[para(19684(a,1),104(a,2,2))].">
      <j1 rule="para" parents="19684 104"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      a(x,y \ a(y,z,u),w) = a(x,y * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(19684(a,1),3061(a,1,2))].">
      <j1 rule="para" parents="19684 3061"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      L(x,y,z \ a(z,u,w)) = L(x,y,z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19684(a,1),3438(a,1,3))].">
      <j1 rule="para" parents="19684 3438"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      a(T(x \ y,y),z,K(u,w)) = a(x * y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,19403,a(flip),b,19648,a),flip(a)].">
      <j1 rule="hyper" parents="370 19403 19648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(x * y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19651,a,19692,a)].">
      <j1 rule="hyper" parents="19651 19692"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      K(x,y) * a(z * u,w,K(y,x)) = K(x,L(y,w,z \ u))
    ]]></literal>
    <justification jstring="[para(19693(a,1),12932(a,1,2))].">
      <j1 rule="para" parents="19693 12932"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      x * a(a(y,z,u) * x,z,K(u,y)) = (a(y,z,u) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(19693(a,1),15832(a,1,2))].">
      <j1 rule="para" parents="19693 15832"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = K(x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(12988,a,19694,a),flip(a)].">
      <j1 rule="hyper" parents="12988 19694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(19694(a,1),12988(a,1))].">
      <j1 rule="para" parents="19694 12988"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u * w,x)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[para(15893(a,1),19694(a,1,2))].">
      <j1 rule="para" parents="15893 19694"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      K(x,L(y / z,u,y * u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16483,a(flip),b,19696,a),flip(a)].">
      <j1 rule="hyper" parents="60 16483 19696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,L(y,z,u * (u * w))) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),19696(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="4 19696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3367(a,1),19700(a,1,2))].">
      <j1 rule="para" parents="3367 19700"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16500(a,1),19697(a,1))].">
      <j1 rule="para" parents="16500 19697"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,y)) \ ((y \ z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,T(y,z),y * z)) = w
    ]]></literal>
    <justification jstring="[para(16691(a,2),19697(a,1))].">
      <j1 rule="para" parents="16691 19697"/>
    </justification>
  </clause>

  <clause id="19704">
    <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(19370(a,2),19697(a,1))].">
      <j1 rule="para" parents="19370 19697"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(z * y) * u)) = K(x,u / (z * ((z * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9124,a(flip),b,19699,a)].">
      <j1 rule="hyper" parents="60 9124 19699"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      K(x,L((y * (z / y)) / u,w,T(z,y) * w)) = K(x,w / (u * ((y * (z / y)) \ w)))
    ]]></literal>
    <justification jstring="[para(19491(a,1),19699(a,1,2))].">
      <j1 rule="para" parents="19491 19699"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * z)) = K(x,((z / u) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(19704,a,18708,a)].">
      <j1 rule="hyper" parents="19704 18708"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      K(x,L(T(y,z \ y) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(19704,a,18627,a)].">
      <j1 rule="hyper" parents="19704 18627"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * y)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19704,a,16580,a)].">
      <j1 rule="hyper" parents="19704 16580"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,15904,a,b,19698,a)].">
      <j1 rule="hyper" parents="31 15904 19698"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[hyper(19649,a,19710,a)].">
      <j1 rule="hyper" parents="19649 19710"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),z)) = a(z,y,K(x,u / (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15871,a,19710,a),flip(a)].">
      <j1 rule="hyper" parents="15871 19710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,w / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19636,a(flip),b,19712,a)].">
      <j1 rule="hyper" parents="60 19636 19712"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,(z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,19642,a(flip),b,19713,a),flip(a)].">
      <j1 rule="hyper" parents="370 19642 19713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z)) = a(z,y,K(x,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15966,a(flip),b,19714,a),flip(a)].">
      <j1 rule="hyper" parents="370 15966 19714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      a(x,y,K(z,u * (x \ w))) = a(z,y,K(x,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15955,a,19715,a),flip(a)].">
      <j1 rule="hyper" parents="15955 19715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      a(x,y,K(z,u * (x \ w))) = a(z,y,K(x,u * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,19716,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 19716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      a(x,y,K(z,(x * u) * w)) = a(z,y,K(x,u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,15966,a,b,19717,a)].">
      <j1 rule="hyper" parents="60 15966 19717"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      K(x,L(T(y,z * y) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(18515,a,19708,a)].">
      <j1 rule="hyper" parents="18515 19708"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      K(x,L(T(y,y * z) \ u,y,y * z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(5485(a,1),19720(a,1,2,1,1))].">
      <j1 rule="para" parents="5485 19720"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y * z) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,12534,a(flip),b,19721,a)].">
      <j1 rule="hyper" parents="60 12534 19721"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) * z)) \ ((y * z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4274(a,1),19722(a,1,2))].">
      <j1 rule="para" parents="4274 19722"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (L(K(y,z),u,w) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(5(a,1),19365(a,2,2,2))].">
      <j1 rule="para" parents="5 19365"/>
    </justification>
  </clause>

  <clause id="19725">
    <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(11011(a,1),19365(a,1,2,1))].">
      <j1 rule="para" parents="11011 19365"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      L(x,y,z * (u * K(w,v5 * v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15795,a(flip),b,19387,a),flip(a)].">
      <j1 rule="hyper" parents="60 15795 19387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y \ z,(w * u) * y))
    ]]></literal>
    <justification jstring="[para(12553(a,1),19497(a,2,2))].">
      <j1 rule="para" parents="12553 19497"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      T(T(x,y / ((z * (z * u)) / z)),K(w,(z * (z * u)) * (z * y))) = T(x,T(y / (T(z,z * u) * u),w))
    ]]></literal>
    <justification jstring="[para(5463(a,1),19503(a,2,2,1,2))].">
      <j1 rule="para" parents="5463 19503"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      (x \ R(T(x,K(y,z)),y,x)) * z = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,10922,a(flip),b,19535,a),flip(a)].">
      <j1 rule="hyper" parents="370 10922 19535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      T((x \ R(x,y,x)) * z,K(x,y)) = K(x,y) * (z * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,16684,a,b,19730,a)].">
      <j1 rule="hyper" parents="60 16684 19730"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      K(x,y) * (z * K(x * y,x)) = T(a(x,y,x) * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11441(a,1),19731(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11441 19731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      K(x,L(y,z \ u,(z \ u) * z)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[hyper(19697,a,19559,a)].">
      <j1 rule="hyper" parents="19697 19559"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * (u \ w))) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(18016,a,19564,a),flip(a)].">
      <j1 rule="hyper" parents="18016 19564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * ((u \ w) \ v5))) = K(x,K(y,(z * (w / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(18038(a,1),19734(a,1,2))].">
      <j1 rule="para" parents="18038 19734"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ u) = T(x,T(u,z * y) / (z / y))
    ]]></literal>
    <justification jstring="[hyper(18326,a,19605,a),flip(a)].">
      <j1 rule="hyper" parents="18326 19605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18346,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="370 18346 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      T((x * y) / x,z \ (x \ (z \ 1))) = T(y,x \ (z \ ((z * x) \ 1)))
    ]]></literal>
    <justification jstring="[para(1284(a,1),19612(a,2,2))].">
      <j1 rule="para" parents="1284 19612"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,(K(u,w) \ z) / (K(u,w) \ y))
    ]]></literal>
    <justification jstring="[para(7506(a,2),19623(a,2,2,2))].">
      <j1 rule="para" parents="7506 19623"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,y \ (L(K(u,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(17770,a,19725,a)].">
      <j1 rule="hyper" parents="17770 19725"/>
    </justification>
  </clause>

  <clause id="19741">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y \ z,w * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19522,a(flip),b,19728,a),flip(a)].">
      <j1 rule="hyper" parents="370 19522 19728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      K(x,L(y,z \ u,T(u,z))) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[para(14013(a,1),19733(a,1,2))].">
      <j1 rule="para" parents="14013 19733"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(1 / (u / z)) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,19296,a(flip),b,19742,a)].">
      <j1 rule="hyper" parents="60 19296 19742"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(u / z) \ z))
    ]]></literal>
    <justification jstring="[para(3376(a,1),19743(a,2,2))].">
      <j1 rule="para" parents="3376 19743"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(z \ u) \ z))
    ]]></literal>
    <justification jstring="[para(19455(a,1),19745(a,2,2))].">
      <j1 rule="para" parents="19455 19745"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,(z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19696,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="370 19696 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(14013(a,1),19747(a,2,2))].">
      <j1 rule="para" parents="14013 19747"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19296,a(flip),b,19748,a),flip(a)].">
      <j1 rule="hyper" parents="370 19296 19748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      (x * K(y,z \ (L(K(u,w),v5,v6) * v7))) \ x = K((z * L(K(w,u),v5,v6)) \ v7,y)
    ]]></literal>
    <justification jstring="[para(19740(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="19740 6294"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      K(x,K((y / z) \ 1,u * (w \ y))) = K(x,K(y * z,w * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17519,a(flip),b,19741,a),flip(a)].">
      <j1 rule="hyper" parents="370 17519 19741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      K(x,K(y / z,u * (w \ z))) = K(x,K(z * y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(8215(a,1),19752(a,1,2))].">
      <j1 rule="para" parents="8215 19752"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      K(x,K(y * z,u * (w \ z))) = K(x,K(z * y,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(17527,a,19753,a)].">
      <j1 rule="hyper" parents="17527 19753"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      K(x,K(y * z,z * (u \ y))) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17601,a(flip),b,19754,a),flip(a)].">
      <j1 rule="hyper" parents="60 17601 19754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8011(a,1),19662(a,1,2,2))].">
      <j1 rule="para" parents="8011 19662"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / L(K(z,u) * y,x,a(x,y,K(z,u))) = (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x
    ]]></literal>
    <justification jstring="[para(19757(a,1),432(a,1,2,3))].">
      <j1 rule="para" parents="19757 432"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      (x * (y \ x)) / (y * ((y \ x) * (y \ x))) = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(1110(a,1),19678(a,2,2))].">
      <j1 rule="para" parents="1110 19678"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(229,a,19686,a),flip(a)].">
      <j1 rule="hyper" parents="229 19686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(14186,a,19760,a)].">
      <j1 rule="hyper" parents="14186 19760"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3101,a(flip),b,19761,a),flip(a)].">
      <j1 rule="hyper" parents="60 3101 19761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(129,a,19763,a(flip),b,83,a)].">
      <j1 rule="hyper" parents="129 19763 83"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,936,a(flip),b,19764,a),flip(a)].">
      <j1 rule="hyper" parents="370 936 19764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = K(L(u,y,x),z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(12965(a,1),19380(a,2,1))].">
      <j1 rule="para" parents="12965 19380"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = K(z,L(u,y,x)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,19767,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 19767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(z,u)) = (K(z,u) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(16493,a,19768,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16493 19768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (u * K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(19768(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="19768 17230"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      T((K(x,y) * z) * T(u,z),K(x,y)) = u * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8717,a,19769,a)].">
      <j1 rule="hyper" parents="8717 19769"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((z \ y) * u)) = T(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(8947(a,1),19496(a,1,1))].">
      <j1 rule="para" parents="8947 19496"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      a((K(x,y) \ (1 / K(x,y))) \ z,u,w) = a(T(1 / z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(15176(a,1),19558(a,2,1))].">
      <j1 rule="para" parents="15176 19558"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      a((K(x,y) \ K(y,x)) \ z,u,w) = a(T(1 / z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(5866(a,1),19773(a,1,1,1,2))].">
      <j1 rule="para" parents="5866 19773"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      a((K(x,y) * K(x,y)) \ z,u,w) = a(T(1 / z,K(y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(7506(a,1),19774(a,1,1,1))].">
      <j1 rule="para" parents="7506 19774"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      a(T(1 / x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(2954,a,19775,a),flip(a)].">
      <j1 rule="hyper" parents="2954 19775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      a(T(x \ 1,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,5181,a(flip),b,19776,a)].">
      <j1 rule="hyper" parents="60 5181 19776"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(9559,a,19778,a)].">
      <j1 rule="hyper" parents="9559 19778"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      (x * a(y,z,u)) / (y \ a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x / (y \ 1),y,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(19688(a,1),2778(a,1))].">
      <j1 rule="para" parents="19688 2778"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      K(x,L(y,z,z) \ ((z * y) * u)) = K(x,y \ (((z \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[para(2074(a,1),19723(a,1,2,1))].">
      <j1 rule="para" parents="2074 19723"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      K(x,L(y \ z,1 / y,1 / y) \ (((y * y) \ z) * u)) = K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u))
    ]]></literal>
    <justification jstring="[para(552(a,1),19781(a,1,2,2,1))].">
      <j1 rule="para" parents="552 19781"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * ((w \ u) \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(19735(a,1),8887(a,1))].">
      <j1 rule="para" parents="19735 8887"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) * (z \ T(u,w))) = K(x,(T(u,w) / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(17748(a,1),19569(a,1,2,1))].">
      <j1 rule="para" parents="17748 19569"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      K(x,(T(y,z) / T(u,y)) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(12637,a,19785,a),flip(a)].">
      <j1 rule="hyper" parents="12637 19785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      K(x,(T(y,z) / T(u,y)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ T(y,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(19785(a,1),12637(a,1))].">
      <j1 rule="para" parents="19785 12637"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      T(x,(T(y,z) / T(u,y)) * w) = x * K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(129,a,19786,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 19786 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      T(x,(T(y,z) / T(u,y)) * w) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,19788,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = T(x,v6) \ T(T(x,y),T(v6,y))
    ]]></literal>
    <justification jstring="[para(19586(a,1),19588(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19586 19588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8967,a(flip),b,19791,a),flip(a)].">
      <j1 rule="hyper" parents="370 8967 19791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(19358,a,19792,a)].">
      <j1 rule="hyper" parents="19358 19792"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(19792(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="19792 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(15809(a,1),19792(a,1,2))].">
      <j1 rule="para" parents="15809 19792"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(17635,a,19795,a)].">
      <j1 rule="hyper" parents="17635 19795"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,19796,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 19796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ w,v5) = K(a(x,y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(17636,a,19799,a)].">
      <j1 rule="hyper" parents="17636 19799"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(82(a,1),19799(a,1,1))].">
      <j1 rule="para" parents="82 19799"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      K(x / T(y,a(z,u,w)),v5) = K(x / y,v5)
    ]]></literal>
    <justification jstring="[para(15505(a,1),19799(a,1,1))].">
      <j1 rule="para" parents="15505 19799"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(x,y) * (z * u),w)
    ]]></literal>
    <justification jstring="[para(15809(a,1),19799(a,1,1))].">
      <j1 rule="para" parents="15809 19799"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[para(19316(a,2),19799(a,1,1))].">
      <j1 rule="para" parents="19316 19799"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) * K(K(y,x),v6) = T(K(x,y) * a(z,u,K(w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(19804(a,1),17409(a,1,2))].">
      <j1 rule="para" parents="19804 17409"/>
    </justification>
  </clause>

  <clause id="19806">
    <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(19802(a,1),14652(a,1))].">
      <j1 rule="para" parents="19802 14652"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z)) * w)) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(107(a,1),19797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 19797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,K(a(y,z,u),w) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(15496(a,2),19797(a,1,2,1,1))].">
      <j1 rule="para" parents="15496 19797"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((u * w) * v5)) = K(x,((K(y,z) * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(16420(a,1),19797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16420 19797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * (w * v5))) * K(x,((K(z,u) * w) * v5) * y) = K(x,y * ((K(z,u) * w) * v5))
    ]]></literal>
    <justification jstring="[para(19797(a,1),17586(a,1,1,2))].">
      <j1 rule="para" parents="19797 17586"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(u,w) * (z * y)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(19797(a,1),17991(a,1,2))].">
      <j1 rule="para" parents="19797 17991"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(17482,a,19801,a)].">
      <j1 rule="hyper" parents="17482 19801"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      K(K(x,y) * (T(z,K(x,y)) * u),w) = K((z * K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(107(a,1),19803(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 19803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(19527,a,19807,a),flip(a)].">
      <j1 rule="hyper" parents="19527 19807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / z) * w)) = K(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(5855(a,1),19814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5855 19814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(y,z))) * v5)
    ]]></literal>
    <justification jstring="[para(12941(a,1),19814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12941 19814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(y,z)) / w) = v5
    ]]></literal>
    <justification jstring="[para(19814(a,1),15472(a,1))].">
      <j1 rule="para" parents="19814 15472"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      K(x,K(y \ 1,T(y,z)) * ((u / T(y,z)) * w)) = K(x,(u / L(T(y,z),y,y)) * w)
    ]]></literal>
    <justification jstring="[para(1335(a,1),19815(a,2,2,1,2))].">
      <j1 rule="para" parents="1335 19815"/>
    </justification>
  </clause>

  <clause id="19819">
    <literal><![CDATA[
      K(x * K(y * x,(z / T(u,w)) * v5),y) = K(x,T(y,K(w,u) * ((z / u) * v5)))
    ]]></literal>
    <justification jstring="[para(19815(a,1),18160(a,1,1,2))].">
      <j1 rule="para" parents="19815 18160"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K((z / u) * v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[para(19815(a,1),18655(a,1,1,2))].">
      <j1 rule="para" parents="19815 18655"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(K(y,z) * (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(17786,a,19813,a),flip(a)].">
      <j1 rule="hyper" parents="17786 19813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <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(19813(a,1),17786(a,1))].">
      <j1 rule="para" parents="19813 17786"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      1 / (x \ K(K(y,z) * (u * w),x)) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(19821(a,1),5767(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19821 5767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19824">
    <literal><![CDATA[
      K(K(x,y) * ((z * x) * u),w) = K((z * T(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),19821(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 19821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) * u),w) = K((z \ K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(15133(a,1),19821(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15133 19821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19826">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * w,v5) = K((K(x,y) * T(z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18662,a(flip),b,19824,a)].">
      <j1 rule="hyper" parents="60 18662 19824"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(z,u) * (y * x),w) = v5
    ]]></literal>
    <justification jstring="[para(17960(a,2),19822(a,1))].">
      <j1 rule="para" parents="17960 19822"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(5768,a,19823,a),flip(a)].">
      <j1 rule="hyper" parents="5768 19823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19829">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y * K(u,w))) = T(x,K(u,w) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18122,a,b,19828,a)].">
      <j1 rule="hyper" parents="60 18122 19828"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,T(w,v5)) * (z * y)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18738,a(flip),b,19828,a),flip(a)].">
      <j1 rule="hyper" parents="60 18738 19828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) * w)) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(15179(a,1),19828(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15179 19828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ z) * w)) = T(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(16774,a,19831,a)].">
      <j1 rule="hyper" parents="16774 19831"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      T(x,K(y * z,y) * ((u \ y) * w)) = T(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(16783,a,19832,a)].">
      <j1 rule="hyper" parents="16783 19832"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      T(x,K(y \ z,u) * ((w \ u) * v5)) = T(x,(w \ T(u,y * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18187,a,b,19832,a)].">
      <j1 rule="hyper" parents="60 18187 19832"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * w,v5) = K(K(x,y) * (T(z,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19803,a(flip),b,19826,a),flip(a)].">
      <j1 rule="hyper" parents="370 19803 19826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * (y * K(u,w)))
    ]]></literal>
    <justification jstring="[para(8706(a,1),19829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8706 19829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      T(x,(y \ T(z,z * u)) * w) = T(x,(y \ T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19832,a(flip),b,19833,a)].">
      <j1 rule="hyper" parents="60 19832 19833"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      K(K(x,y) * (T(T(z,K(x,y)),u) * w),v5) = K(T(z * K(x,y),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(107(a,1),19835(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 19835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u * w,u) * (y * z)) = T(x,z * T(K(u * w,u) * y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8952(a,2),19836(a,2,2,2))].">
      <j1 rule="para" parents="8952 19836"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(y,z) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(19827,a,17693,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19827 17693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      K(x * (T(y,z) * K(u,w)),T(v5,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(u,w) * (T(y,z) * x),v5) = v6
    ]]></literal>
    <justification jstring="[para(17162(a,1),19827(a,1))].">
      <j1 rule="para" parents="17162 19827"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,a(y,z,K(u,w)) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(15496(a,2),19808(a,2,2,1))].">
      <j1 rule="para" parents="15496 19808"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K((u \ z) * v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,18663,a(flip),b,19820,a),flip(a)].">
      <j1 rule="hyper" parents="370 18663 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (z * y)) = T(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17744,a,19830,a)].">
      <j1 rule="hyper" parents="17744 19830"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ w)) * v5) = T(x,(y \ T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,19832,a(flip),b,19834,a)].">
      <j1 rule="hyper" parents="60 19832 19834"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,19795,a(flip),b,19843,a),flip(a)].">
      <j1 rule="hyper" parents="370 19795 19843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * (v5 \ 1)) * v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,19848,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 19848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(12949(a,1),19848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12949 19848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(19316(a,1),19848(a,1,2,1))].">
      <j1 rule="para" parents="19316 19848"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(19770,a,19851,a),flip(a)].">
      <j1 rule="hyper" parents="19770 19851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = x \ T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,19851,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 19851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      K(x,K((y * z) \ u,w) * v5) = K(x,K(z \ (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[para(12972(a,1),19851(a,1,2,1))].">
      <j1 rule="para" parents="12972 19851"/>
    </justification>
  </clause>

  <clause id="19856">
    <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(19851(a,1),19770(a,1))].">
      <j1 rule="para" parents="19851 19770"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17620,a,19853,a),flip(a)].">
      <j1 rule="hyper" parents="17620 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16731,a,19853,a)].">
      <j1 rule="hyper" parents="16731 19853"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17687,a,b,19853,a),flip(a)].">
      <j1 rule="hyper" parents="370 17687 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w / z))) = K(x,u * (w / T(z,y)))
    ]]></literal>
    <justification jstring="[para(5855(a,1),19853(a,2,2,2))].">
      <j1 rule="para" parents="5855 19853"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * y))) = K(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),19853(a,2,2,2))].">
      <j1 rule="para" parents="6270 19853"/>
    </justification>
  </clause>

  <clause id="19862">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u * (w * (z / y)))) = K(x,u * (w * (y \ z)))
    ]]></literal>
    <justification jstring="[para(6298(a,1),19853(a,2,2,2))].">
      <j1 rule="para" parents="6298 19853"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * (y * z)) = v5
    ]]></literal>
    <justification jstring="[para(19853(a,1),16731(a,1))].">
      <j1 rule="para" parents="19853 16731"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      K(x,((y \ 1) * K(z,y \ 1)) * u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18161,a,b,19857,a)].">
      <j1 rule="hyper" parents="60 18161 19857"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5254(a,1),19857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5254 19857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z * u)))) = K(x,y * T(z * u,w))
    ]]></literal>
    <justification jstring="[para(15234(a,1),19857(a,1,2,2))].">
      <j1 rule="para" parents="15234 19857"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17687,a,b,19858,a),flip(a)].">
      <j1 rule="hyper" parents="370 17687 19858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * z))) = K(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),19858(a,2,2,2))].">
      <j1 rule="para" parents="6270 19858"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (y * z)))) = K(x,u * (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(12347(a,1),19858(a,2,2,2))].">
      <j1 rule="para" parents="12347 19858"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(15133(a,1),19858(a,2,2,2))].">
      <j1 rule="para" parents="15133 19858"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(y,z)))) = K(x,u * (w \ 1))
    ]]></literal>
    <justification jstring="[para(15182(a,1),19858(a,2,2,2))].">
      <j1 rule="para" parents="15182 19858"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19858,a(flip),b,19859,a),flip(a)].">
      <j1 rule="hyper" parents="60 19858 19859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(19859(a,1),14519(a,1))].">
      <j1 rule="para" parents="19859 14519"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19859,a(flip),b,19868,a)].">
      <j1 rule="hyper" parents="60 19859 19868"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z * w))) = K(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(7864(a,1),19868(a,2,2,2))].">
      <j1 rule="para" parents="7864 19868"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(17765,a,19873,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17765 19873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      K(x,y * (K(z,u) * K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5867(a,1),19873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5867 19873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * ((u * w) / u))) = K(x,y * (T(u,w) * T(u \ w,z)))
    ]]></literal>
    <justification jstring="[para(6352(a,1),19873(a,2,2,2))].">
      <j1 rule="para" parents="6352 19873"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(19873(a,2),17305(a,1))].">
      <j1 rule="para" parents="19873 17305"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(u,z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(19873(a,2),17737(a,1))].">
      <j1 rule="para" parents="19873 17737"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(18950(a,1),19878(a,1,2))].">
      <j1 rule="para" parents="18950 19878"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      K((x * y) / x,z * u) = K(y,T(T(T(z,w),w) * u,x))
    ]]></literal>
    <justification jstring="[hyper(8790,a,19882,a),flip(a)].">
      <j1 rule="hyper" parents="8790 19882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),19882(a,1,2,1,1))].">
      <j1 rule="para" parents="109 19882"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(262(a,1),19882(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="262 19882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) = K(x,(z / (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(5839(a,1),19882(a,1,2,1,1))].">
      <j1 rule="para" parents="5839 19882"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      K(x,(y / z) * ((y / z) * u)) = K(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16982,a(flip),b,19884,a),flip(a)].">
      <j1 rule="hyper" parents="60 16982 19884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      K(x,L(((y * z) / y) * u,w,v5)) = L(K(x,T(z,y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(19885(a,1),12922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19885 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (u / w))) = K(x,y * (T(u,z) / w))
    ]]></literal>
    <justification jstring="[para(15370(a,1),19875(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15370 19875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19890">
    <literal><![CDATA[
      K(x,(y / (y / z)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(14534,a,19886,a),flip(a)].">
      <j1 rule="hyper" parents="14534 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(74(a,1),19890(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="74 19890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      K(x,K(y,T(z,u) * w)) * K(x,y \ ((u / (u / z)) * w)) = K(x,((u / (u / z)) * w) / y)
    ]]></literal>
    <justification jstring="[para(19890(a,1),9355(a,1,1,2))].">
      <j1 rule="para" parents="19890 9355"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      K(x,(y \ a(z,u,K(w,v5))) * v6) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(19450(a,1),19850(a,1,2,1))].">
      <j1 rule="para" parents="19450 19850"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      K(x,(T(a(y,z,u),w) \ 1) * v5) = K(x,a(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(15835(a,1),19893(a,1,2,1))].">
      <j1 rule="para" parents="15835 19893"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(5264,a,19854,a)].">
      <j1 rule="hyper" parents="5264 19854"/>
    </justification>
  </clause>

  <clause id="19896">
    <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(19854(a,2),5290(a,1))].">
      <j1 rule="para" parents="19854 5290"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ L(z,u,w))) = T(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(17499,a,19895,a),flip(a)].">
      <j1 rule="hyper" parents="17499 19895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      T(x,y * K(z,L(u,w,v5))) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(17210,a,19895,a)].">
      <j1 rule="hyper" parents="17210 19895"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = v5 / T(v5,K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(19895(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="19895 5701"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(7553(a,1),19895(a,1,2))].">
      <j1 rule="para" parents="7553 19895"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      T(x,K(L(y,z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(12966(a,2),19895(a,1,2,1))].">
      <j1 rule="para" parents="12966 19895"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[para(11016(a,1),19898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 19898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * K(z,y)))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(12939(a,1),19898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12939 19898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * y))) = T(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(12980(a,1),19898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12980 19898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(7506(a,2),19900(a,2,2))].">
      <j1 rule="para" parents="7506 19900"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(125,a,19905,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 19905 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      T(x,K(L(y,z,u),w) * (v5 * (u * (z * y)))) = T(x,v5 * ((u * z) * T(L(y,z,u),w)))
    ]]></literal>
    <justification jstring="[para(6334(a,1),19902(a,2,2,2))].">
      <j1 rule="para" parents="6334 19902"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = v6
    ]]></literal>
    <justification jstring="[para(19902(a,1),17946(a,1,2))].">
      <j1 rule="para" parents="19902 17946"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(8202(a,2),19880(a,1,2))].">
      <j1 rule="para" parents="8202 19880"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = K(K(x,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,19899,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      K(K(x,y) * R(y,z,u),T(w,y)) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,19618,a(flip),b,19910,a),flip(a)].">
      <j1 rule="hyper" parents="60 19618 19910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      K(K(x,T((y * z) \ u,w)) * v5,v6) = K(K(x,T(z \ (y \ u),w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(745(a,1),19910(a,1,1,1,2))].">
      <j1 rule="para" parents="745 19910"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,v5) = K(K(x,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(12966(a,2),19910(a,1,1,1))].">
      <j1 rule="para" parents="12966 19910"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      K(K((x * y) \ z,u) * w,v5) = K(K(y \ (x \ z),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(12972(a,1),19910(a,1,1,1))].">
      <j1 rule="para" parents="12972 19910"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),v5) = K(K(y,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(17250,a,19913,a)].">
      <j1 rule="hyper" parents="17250 19913"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),v5) = K(K(y,z) * x,v5)
    ]]></literal>
    <justification jstring="[para(6763(a,1),19915(a,1,1,2))].">
      <j1 rule="para" parents="6763 19915"/>
    </justification>
  </clause>

  <clause id="19917">
    <literal><![CDATA[
      K(x * ((x \ y) * K(z,u)),w) = K(K(z,u) * y,w)
    ]]></literal>
    <justification jstring="[para(530(a,1),19916(a,1,1))].">
      <j1 rule="para" parents="530 19916"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      K(((x \ y) * K(z,u)) * x,w) = K(K(z,u) * y,T(w,x))
    ]]></literal>
    <justification jstring="[hyper(12588,a,19917,a)].">
      <j1 rule="hyper" parents="12588 19917"/>
    </justification>
  </clause>

  <clause id="19919">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,19906,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <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(19906(a,2),5290(a,1))].">
      <j1 rule="para" parents="19906 5290"/>
    </justification>
  </clause>

  <clause id="19921">
    <literal><![CDATA[
      K(x,K(y * z,(y \ 1) \ 1) * (u * (w / ((y \ 1) \ 1)))) = K(x,u * (w / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[para(15450(a,1),19860(a,2,2,2,2))].">
      <j1 rule="para" parents="15450 19860"/>
    </justification>
  </clause>

  <clause id="19922">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * (y * z)))) = K(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(14537,a,19861,a)].">
      <j1 rule="hyper" parents="14537 19861"/>
    </justification>
  </clause>

  <clause id="19923">
    <literal><![CDATA[
      a(K(x,y) * (z * (u * y)),w,K(v5,v6)) = v7 / (v7 * a(v6,w,K(v5,z * (u * T(y,x)))))
    ]]></literal>
    <justification jstring="[para(19869(a,1),19403(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="19869 19403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(19817,a,19871,a)].">
      <j1 rule="hyper" parents="19817 19871"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(5912(a,1),19924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5912 19924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      K(x,y / T(z,u)) * a(w,v5,K(y / T(z,u),x)) = K(x,L(y * (z \ K(z,u)),v5,w))
    ]]></literal>
    <justification jstring="[para(19925(a,1),17577(a,1,1))].">
      <j1 rule="para" parents="19925 17577"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(y,z)))) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(370,a,15155,a(flip),b,19872,a),flip(a)].">
      <j1 rule="hyper" parents="370 15155 19872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19928">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ K(z,y)))) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(16731,a,19927,a)].">
      <j1 rule="hyper" parents="16731 19927"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z * w))) = x \ T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,19876,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 19876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19930">
    <literal><![CDATA[
      K(x * K(y,z * (T(u,w) * v5)),v6) = K(K(z * (u * v5),y) * x,v6)
    ]]></literal>
    <justification jstring="[para(19876(a,1),18655(a,1,1,2))].">
      <j1 rule="para" parents="19876 18655"/>
    </justification>
  </clause>

  <clause id="19931">
    <literal><![CDATA[
      K(x,y * ((z \ K(u,z \ 1)) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(8208(a,1),19877(a,1,2,2))].">
      <j1 rule="para" parents="8208 19877"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * u,w)) = v5
    ]]></literal>
    <justification jstring="[para(19883(a,1),8790(a,1))].">
      <j1 rule="para" parents="19883 8790"/>
    </justification>
  </clause>

  <clause id="19933">
    <literal><![CDATA[
      K(x,y * (K(z * u,w) * (w / v5))) = K(x,y * (T(w,z \ u) / v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,18685,a(flip),b,19889,a)].">
      <j1 rule="hyper" parents="60 18685 19889"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) / w)) = K(x,y * (T(u,z) / w))
    ]]></literal>
    <justification jstring="[para(15604(a,2),19889(a,1,2,2))].">
      <j1 rule="para" parents="15604 19889"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      K(x,T(a(y,z,u),w) \ v5) = K(x,a(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(15233,a,19894,a)].">
      <j1 rule="hyper" parents="15233 19894"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      T(x,T(y,z) \ L(z,u,w)) = T(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(16775,a,19897,a)].">
      <j1 rule="hyper" parents="16775 19897"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (y * z)))) = T(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(16900,a,19904,a)].">
      <j1 rule="hyper" parents="16900 19904"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * z))) = T(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16774,a,19904,a)].">
      <j1 rule="hyper" parents="16774 19904"/>
    </justification>
  </clause>

  <clause id="19939">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),w) = K(R(x,y,z),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(19423,a,19911,a)].">
      <j1 rule="hyper" parents="19423 19911"/>
    </justification>
  </clause>

  <clause id="19941">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(w,u),y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19939(a,2),16428(a,1))].">
      <j1 rule="para" parents="19939 16428"/>
    </justification>
  </clause>

  <clause id="19942">
    <literal><![CDATA[
      K(K(x,y) * ((z \ u) * z),w) = K(K(x,y) * u,T(w,z))
    ]]></literal>
    <justification jstring="[hyper(19822,a,19918,a)].">
      <j1 rule="hyper" parents="19822 19918"/>
    </justification>
  </clause>

  <clause id="19943">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,y) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(16741(a,1),19920(a,1))].">
      <j1 rule="para" parents="16741 19920"/>
    </justification>
  </clause>

  <clause id="19944">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) / w)) = K(x,y * (z / w))
    ]]></literal>
    <justification jstring="[para(263(a,1),19934(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="263 19934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19945">
    <literal><![CDATA[
      K(x,K(((y * z) / y) / u,w) * (T(z,y) / u)) = K(x,T(((y * z) / y) / u,w))
    ]]></literal>
    <justification jstring="[para(5275(a,2),19934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5275 19934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19946">
    <literal><![CDATA[
      K(x,T(y,T(T(z,u),u) / w) * (z / w)) = K(x,(T(T(z,u),u) / w) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,19944,a),flip(a)].">
      <j1 rule="hyper" parents="12637 19944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19947">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14513,a(flip),b,19944,a)].">
      <j1 rule="hyper" parents="60 14513 19944"/>
    </justification>
  </clause>

  <clause id="19948">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1289(a,1),19947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1289 19947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      K(K(x,y) * T(z,u),w) = K(K(x,y) * z,T(w,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17867,a(flip),b,19942,a)].">
      <j1 rule="hyper" parents="60 17867 19942"/>
    </justification>
  </clause>

  <clause id="19950">
    <literal><![CDATA[
      (((x * x) * y) / (x * x)) / (((x * x) * (y * K(K(z,u) * w,T(y,v5)))) / (x * x)) = K(y,K(z,u) * T(w,x * (x * v5)))
    ]]></literal>
    <justification jstring="[para(19949(a,1),18205(a,1,2,1,2,2))].">
      <j1 rule="para" parents="19949 18205"/>
    </justification>
  </clause>

  <clause id="19952">
    <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(17235(a,1),19856(a,1))].">
      <j1 rule="para" parents="17235 19856"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,v5)) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[hyper(19952,a,18352,a),flip(a)].">
      <j1 rule="hyper" parents="19952 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      K(x,K((y * z) \ u,w) * v5) = K(x,K(z * (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,18359,a(flip),b,19855,a),flip(a)].">
      <j1 rule="hyper" parents="370 18359 19855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19957">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(7438(a,1),19867(a,1,2,2))].">
      <j1 rule="para" parents="7438 19867"/>
    </justification>
  </clause>

  <clause id="19958">
    <literal><![CDATA[
      K(x,L(((y * z) / y) * u,w,v5)) = K(x,L(T(z,y) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,12922,a(flip),b,19888,a),flip(a)].">
      <j1 rule="hyper" parents="370 12922 19888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      K(K(x \ (y \ z),u) * w,v5) = K(K((y * x) * z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(18390,a,19914,a),flip(a)].">
      <j1 rule="hyper" parents="18390 19914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(5264,a,19929,a)].">
      <j1 rule="hyper" parents="5264 19929"/>
    </justification>
  </clause>

  <clause id="19961">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (T(z,w) * v5))) = T(x,u * (T(T(z,w),y) * v5))
    ]]></literal>
    <justification jstring="[hyper(17720,a,19960,a)].">
      <j1 rule="hyper" parents="17720 19960"/>
    </justification>
  </clause>

  <clause id="19962">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (T(z,w) * v5))) = T(x,u * (T(z,y) * (v5 * K(z,w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,17772,a(flip),b,19960,a)].">
      <j1 rule="hyper" parents="60 17772 19960"/>
    </justification>
  </clause>

  <clause id="19963">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(u * w,u)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[para(6442(a,1),19955(a,2,2,2))].">
      <j1 rule="para" parents="6442 19955"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      K(x,K((y * z) * u,w) * v5) = K(x,K(z * (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(18381,a,19956,a)].">
      <j1 rule="hyper" parents="18381 19956"/>
    </justification>
  </clause>

  <clause id="19965">
    <literal><![CDATA[
      K(x,L(y * (K(z,y) * u),w,v5)) = K(x,L(T(y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[para(8202(a,1),19958(a,1,2,1))].">
      <j1 rule="para" parents="8202 19958"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      K(K((x * y) * z,u) * w,v5) = K(K(y * (x \ z),u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(18390,a,19959,a),flip(a)].">
      <j1 rule="hyper" parents="18390 19959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      K(x,K(y * ((z \ 1) \ u),w) * v5) = K(x,v5 * K((z * y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18786,a(flip),b,19964,a),flip(a)].">
      <j1 rule="hyper" parents="60 18786 19964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = K(x,L(T(y,z) * (u \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(15723,a,19965,a)].">
      <j1 rule="hyper" parents="15723 19965"/>
    </justification>
  </clause>

  <clause id="19970">
    <literal><![CDATA[
      K(K(x * (y \ z),T(u,w)) * v5,v6) = K(v5 * K(u,(y * x) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(17753,a,19966,a),flip(a)].">
      <j1 rule="hyper" parents="17753 19966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,18314,a(flip),b,19957,a),flip(a)].">
      <j1 rule="hyper" parents="370 18314 19957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14423,a(flip),b,19971,a),flip(a)].">
      <j1 rule="hyper" parents="370 14423 19971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19973">
    <literal><![CDATA[
      K(K(x * (T(y,z) \ u),w) * v5,v6) = K(K((y \ u) * x,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,18903,a,b,19844,a)].">
      <j1 rule="hyper" parents="60 18903 19844"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      K(x,K(y * z,y) * (u * (w * (z / y)))) = K(x,u * (w * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(18381,a,19862,a)].">
      <j1 rule="hyper" parents="18381 19862"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19870,a(flip),b,19922,a),flip(a)].">
      <j1 rule="hyper" parents="60 19870 19922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * ((1 / u) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18881,a,b,19975,a)].">
      <j1 rule="hyper" parents="60 18881 19975"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),19975(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 19975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),19975(a,1,2,2))].">
      <j1 rule="para" parents="107 19975"/>
    </justification>
  </clause>

  <clause id="19979">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,u * w)))) = K(x,y * (z * (T(u,u * w) * w)))
    ]]></literal>
    <justification jstring="[para(5488(a,2),19975(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5488 19975"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = x \ T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,19977,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 19977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19981">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,u))) = K(x,y * (z * (T(u,w) * w)))
    ]]></literal>
    <justification jstring="[para(5448(a,2),19977(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5448 19977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w,z))) = K(x,y * (T(z,u) * (w / z)))
    ]]></literal>
    <justification jstring="[para(7864(a,1),19977(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7864 19977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      T(x,y * (z * (u * (w / u)))) = T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5264,a,19980,a)].">
      <j1 rule="hyper" parents="5264 19980"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(19980(a,2),5290(a,1))].">
      <j1 rule="para" parents="19980 5290"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w / u)) * T(w,u))) = T(x,y * ((u * (w / u)) * z))
    ]]></literal>
    <justification jstring="[hyper(16863,a,19983,a),flip(a)].">
      <j1 rule="hyper" parents="16863 19983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      T(x,T(y,z * (u * (w / u))) * (z * T(w,u))) = T(x,(z * (u * (w / u))) * y)
    ]]></literal>
    <justification jstring="[hyper(12606,a,19983,a),flip(a)].">
      <j1 rule="hyper" parents="12606 19983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,w))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),19983(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 19983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,u))) = T(x,y * (z * (T(u,w) * w)))
    ]]></literal>
    <justification jstring="[para(5448(a,2),19983(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5448 19983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),1 / z))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(951(a,2),19987(a,2,2,2))].">
      <j1 rule="para" parents="951 19987"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) * (1 / u),u \ 1))) = T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w))))
    ]]></literal>
    <justification jstring="[para(4434(a,1),19987(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4434 19987"/>
    </justification>
  </clause>

  <clause id="19991">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w,z))) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,17875,a(flip),b,19982,a),flip(a)].">
      <j1 rule="hyper" parents="370 17875 19982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      K(x,y * T(K(z,u) * w,z)) = K(x,y * (z * (w / T(z,u))))
    ]]></literal>
    <justification jstring="[para(8359(a,2),19991(a,1,2,2))].">
      <j1 rule="para" parents="8359 19991"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * T(K(y,z) * z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,17583,a,b,19992,a)].">
      <j1 rule="hyper" parents="370 17583 19992"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      K(K(x * (T(y,z) * u),w) * v5,v6) = K(K(x * (y * u),w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17367,a,19930,a)].">
      <j1 rule="hyper" parents="17367 19930"/>
    </justification>
  </clause>

  <clause id="19995">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19889,a(flip),b,19933,a),flip(a)].">
      <j1 rule="hyper" parents="60 19889 19933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / T(v5,T(z,u \ w)))) = K(x,y * (v5 \ T(z,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14516,a(flip),b,19995,a),flip(a)].">
      <j1 rule="hyper" parents="60 14516 19995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19997">
    <literal><![CDATA[
      T(x,K(y,y * z) * (u * (w * (y * z)))) = T(x,u * (w * T(y * z,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14342,a,b,19937,a)].">
      <j1 rule="hyper" parents="60 14342 19937"/>
    </justification>
  </clause>

  <clause id="19998">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(w * u,u)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17784,a,19963,a)].">
      <j1 rule="hyper" parents="17784 19963"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      K(x,y * K(z,u * ((w \ 1) \ v5))) = K(x,y * K((w * u) * v5,z))
    ]]></literal>
    <justification jstring="[hyper(17484,a,19968,a)].">
      <j1 rule="hyper" parents="17484 19968"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      K(x,L((y * K(z,y)) / u,w,v5)) = K(x,L(T(y,z) / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,15592,a(flip),b,19969,a),flip(a)].">
      <j1 rule="hyper" parents="370 15592 19969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16456,a(flip),b,20000,a),flip(a)].">
      <j1 rule="hyper" parents="60 16456 20000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      K(x,L(T(y * z,y \ 1) / u,u,y \ 1)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(951(a,1),20001(a,2,2,1))].">
      <j1 rule="para" parents="951 20001"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      K(x * K(y,(z * u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,u * (z \ w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(19970(a,1),17753(a,1))].">
      <j1 rule="para" parents="19970 17753"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      K(x,(y * (z * (u / w))) * K(u,w)) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17483,a,19974,a)].">
      <j1 rule="hyper" parents="17483 19974"/>
    </justification>
  </clause>

  <clause id="20006">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(u,w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(19952,a,20005,a)].">
      <j1 rule="hyper" parents="19952 20005"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      K(x,(y * (z / (u \ w))) * K(u,w)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18324,a(flip),b,19998,a)].">
      <j1 rule="hyper" parents="60 18324 19998"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(17727,a,20007,a),flip(a)].">
      <j1 rule="hyper" parents="17727 20007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w) / v5) / (v5 \ K(u,w)))) = K(x,y * ((K(u,w) / v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14513,a(flip),b,20008,a),flip(a)].">
      <j1 rule="hyper" parents="60 14513 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) \ w)) \ v5) = K(x,(y \ v5) * K((u * z) * w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17451,a(flip),b,19999,a)].">
      <j1 rule="hyper" parents="60 17451 19999"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(19896,a,19809,a),flip(a)].">
      <j1 rule="hyper" parents="19896 19809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(u,w) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(19896,a,19816,a),flip(a)].">
      <j1 rule="hyper" parents="19896 19816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,(y * z) * (v5 * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19853,a(flip),b,20013,a),flip(a)].">
      <j1 rule="hyper" parents="370 19853 20013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(z,w))) = K(x,(y * T(z,w)) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,2),20015(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5256 20015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * z) * w)) = K(x,(u * T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(19863,a,20016,a)].">
      <j1 rule="hyper" parents="19863 20016"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(w,z))) = K(x,(y * T(z,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(19856,a,20017,a)].">
      <j1 rule="hyper" parents="19856 20017"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      K(x,(T(y,z) * T(z,u)) * w) = K(x,(z * y) * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(16973,a,20018,a),flip(a)].">
      <j1 rule="hyper" parents="16973 20018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      K(x,(y * z) * (u * K(w,y))) = K(x,(T(y,w) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17876,a,20019,a),flip(a)].">
      <j1 rule="hyper" parents="17876 20019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      K(x,(T(y,z) * u) * (y \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) * (T(y,z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20020(a,1),17765(a,1))].">
      <j1 rule="para" parents="20020 17765"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      K(K(x,y * (y * K(z,u))) * K(u,(w / x) * (w \ z)),v5) = K(K(u,(w * (w / x)) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(20003,a,18847,a)].">
      <j1 rule="hyper" parents="20003 18847"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      K(T(x * K(y,z),u) * w,v5) = K(K(y,z) * (T(x,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(17843,a,19838,a),flip(a)].">
      <j1 rule="hyper" parents="17843 19838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      K(T(x * K(y,z),u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * (T(x,u) * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(19838(a,1),17843(a,1))].">
      <j1 rule="para" parents="19838 17843"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      K(K(x,T(y \ (z \ u),w)) * v5,v6) = K(v5 * K((z * y) \ u,x),v6)
    ]]></literal>
    <justification jstring="[hyper(17753,a,19912,a),flip(a)].">
      <j1 rule="hyper" parents="17753 19912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      K(K(x,T(y \ (z \ u),w)) * v5,v6) = K(v5 * K((z * y) * u,x),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,18287,a(flip),b,20025,a),flip(a)].">
      <j1 rule="hyper" parents="370 18287 20025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      K(x * K(y \ (z \ u),w),v5) = K(x * K((z * y) * u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(17753,a,20027,a)].">
      <j1 rule="hyper" parents="17753 20027"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      K(x * K((y * z) * u,w),v5) = K(x * K(z * (y \ u),w),v5)
    ]]></literal>
    <justification jstring="[hyper(18288,a,20028,a),flip(a)].">
      <j1 rule="hyper" parents="18288 20028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      K(x * K(K(y,z) * (u * w),v5),v6) = K(x * K(u * (K(y,z) \ w),v5),v6)
    ]]></literal>
    <justification jstring="[para(19803(a,1),20029(a,1,1,2))].">
      <j1 rule="para" parents="19803 20029"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z / u)) = K(x,(T(T(z,w),w) / u) * y)
    ]]></literal>
    <justification jstring="[para(16719(a,1),19946(a,1,2,1))].">
      <j1 rule="para" parents="16719 19946"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) / u) * w) = K(x,(y / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12637,a,20031,a),flip(a)].">
      <j1 rule="hyper" parents="12637 20031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(z / T(y,T(z,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(19787,a,20032,a)].">
      <j1 rule="hyper" parents="19787 20032"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14480,a(flip),b,20032,a)].">
      <j1 rule="hyper" parents="60 14480 20032"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      K(x,((y / z) / z) * u) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20035(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 20035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20037">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5749(a,2),20035(a,1,2,1))].">
      <j1 rule="para" parents="5749 20035"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = x * K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,20037,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 20037 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      K((T(x,y) \ y) * z,u) = (w * K(u,(y / x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(20037(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20037 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20040">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,20038,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 20038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),20040(a,1,2,1))].">
      <j1 rule="para" parents="5749 20040"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      T(x,((y / z) / z) * u) = T(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20041(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u \ y)) * z) = T(x,z * ((y / u) / u))
    ]]></literal>
    <justification jstring="[hyper(18964,a,20042,a),flip(a)].">
      <j1 rule="hyper" parents="18964 20042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20044">
    <literal><![CDATA[
      K((T(x,y) \ y) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,20039,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 20039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20045">
    <literal><![CDATA[
      K((x \ T(y,x)) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),20044(a,1,1,1))].">
      <j1 rule="para" parents="5749 20044"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      K((T(x,y * z) \ T(u,T(x,y \ z))) * w,v5) = K((u / T(x,y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(18880,a,20045,a)].">
      <j1 rule="hyper" parents="18880 20045"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      T(x,y * ((z / u) / u)) = T(x,y * (u \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(17558,a,20043,a),flip(a)].">
      <j1 rule="hyper" parents="17558 20043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20048">
    <literal><![CDATA[
      T(x,y * (T(z,u) * (w * K(z,v5)))) = T(x,y * (T(T(z,v5),u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19961,a(flip),b,19962,a),flip(a)].">
      <j1 rule="hyper" parents="60 19961 19962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      T(x,y * (T(T(z,u),u) * (z \ w))) = T(x,y * (K(z,u) * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,14733,a(flip),b,20048,a),flip(a)].">
      <j1 rule="hyper" parents="60 14733 20048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w)) * T(u,w))) = T(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[para(12547(a,1),19985(a,1,2,2,1))].">
      <j1 rule="para" parents="12547 19985"/>
    </justification>
  </clause>

  <clause id="20051">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(16863,a,20050,a),flip(a)].">
      <j1 rule="hyper" parents="16863 20050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20052">
    <literal><![CDATA[
      T(x,(y * (z / y)) * u) = T(x,1 * (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(2(a,1),20051(a,1,2))].">
      <j1 rule="para" parents="2 20051"/>
    </justification>
  </clause>

  <clause id="20053">
    <literal><![CDATA[
      T(x,(y * (z / y)) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2(a,1),20052(a,2,2))].">
      <j1 rule="para" parents="2 20052"/>
    </justification>
  </clause>

  <clause id="20054">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(T(y,z) * z) * u)
    ]]></literal>
    <justification jstring="[para(5448(a,2),20053(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5448 20053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20055">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(16887,a,20054,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16887 20054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20056">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(20054(a,2),16887(a,1))].">
      <j1 rule="para" parents="20054 16887"/>
    </justification>
  </clause>

  <clause id="20057">
    <literal><![CDATA[
      T(x,(y * z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(20055(a,1),12606(a,1))].">
      <j1 rule="para" parents="20055 12606"/>
    </justification>
  </clause>

  <clause id="20058">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z \ 1))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(4443(a,1),19989(a,1,2,2,2))].">
      <j1 rule="para" parents="4443 19989"/>
    </justification>
  </clause>

  <clause id="20059">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,w))) = T(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19938,a(flip),b,19997,a),flip(a)].">
      <j1 rule="hyper" parents="60 19938 19997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20060">
    <literal><![CDATA[
      T(x,y * (z * T(u * w,u))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19987,a(flip),b,20059,a),flip(a)].">
      <j1 rule="hyper" parents="60 19987 20059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20061">
    <literal><![CDATA[
      T(x,y \ (z * T(u * w,u))) = T(x,(y \ 1) * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(15260,a,20060,a)].">
      <j1 rule="hyper" parents="15260 20060"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      T(x,y * (z * (T(u,w) * w))) = T(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19988,a(flip),b,20060,a)].">
      <j1 rule="hyper" parents="60 19988 20060"/>
    </justification>
  </clause>

  <clause id="20063">
    <literal><![CDATA[
      T(x,T(y,z * (u * w)) * (z * (u * w))) = T(x,(z * (T(w,u) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(16858,a,20062,a),flip(a)].">
      <j1 rule="hyper" parents="16858 20062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20064">
    <literal><![CDATA[
      T(x,y * (z * (T(u,(w \ v5) \ v5) * ((w \ v5) \ v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[para(362(a,2),20062(a,2,2,2,2))].">
      <j1 rule="para" parents="362 20062"/>
    </justification>
  </clause>

  <clause id="20065">
    <literal><![CDATA[
      T(x,y \ (z * T(u * w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(20061(a,2),15260(a,1))].">
      <j1 rule="para" parents="20061 15260"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      K(x,T(y / T(z,(u * w) * v5),z)) = K(x,T(z,w * ((1 / u) \ v5)) \ y)
    ]]></literal>
    <justification jstring="[para(9096(a,2),20010(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9096 20010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      K(x * K(y * (K(z,u) \ w),v5),v6) = K(K(y * w,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,18657,a(flip),b,20030,a),flip(a)].">
      <j1 rule="hyper" parents="60 18657 20030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20069">
    <literal><![CDATA[
      K(x * K((y * z) * (K(u,w) \ v5),v6),v7) = K(K(z * (y \ v5),v6) * x,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,19966,a(flip),b,20067,a),flip(a)].">
      <j1 rule="hyper" parents="370 19966 20067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * K(z,u)))) = T(x,y * (z * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18952,a(flip),b,20049,a),flip(a)].">
      <j1 rule="hyper" parents="60 18952 20049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20072">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (w * K(z,u)))) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),20070(a,2,2,2))].">
      <j1 rule="para" parents="5 20070"/>
    </justification>
  </clause>

  <clause id="20074">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(6281(a,1),20072(a,1,2,2,2))].">
      <j1 rule="para" parents="6281 20072"/>
    </justification>
  </clause>

  <clause id="20075">
    <literal><![CDATA[
      T(x,(y \ 1) * (z * K(u,w))) = T(x,y \ (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(15260,a,20074,a),flip(a)].">
      <j1 rule="hyper" parents="15260 20074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20076">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (z * y)) = T(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19845,a,b,20074,a)].">
      <j1 rule="hyper" parents="370 19845 20074"/>
    </justification>
  </clause>

  <clause id="20077">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (z \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,u) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20074(a,2),17761(a,1))].">
      <j1 rule="para" parents="20074 17761"/>
    </justification>
  </clause>

  <clause id="20078">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(20075(a,1),15260(a,1))].">
      <j1 rule="para" parents="20075 15260"/>
    </justification>
  </clause>

  <clause id="20079">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u * w,v5) * (z * y)) = T(x,y * (K(u \ w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(18188,a,20076,a)].">
      <j1 rule="hyper" parents="18188 20076"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z * 1))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18574,a(flip),b,20058,a)].">
      <j1 rule="hyper" parents="60 18574 20058"/>
    </justification>
  </clause>

  <clause id="20081">
    <literal><![CDATA[
      T(x,(y * (T(z,u) * u)) * w) = T(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(12606,a,20063,a),flip(a)].">
      <j1 rule="hyper" parents="12606 20063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      K(x,T(y,z * ((1 / u) \ w)) \ v5) = K(x,T(y,(u * z) * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(17304,a,20066,a),flip(a)].">
      <j1 rule="hyper" parents="17304 20066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20084">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) \ v5) = K(x,T(y,(u * z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(4671(a,1),20083(a,1,2,1))].">
      <j1 rule="para" parents="4671 20083"/>
    </justification>
  </clause>

  <clause id="20085">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) \ v5) = K(x,T(y,u * (z \ w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18573,a(flip),b,20084,a),flip(a)].">
      <j1 rule="hyper" parents="60 18573 20084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20086">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) * w)) \ v5) = K(x,T(y,w * (u \ z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18791,a,b,20085,a)].">
      <j1 rule="hyper" parents="60 18791 20085"/>
    </justification>
  </clause>

  <clause id="20087">
    <literal><![CDATA[
      K(x * K((T(y,z) * u) * (K(w,v5) \ v6),v7),v8) = K(K((y \ v6) * u,v7) * x,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,19973,a(flip),b,20069,a),flip(a)].">
      <j1 rule="hyper" parents="370 19973 20069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20088">
    <literal><![CDATA[
      T(x,y * (K(z \ u,w) * v5)) = T(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,20076,a(flip),b,20079,a),flip(a)].">
      <j1 rule="hyper" parents="60 20076 20079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20089">
    <literal><![CDATA[
      T(x,y * (K(z * u,w) * (w \ v5))) = T(x,y * (T(w,z \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),20088(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 20088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) \ v5)) = T(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),20089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 20089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20091">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,y * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(17810,a,20090,a)].">
      <j1 rule="hyper" parents="17810 20090"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) \ v5)) = T(x,y \ (T(z,u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(15260,a,20090,a),flip(a)].">
      <j1 rule="hyper" parents="15260 20090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,17861,a,b,20091,a),flip(a)].">
      <j1 rule="hyper" parents="370 17861 20091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20094">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) \ v5)) = T(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(15260,a,20092,a),flip(a)].">
      <j1 rule="hyper" parents="15260 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20095">
    <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(20092(a,1),15260(a,1))].">
      <j1 rule="para" parents="20092 15260"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      T(x,y \ (T(z,u * u) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(227(a,1),20094(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="227 20094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20097">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ (u \ 1)) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(15252(a,1),20096(a,1,2,2,1))].">
      <j1 rule="para" parents="15252 20096"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      T(x,y \ ((z * (u * (z \ (1 / z)))) \ w)) = T(x,y \ (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[para(7124(a,1),20097(a,1,2,2,1))].">
      <j1 rule="para" parents="7124 20097"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      T(x,y * (z * T(u * (1 / z),z))) = T(x,y * ((z \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(3(a,1),20080(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3 20080"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (z * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[para(2059(a,1),20099(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2059 20099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      T(x,y * (z * ((1 / z) * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[para(951(a,1),20100(a,1,2,2))].">
      <j1 rule="para" parents="951 20100"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      T(x,y * (z * ((z \ 1) * u))) = T(x,y * R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16049,a(flip),b,20101,a)].">
      <j1 rule="hyper" parents="60 16049 20101"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      T(x,y * R(z,u,u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(2074(a,1),20102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2074 20102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20104">
    <literal><![CDATA[
      K(x,T(y,z * L(T(u,w),v5,v5))) = K(x,T(y,z * R(u,v5,v5)))
    ]]></literal>
    <justification jstring="[para(20103(a,2),17972(a,2,2))].">
      <j1 rule="para" parents="20103 17972"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      K(x,T(y,z * R(u,w,w))) = K(x,T(y,z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17972,a(flip),b,20104,a),flip(a)].">
      <j1 rule="hyper" parents="60 17972 20104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      T(x,y \ (z * ((z \ 1) \ ((z * u) \ w)))) = T(x,y \ (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[para(3342(a,1),20098(a,1,2,2))].">
      <j1 rule="para" parents="3342 20098"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y * z) \ u)) = T(x,y \ (((y \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),20106(a,1,2))].">
      <j1 rule="para" parents="4 20106"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) * z) \ u)) = T(x,y * ((y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(15396,a,20107,a),flip(a)].">
      <j1 rule="hyper" parents="15396 20107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((y * z) \ u)) = w
    ]]></literal>
    <justification jstring="[para(20107(a,1),15396(a,1))].">
      <j1 rule="para" parents="20107 15396"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      T(T(x,K((y * z) \ u,y)),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12569,a(flip),b,20108,a),flip(a)].">
      <j1 rule="hyper" parents="370 12569 20108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20111">
    <literal><![CDATA[
      T(x,y \ (((y \ 1) * ((y \ z) * (y \ z))) \ u)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[para(857(a,1),20108(a,2,2,2,1))].">
      <j1 rule="para" parents="857 20108"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y * (w \ v5),y)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(19710(a,1),19638(a,1,2))].">
      <j1 rule="para" parents="19710 19638"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      a(x,y,K(T(z * K(u * w,z),v5) * w,u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19718,a(flip),b,19656,a),flip(a)].">
      <j1 rule="hyper" parents="370 19718 19656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20115">
    <literal><![CDATA[
      a(x,y,K(K(z * u,w) * (T(w,v5) * u),z)) = a(x,y,K(z,u * T(w,v5)))
    ]]></literal>
    <justification jstring="[para(20023(a,1),20114(a,1,3))].">
      <j1 rule="para" parents="20023 20114"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      K((x * L(K(y,z),u,w)) \ v5,v6) = K(x \ (L(K(z,y),u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(19552,a,19751,a),flip(a)].">
      <j1 rule="hyper" parents="19552 19751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20117">
    <literal><![CDATA[
      K(((x \ y) * x) / T(L(K(z,u),w,v5) * x,K(v6,v7)),v8) = K(x \ (L(K(u,z),w,v5) * y),v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,17932,a,b,20116,a)].">
      <j1 rule="hyper" parents="60 17932 20116"/>
    </justification>
  </clause>

  <clause id="20118">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) * K(x,K(y,v6)) = T(K(x,y) * a(z,u,K(w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(8637(a,1),19805(a,1,2))].">
      <j1 rule="para" parents="8637 19805"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * T(w,u))) = K(x,y * (T(u,w) * T(u \ w,z)))
    ]]></literal>
    <justification jstring="[hyper(16902,a,19879,a)].">
      <j1 rule="hyper" parents="16902 19879"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(w,z * u) * T(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(20119(a,1),18606(a,1))].">
      <j1 rule="para" parents="20119 18606"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w) * (T(y,z) / u)) = K(x,T(((z * y) / z) / u,w))
    ]]></literal>
    <justification jstring="[para(16748(a,1),19945(a,1,2,1))].">
      <j1 rule="para" parents="16748 19945"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      K(x,T(((y * z) / y) / u,w)) = K(x,T(T(z,y) / u,w))
    ]]></literal>
    <justification jstring="[para(5275(a,2),20121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5275 20121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      T(x,T(y,z * T(u,w)) * (z * T(u,w))) = T(x,(z * (w * (u / w))) * y)
    ]]></literal>
    <justification jstring="[para(16870(a,1),19986(a,1,2,1))].">
      <j1 rule="para" parents="16870 19986"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      T(x,(y * (z * (u / z))) * w) = T(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(12606,a,20123,a),flip(a)].">
      <j1 rule="hyper" parents="12606 20123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      K(x,(y * (z * (u / z))) * w) = x \ T(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(125,a,20124,a(flip),b,5256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 20124 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      T(x,(y * T(z * u,z)) * w) = T(x,(y * (T(z,u) * u)) * w)
    ]]></literal>
    <justification jstring="[para(5448(a,2),20124(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5448 20124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      K(x,(y * (z * (u / z))) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a,b,20125,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 20125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      K(x,(y * (z * (u / z))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * T(u,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(20125(a,2),5290(a,1))].">
      <j1 rule="para" parents="20125 5290"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      K(x,(y * T(z * u,u)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(6(a,1),20127(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 20127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),1 / y)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(951(a,2),20129(a,2,2,1))].">
      <j1 rule="para" parents="951 20129"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      T(x,(y * T((z \ u) * w,z * u)) * v5) = T(x,(y * (T(z \ u,w) * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18798,a,20126,a)].">
      <j1 rule="hyper" parents="18798 20126"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y \ 1)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(4443(a,1),20130(a,1,2,1,2))].">
      <j1 rule="para" parents="4443 20130"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y * 1)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(18800,a,20132,a)].">
      <j1 rule="hyper" parents="18800 20132"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      K(x,(y * T(z * (1 / y),y)) * u) = K(x,((y \ 1) * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(3(a,1),20133(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3 20133"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[para(2059(a,1),20134(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2059 20134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[para(951(a,1),20135(a,1,2,1))].">
      <j1 rule="para" parents="951 20135"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      K(x,(y * ((y \ 1) * z)) * u) = K(x,R(z,y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(16141,a,20136,a)].">
      <j1 rule="hyper" parents="16141 20136"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      K(x,R(y,z,z) * u) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),20137(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2074 20137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / T(v5,T(z,u * w)))) = K(x,y * (v5 \ T(z,u \ w)))
    ]]></literal>
    <justification jstring="[para(17155(a,1),19996(a,1,2,2,2))].">
      <j1 rule="para" parents="17155 19996"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      K(x,y * (T(z,u \ K(w,v5)) / (u \ K(w,v5)))) = K(x,y * ((K(w,v5) / u) \ z))
    ]]></literal>
    <justification jstring="[para(17198(a,1),20009(a,1,2,2,1))].">
      <j1 rule="para" parents="17198 20009"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      K((T(x,y * z) \ T(u,T(x,y * z))) * w,v5) = K((u / T(x,y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(17155(a,1),20046(a,1,1,1,2))].">
      <j1 rule="para" parents="17155 20046"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      K(x * K((T(y,z) * u) * (K(w,v5) * v6),v7),v8) = K(K((y \ v6) * u,v7) * x,v8)
    ]]></literal>
    <justification jstring="[para(7506(a,1),20087(a,1,1,2,1,2))].">
      <j1 rule="para" parents="7506 20087"/>
    </justification>
  </clause>

  <clause id="20143">
    <literal><![CDATA[
      T(T(x,K(y \ (z \ u),z)),z \ (((z \ 1) * y) \ u)) = T(x,((z * y) \ u) * z)
    ]]></literal>
    <justification jstring="[para(11025(a,1),20110(a,1,1,2))].">
      <j1 rule="para" parents="11025 20110"/>
    </justification>
  </clause>

  <clause id="20144">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y,w \ v5)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(15954(a,1),20113(a,1,2))].">
      <j1 rule="para" parents="15954 20113"/>
    </justification>
  </clause>

  <clause id="20145">
    <literal><![CDATA[
      K(x,T(y,z)) * a(x,u,K(y,w * v5)) = K(x,L(T(y,z),u,(w * y) \ v5))
    ]]></literal>
    <justification jstring="[para(15958(a,1),20144(a,1,2))].">
      <j1 rule="para" parents="15958 20144"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,K(w,v5)),v6) = K(x,T(y,v6)) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(17345,a,20118,a),flip(a)].">
      <j1 rule="hyper" parents="17345 20118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      T(K(x,y) * a(x,z,K(y,u * w)),v5) = K(x,L(T(y,v5),z,(u * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20145,a(flip),b,20146,a),flip(a)].">
      <j1 rule="hyper" parents="370 20145 20146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) \ v5)) = T(K(x,L(y,u,w * v5)),z)
    ]]></literal>
    <justification jstring="[para(15909(a,1),20147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15909 20147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) \ v5)) = K(x,L(T(y,z),u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,8042,a,b,20148,a),flip(a)].">
      <j1 rule="hyper" parents="370 8042 20148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20150">
    <literal><![CDATA[
      K(x,L(T(y,z),u,(w * y) * v5)) = K(x,L(T(y,z),u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(19697,a,20149,a)].">
      <j1 rule="hyper" parents="19697 20149"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      K(x,y / (z * ((z * u) \ y))) = K(x,L(T(u,z),y,z * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,19705,a(flip),b,20150,a)].">
      <j1 rule="hyper" parents="60 19705 20150"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      T(x,(y * T((z \ 1) * u,z)) * w) = T(x,(y * (T(z \ 1,u) * u)) * w)
    ]]></literal>
    <justification jstring="[para(3(a,1),20131(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3 20131"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      T(x,(y * T((z \ 1) * u,z)) * w) = T(x,(y * (u * (z \ 1))) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20081,a(flip),b,20152,a),flip(a)].">
      <j1 rule="hyper" parents="370 20081 20152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14516,a(flip),b,20139,a),flip(a)].">
      <j1 rule="hyper" parents="60 14516 20139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w * v5)) * (z \ T(u,w * v5))) = K(x,(z \ T(u,w \ v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(18487,a,20155,a),flip(a)].">
      <j1 rule="hyper" parents="18487 20155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z * 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19948,a,b,20155,a)].">
      <j1 rule="hyper" parents="60 19948 20155"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (z \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(3(a,1),20157(a,2,2,2,2,2))].">
      <j1 rule="para" parents="3 20157"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y * z) * (u / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19947,a(flip),b,20158,a),flip(a)].">
      <j1 rule="hyper" parents="370 19947 20158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20160">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) \ v5)) = K(x,y * ((w \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,14513,a(flip),b,20140,a),flip(a)].">
      <j1 rule="hyper" parents="60 14513 20140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20161">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * ((z \ K(u,z \ 1)) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18687,a,b,20160,a)].">
      <j1 rule="hyper" parents="60 18687 20160"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      K((x / T(y,z \ u)) * w,v5) = K((x / T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20045,a(flip),b,20141,a),flip(a)].">
      <j1 rule="hyper" parents="60 20045 20141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      K((x / T(y,z * u)) * (w \ 1),v5) = K((x / T(y,z \ u)) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(15417,a,20162,a),flip(a)].">
      <j1 rule="hyper" parents="15417 20162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      K((x / T(y,z \ u)) / w,v5) = K((x / T(y,z * u)) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(15417,a,20163,a),flip(a)].">
      <j1 rule="hyper" parents="15417 20163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      K((x / T(y,y * z)) / u,w) = K((x / ((y \ z) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[para(108(a,1),20164(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="108 20164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      K((x / T((y * y) * z,y \ y)) / u,w) = K((x / (z * (y * y))) / u,w)
    ]]></literal>
    <justification jstring="[para(261(a,1),20164(a,2,1,1,2))].">
      <j1 rule="para" parents="261 20164"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      K((x / ((y * y) * z)) / u,w) = K((x / (z * (y * y))) / u,w)
    ]]></literal>
    <justification jstring="[para(227(a,1),20166(a,1,1,1,2))].">
      <j1 rule="para" parents="227 20166"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      K((x / ((y \ z) * (y * y))) / u,w) = K((x / ((y \ 1) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[para(936(a,1),20167(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="936 20167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20170">
    <literal><![CDATA[
      K((x / (y * (z * z))) / u,w) = K((x / y) / (u * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(979(a,1),20167(a,1,1)),flip(a)].">
      <j1 rule="para" parents="979 20167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20171">
    <literal><![CDATA[
      K((x / (y * (z * z))) / u,w) = K(z \ (z \ ((x / y) / u)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,18503,a(flip),b,20170,a),flip(a)].">
      <j1 rule="hyper" parents="370 18503 20170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      K(x \ (x \ ((y / (x \ z)) / u)),w) = K((y / ((x \ 1) \ z)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20171,a(flip),b,20169,a)].">
      <j1 rule="hyper" parents="60 20171 20169"/>
    </justification>
  </clause>

  <clause id="20174">
    <literal><![CDATA[
      T(T(x,K(y,z * (y \ u))),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(17531(a,1),20143(a,1,1))].">
      <j1 rule="para" parents="17531 20143"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      K(x,y * (K(z * 1,u) * ((1 / z) \ w))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,19931,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="370 19931 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((1 / z) \ w))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(3(a,1),20175(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3 20175"/>
    </justification>
  </clause>

  <clause id="20177">
    <literal><![CDATA[
      K(x,y * ((1 / T(z,u)) \ w)) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[para(9167(a,1),20176(a,1,2,2))].">
      <j1 rule="para" parents="9167 20176"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (((y \ 1) * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[para(12330(a,1),20174(a,1,1))].">
      <j1 rule="para" parents="12330 20174"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * ((y * z) \ u)) = T(x,((y * z) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(20109,a,20178,a)].">
      <j1 rule="hyper" parents="20109 20178"/>
    </justification>
  </clause>

  <clause id="20180">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(37,a,17545,a,b,20179,a)].">
      <j1 rule="hyper" parents="37 17545 20179"/>
    </justification>
  </clause>

  <clause id="20181">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ (y * z))) = T(x,(u \ (y * z)) \ y)
    ]]></literal>
    <justification jstring="[para(20180(a,1),17535(a,1,1))].">
      <j1 rule="para" parents="20180 17535"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((y \ u) \ z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[para(20180(a,1),17536(a,1,1))].">
      <j1 rule="para" parents="20180 17536"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * ((z / T(y,u)) * w)) = K(x,(z / L(T(y,u),y,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(17749,a,19818,a)].">
      <j1 rule="hyper" parents="17749 19818"/>
    </justification>
  </clause>

  <clause id="20184">
    <literal><![CDATA[
      K(x,(y / L(T(z,u),z,z)) * w) = K(x,(y / T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(6058,a,20183,a),flip(a)].">
      <j1 rule="hyper" parents="6058 20183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20186">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * w) * K(x,K(w,T(z,u) * y)) = K(x,w * (y / T(T(z,u),z \ 1)))
    ]]></literal>
    <justification jstring="[para(20184(a,1),18172(a,1,1))].">
      <j1 rule="para" parents="20184 18172"/>
    </justification>
  </clause>

  <clause id="20187">
    <literal><![CDATA[
      K(x,y * (z * (a(z,u,1 / u) * K(u,u \ 1)))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(579(a,1),19976(a,2,2,2))].">
      <j1 rule="para" parents="579 19976"/>
    </justification>
  </clause>

  <clause id="20188">
    <literal><![CDATA[
      K(x,y * ((z * u) * (1 / u))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(4552(a,1),20187(a,1,2,2))].">
      <j1 rule="para" parents="4552 20187"/>
    </justification>
  </clause>

  <clause id="20189">
    <literal><![CDATA[
      K(x,y * ((z * u) * (u \ 1))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(6081,a,20188,a)].">
      <j1 rule="hyper" parents="6081 20188"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y \ z) * ((u * y) * y))
    ]]></literal>
    <justification jstring="[hyper(17419,a,20189,a),flip(a)].">
      <j1 rule="hyper" parents="17419 20189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      K(x,y * R(z,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(1111(a,1),20189(a,1,2,2))].">
      <j1 rule="para" parents="1111 20189"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      K(x,R(y,z,z) * (y \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(16455(a,2),20191(a,1,2))].">
      <j1 rule="para" parents="16455 20191"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      K(x,R(y \ 1,z,z) * ((y \ 1) \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(2302(a,2),20192(a,1,2))].">
      <j1 rule="para" parents="2302 20192"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y \ z) * (y * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19978,a(flip),b,20190,a),flip(a)].">
      <j1 rule="hyper" parents="370 19978 20190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20195">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) * ((y \ 1) \ u)) = K(x,(u / y) * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20138,a(flip),b,20193,a)].">
      <j1 rule="hyper" parents="60 20138 20193"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      K(x,a(y,y,z \ 1) \ u) = K(x,(u / z) * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(16605,a,20195,a)].">
      <j1 rule="hyper" parents="16605 20195"/>
    </justification>
  </clause>

  <clause id="20197">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,u)) = K(x,a(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(3091(a,1),20196(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3091 20196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20198">
    <literal><![CDATA[
      L(x,y,(((T(z,u * u) * w) / z) * (u * u)) * v5) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(997(a,1),19492(a,1,3,1,1,1))].">
      <j1 rule="para" parents="997 19492"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      L(x,y,(((z * z) \ ((u * w) / u)) * (z * z)) * v5) = L(x,y,T(w,(z * z) \ u) * v5)
    ]]></literal>
    <justification jstring="[para(1000(a,1),19492(a,1,3,1,1))].">
      <j1 rule="para" parents="1000 19492"/>
    </justification>
  </clause>

  <clause id="20200">
    <literal><![CDATA[
      T(x,T(T(y * (z \ 1),z) \ u,w)) = T(x,T(((z \ 1) * y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,9813,a(flip),b,19606,a),flip(a)].">
      <j1 rule="hyper" parents="370 9813 19606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(K(u,z) * w,v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(15263(a,1),19614(a,1,2,2,2))].">
      <j1 rule="para" parents="15263 19614"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      (x * K(y,T(z,x))) * R(u,x,K(y,T(z,x))) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(16009,a,19640,a),flip(a)].">
      <j1 rule="hyper" parents="16009 19640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20205">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(8011(a,1),20203(a,1,1))].">
      <j1 rule="para" parents="8011 20203"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(12405(a,1),20205(a,1,2))].">
      <j1 rule="para" parents="12405 20205"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(625,a,20206,a),flip(a)].">
      <j1 rule="hyper" parents="625 20206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6314,a,20207,a),flip(a)].">
      <j1 rule="hyper" parents="6314 20207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      ((x * y) * K(z,T(u,y))) / (K(z,u) * y) = L(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,8108,a,b,20207,a)].">
      <j1 rule="hyper" parents="60 8108 20207"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      L((x * y) / z,z,K(y,x)) = (y * x) / (z * ((x * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,1046,a(flip),b,20207,a),flip(a)].">
      <j1 rule="hyper" parents="60 1046 20207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(20207(a,1),103(a,1,1))].">
      <j1 rule="para" parents="20207 103"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(20207(a,1),675(a,1,1))].">
      <j1 rule="para" parents="20207 675"/>
    </justification>
  </clause>

  <clause id="20213">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(20207(a,1),5902(a,1,1))].">
      <j1 rule="para" parents="20207 5902"/>
    </justification>
  </clause>

  <clause id="20214">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * y) * T(K(z,u),y)
    ]]></literal>
    <justification jstring="[para(20207(a,1),12402(a,1,1))].">
      <j1 rule="para" parents="20207 12402"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(20208(a,1),19280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20208 19280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(17767,a,20215,a)].">
      <j1 rule="hyper" parents="17767 20215"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19924,a(flip),b,20215,a),flip(a)].">
      <j1 rule="hyper" parents="60 19924 20215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20218">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17833,a(flip),b,20216,a),flip(a)].">
      <j1 rule="hyper" parents="370 17833 20216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17833,a(flip),b,20217,a)].">
      <j1 rule="hyper" parents="60 17833 20217"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y * ((z * u) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(5630(a,1),20217(a,1,2,2))].">
      <j1 rule="para" parents="5630 20217"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),20217(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 20217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),u,u)) = K(x,y * (L(z,u,u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(11664(a,2),20217(a,1,2,2))].">
      <j1 rule="para" parents="11664 20217"/>
    </justification>
  </clause>

  <clause id="20223">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,(K(u,w) * y) / z)
    ]]></literal>
    <justification jstring="[hyper(129,a,20218,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 20218 5230"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(z \ y,z)))
    ]]></literal>
    <justification jstring="[para(8365(a,1),20218(a,1,2,1))].">
      <j1 rule="para" parents="8365 20218"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * w) * K(x,K(y \ K(z,u),w)) = K(x,w * (y \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(17594,a,20219,a)].">
      <j1 rule="hyper" parents="17594 20219"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,v5))) = K(x,y * (z \ K(v5,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18512,a(flip),b,20219,a)].">
      <j1 rule="hyper" parents="370 18512 20219"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(w,z))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15595,a(flip),b,20219,a),flip(a)].">
      <j1 rule="hyper" parents="370 15595 20219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * (z \ K(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ K(u,w)) * y) = v5
    ]]></literal>
    <justification jstring="[para(20219(a,1),18467(a,1))].">
      <j1 rule="para" parents="20219 18467"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,13005,a(flip),b,20211,a),flip(a)].">
      <j1 rule="hyper" parents="32 13005 20211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      (x * y) * K(z \ 1,y * z) = x * (y * K(z \ 1,y * z))
    ]]></literal>
    <justification jstring="[para(12484(a,1),20211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12484 20211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      (x * (y / z)) * K(y,z) = x * ((y / z) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14011(a,1),20211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14011 20211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[para(16476(a,1),20211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16476 20211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(5272,a,20229,a)].">
      <j1 rule="hyper" parents="5272 20229"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      (T(x * x,y) * z) \ u = z \ (T(x * x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(747,a,20234,a),flip(a)].">
      <j1 rule="hyper" parents="747 20234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      (T(x * x,y) * z) \ (u * T(x * x,y)) = z \ T(u,x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,17147,a(flip),b,20234,a)].">
      <j1 rule="hyper" parents="60 17147 20234"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      (x * (y / z)) * K(y,z) = x * (y / T(z,y))
    ]]></literal>
    <justification jstring="[para(5855(a,1),20232(a,2,2))].">
      <j1 rule="para" parents="5855 20232"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(20237(a,1),20006(a,1,2,2))].">
      <j1 rule="para" parents="20237 20006"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      (x * K(y,x * z)) * z = x * (z * K(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,16479,a,b,20233,a)].">
      <j1 rule="hyper" parents="60 16479 20233"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      x / (y * (z * K(u,z * y))) = (x / (y * z)) * K(z * y,u)
    ]]></literal>
    <justification jstring="[para(20233(a,1),12707(a,1,2))].">
      <j1 rule="para" parents="20233 12707"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      (x * (y * K(z,y * x))) / u = (x * y) / (u * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(20233(a,1),15988(a,1,1))].">
      <j1 rule="para" parents="20233 15988"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      (x * (y * K(z,y * x))) / (y * (x * K(z,x * y))) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(128,a,20239,a(flip),b,7481,a)].">
      <j1 rule="hyper" parents="128 20239 7481"/>
    </justification>
  </clause>

  <clause id="20243">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17835,a,b,20221,a)].">
      <j1 rule="hyper" parents="60 17835 20221"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,20223,a),flip(a)].">
      <j1 rule="hyper" parents="5265 20223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20246">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,y \ (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18027,a(flip),b,20244,a),flip(a)].">
      <j1 rule="hyper" parents="60 18027 20244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(w,z))) = x * K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,20227,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 20227 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      K(x,T(y,z * (u / T(w,u))) * (z * (w \ u))) = K(x,(z * (u / T(w,u))) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,20238,a),flip(a)].">
      <j1 rule="hyper" parents="12637 20238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = x \ T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,20238,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 20238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      K(x,y / (z * ((u \ w) \ w))) = K(x,y / (z * (u * K(u \ w,u))))
    ]]></literal>
    <justification jstring="[para(108(a,1),20243(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="108 20243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5254(a,1),20243(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5254 20243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20252">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18479,a(flip),b,20251,a)].">
      <j1 rule="hyper" parents="60 18479 20251"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      K(x,y / (T(z,u) * u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),20251(a,1,2,2))].">
      <j1 rule="para" parents="107 20251"/>
    </justification>
  </clause>

  <clause id="20254">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,y * z)) = K(x,u / (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,14576,a,b,20253,a)].">
      <j1 rule="hyper" parents="370 14576 20253"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (T(y,z) \ z)) = K(x,(T(y,z) * u) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,18129,a,b,20253,a)].">
      <j1 rule="hyper" parents="60 18129 20253"/>
    </justification>
  </clause>

  <clause id="20256">
    <literal><![CDATA[
      K(x,T(y * z,u \ y) / ((u \ 1) * y)) = K(x,L((1 / T(u,y)) \ z,u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16147,a(flip),b,20252,a),flip(a)].">
      <j1 rule="hyper" parents="60 16147 20252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      K(x,y / (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(20254(a,1),14580(a,1))].">
      <j1 rule="para" parents="20254 14580"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[para(16474(a,1),20212(a,1,1))].">
      <j1 rule="para" parents="16474 20212"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5233(a,2),20258(a,1,2))].">
      <j1 rule="para" parents="5233 20258"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(5279(a,1),20258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5279 20258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20261">
    <literal><![CDATA[
      x \ (y / (y / z)) = (x \ z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(5683(a,2),20258(a,1,2))].">
      <j1 rule="para" parents="5683 20258"/>
    </justification>
  </clause>

  <clause id="20263">
    <literal><![CDATA[
      ((x \ y) * K(z,y)) * K(y * K(z,y),y * z) = x \ L(y,z,y)
    ]]></literal>
    <justification jstring="[para(20258(a,1),15281(a,1,1))].">
      <j1 rule="para" parents="20258 15281"/>
    </justification>
  </clause>

  <clause id="20264">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) / u)) = L(x,y,(z \ w) * K(w,u))
    ]]></literal>
    <justification jstring="[para(20259(a,2),5884(a,1,3))].">
      <j1 rule="para" parents="20259 5884"/>
    </justification>
  </clause>

  <clause id="20266">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(20259(a,2),18485(a,1,2))].">
      <j1 rule="para" parents="20259 18485"/>
    </justification>
  </clause>

  <clause id="20270">
    <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(17789(a,1),20266(a,1))].">
      <j1 rule="para" parents="17789 20266"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) / u)) = L(x,y,z \ T(w,u))
    ]]></literal>
    <justification jstring="[para(15179(a,1),20264(a,2,3))].">
      <j1 rule="para" parents="15179 20264"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,y \ T(u,z))) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[para(20271(a,1),16771(a,1,2))].">
      <j1 rule="para" parents="20271 16771"/>
    </justification>
  </clause>

  <clause id="20273">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,8034,a,b,20214,a),flip(a)].">
      <j1 rule="hyper" parents="370 8034 20214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(u \ z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18522,a,b,20220,a)].">
      <j1 rule="hyper" parents="60 18522 20220"/>
    </justification>
  </clause>

  <clause id="20275">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ v5))) = K(x,y * (z \ K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20219,a,b,20226,a),flip(a)].">
      <j1 rule="hyper" parents="60 20219 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z * y) = x * (y * K(z \ 1,y * z))
    ]]></literal>
    <justification jstring="[para(7436(a,1),20231(a,1,2))].">
      <j1 rule="para" parents="7436 20231"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      ((T(x * x,y) * z) \ u) * T(x * x,y) = z \ T(u,x * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,1525,a(flip),b,20236,a)].">
      <j1 rule="hyper" parents="60 1525 20236"/>
    </justification>
  </clause>

  <clause id="20279">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(w,z))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,20247,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 20247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      T(x,y * (z * (u / T(w,u)))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(5264,a,20249,a)].">
      <j1 rule="hyper" parents="5264 20249"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      T(x,y * (T(z,u / T(w,u)) * (w \ u))) = T(x,y * ((u / T(w,u)) * z))
    ]]></literal>
    <justification jstring="[hyper(16863,a,20281,a),flip(a)].">
      <j1 rule="hyper" parents="16863 20281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      T(x,y * (z * (T(u,w) / w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5747(a,2),20281(a,1,2,2,2))].">
      <j1 rule="para" parents="5747 20281"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      T(x,y * (z * ((u \ w) / u))) = T(x,y * (z * (u \ (w / u))))
    ]]></literal>
    <justification jstring="[para(5782(a,1),20281(a,1,2,2,2))].">
      <j1 rule="para" parents="5782 20281"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      T(x,T(y,z * (u \ w)) * (z * (u \ w))) = T(x,(z * (T(w,u) / u)) * y)
    ]]></literal>
    <justification jstring="[hyper(14451,a,20283,a),flip(a)].">
      <j1 rule="hyper" parents="14451 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(T(y,z \ y) / T(z,y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14502,a(flip),b,20283,a)].">
      <j1 rule="hyper" parents="60 14502 20283"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      K(x,y * (z \ K(u,T(w / v5,w)))) = K(x,y * (z \ K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(7329(a,2),20275(a,1,2,2,2))].">
      <j1 rule="para" parents="7329 20275"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y,x,x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5342,a(flip),b,20276,a),flip(a)].">
      <j1 rule="hyper" parents="60 5342 20276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1492(a,1),20288(a,2,1))].">
      <j1 rule="para" parents="1492 20288"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      L(x / (y \ 1),y,y) = L(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(6827,a,20289,a)].">
      <j1 rule="hyper" parents="6827 20289"/>
    </justification>
  </clause>

  <clause id="20291">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y \ 1,y \ 1) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(108(a,2),20290(a,1,1,2))].">
      <j1 rule="para" parents="108 20290"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      L(x / (T(y,y \ 1) \ 1),T(y,y \ 1),T(y,y \ 1)) = L(x,T(y,y \ 1),T(y,y \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(308(a,1),20290(a,2,2))].">
      <j1 rule="para" parents="308 20290"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      (x \ (T(y * y,z) \ u)) * T(y * y,z) = x \ T(u,y * y)
    ]]></literal>
    <justification jstring="[para(20235(a,1),20278(a,1,1))].">
      <j1 rule="para" parents="20235 20278"/>
    </justification>
  </clause>

  <clause id="20294">
    <literal><![CDATA[
      (T(x * x,y) \ z) * T(x * x,y) = T(z,x * x)
    ]]></literal>
    <justification jstring="[hyper(1575,a,20293,a(flip))].">
      <j1 rule="hyper" parents="1575 20293"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      K(x * x,y) * (((T(x * x,y) * z) \ u) * (x * x)) = K(z,x * x) * T(z \ u,x * x)
    ]]></literal>
    <justification jstring="[para(20294(a,1),19045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20294 19045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20296">
    <literal><![CDATA[
      (x * y) / (z * ((y * x) \ (x * y))) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,16478,a(flip),b,20210,a),flip(a)].">
      <j1 rule="hyper" parents="60 16478 20210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[para(11(a,2),20296(a,1,2,2))].">
      <j1 rule="para" parents="11 20296"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = ((y * z) * x) / (y * (z * x))
    ]]></literal>
    <justification jstring="[para(15589(a,1),20297(a,1,2))].">
      <j1 rule="para" parents="15589 20297"/>
    </justification>
  </clause>

  <clause id="20299">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17893(a,2),20270(a,1))].">
      <j1 rule="para" parents="17893 20270"/>
    </justification>
  </clause>

  <clause id="20300">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18512,a(flip),b,20224,a),flip(a)].">
      <j1 rule="hyper" parents="370 18512 20224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      K(x,y / (z * T(u,T(w / v5,w)))) = K(x,y * ((z * u) \ K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20221,a(flip),b,20287,a)].">
      <j1 rule="hyper" parents="60 20221 20287"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(14004(a,1),20213(a,1,1))].">
      <j1 rule="para" parents="14004 20213"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(16474(a,1),20302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16474 20302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20304">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,19661,a,b,20298,a)].">
      <j1 rule="hyper" parents="370 19661 20298"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      K((L(x,y,z) * (z * y)) / (x * (z * y)),u) = K(a(z,y,x) \ 1,u)
    ]]></literal>
    <justification jstring="[para(20304(a,2),8215(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20304 8215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16561,a(flip),b,20305,a),flip(a)].">
      <j1 rule="hyper" parents="60 16561 20305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      K(x,((a(y,z,u) \ 1) \ w) * T(a(y,z,u) \ 1,v5)) = K(x,T(a(y,z,K(v5,u)) * w,a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(20306(a,1),17433(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="20306 17433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(u * z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18512,a(flip),b,20274,a),flip(a)].">
      <j1 rule="hyper" parents="370 18512 20274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (u \ w))) = T(x,y * ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(14346(a,1),20282(a,1,2,2,1))].">
      <j1 rule="para" parents="14346 20282"/>
    </justification>
  </clause>

  <clause id="20311">
    <literal><![CDATA[
      T(x,y * ((z / T(u,z)) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(16863,a,20310,a),flip(a)].">
      <j1 rule="hyper" parents="16863 20310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      T(x,y * (((z \ u) / z) * w)) = T(x,y * ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[para(5782(a,1),20311(a,1,2,2,1))].">
      <j1 rule="para" parents="5782 20311"/>
    </justification>
  </clause>

  <clause id="20313">
    <literal><![CDATA[
      T(x,(y * (T(z,u) / u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * (u \ z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(20285(a,1),12606(a,1))].">
      <j1 rule="para" parents="20285 12606"/>
    </justification>
  </clause>

  <clause id="20314">
    <literal><![CDATA[
      T(x,(y * (1 / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(224(a,1),20313(a,1,2,1,2,1))].">
      <j1 rule="para" parents="224 20313"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      K(x,y / (z * T(u,T(w / v5,w)))) = K(x,y / (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20221,a(flip),b,20301,a),flip(a)].">
      <j1 rule="hyper" parents="370 20221 20301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20317">
    <literal><![CDATA[
      K(x,y / (z * T(u,w \ v5))) = K(x,y / (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(7314(a,1),20316(a,1,2,2,2))].">
      <j1 rule="para" parents="7314 20316"/>
    </justification>
  </clause>

  <clause id="20318">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,T(v5,y * T(z,u * w)) / (y * T(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19090,a,b,20317,a)].">
      <j1 rule="hyper" parents="60 19090 20317"/>
    </justification>
  </clause>

  <clause id="20319">
    <literal><![CDATA[
      K(x,L((1 / T(y,z)) \ u,y,z)) = K(x,((y \ 1) * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(15335,a,20256,a),flip(a)].">
      <j1 rule="hyper" parents="15335 20256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20320">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z)) = K(x,((y \ 1) * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(18542,a,20319,a)].">
      <j1 rule="hyper" parents="18542 20319"/>
    </justification>
  </clause>

  <clause id="20321">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,L((y \ K(y,z)) * u,y,z))
    ]]></literal>
    <justification jstring="[para(9802(a,1),20320(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9802 20320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20323">
    <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(20225(a,1),17629(a,1))].">
      <j1 rule="para" parents="20225 17629"/>
    </justification>
  </clause>

  <clause id="20324">
    <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(15268(a,2),20323(a,1))].">
      <j1 rule="para" parents="15268 20323"/>
    </justification>
  </clause>

  <clause id="20325">
    <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(20217(a,2),20323(a,1))].">
      <j1 rule="para" parents="20217 20323"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(w * v5,u))) = v6
    ]]></literal>
    <justification jstring="[para(20275(a,2),20323(a,1))].">
      <j1 rule="para" parents="20275 20323"/>
    </justification>
  </clause>

  <clause id="20327">
    <literal><![CDATA[
      K(x,y / L(K(z,u) * w,z,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (L(w,z,z) \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(11663(a,2),20324(a,1,2,2))].">
      <j1 rule="para" parents="11663 20324"/>
    </justification>
  </clause>

  <clause id="20328">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y * K(z,u)) * (y \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(14353(a,1),20325(a,1))].">
      <j1 rule="para" parents="14353 20325"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      ((x * (y * K(z,y * x))) / (y * x)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20240,a(flip),b,20242,a)].">
      <j1 rule="hyper" parents="60 20240 20242"/>
    </justification>
  </clause>

  <clause id="20331">
    <literal><![CDATA[
      K(x,T(y,z * (u \ w)) * (z * (u \ w))) = K(x,(z * (w / T(u,w))) * y)
    ]]></literal>
    <justification jstring="[para(14450(a,1),20248(a,1,2,1))].">
      <j1 rule="para" parents="14450 20248"/>
    </justification>
  </clause>

  <clause id="20332">
    <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(20331(a,1),12637(a,1))].">
      <j1 rule="para" parents="20331 12637"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      K(x,(y * (z / T(u,z))) / w) = K(x,(y * (u \ z)) * (w \ 1))
    ]]></literal>
    <justification jstring="[hyper(20332,a,15155,a),flip(a)].">
      <j1 rule="hyper" parents="20332 15155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20334">
    <literal><![CDATA[
      K(x,(y * (z / T(u,z))) / w) = K(x,(y * (u \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(370,a,15155,a(flip),b,20333,a),flip(a)].">
      <j1 rule="hyper" parents="370 15155 20333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20335">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(y,(z * (u \ w)) / x) = K(y,x \ (z * (w / T(u,w))))
    ]]></literal>
    <justification jstring="[para(20334(a,1),14517(a,1,2))].">
      <j1 rule="para" parents="20334 14517"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y,y) / (1 / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3407(a,1),20291(a,2,1))].">
      <j1 rule="para" parents="3407 20291"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y \ 1,y \ 1) = L(x,y,y) / y
    ]]></literal>
    <justification jstring="[para(74(a,1),20337(a,2,2))].">
      <j1 rule="para" parents="74 20337"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      L(x / T(y,y \ 1),y,y) = L(x,y,y) / y
    ]]></literal>
    <justification jstring="[hyper(3529,a,20338,a)].">
      <j1 rule="hyper" parents="3529 20338"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      L(x / T(L(y,y * z,y),L(y,y * z,y) \ 1),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,14604,a(flip),b,20340,a),flip(a)].">
      <j1 rule="hyper" parents="370 14604 20340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20342">
    <literal><![CDATA[
      ((x * y) / ((y * x) * K(y * x,z))) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(20241(a,1),20330(a,1,1))].">
      <j1 rule="para" parents="20241 20330"/>
    </justification>
  </clause>

  <clause id="20343">
    <literal><![CDATA[
      ((x * y) / T(y * x,z)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(5256(a,2),20342(a,1,1,2))].">
      <j1 rule="para" parents="5256 20342"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      (K(x,y) * K(z,y * x)) * K(x * y,z) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[para(7486(a,1),20343(a,1,1))].">
      <j1 rule="para" parents="7486 20343"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * K(z,y * x)) = K(x * K(z,x * y),y)
    ]]></literal>
    <justification jstring="[hyper(11593,a,20344,a)].">
      <j1 rule="hyper" parents="11593 20344"/>
    </justification>
  </clause>

  <clause id="20346">
    <literal><![CDATA[
      K(x * K(y,x * z),z) = K(x,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(17592(a,1),20345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17592 20345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      K(x * K(y,x * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(20346(a,2),8920(a,1))].">
      <j1 rule="para" parents="20346 8920"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = w
    ]]></literal>
    <justification jstring="[para(18168(a,1),19702(a,1))].">
      <j1 rule="para" parents="18168 19702"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * T(K(w * u,w) * y,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(16898,a,19839,a)].">
      <j1 rule="hyper" parents="16898 19839"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      T(x,y * T(K(z * u,z) * w,K(z,u))) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19836,a(flip),b,20349,a),flip(a)].">
      <j1 rule="hyper" parents="60 19836 20349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      T(x,y * (K(z * u,z) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(17718,a,20350,a)].">
      <j1 rule="hyper" parents="17718 20350"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      T(x,y * (K(z \ u,z) * w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20088,a,b,20351,a)].">
      <j1 rule="hyper" parents="60 20088 20351"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ w) * K(u,z))) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(8210(a,1),20352(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8210 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * ((w * v5) * T(L(y,v5,w),z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19901,a(flip),b,19907,a)].">
      <j1 rule="hyper" parents="60 19901 19907"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * (w * (v5 * T(y,z))))
    ]]></literal>
    <justification jstring="[para(531(a,1),20355(a,2,2,2))].">
      <j1 rule="para" parents="531 20355"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * (v5 * y)))) = T(x,u * (w * (v5 * T(y,y * z))))
    ]]></literal>
    <justification jstring="[hyper(16784,a,20357,a)].">
      <j1 rule="hyper" parents="16784 20357"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,w * v5)))) = T(x,y * (z * (u * T(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(60,a,20357,a(flip),b,20358,a),flip(a)].">
      <j1 rule="hyper" parents="60 20357 20358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      T(x,y * (z * (u * ((w \ v5) \ v5)))) = T(x,y * (z * (u * T(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(60,a,16121,a(flip),b,20359,a)].">
      <j1 rule="hyper" parents="60 16121 20359"/>
    </justification>
  </clause>

  <clause id="20361">
    <literal><![CDATA[
      a(K(x,y) * (z * (u * y)),w,K(v5,v6)) = a(z * (u * T(y,x)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,19403,a(flip),b,19923,a),flip(a)].">
      <j1 rule="hyper" parents="370 19403 19923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      a(K(x,y) * (z * T(x,y)),u,K(w,v5)) = a(z * x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(7500(a,1),20361(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7500 20361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20363">
    <literal><![CDATA[
      K(x,L(y * (z \ K(z,u)),w,v5)) = K(x,L(y / T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(12988,a,19926,a),flip(a)].">
      <j1 rule="hyper" parents="12988 19926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20364">
    <literal><![CDATA[
      K(x,L(y / ((z * u) / z),w,v5)) = K(x,L(y / T(u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(15722,a,20363,a)].">
      <j1 rule="hyper" parents="15722 20363"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,z \ 1)),w,v5)) = K(x,L(y / T(z \ 1,u),w,v5))
    ]]></literal>
    <justification jstring="[para(5257(a,2),20364(a,1,2,1,2))].">
      <j1 rule="para" parents="5257 20364"/>
    </justification>
  </clause>

  <clause id="20366">
    <literal><![CDATA[
      K(x,L(y / (T(z,u \ z) / u),w,v5)) = K(x,L(y / T(z / u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(5471(a,2),20364(a,1,2,1,2))].">
      <j1 rule="para" parents="5471 20364"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      K(x,L(y / (T(z,u \ z) / u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20366(a,2),18170(a,1))].">
      <j1 rule="para" parents="20366 18170"/>
    </justification>
  </clause>

  <clause id="20368">
    <literal><![CDATA[
      T(x,y \ ((y \ ((y \ z) * (y \ z))) \ u)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[para(519(a,1),20111(a,1,2,2,1))].">
      <j1 rule="para" parents="519 20111"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) * v5) = K(x,(y \ T(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18467,a,20156,a),flip(a)].">
      <j1 rule="hyper" parents="18467 20156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      (x * K(y,(z \ T(u,w * v5)) * v6)) \ x = K((z \ T(u,w \ v5)) * v6,y)
    ]]></literal>
    <justification jstring="[para(20369(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="20369 6294"/>
    </justification>
  </clause>

  <clause id="20371">
    <literal><![CDATA[
      K((x \ T(y,z \ u)) * w,v5) = K((x \ T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(19552,a,20370,a),flip(a)].">
      <j1 rule="hyper" parents="19552 20370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      L(x,y,T((z * u) / z,w * w) * v5) = L(x,y,T(u,(w * w) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(847(a,1),20199(a,1,3,1))].">
      <j1 rule="para" parents="847 20199"/>
    </justification>
  </clause>

  <clause id="20374">
    <literal><![CDATA[
      L(x,y,T(z,(u * u) \ w) * v5) = L(x,y,((w * z) / w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,4108,a(flip),b,20373,a),flip(a)].">
      <j1 rule="hyper" parents="60 4108 20373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20376">
    <literal><![CDATA[
      L(x,y,T(z,(u * u) \ w) * v5) = L(x,y,T(z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19481,a(flip),b,20374,a),flip(a)].">
      <j1 rule="hyper" parents="370 19481 20374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20377">
    <literal><![CDATA[
      K(x,y \ (z * (u / T(w,u)))) = K(x,y \ (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(9366,a,20335,a),flip(a)].">
      <j1 rule="hyper" parents="9366 20335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20378">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) / w))) = K(x,y \ (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5747(a,2),20377(a,1,2,2,2))].">
      <j1 rule="para" parents="5747 20377"/>
    </justification>
  </clause>

  <clause id="20379">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * (u \ w))) = K(x,y \ ((w / T(u,w)) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16961,a(flip),b,20378,a),flip(a)].">
      <j1 rule="hyper" parents="60 16961 20378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(16874,a,20379,a),flip(a)].">
      <j1 rule="hyper" parents="16874 20379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20383">
    <literal><![CDATA[
      K(x,(L(1 / y,z,y) * a(u,w,K(v5,v6))) * v7) = K(x,(a(u,w,K(v5,v6)) / y) * v7)
    ]]></literal>
    <justification jstring="[para(1488(a,1),19459(a,1,2,1,1))].">
      <j1 rule="para" parents="1488 19459"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      K(x,L(1 / y,z,y) * u) = K(x,(a(w,v5,K(v6,v7)) / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19852,a(flip),b,20383,a)].">
      <j1 rule="hyper" parents="60 19852 20383"/>
    </justification>
  </clause>

  <clause id="20386">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) / v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(v5 \ 1,v8,v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(20384(a,1),6555(a,1))].">
      <j1 rule="para" parents="20384 6555"/>
    </justification>
  </clause>

  <clause id="20387">
    <literal><![CDATA[
      K(x,L(T(y * z,y \ 1) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1492(a,1),20002(a,1,2))].">
      <j1 rule="para" parents="1492 20002"/>
    </justification>
  </clause>

  <clause id="20388">
    <literal><![CDATA[
      K(x,L(T(y * z,y * 1) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18536,a,20387,a)].">
      <j1 rule="hyper" parents="18536 20387"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      K(x,L(T(y * z,y) / u,u,y)) = K(x,(y * ((1 / y) * z)) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3(a,1),20388(a,1,2,1,1,2))].">
      <j1 rule="para" parents="3 20388"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      K(x,(y * ((1 / y) * z)) / (u * (y \ 1))) = K(x,(y * (y * z)) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,20001,a(flip),b,20389,a),flip(a)].">
      <j1 rule="hyper" parents="60 20001 20389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20391">
    <literal><![CDATA[
      K(x,L(y,z,z) / (u * (z \ 1))) = K(x,(z * (z * y)) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,9947,a(flip),b,20390,a)].">
      <j1 rule="hyper" parents="60 9947 20390"/>
    </justification>
  </clause>

  <clause id="20392">
    <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(8718(a,1),19384(a,1,1))].">
      <j1 rule="para" parents="8718 19384"/>
    </justification>
  </clause>

  <clause id="20394">
    <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(8837(a,1),20392(a,2,2))].">
      <j1 rule="para" parents="8837 20392"/>
    </justification>
  </clause>

  <clause id="20395">
    <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(370,a,8046,a(flip),b,20394,a),flip(a)].">
      <j1 rule="hyper" parents="370 8046 20394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20396">
    <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(60,a,15809,a,b,20395,a)].">
      <j1 rule="hyper" parents="60 15809 20395"/>
    </justification>
  </clause>

  <clause id="20397">
    <literal><![CDATA[
      (K(x,y) * z) * a(x,u,K(w,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(15820(a,1),20395(a,1,2))].">
      <j1 rule="para" parents="15820 20395"/>
    </justification>
  </clause>

  <clause id="20398">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(15200(a,1),19526(a,1,1,2))].">
      <j1 rule="para" parents="15200 19526"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) * K(K(x,y),K(w,z * u)) = K(x,K(y,w * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(17508(a,1),20398(a,1,1))].">
      <j1 rule="para" parents="17508 20398"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) = K(x,K(y,u * (w \ z))) * 1
    ]]></literal>
    <justification jstring="[para(17191(a,1),20399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17191 20399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) = K(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,20400,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 20400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ 1) * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * (w \ z))) = v5
    ]]></literal>
    <justification jstring="[para(20400(a,2),143(a,1)),flip(b)].">
      <j1 rule="para" parents="20400 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,y \ ((w / (w / z)) * u)) = K(x,((w / (w / z)) * u) / y)
    ]]></literal>
    <justification jstring="[para(17985(a,1),19892(a,1,1))].">
      <j1 rule="para" parents="17985 19892"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      K(x,K(y * z,y) * (u * (w / ((y \ 1) \ 1)))) = K(x,u * (w / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[para(5428(a,1),19921(a,1,2,1))].">
      <j1 rule="para" parents="5428 19921"/>
    </justification>
  </clause>

  <clause id="20407">
    <literal><![CDATA[
      K(x,(y * (z / ((u \ 1) \ 1))) * K(w,u)) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(17483,a,20406,a)].">
      <j1 rule="hyper" parents="17483 20406"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      K(x,y * ((z / ((u \ 1) \ 1)) * K(w,u))) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[hyper(19952,a,20407,a)].">
      <j1 rule="hyper" parents="19952 20407"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,u \ w)))
    ]]></literal>
    <justification jstring="[para(5931(a,1),20408(a,1,2,2))].">
      <j1 rule="para" parents="5931 20408"/>
    </justification>
  </clause>

  <clause id="20410">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,u * w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18510,a(flip),b,20409,a),flip(a)].">
      <j1 rule="hyper" parents="370 18510 20409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20411">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,u * w)))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16896,a(flip),b,19979,a),flip(a)].">
      <j1 rule="hyper" parents="370 16896 19979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20412">
    <literal><![CDATA[
      K(x,y * (z * T((u * (w * u)) / u,T(u,w)))) = K(x,y * (z * T(u * w,u)))
    ]]></literal>
    <justification jstring="[para(7318(a,1),20411(a,1,2,2,2))].">
      <j1 rule="para" parents="7318 20411"/>
    </justification>
  </clause>

  <clause id="20413">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,K(w,u)))) = K(x,y * (z * T(w * u,w)))
    ]]></literal>
    <justification jstring="[para(8586(a,1),20412(a,1,2,2,2))].">
      <j1 rule="para" parents="8586 20412"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(20413(a,1),17738(a,1))].">
      <j1 rule="para" parents="20413 17738"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) * w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(20414,a,19981,a),flip(a)].">
      <j1 rule="hyper" parents="20414 19981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20416">
    <literal><![CDATA[
      K(x,y * (z * ((1 / u) * (u * w)))) = K(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(20414,a,14737,a)].">
      <j1 rule="hyper" parents="20414 14737"/>
    </justification>
  </clause>

  <clause id="20417">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (z * (u * w))) = K(x,(z * (T(w,u) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(16859,a,20415,a),flip(a)].">
      <j1 rule="hyper" parents="16859 20415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20418">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) * w))) = K(x,(y \ 1) * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,20415,a)].">
      <j1 rule="hyper" parents="15233 20415"/>
    </justification>
  </clause>

  <clause id="20419">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,w) * w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15200,a(flip),b,20418,a),flip(a)].">
      <j1 rule="hyper" parents="370 15200 20418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20420">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ ((T(w,u) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(16885,a,20419,a),flip(a)].">
      <j1 rule="hyper" parents="16885 20419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20421">
    <literal><![CDATA[
      K(x,y * (z * R(u,w,w))) = K(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(579(a,1),20416(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="579 20416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20422">
    <literal><![CDATA[
      K(x,y * ((z * u) * R(L(w,u,z),v5,v5))) = K(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(528(a,1),20421(a,2,2,2))].">
      <j1 rule="para" parents="528 20421"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(16874,a,20420,a),flip(a)].">
      <j1 rule="hyper" parents="16874 20420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20425">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * z) * u) * w)) = K(x,y \ ((u * L(z,u,z)) * w))
    ]]></literal>
    <justification jstring="[para(5486(a,1),20423(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5486 20423"/>
    </justification>
  </clause>

  <clause id="20426">
    <literal><![CDATA[
      K(x,y \ (((K(z,u) * K(z,u)) * w) * v5)) = K(x,y \ ((w * (K(z,u) * K(z,u))) * v5))
    ]]></literal>
    <justification jstring="[para(16718(a,1),20423(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="16718 20423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20427">
    <literal><![CDATA[
      K(x,(y * (T(z,u) * u)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(12637,a,20417,a),flip(a)].">
      <j1 rule="hyper" parents="12637 20417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20428">
    <literal><![CDATA[
      K(x,(y * (z * ((z * u) / z))) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(262(a,1),20427(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="262 20427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20429">
    <literal><![CDATA[
      K(x,(y * T(z * u,z)) * w) = K(x,(y * (u * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(20128,a,20428,a)].">
      <j1 rule="hyper" parents="20128 20428"/>
    </justification>
  </clause>

  <clause id="20430">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * (z * u))) * w) = K(x,(y * R(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18902,a(flip),b,20429,a),flip(a)].">
      <j1 rule="hyper" parents="60 18902 20429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      K(x,(y * ((z \ u) * z)) * w) = K(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),20429(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 20429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      K(x,(y * T(z,u)) * K(u,y * (u \ z))) = K(x,L(u,u \ z,y) * (y * (u \ z)))
    ]]></literal>
    <justification jstring="[para(15589(a,1),20431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15589 20431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      K(x,(y * R(z,u,u)) * w) = K(x,(y * L(z,u,u)) * w)
    ]]></literal>
    <justification jstring="[para(579(a,1),20430(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="579 20430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      K(x,(y * L(1 / y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16560,a(flip),b,20433,a),flip(a)].">
      <j1 rule="hyper" parents="60 16560 20433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20435">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14477,a(flip),b,20434,a)].">
      <j1 rule="hyper" parents="60 14477 20434"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * u) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(3816(a,1),20435(a,1,2,1))].">
      <j1 rule="para" parents="3816 20435"/>
    </justification>
  </clause>

  <clause id="20437">
    <literal><![CDATA[
      K(x,a(y,y,z) \ u) = K(x,a(z,y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15462,a,20436,a)].">
      <j1 rule="hyper" parents="15462 20436"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) = K(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16598,a(flip),b,20436,a)].">
      <j1 rule="hyper" parents="60 16598 20436"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,u)) = K(x,a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20197,a,b,20437,a)].">
      <j1 rule="hyper" parents="60 20197 20437"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      K(x,a(y,z,z) * (u * y)) = K(x,u * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),20439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 20439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      K(x,y * (z * (u * R(w,v5,v5)))) = K(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(529(a,1),20422(a,1,2,2))].">
      <j1 rule="para" parents="529 20422"/>
    </justification>
  </clause>

  <clause id="20442">
    <literal><![CDATA[
      K(x,y * (z * (u * L(1 / u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16645,a(flip),b,20441,a),flip(a)].">
      <j1 rule="hyper" parents="60 16645 20441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      K(x,y * (z * (u \ L(u,w,w)))) = K(x,y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16543,a(flip),b,20442,a)].">
      <j1 rule="hyper" parents="60 16543 20442"/>
    </justification>
  </clause>

  <clause id="20444">
    <literal><![CDATA[
      K(x,y * ((z \ L(z,u,u)) * w)) = K(x,y * (w * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15381,a,b,20443,a)].">
      <j1 rule="hyper" parents="60 15381 20443"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      K(x,L(y,y \ z,u) * (u * (y \ z))) = K(x,K(y,u * z) * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18398,a(flip),b,20432,a),flip(a)].">
      <j1 rule="hyper" parents="60 18398 20432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      K(x,y \ ((z * (T(T(z,u),u) \ w)) * v5)) = K(x,y \ ((w * (K(u,z) * K(u,z))) * v5))
    ]]></literal>
    <justification jstring="[para(10839(a,1),20426(a,1,2,2,1))].">
      <j1 rule="para" parents="10839 20426"/>
    </justification>
  </clause>

  <clause id="20447">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,y \ (w * (T(T(w,u),u) \ (z * v5))))
    ]]></literal>
    <justification jstring="[para(16638(a,1),20446(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16638 20446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      K(K(x,K(y,z)) * K(z,(u / x) * (u \ y)),w) = K(K(z,(u * (u / x)) \ y),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18289,a(flip),b,20022,a)].">
      <j1 rule="hyper" parents="60 18289 20022"/>
    </justification>
  </clause>

  <clause id="20449">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(K(x,(y / z) * (y \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(17690,a,20448,a),flip(a)].">
      <j1 rule="hyper" parents="17690 20448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(x,K(w,(y / z) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,8645,a(flip),b,20449,a),flip(a)].">
      <j1 rule="hyper" parents="370 8645 20449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20452">
    <literal><![CDATA[
      K(K(x,(y * (y / z)) \ u),w) = K(x,K(w,y * (z * (y \ u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,19485,a(flip),b,20451,a),flip(a)].">
      <j1 rule="hyper" parents="370 19485 20451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20453">
    <literal><![CDATA[
      K(x,K(y,(z * (z / u)) \ w)) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(8879,a,20452,a)].">
      <j1 rule="hyper" parents="8879 20452"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) \ w))) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(19783,a,20453,a)].">
      <j1 rule="hyper" parents="19783 20453"/>
    </justification>
  </clause>

  <clause id="20455">
    <literal><![CDATA[
      T(x,y * (z * (T(u,T(w,v5)) * ((w \ v5) \ v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[para(7334(a,1),20064(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7334 20064"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      T(x,y * (z * (T(u,T(w,v5)) * T(w,v5)))) = T(x,y * (z * (T(w,w \ v5) * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20360,a(flip),b,20455,a)].">
      <j1 rule="hyper" parents="60 20360 20455"/>
    </justification>
  </clause>

  <clause id="20457">
    <literal><![CDATA[
      T(x,y * (z * (T(u,u \ w) * v5))) = T(x,y * (z * (T(u,w) * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20062,a(flip),b,20456,a),flip(a)].">
      <j1 rule="hyper" parents="60 20062 20456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20458">
    <literal><![CDATA[
      K(((x \ y) * x) / (L(K(z,u),w,v5) * x),v6) = K(x \ (L(K(u,z),w,v5) * y),v6)
    ]]></literal>
    <justification jstring="[hyper(17735,a,20117,a)].">
      <j1 rule="hyper" parents="17735 20117"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),u \ 1))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17637,a,20186,a),flip(a)].">
      <j1 rule="hyper" parents="17637 20186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20460">
    <literal><![CDATA[
      K(x,y * (z / T((u \ 1) \ 1,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19561,a(flip),b,20459,a)].">
      <j1 rule="hyper" parents="60 19561 20459"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      K(x,y * (z / T(u,u * w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20410,a(flip),b,20460,a)].">
      <j1 rule="hyper" parents="60 20410 20460"/>
    </justification>
  </clause>

  <clause id="20462">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18511,a(flip),b,20461,a)].">
      <j1 rule="hyper" parents="60 18511 20461"/>
    </justification>
  </clause>

  <clause id="20463">
    <literal><![CDATA[
      K(x,y * (T(z,(u \ w) \ w) / T(u,w))) = K(x,y * (((u \ w) \ w) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14513,a(flip),b,20462,a),flip(a)].">
      <j1 rule="hyper" parents="60 14513 20462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20464">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) / T(u,w))) = K(x,y * (((u \ w) \ w) \ z))
    ]]></literal>
    <justification jstring="[para(7334(a,1),20463(a,1,2,2,1))].">
      <j1 rule="para" parents="7334 20463"/>
    </justification>
  </clause>

  <clause id="20465">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14513,a(flip),b,20464,a),flip(a)].">
      <j1 rule="hyper" parents="60 14513 20464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20466">
    <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(18486,a,20465,a),flip(a)].">
      <j1 rule="hyper" parents="18486 20465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20467">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(18467,a,20466,a),flip(a)].">
      <j1 rule="hyper" parents="18467 20466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20468">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(363(a,2),20467(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="363 20467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20469">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / w) = K(x,(T(y,z) \ u) * (1 / w))
    ]]></literal>
    <justification jstring="[hyper(15319,a,20468,a)].">
      <j1 rule="hyper" parents="15319 20468"/>
    </justification>
  </clause>

  <clause id="20470">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / w) = v5
    ]]></literal>
    <justification jstring="[para(20469(a,2),15319(a,1))].">
      <j1 rule="para" parents="20469 15319"/>
    </justification>
  </clause>

  <clause id="20471">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = K(y * y,u) * (((T(y * y,u) * x) \ z) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18200,a,b,20295,a)].">
      <j1 rule="hyper" parents="370 18200 20295"/>
    </justification>
  </clause>

  <clause id="20473">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = K(y * y,u) * ((x \ (T(y * y,u) \ z)) * (y * y))
    ]]></literal>
    <justification jstring="[para(20235(a,1),20471(a,2,2,1))].">
      <j1 rule="para" parents="20235 20471"/>
    </justification>
  </clause>

  <clause id="20474">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = (x \ (T(y * y,u) \ z)) * T(y * y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17139,a(flip),b,20473,a),flip(a)].">
      <j1 rule="hyper" parents="370 17139 20473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20475">
    <literal><![CDATA[
      T(K(x,y * y) * (x \ z),y * y) = x \ T(z,y * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,20293,a(flip),b,20474,a),flip(a)].">
      <j1 rule="hyper" parents="370 20293 20474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20476">
    <literal><![CDATA[
      (((x * x) * y) \ z) * ((x * x) * u) = (y \ T(z,x * x)) * u
    ]]></literal>
    <justification jstring="[para(20475(a,1),12301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20475 12301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20477">
    <literal><![CDATA[
      (x \ ((y * y) \ z)) * ((y * y) * u) = (x \ T(z,y * y)) * u
    ]]></literal>
    <justification jstring="[para(518(a,1),20476(a,1,1))].">
      <j1 rule="para" parents="518 20476"/>
    </justification>
  </clause>

  <clause id="20478">
    <literal><![CDATA[
      T(x / K(y,L(T(z,u),w,v5)),K(K(y,L(z,w,v5)),u)) = K(u,K(y,z)) * (x / K(y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(8042(a,2),19245(a,1,1,2))].">
      <j1 rule="para" parents="8042 19245"/>
    </justification>
  </clause>

  <clause id="20479">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (y * w)) = u \ (T(y,K(x,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(19277,a,19505,a)].">
      <j1 rule="hyper" parents="19277 19505"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * v5)) = v6
    ]]></literal>
    <justification jstring="[para(20479(a,1),17677(a,1,2))].">
      <j1 rule="para" parents="20479 17677"/>
    </justification>
  </clause>

  <clause id="20482">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,L(u * K(y,u),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(16404(a,1),19525(a,1,2))].">
      <j1 rule="para" parents="16404 19525"/>
    </justification>
  </clause>

  <clause id="20483">
    <literal><![CDATA[
      T(x * K(L(T(y,z),u,w),v5),K(K(v5,L(y,u,w)),z)) = K(z,K(v5,y)) * (x / K(v5,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(6291(a,1),20478(a,1,1))].">
      <j1 rule="para" parents="6291 20478"/>
    </justification>
  </clause>

  <clause id="20484">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) * K(x,L(T(u,y),y,z)) = K(x,(y * z) \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(9125(a,1),20482(a,1,2))].">
      <j1 rule="para" parents="9125 20482"/>
    </justification>
  </clause>

  <clause id="20485">
    <literal><![CDATA[
      T(x * K(T(y,z),L(u,w,v5)),K(K(u,L(y,w,v5)),z)) = K(z,K(u,y)) * (x / K(u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(12966(a,1),20483(a,1,1,2))].">
      <j1 rule="para" parents="12966 20483"/>
    </justification>
  </clause>

  <clause id="20486">
    <literal><![CDATA[
      T(x * K(y,T(L(z,u,w),v5)),K(K(z,L(y,u,w)),v5)) = K(v5,K(z,y)) * (x / K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(8024(a,1),20485(a,1,1,2))].">
      <j1 rule="para" parents="8024 20485"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      T(x * K(y,L(T(z,u),w,v5)),K(K(z,L(y,w,v5)),u)) = K(u,K(z,y)) * (x / K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(20(a,2),20486(a,1,1,2,2))].">
      <j1 rule="para" parents="20 20486"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      T(x * K(y,L(T(z,u),w,v5)),K(z,K(L(y,w,v5),u))) = K(u,K(z,y)) * (x / K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(8605(a,1),20487(a,1,2))].">
      <j1 rule="para" parents="8605 20487"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / K(y,L(z,w,v5))) = u * K(z,L(T(y,x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17204,a,20488,a)].">
      <j1 rule="hyper" parents="17204 20488"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / K(x,L(y,w,v5))) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(8636(a,2),20489(a,1,1))].">
      <j1 rule="para" parents="8636 20489"/>
    </justification>
  </clause>

  <clause id="20492">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(L(y,w,v5),x)) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(6291(a,1),20491(a,1,2))].">
      <j1 rule="para" parents="6291 20491"/>
    </justification>
  </clause>

  <clause id="20493">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,L(x,w,v5))) = u * K(y,L(T(x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(12966(a,1),20492(a,1,2,2))].">
      <j1 rule="para" parents="12966 20492"/>
    </justification>
  </clause>

  <clause id="20494">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(x,K(y,w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(19466,a,20493,a)].">
      <j1 rule="hyper" parents="19466 20493"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      K(K(x,y),z) * (u * K(x,L(T(z,y),w,v5))) = u * K(x,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(7518,a,20493,a)].">
      <j1 rule="hyper" parents="7518 20493"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) = T(K(x,L(T(y,v5),u,w)),z)
    ]]></literal>
    <justification jstring="[para(20494(a,1),17816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20494 17816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,L(T(z,y),w,v5))) = u * K(x,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(8605(a,1),20495(a,1,1))].">
      <j1 rule="para" parents="8605 20495"/>
    </justification>
  </clause>

  <clause id="20498">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(T(y,v5),z),u,w)) = v6
    ]]></literal>
    <justification jstring="[para(20496(a,2),9078(a,1))].">
      <j1 rule="para" parents="20496 9078"/>
    </justification>
  </clause>

  <clause id="20499">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10854,a,20497,a)].">
      <j1 rule="hyper" parents="10854 20497"/>
    </justification>
  </clause>

  <clause id="20501">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,L(T(T(z,x),u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17341(a,2),20498(a,1))].">
      <j1 rule="para" parents="17341 20498"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(y,w)) = (K(z,u) * T(y,w)) \ (K(z,u) * (T(y,w) * x))
    ]]></literal>
    <justification jstring="[para(17244(a,1),19567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17244 19567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,w),K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(20502(a,2),629(a,1))].">
      <j1 rule="para" parents="20502 629"/>
    </justification>
  </clause>

  <clause id="20504">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,((K(w,v5) * z) * u) * y) = K(x,y * ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(17979(a,1),19810(a,1,1))].">
      <j1 rule="para" parents="17979 19810"/>
    </justification>
  </clause>

  <clause id="20506">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,K(w,v5) * ((z * u) * y)) = K(x,y * ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(20011(a,1),20504(a,1,2))].">
      <j1 rule="para" parents="20011 20504"/>
    </justification>
  </clause>

  <clause id="20507">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) * v5)) = K(x,y * (K(z,u) * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19811,a(flip),b,20506,a),flip(a)].">
      <j1 rule="hyper" parents="60 19811 20506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(19576,a,20507,a)].">
      <j1 rule="hyper" parents="19576 20507"/>
    </justification>
  </clause>

  <clause id="20509">
    <literal><![CDATA[
      K(x,(y \ 1) * (K(z,u) * (w * v5))) = K(x,y \ ((w * K(z,u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(15233,a,20508,a),flip(a)].">
      <j1 rule="hyper" parents="15233 20508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20510">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * K(u,w)) * K(v5,v6))) = K(x,y * (K(u,w) * (z \ K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(15133(a,1),20508(a,2,2,2,2))].">
      <j1 rule="para" parents="15133 20508"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w \ z) * v5))) = K(x,y * ((w \ T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(15179(a,1),20508(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15179 20508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20512">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) * v5)) = K(x,y \ (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,20509,a),flip(a)].">
      <j1 rule="hyper" parents="15233 20509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w \ u) * v5))) = K(x,y * ((w \ T(u,z)) * v5))
    ]]></literal>
    <justification jstring="[hyper(19881,a,20511,a)].">
      <j1 rule="hyper" parents="19881 20511"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w * w)) * v5)) = K(x,y * ((z \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,18433,a(flip),b,20513,a),flip(a)].">
      <j1 rule="hyper" parents="60 18433 20513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      K(x,y * ((z \ K(u,w)) * K(v5,v6))) = K(x,y * (K(u,w) * (z \ K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(15133(a,1),20510(a,1,2,2,1))].">
      <j1 rule="para" parents="15133 20510"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * ((z \ w) \ K(z,u)))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16172,a(flip),b,20515,a),flip(a)].">
      <j1 rule="hyper" parents="60 16172 20515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      K(x,K(y,z) * (u * ((z \ w) \ K(z,y)))) = K(x,u / (R(z,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(19874,a,20516,a)].">
      <j1 rule="hyper" parents="19874 20516"/>
    </justification>
  </clause>

  <clause id="20518">
    <literal><![CDATA[
      K(x,y / (R(z,u,z) \ w)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19928,a(flip),b,20517,a),flip(a)].">
      <j1 rule="hyper" parents="60 19928 20517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      K(x,y / (((z \ u) \ u) \ w)) = K(x,y / (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(7378(a,1),20518(a,1,2,2,1))].">
      <j1 rule="para" parents="7378 20518"/>
    </justification>
  </clause>

  <clause id="20521">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18168,a(flip),b,20520,a)].">
      <j1 rule="hyper" parents="60 18168 20520"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      K(x,(y \ K(z,y \ 1)) * u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(4781(a,1),19865(a,1,1,2,1))].">
      <j1 rule="para" parents="4781 19865"/>
    </justification>
  </clause>

  <clause id="20523">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) * (1 / u),u * 1))) = T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,18574,a(flip),b,19990,a)].">
      <j1 rule="hyper" parents="60 18574 19990"/>
    </justification>
  </clause>

  <clause id="20524">
    <literal><![CDATA[
      K(x,T(K(y * (z / y),y) * u,y * (z / y))) = K(x,((y * (z / y)) \ u) * z)
    ]]></literal>
    <justification jstring="[para(5236(a,1),19993(a,2,2,2))].">
      <j1 rule="para" parents="5236 19993"/>
    </justification>
  </clause>

  <clause id="20525">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,z * (y / z))) = K(x,((z * (y / z)) \ u) * y)
    ]]></literal>
    <justification jstring="[para(6558(a,1),20524(a,1,2,1,1))].">
      <j1 rule="para" parents="6558 20524"/>
    </justification>
  </clause>

  <clause id="20526">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,T(y,z))) = K(x,((z * (y / z)) \ u) * y)
    ]]></literal>
    <justification jstring="[para(12547(a,1),20525(a,1,2))].">
      <j1 rule="para" parents="12547 20525"/>
    </justification>
  </clause>

  <clause id="20527">
    <literal><![CDATA[
      K(x,((y * (z / y)) \ u) * z) = K(x,T(u * K(z,y),z))
    ]]></literal>
    <justification jstring="[para(8599(a,1),20526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8599 20526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      L(x,y,((T(z,u * u) * w) / z) * ((u * u) * v5)) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),20198(a,1,3))].">
      <j1 rule="para" parents="29 20198"/>
    </justification>
  </clause>

  <clause id="20529">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * T((u * w) * (1 / u),u)))
    ]]></literal>
    <justification jstring="[para(3(a,1),20523(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3 20523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20530">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * ((w * u) * (1 / u))))
    ]]></literal>
    <justification jstring="[para(3281(a,1),20529(a,2,2,2,2))].">
      <j1 rule="para" parents="3281 20529"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * ((w * u) * (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(370,a,4709,a(flip),b,20530,a),flip(a)].">
      <j1 rule="hyper" parents="370 4709 20530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20532">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (T(u,u \ 1) * w)))) = T(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(1111(a,1),20531(a,2,2,2,2))].">
      <j1 rule="para" parents="1111 20531"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      T(x,y * (z * ((1 / u) * (u * w)))) = T(x,y * (z * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(8527(a,1),20532(a,1,2,2,2))].">
      <j1 rule="para" parents="8527 20532"/>
    </justification>
  </clause>

  <clause id="20534">
    <literal><![CDATA[
      T(x,y * (z * R(u,w,w))) = T(x,y * (z * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(579(a,1),20533(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="579 20533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20535">
    <literal><![CDATA[
      T(x,y * (z * L(1 / z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16533,a(flip),b,20534,a),flip(a)].">
      <j1 rule="hyper" parents="60 16533 20534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      T(x,y * ((z * u) * R(L(w,u,z),v5,v5))) = T(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(528(a,1),20534(a,2,2,2))].">
      <j1 rule="para" parents="528 20534"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) = T(x,y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14668,a(flip),b,20535,a)].">
      <j1 rule="hyper" parents="60 14668 20535"/>
    </justification>
  </clause>

  <clause id="20538">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,u))) = T(x,a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,19324,a,b,20537,a),flip(a)].">
      <j1 rule="hyper" parents="370 19324 20537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20539">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ 1)) = T(x,y * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(14176(a,2),20537(a,1,2,2))].">
      <j1 rule="para" parents="14176 20537"/>
    </justification>
  </clause>

  <clause id="20540">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) * u) = T(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(19364,a,20538,a)].">
      <j1 rule="hyper" parents="19364 20538"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      T(x,y * a(z \ (z \ u),z,z)) = T(x,y * ((z \ ((1 / z) \ u)) \ u))
    ]]></literal>
    <justification jstring="[para(14215(a,1),20539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14215 20539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      T(x,y * (z * (u * R(w,v5,v5)))) = T(x,y * (z * (u * L(w,v5,v5))))
    ]]></literal>
    <justification jstring="[para(529(a,1),20536(a,1,2,2))].">
      <j1 rule="para" parents="529 20536"/>
    </justification>
  </clause>

  <clause id="20543">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,((T(w,z * z) * u) / w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,4106,a(flip),b,20528,a),flip(a)].">
      <j1 rule="hyper" parents="60 4106 20528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20545">
    <literal><![CDATA[
      L(x,y,T(K(z,u * u) * w,z) * v5) = L(x,y,T((u * u) * w,(u * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19493,a(flip),b,20543,a)].">
      <j1 rule="hyper" parents="370 19493 20543"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,T(u,w) * (v5 * K(w,z * z)))
    ]]></literal>
    <justification jstring="[para(18132(a,1),20545(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18132 20545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,(z * z) \ w) * v5) = L(x,y,T(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19726,a(flip),b,20546,a),flip(a)].">
      <j1 rule="hyper" parents="370 19726 20546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      L(x,y,T((z * z) * u,w) * v5) = L(x,y,T(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20376,a(flip),b,20547,a)].">
      <j1 rule="hyper" parents="60 20376 20547"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      L(x,y,T(((z \ 1) * z) * (1 / z),u) * w) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[para(1288(a,1),20549(a,1,3,1,1))].">
      <j1 rule="para" parents="1288 20549"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      L(x,y,T(z \ 1,u) * w) = L(x,y,T(z,u) * w)
    ]]></literal>
    <justification jstring="[para(1505(a,1),20551(a,1,3,1,1))].">
      <j1 rule="para" parents="1505 20551"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      L(x,y,T(z,u) * (z \ w)) = L(x,y,K(z \ 1,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7903,a(flip),b,20552,a),flip(a)].">
      <j1 rule="hyper" parents="60 7903 20552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u) * w) = L(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(7860(a,1),20553(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7860 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20556">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ ((x * K(y,K(z,u))) * (w * v5)) = L(v5,L(w,K(y,K(z,u)),x),K(y,K(z,u)) * x)
    ]]></literal>
    <justification jstring="[para(19488(a,1),19386(a,1,2,2,1))].">
      <j1 rule="para" parents="19488 19386"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(w,u)) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(19374(a,1),19293(a,1,2,1))].">
      <j1 rule="para" parents="19374 19293"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(u,w)) \ (K(w,L(u,z,y)) \ v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(8700(a,1),20558(a,1,2,1))].">
      <j1 rule="para" parents="8700 20558"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      K(x,T(y * (z * u),K(u,w)) \ (K(L(u,z,y),w) * v5)) = K(x,(y * (z * (u * K(w,u)))) \ v5)
    ]]></literal>
    <justification jstring="[para(7506(a,1),20559(a,1,2,2))].">
      <j1 rule="para" parents="7506 20559"/>
    </justification>
  </clause>

  <clause id="20562">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(x * y,y * (((x / (1 / y)) * z) \ x)))
    ]]></literal>
    <justification jstring="[hyper(20402,a,19498,a),flip(a)].">
      <j1 rule="hyper" parents="20402 19498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K((x / (1 / y)) * z,y * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,19755,a(flip),b,20562,a),flip(a)].">
      <j1 rule="hyper" parents="370 19755 20562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20564">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K((x / (y \ 1)) * z,y * x))
    ]]></literal>
    <justification jstring="[para(6019(a,1),20563(a,2,2))].">
      <j1 rule="para" parents="6019 20563"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,(x / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8648,a,b,20564,a),flip(a)].">
      <j1 rule="hyper" parents="370 8648 20564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20566">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,x * ((y \ 1) * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19485,a(flip),b,20565,a),flip(a)].">
      <j1 rule="hyper" parents="370 19485 20565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20567">
    <literal><![CDATA[
      K((x / (y \ 1)) * (1 / T(x / (1 / y),z)),u) = K(u,K(y * x,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20401,a(flip),b,20566,a),flip(a)].">
      <j1 rule="hyper" parents="370 20401 20566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      K((x / (y \ 1)) / T(x / (1 / y),z),u) = K(u,K(y * x,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(15432,a,20567,a)].">
      <j1 rule="hyper" parents="15432 20567"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      T(T(x,y / T(z * u,z)),K(w,(z * (z * u)) * (z * y))) = T(x,T(y / (T(z,z * u) * u),w))
    ]]></literal>
    <justification jstring="[para(17456(a,1),19729(a,1,1))].">
      <j1 rule="para" parents="17456 19729"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * (u * z)) * (u * y))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[para(14650(a,1),20569(a,1,1))].">
      <j1 rule="para" parents="14650 20569"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * z) * (u \ (u * y)))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[hyper(19572,a,20570,a)].">
      <j1 rule="hyper" parents="19572 20570"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,(u * z) * y)) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[para(4(a,1),20571(a,1,2,2,2))].">
      <j1 rule="para" parents="4 20571"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / (T(u,u * z) * z),w))
    ]]></literal>
    <justification jstring="[hyper(19572,a,20572,a)].">
      <j1 rule="hyper" parents="19572 20572"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / ((u * (u * z)) / u),w))
    ]]></literal>
    <justification jstring="[para(5463(a,2),20573(a,2,2,1,2))].">
      <j1 rule="para" parents="5463 20573"/>
    </justification>
  </clause>

  <clause id="20576">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / T(u * z,u),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,18150,a(flip),b,20575,a),flip(a)].">
      <j1 rule="hyper" parents="370 18150 20575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20577">
    <literal><![CDATA[
      T(T(x,y / (z * u)),K(w,z * (u \ y))) = T(x,T(y / (z * u),w))
    ]]></literal>
    <justification jstring="[hyper(370,a,18642,a(flip),b,20576,a),flip(a)].">
      <j1 rule="hyper" parents="370 18642 20576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),w)) = T(x,T(y / (u * z),w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20573,a(flip),b,20577,a)].">
      <j1 rule="hyper" parents="60 20573 20577"/>
    </justification>
  </clause>

  <clause id="20579">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z \ y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19789,a(flip),b,20286,a),flip(a)].">
      <j1 rule="hyper" parents="370 19789 20286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z * y)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19847,a(flip),b,20579,a),flip(a)].">
      <j1 rule="hyper" parents="370 19847 20579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,y * z)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[para(5485(a,1),20580(a,2,2,1,2))].">
      <j1 rule="para" parents="5485 20580"/>
    </justification>
  </clause>

  <clause id="20582">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ T(y,z)) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19837,a(flip),b,20581,a),flip(a)].">
      <j1 rule="hyper" parents="370 19837 20581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(y / z) * (y * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20041,a(flip),b,20582,a),flip(a)].">
      <j1 rule="hyper" parents="370 20041 20582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20584">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (y \ (y * (T(y,z) / z)))) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17934,a(flip),b,20583,a),flip(a)].">
      <j1 rule="hyper" parents="370 17934 20583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20585">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (T(y,z) / z)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[para(4(a,1),20584(a,1,2,2))].">
      <j1 rule="para" parents="4 20584"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      T(x,(y * (T(y,z) / z)) * (z \ y)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(14514,a,20585,a)].">
      <j1 rule="hyper" parents="14514 20585"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * (z \ y)) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(20313,a,20586,a)].">
      <j1 rule="hyper" parents="20313 20586"/>
    </justification>
  </clause>

  <clause id="20589">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * z)) = T(x,(y \ z) * (z * (z / y)))
    ]]></literal>
    <justification jstring="[hyper(20057,a,20588,a)].">
      <j1 rule="hyper" parents="20057 20588"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      T(x,y * (y / (z * ((z \ y) \ 1)))) = T(x,(z \ y) * (y * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15992,a,b,20589,a)].">
      <j1 rule="hyper" parents="60 15992 20589"/>
    </justification>
  </clause>

  <clause id="20591">
    <literal><![CDATA[
      T(x,(y \ z) * (z * (z / y))) = T(x,z * (z * ((y \ z) / y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16060,a(flip),b,20590,a),flip(a)].">
      <j1 rule="hyper" parents="60 16060 20590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      T(x,(y \ z) * (z * (z / y))) = T(x,z * (z * (y \ (z / y))))
    ]]></literal>
    <justification jstring="[hyper(370,a,20284,a(flip),b,20591,a),flip(a)].">
      <j1 rule="hyper" parents="370 20284 20591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20593">
    <literal><![CDATA[
      L(x / (T(y,y \ 1) \ 1),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(16264(a,1),20292(a,2,1))].">
      <j1 rule="para" parents="16264 20292"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      L(x / T(y \ 1,y),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(1332(a,1),20593(a,1,1,2))].">
      <j1 rule="para" parents="1332 20593"/>
    </justification>
  </clause>

  <clause id="20596">
    <literal><![CDATA[
      L(x / (1 / y),T(y,y \ 1),T(y,y \ 1)) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(955(a,1),20594(a,1,1,2))].">
      <j1 rule="para" parents="955 20594"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      L(x / (1 / y),y,y) = L(x,y,y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,16264,a(flip),b,20596,a)].">
      <j1 rule="hyper" parents="60 16264 20596"/>
    </justification>
  </clause>

  <clause id="20599">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * K(L(x,z,u),T(y,v5))
    ]]></literal>
    <justification jstring="[para(9076(a,1),19301(a,2,2))].">
      <j1 rule="para" parents="9076 19301"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      T(K(x,L(y,z,u)),w) * K(v5 / y,K(x,L(y,z,u))) = K(x,K(y,w)) * K(x,L(T(y,v5),z,u))
    ]]></literal>
    <justification jstring="[para(12966(a,1),20599(a,2,2))].">
      <j1 rule="para" parents="12966 20599"/>
    </justification>
  </clause>

  <clause id="20602">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(v5 / y,K(x,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(8042(a,2),20601(a,1,1))].">
      <j1 rule="para" parents="8042 20601"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(v5 / y,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(8630(a,1),20602(a,1,2))].">
      <j1 rule="para" parents="8630 20602"/>
    </justification>
  </clause>

  <clause id="20604">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y \ v5,L(y,u,w))) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(8142(a,1),20603(a,1,2,2))].">
      <j1 rule="para" parents="8142 20603"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y \ v5,y)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(19233(a,1),20604(a,1,2))].">
      <j1 rule="para" parents="19233 20604"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,y * v5)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(17512(a,1),20605(a,1,2))].">
      <j1 rule="para" parents="17512 20605"/>
    </justification>
  </clause>

  <clause id="20608">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * K(x,K(y,v5)) = K(x,K(y,z)) * K(x,L(T(y,v5),u,w))
    ]]></literal>
    <justification jstring="[para(8692(a,1),20606(a,1,2))].">
      <j1 rule="para" parents="8692 20606"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(T(y,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(T(y,u),z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20608(a,1),20498(a,1))].">
      <j1 rule="para" parents="20608 20498"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      K(x,L(y \ z,y,y) \ (((y * y) \ z) * u)) = K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u))
    ]]></literal>
    <justification jstring="[para(3400(a,1),19782(a,1,2,1))].">
      <j1 rule="para" parents="3400 19782"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((1 / y) * z) \ (((y * y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(586(a,1),20610(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="586 20610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20612">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((1 / y) * z) \ (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18603,a(flip),b,20611,a),flip(a)].">
      <j1 rule="hyper" parents="370 18603 20611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20613">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,((y \ 1) * z) \ (z * ((y * y) \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,5591,a(flip),b,20612,a),flip(a)].">
      <j1 rule="hyper" parents="370 5591 20612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20614">
    <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))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19297,a(flip),b,19278,a),flip(a)].">
      <j1 rule="hyper" parents="370 19297 19278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,L(w,K(y,K(z,u)),x),K(y,K(z,u)) * x)
    ]]></literal>
    <justification jstring="[para(19473(a,1),20556(a,1,2))].">
      <j1 rule="para" parents="19473 20556"/>
    </justification>
  </clause>

  <clause id="20616">
    <literal><![CDATA[
      L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v5 * K(z,K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(20556(a,1),19489(a,1))].">
      <j1 rule="para" parents="20556 19489"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * ((w * v5) * K(x,K(y,z)))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19435(a,1),20614(a,1,2))].">
      <j1 rule="para" parents="19435 20614"/>
    </justification>
  </clause>

  <clause id="20618">
    <literal><![CDATA[
      L(L(x,y,K(z,K(u,w))),K(z,K(u,w)) * y,v5) = L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(1199,a,20615,a)].">
      <j1 rule="hyper" parents="1199 20615"/>
    </justification>
  </clause>

  <clause id="20619">
    <literal><![CDATA[
      L(x,L(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = L(x,K(z,K(u,w)) * y,v5)
    ]]></literal>
    <justification jstring="[para(19271(a,1),20618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19271 20618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(20616,a,20619,a),flip(a)].">
      <j1 rule="hyper" parents="20616 20619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20621">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,L(w,u,K(x,K(y,z))),u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19248(a,1),20617(a,1,2,2))].">
      <j1 rule="para" parents="19248 20617"/>
    </justification>
  </clause>

  <clause id="20622">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19271(a,1),20621(a,2,2))].">
      <j1 rule="para" parents="19271 20621"/>
    </justification>
  </clause>

  <clause id="20623">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(19590,a,20622,a)].">
      <j1 rule="hyper" parents="19590 20622"/>
    </justification>
  </clause>

  <clause id="20624">
    <literal><![CDATA[
      L(x,y,z * K(u,K(w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19277,a,20623,a),flip(a)].">
      <j1 rule="hyper" parents="19277 20623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20625">
    <literal><![CDATA[
      L(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20623(a,1),19277(a,1))].">
      <j1 rule="para" parents="20623 19277"/>
    </justification>
  </clause>

  <clause id="20627">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20620,a,b,20624,a)].">
      <j1 rule="hyper" parents="60 20620 20624"/>
    </justification>
  </clause>

  <clause id="20630">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(8027(a,1),20627(a,1,2))].">
      <j1 rule="para" parents="8027 20627"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5883,a,b,20630,a),flip(a)].">
      <j1 rule="hyper" parents="370 5883 20630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20632">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18870,a(flip),b,20630,a)].">
      <j1 rule="hyper" parents="60 18870 20630"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6315,a,20632,a),flip(a)].">
      <j1 rule="hyper" parents="6315 20632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(20632(a,1),103(a,1,1))].">
      <j1 rule="para" parents="20632 103"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) != w
    ]]></literal>
    <literal><![CDATA[
      x / (K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(20632(a,1),6315(a,1))].">
      <j1 rule="para" parents="20632 6315"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(20632(a,1),7517(a,1,1))].">
      <j1 rule="para" parents="20632 7517"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(y,z)) = (x * K(y,z)) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(20632(a,1),12402(a,1,1))].">
      <j1 rule="para" parents="20632 12402"/>
    </justification>
  </clause>

  <clause id="20639">
    <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(8028(a,1),20625(a,1,3))].">
      <j1 rule="para" parents="8028 20625"/>
    </justification>
  </clause>

  <clause id="20642">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,(y / (K(w,u) * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(20633(a,1),13055(a,2,2,1))].">
      <j1 rule="para" parents="20633 13055"/>
    </justification>
  </clause>

  <clause id="20643">
    <literal><![CDATA[
      (x * K(y,z)) * u != w * (K(y,z) * u)
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(20635(a,1),41(a,1))].">
      <j1 rule="para" parents="20635 41"/>
    </justification>
  </clause>

  <clause id="20644">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),u) * (u * K(y,z)) = (x * K(y,T(z,u))) * u
    ]]></literal>
    <justification jstring="[para(8758(a,1),20635(a,1,2))].">
      <j1 rule="para" parents="8758 20635"/>
    </justification>
  </clause>

  <clause id="20645">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (K(z,y) * (K(z,y) * x)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(20637(a,2),10842(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20637 10842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(z,y)) = (x * K(z,T(y,u))) * u
    ]]></literal>
    <justification jstring="[para(20631(a,1),20644(a,1,1))].">
      <j1 rule="para" parents="20631 20644"/>
    </justification>
  </clause>

  <clause id="20647">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = ((K(y,T(z,u)) * K(y,T(z,u))) \ x) \ u
    ]]></literal>
    <justification jstring="[para(20646(a,2),849(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20646 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20649">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,(K(w,u) * z) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9704,a(flip),b,20642,a),flip(a)].">
      <j1 rule="hyper" parents="370 9704 20642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20650">
    <literal><![CDATA[
      T(x,L(((y / z) * K(u,w)) \ 1,K(w,u),z)) = T(x,z * (y \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20244,a(flip),b,20649,a),flip(a)].">
      <j1 rule="hyper" parents="370 20244 20649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20651">
    <literal><![CDATA[
      T(x,L(K(y,z) * ((u / w) \ 1),K(y,z),w)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(15550(a,1),20650(a,1,2,1))].">
      <j1 rule="para" parents="15550 20650"/>
    </justification>
  </clause>

  <clause id="20652">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (y * (T(T(y,z),z) \ x)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9604(a,1),20645(a,2,1))].">
      <j1 rule="para" parents="9604 20645"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = ((K(y,z) * K(y,z)) \ x) \ u
    ]]></literal>
    <justification jstring="[para(17572(a,1),20647(a,2,1,1))].">
      <j1 rule="para" parents="17572 20647"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = (K(z,y) * (K(z,y) * x)) \ u
    ]]></literal>
    <justification jstring="[para(10828(a,1),20653(a,2,1))].">
      <j1 rule="para" parents="10828 20653"/>
    </justification>
  </clause>

  <clause id="20656">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = (y * (T(T(y,z),z) \ x)) \ u
    ]]></literal>
    <justification jstring="[para(9604(a,1),20654(a,2,1))].">
      <j1 rule="para" parents="9604 20654"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      x \ (L(K(y,T(z,u)),K(z,y),u) * (u * K(y,z))) = x \ (z * (T(T(z,y),y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,10888,a(flip),b,20656,a),flip(a)].">
      <j1 rule="hyper" parents="370 10888 20656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20658">
    <literal><![CDATA[
      x \ (K(y,T(z,u)) * (u * K(y,z))) = x \ (z * (T(T(z,y),y) \ u))
    ]]></literal>
    <justification jstring="[para(11399(a,1),20657(a,1,2,1))].">
      <j1 rule="para" parents="11399 20657"/>
    </justification>
  </clause>

  <clause id="20661">
    <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(19916(a,1),20396(a,1,2,3))].">
      <j1 rule="para" parents="19916 20396"/>
    </justification>
  </clause>

  <clause id="20662">
    <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(5857(a,1),20661(a,1,2,3,1))].">
      <j1 rule="para" parents="5857 20661"/>
    </justification>
  </clause>

  <clause id="20664">
    <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(443(a,1),20662(a,1,2))].">
      <j1 rule="para" parents="443 20662"/>
    </justification>
  </clause>

  <clause id="20666">
    <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(144,a,20664,a)].">
      <j1 rule="hyper" parents="144 20664"/>
    </justification>
  </clause>

  <clause id="20668">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,K(w,y))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(15820(a,1),20666(a,1,2,2))].">
      <j1 rule="para" parents="15820 20666"/>
    </justification>
  </clause>

  <clause id="20669">
    <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(20668(a,1),16432(a,1,2,1))].">
      <j1 rule="para" parents="20668 16432"/>
    </justification>
  </clause>

  <clause id="20670">
    <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(19265(a,1),20669(a,1,1))].">
      <j1 rule="para" parents="19265 20669"/>
    </justification>
  </clause>

  <clause id="20671">
    <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(19366(a,1),20670(a,1,2))].">
      <j1 rule="para" parents="19366 20670"/>
    </justification>
  </clause>

  <clause id="20672">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * (w * K(v5,v6))) = (w * a(y,z,K(u,x))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(7521,a,20671,a)].">
      <j1 rule="hyper" parents="7521 20671"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(v5,v6) = a(y,z,K(u,w)) * (x * K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,15824,a(flip),b,20672,a),flip(a)].">
      <j1 rule="hyper" parents="60 15824 20672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * K(w * a(x,y,K(z,u)),v5)) = T(w * a(x,y,K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(5265,a,20673,a),flip(a)].">
      <j1 rule="hyper" parents="5265 20673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * K(w,v5)) = T(w * a(x,y,K(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(19799(a,1),20674(a,1,2,2))].">
      <j1 rule="para" parents="19799 20674"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = a(y,z,K(u,w)) * T(x,v5)
    ]]></literal>
    <justification jstring="[para(5256(a,2),20675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5256 20675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20678">
    <literal><![CDATA[
      x \ (y * T((a(z,u,K(w,v5)) * (y \ x)) * a(v5,u,K(w,z)),v6)) = K((x \ (y * a(v5,u,K(w,z)))) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(20676(a,2),15877(a,1,2,2))].">
      <j1 rule="para" parents="20676 15877"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) = x \ (y * T(y \ x,v6))
    ]]></literal>
    <justification jstring="[para(19404(a,1),20678(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="19404 20678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      K((x \ (y * a(z,u,K(w,v5)))) \ 1,v6) = K((x \ y) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,5397,a(flip),b,20679,a),flip(a)].">
      <j1 rule="hyper" parents="370 5397 20679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      K((T(x,y) \ y) \ 1,z) = K(((y * a(u,w,K(v5,v6))) / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,19587,a(flip),b,20680,a),flip(a)].">
      <j1 rule="hyper" parents="60 19587 20680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      K(((x * a(y,z,K(u,w))) / v5) \ 1,v6) = K((x / v5) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,14680,a(flip),b,20682,a),flip(a)].">
      <j1 rule="hyper" parents="60 14680 20682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20685">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K((y / x) \ 1,v6)
    ]]></literal>
    <justification jstring="[hyper(9021,a,20684,a)].">
      <j1 rule="hyper" parents="9021 20684"/>
    </justification>
  </clause>

  <clause id="20686">
    <literal><![CDATA[
      K(x / (y * a(z,u,K(w,v5))),v6) = K(x / y,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,8215,a(flip),b,20685,a),flip(a)].">
      <j1 rule="hyper" parents="370 8215 20685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20687">
    <literal><![CDATA[
      K(x / (L(K(y,z),u,w) * v5),v6) = K(x / (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(20397(a,1),20686(a,1,1,2))].">
      <j1 rule="para" parents="20397 20686"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(((x \ v5) * x) / (K(z,y) * x),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,20458,a(flip),b,20687,a)].">
      <j1 rule="hyper" parents="60 20458 20687"/>
    </justification>
  </clause>

  <clause id="20690">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * (x * (x \ v5))),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,19476,a(flip),b,20688,a),flip(a)].">
      <j1 rule="hyper" parents="370 19476 20688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20691">
    <literal><![CDATA[
      K(x \ (L(K(y,z),u,w) * v5),v6) = K(x \ (K(y,z) * v5),v6)
    ]]></literal>
    <justification jstring="[para(5(a,1),20690(a,2,1,2,2))].">
      <j1 rule="para" parents="5 20690"/>
    </justification>
  </clause>

  <clause id="20692">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K((x * K(z,y)) \ (K(u,y) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,19477,a,b,20691,a)].">
      <j1 rule="hyper" parents="60 19477 20691"/>
    </justification>
  </clause>

  <clause id="20695">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,u) \ 1,w,v5)) * v6),v7) = K(x \ (K(y,z) * (K(u,y) * v6)),v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,19441,a(flip),b,20692,a),flip(a)].">
      <j1 rule="hyper" parents="370 19441 20692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20696">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(y,z) \ 1,u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(7500(a,1),20695(a,2,1,2))].">
      <j1 rule="para" parents="7500 20695"/>
    </justification>
  </clause>

  <clause id="20697">
    <literal><![CDATA[
      K(x \ ((K(y,z) * L(K(z,y),u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(5865(a,1),20696(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="5865 20696"/>
    </justification>
  </clause>

  <clause id="20698">
    <literal><![CDATA[
      K(x \ (a(y,z,K(u,w)) * v5),v6) = K(x \ v5,v6)
    ]]></literal>
    <justification jstring="[para(11889(a,1),20697(a,1,1,2,1))].">
      <j1 rule="para" parents="11889 20697"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      K(x \ ((y * z) * K(u,w)),v5) = K(x \ (y * (z * K(u,w))),v5)
    ]]></literal>
    <justification jstring="[para(19665(a,1),20698(a,1,1,2))].">
      <j1 rule="para" parents="19665 20698"/>
    </justification>
  </clause>

  <clause id="20700">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(19625,a,20699,a),flip(a)].">
      <j1 rule="hyper" parents="19625 20699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20701">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(270(a,1),20700(a,1,1))].">
      <j1 rule="para" parents="270 20700"/>
    </justification>
  </clause>

  <clause id="20702">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8193,a,20701,a)].">
      <j1 rule="hyper" parents="8193 20701"/>
    </justification>
  </clause>

  <clause id="20703">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(T(x,K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(6224(a,1),20701(a,1,1,1))].">
      <j1 rule="para" parents="6224 20701"/>
    </justification>
  </clause>

  <clause id="20704">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17230,a,20702,a)].">
      <j1 rule="hyper" parents="17230 20702"/>
    </justification>
  </clause>

  <clause id="20705">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(18148,a,20704,a)].">
      <j1 rule="hyper" parents="18148 20704"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13036,a,20704,a)].">
      <j1 rule="hyper" parents="13036 20704"/>
    </justification>
  </clause>

  <clause id="20707">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12983,a,20704,a)].">
      <j1 rule="hyper" parents="12983 20704"/>
    </justification>
  </clause>

  <clause id="20713">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19475,a(flip),b,20704,a)].">
      <j1 rule="hyper" parents="60 19475 20704"/>
    </justification>
  </clause>

  <clause id="20714">
    <literal><![CDATA[
      K((x / y) * K(z,T(u,y)),w) = K(x / (y * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16630,a(flip),b,20704,a),flip(a)].">
      <j1 rule="hyper" parents="60 16630 20704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,20704,a(flip),b,12965,a)].">
      <j1 rule="hyper" parents="129 20704 12965"/>
    </justification>
  </clause>

  <clause id="20718">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(20704(a,1),12967(a,1,2))].">
      <j1 rule="para" parents="20704 12967"/>
    </justification>
  </clause>

  <clause id="20719">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K((x / u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(20633(a,1),20704(a,1,1))].">
      <j1 rule="para" parents="20633 20704"/>
    </justification>
  </clause>

  <clause id="20722">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16572,a(flip),b,20706,a),flip(a)].">
      <j1 rule="hyper" parents="60 16572 20706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20723">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16410,a(flip),b,20706,a),flip(a)].">
      <j1 rule="hyper" parents="60 16410 20706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20724">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(7539(a,1),20706(a,1,2))].">
      <j1 rule="para" parents="7539 20706"/>
    </justification>
  </clause>

  <clause id="20726">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(20633(a,1),20706(a,1,2))].">
      <j1 rule="para" parents="20633 20706"/>
    </justification>
  </clause>

  <clause id="20733">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6591(a,1),20707(a,1,2))].">
      <j1 rule="para" parents="6591 20707"/>
    </justification>
  </clause>

  <clause id="20737">
    <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(60,a,12942,a(flip),b,20733,a)].">
      <j1 rule="hyper" parents="60 12942 20733"/>
    </justification>
  </clause>

  <clause id="20740">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(20703(a,2),17231(a,1))].">
      <j1 rule="para" parents="20703 17231"/>
    </justification>
  </clause>

  <clause id="20741">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(12966(a,1),20740(a,1))].">
      <j1 rule="para" parents="12966 20740"/>
    </justification>
  </clause>

  <clause id="20742">
    <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(7539(a,1),20741(a,1,2))].">
      <j1 rule="para" parents="7539 20741"/>
    </justification>
  </clause>

  <clause id="20745">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(17734,a,20705,a)].">
      <j1 rule="hyper" parents="17734 20705"/>
    </justification>
  </clause>

  <clause id="20747">
    <literal><![CDATA[
      K(((x \ 1) \ y) * K(z,u),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(15133(a,1),20705(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15133 20705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20749">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17237,a,b,20713,a),flip(a)].">
      <j1 rule="hyper" parents="370 17237 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20750">
    <literal><![CDATA[
      K(x \ (K(y,K(z,u)) * w),v5) = K(x \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,17692,a(flip),b,20713,a),flip(a)].">
      <j1 rule="hyper" parents="370 17692 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20751">
    <literal><![CDATA[
      K(x \ (y * T(z,K(u,w))),v5) = K(x \ (y * z),v5)
    ]]></literal>
    <justification jstring="[para(6130(a,1),20750(a,1,1,2))].">
      <j1 rule="para" parents="6130 20750"/>
    </justification>
  </clause>

  <clause id="20752">
    <literal><![CDATA[
      K(x \ (T(y,T(z,u)) * w),v5) = K(x \ (T(y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(9669(a,1),20750(a,1,1,2))].">
      <j1 rule="para" parents="9669 20750"/>
    </justification>
  </clause>

  <clause id="20753">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19553,a,20715,a)].">
      <j1 rule="hyper" parents="19553 20715"/>
    </justification>
  </clause>

  <clause id="20755">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * K(y,y * z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(7394(a,1),20715(a,1,1,2))].">
      <j1 rule="para" parents="7394 20715"/>
    </justification>
  </clause>

  <clause id="20757">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(20643,a,20718,a)].">
      <j1 rule="hyper" parents="20643 20718"/>
    </justification>
  </clause>

  <clause id="20759">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17965,a,b,20718,a)].">
      <j1 rule="hyper" parents="60 17965 20718"/>
    </justification>
  </clause>

  <clause id="20763">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(w,u) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(17217(a,2),20718(a,2,2))].">
      <j1 rule="para" parents="17217 20718"/>
    </justification>
  </clause>

  <clause id="20765">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,7618,a(flip),b,20757,a)].">
      <j1 rule="hyper" parents="60 7618 20757"/>
    </justification>
  </clause>

  <clause id="20766">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(20757(a,1),47(a,2))].">
      <j1 rule="para" parents="20757 47"/>
    </justification>
  </clause>

  <clause id="20772">
    <literal><![CDATA[
      K((x / y) * K(z,u),w) = K(x * (y \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(15482,a,20719,a),flip(a)].">
      <j1 rule="hyper" parents="15482 20719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20773">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(K(z,y) * (x / u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17237,a,b,20719,a),flip(a)].">
      <j1 rule="hyper" parents="370 17237 20719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20775">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19480,a(flip),b,20722,a),flip(a)].">
      <j1 rule="hyper" parents="60 19480 20722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(7506(a,2),20723(a,2,2,2))].">
      <j1 rule="para" parents="7506 20723"/>
    </justification>
  </clause>

  <clause id="20777">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * (z \ K(w,u))) = K(x,K(w,u) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(20328,a,20724,a)].">
      <j1 rule="hyper" parents="20328 20724"/>
    </justification>
  </clause>

  <clause id="20778">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(17730,a,20724,a)].">
      <j1 rule="hyper" parents="17730 20724"/>
    </justification>
  </clause>

  <clause id="20779">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19448,a(flip),b,20724,a)].">
      <j1 rule="hyper" parents="60 19448 20724"/>
    </justification>
  </clause>

  <clause id="20780">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) \ w)) = K(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5855(a,1),20724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5855 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20781">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * z) \ w)) = K(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),20724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6270 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20782">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * (u * z)) \ v5)) = K(x,(w * (u * T(z,y))) \ v5)
    ]]></literal>
    <justification jstring="[para(6930(a,1),20724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6930 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20783">
    <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(12967(a,1),20724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12967 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20784">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(15179(a,1),20724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15179 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(20324,a,20726,a),flip(a)].">
      <j1 rule="hyper" parents="20324 20726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20786">
    <literal><![CDATA[
      K(((x \ 1) \ y) * K(z,u),w) = K((x * K(z,u)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(15555,a,20745,a),flip(a)].">
      <j1 rule="hyper" parents="15555 20745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20789">
    <literal><![CDATA[
      K(K(x,y) * ((y / z) \ u),w) = K((T(y,x) / z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19443,a(flip),b,20749,a),flip(a)].">
      <j1 rule="hyper" parents="60 19443 20749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20790">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u,w))),v5) = K(x \ (y * T(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(8587(a,1),20751(a,1,1,2,2))].">
      <j1 rule="para" parents="8587 20751"/>
    </justification>
  </clause>

  <clause id="20795">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * (K(x,y) \ K(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(60,a,19565,a,b,20763,a)].">
      <j1 rule="hyper" parents="60 19565 20763"/>
    </justification>
  </clause>

  <clause id="20797">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(u,z) * (x / y),w) = v5
    ]]></literal>
    <justification jstring="[para(20772(a,1),17367(a,1))].">
      <j1 rule="para" parents="20772 17367"/>
    </justification>
  </clause>

  <clause id="20798">
    <literal><![CDATA[
      K(K(x,y) * ((((z * y) \ u) * (z * y)) / (z * y)),w) = K((z * T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17309,a,20773,a),flip(a)].">
      <j1 rule="hyper" parents="17309 20773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20799">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y / (K(u,z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,18891,a,b,20773,a)].">
      <j1 rule="hyper" parents="370 18891 20773"/>
    </justification>
  </clause>

  <clause id="20800">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(17487,a,20775,a)].">
      <j1 rule="hyper" parents="17487 20775"/>
    </justification>
  </clause>

  <clause id="20801">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(17300,a,20776,a),flip(a)].">
      <j1 rule="hyper" parents="17300 20776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20802">
    <literal><![CDATA[
      K(L(x,y,z),K(u,w) * (v5 \ v6)) = K(x,L((K(w,u) * v5) \ v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,20778,a),flip(a)].">
      <j1 rule="hyper" parents="13036 20778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20803">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,(K(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,20778,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 20778 5230"/>
    </justification>
  </clause>

  <clause id="20804">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) \ w)) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),20778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7864 20778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20805">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) \ w) = K(x,K(y,z) * ((y * u) \ w))
    ]]></literal>
    <justification jstring="[para(7967(a,1),20778(a,1,2,1))].">
      <j1 rule="para" parents="7967 20778"/>
    </justification>
  </clause>

  <clause id="20806">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((z * u) \ v5)) = K(x,((K(w,y) * z) * u) \ v5)
    ]]></literal>
    <justification jstring="[para(16420(a,1),20778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16420 20778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20807">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16730,a,b,20779,a),flip(a)].">
      <j1 rule="hyper" parents="370 16730 20779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20808">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(7864(a,1),20779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7864 20779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20809">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (T(z,y) \ w))) = K(x,u \ (T(T(z,y),y) \ w))
    ]]></literal>
    <justification jstring="[para(7948(a,1),20779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7948 20779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20810">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (T(y,z) \ v5))) = K(x,w \ (T(y,K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(9718(a,1),20779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9718 20779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20811">
    <literal><![CDATA[
      K(x,y \ L(K(z,u) * w,z,z)) = K(x,K(z,u) * (y \ L(w,z,z)))
    ]]></literal>
    <justification jstring="[para(11663(a,2),20779(a,1,2,2))].">
      <j1 rule="para" parents="11663 20779"/>
    </justification>
  </clause>

  <clause id="20812">
    <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(20779(a,2),16731(a,1))].">
      <j1 rule="para" parents="20779 16731"/>
    </justification>
  </clause>

  <clause id="20813">
    <literal><![CDATA[
      x * K(x,y * (z \ K(u,w))) = T(x,(y / z) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,20785,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 20785 5230"/>
    </justification>
  </clause>

  <clause id="20814">
    <literal><![CDATA[
      K(x,y \ (K(z,L(u,w,v5)) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(19943,a,20800,a),flip(a)].">
      <j1 rule="hyper" parents="19943 20800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20815">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,19474,a(flip),b,20800,a),flip(a)].">
      <j1 rule="hyper" parents="370 19474 20800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20816">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w) \ y)) = K(x,K(w,u) \ ((K(u,w) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,19739,a,b,20801,a)].">
      <j1 rule="hyper" parents="60 19739 20801"/>
    </justification>
  </clause>

  <clause id="20817">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) * v5)) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20512,a,b,20807,a)].">
      <j1 rule="hyper" parents="60 20512 20807"/>
    </justification>
  </clause>

  <clause id="20818">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (T(w * (u * z),K(z,y)) \ v5)) = K(x,(w * (u * (z * K(y,z)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20561,a(flip),b,20807,a),flip(a)].">
      <j1 rule="hyper" parents="60 20561 20807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20819">
    <literal><![CDATA[
      K(x,K(y,y \ z) * ((u * (y \ z)) \ w)) = K(x,(u * (z / y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19479,a(flip),b,20807,a),flip(a)].">
      <j1 rule="hyper" parents="60 19479 20807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20820">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y \ w))) = K(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(7873(a,1),20807(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 20807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20821">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) / K(y * z,y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6381,a,20755,a)].">
      <j1 rule="hyper" parents="6381 20755"/>
    </justification>
  </clause>

  <clause id="20822">
    <literal><![CDATA[
      ((x * (y \ R(y,z,y))) / (K(y,z) * x)) / (K(y,z) * x) = K(y * z,T(y,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20821(a,1),18092(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20821 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20823">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K((x / y) * K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(17736,a,20714,a),flip(a)].">
      <j1 rule="hyper" parents="17736 20714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20826">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(K(z,u) \ (x / y),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17262,a,b,20823,a),flip(a)].">
      <j1 rule="hyper" parents="370 17262 20823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20828">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(x * (y \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20772,a(flip),b,20823,a),flip(a)].">
      <j1 rule="hyper" parents="370 20772 20823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20829">
    <literal><![CDATA[
      K(x / (K(y,z) \ u),w) = K(K(z,y) \ (x / u),w)
    ]]></literal>
    <justification jstring="[hyper(17771,a,20826,a)].">
      <j1 rule="hyper" parents="17771 20826"/>
    </justification>
  </clause>

  <clause id="20831">
    <literal><![CDATA[
      K(x * ((y * z) \ K(u,z)),w) = K(x / (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),20828(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 20828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      K(K(x,y) \ (z / (x * u)),w) = K(z / (T(x,y) * u),w)
    ]]></literal>
    <justification jstring="[para(7907(a,1),20829(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7907 20829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) \ u),w) = K((z \ K(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17367,a,20747,a)].">
      <j1 rule="hyper" parents="17367 20747"/>
    </justification>
  </clause>

  <clause id="20834">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = x \ (u * (K(z,y) * K(z,y)))
    ]]></literal>
    <justification jstring="[para(20759(a,1),20658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20759 20658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20835">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(w,z)) = K(x,(y * T(z,w)) \ u)
    ]]></literal>
    <justification jstring="[hyper(17252,a,20781,a)].">
      <j1 rule="hyper" parents="17252 20781"/>
    </justification>
  </clause>

  <clause id="20836">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(20781(a,1),17723(a,1))].">
      <j1 rule="para" parents="20781 17723"/>
    </justification>
  </clause>

  <clause id="20837">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(16731,a,20784,a)].">
      <j1 rule="hyper" parents="16731 20784"/>
    </justification>
  </clause>

  <clause id="20838">
    <literal><![CDATA[
      K((x \ K(y,z)) \ u,w) = K((x * K(z,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20747,a(flip),b,20786,a)].">
      <j1 rule="hyper" parents="60 20747 20786"/>
    </justification>
  </clause>

  <clause id="20839">
    <literal><![CDATA[
      K((x \ K(y,z)) \ u,w) = K(K(z,y) * (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,19821,a(flip),b,20838,a),flip(a)].">
      <j1 rule="hyper" parents="370 19821 20838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20841">
    <literal><![CDATA[
      K((T(x,y) / y) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18325,a(flip),b,20789,a),flip(a)].">
      <j1 rule="hyper" parents="60 18325 20789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20842">
    <literal><![CDATA[
      K((x / T(y,x)) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17825,a(flip),b,20841,a)].">
      <j1 rule="hyper" parents="60 17825 20841"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      K((x / (x \ y)) \ z,u) = K(((y / x) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5790(a,1),20841(a,1,1,1))].">
      <j1 rule="para" parents="5790 20841"/>
    </justification>
  </clause>

  <clause id="20844">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,(w \ u) \ z)),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,18801,a(flip),b,20790,a)].">
      <j1 rule="hyper" parents="60 18801 20790"/>
    </justification>
  </clause>

  <clause id="20845">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * u),w) = K(K(z,y) * (u \ x),T(w,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17364,a(flip),b,20799,a),flip(a)].">
      <j1 rule="hyper" parents="60 17364 20799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(5265,a,20803,a),flip(a)].">
      <j1 rule="hyper" parents="5265 20803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20847">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20803(a,1),5265(a,1))].">
      <j1 rule="para" parents="20803 5265"/>
    </justification>
  </clause>

  <clause id="20848">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(17721,a,20846,a)].">
      <j1 rule="hyper" parents="17721 20846"/>
    </justification>
  </clause>

  <clause id="20849">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) * w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(15490,a,20846,a)].">
      <j1 rule="hyper" parents="15490 20846"/>
    </justification>
  </clause>

  <clause id="20850">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * u) \ w)) = T(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),20846(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7864 20846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20852">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * (y \ K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(18121,a,20848,a)].">
      <j1 rule="hyper" parents="18121 20848"/>
    </justification>
  </clause>

  <clause id="20853">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5855(a,1),20848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5855 20848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20854">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ z) \ w)) = T(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(15179(a,1),20848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15179 20848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(K(z,y) * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(20848(a,1),17717(a,1))].">
      <j1 rule="para" parents="20848 17717"/>
    </justification>
  </clause>

  <clause id="20856">
    <literal><![CDATA[
      T(x,(y \ K(y * z,y \ 1)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18234,a(flip),b,20849,a),flip(a)].">
      <j1 rule="hyper" parents="370 18234 20849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20857">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(y,w)) = K(x,(T(y,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17484,a,20804,a)].">
      <j1 rule="hyper" parents="17484 20804"/>
    </justification>
  </clause>

  <clause id="20858">
    <literal><![CDATA[
      K(x,(T(y,y * z) * u) \ w) = K(x,((y * u) \ w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17483,a,20804,a),flip(a)].">
      <j1 rule="hyper" parents="17483 20804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20859">
    <literal><![CDATA[
      K(x,((y * z) \ u) * K(w,y)) = K(x,(T(y,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17252,a,20804,a)].">
      <j1 rule="hyper" parents="17252 20804"/>
    </justification>
  </clause>

  <clause id="20860">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(16731,a,20804,a)].">
      <j1 rule="hyper" parents="16731 20804"/>
    </justification>
  </clause>

  <clause id="20861">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,z)) = K(x,y \ (T(z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(17484,a,20808,a)].">
      <j1 rule="hyper" parents="17484 20808"/>
    </justification>
  </clause>

  <clause id="20862">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * z) * w))) = K(x,u \ (T(y * z,z) * w))
    ]]></literal>
    <justification jstring="[hyper(14537,a,20808,a)].">
      <j1 rule="hyper" parents="14537 20808"/>
    </justification>
  </clause>

  <clause id="20863">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ (T(z * y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(14519,a,20808,a)].">
      <j1 rule="hyper" parents="14519 20808"/>
    </justification>
  </clause>

  <clause id="20864">
    <literal><![CDATA[
      K(x,K(R(y,z,u),w) * (v5 \ ((y * z) * u))) = K(x,v5 \ (T(R(y,z,u),w) * (z * u)))
    ]]></literal>
    <justification jstring="[para(103(a,1),20808(a,1,2,2,2))].">
      <j1 rule="para" parents="103 20808"/>
    </justification>
  </clause>

  <clause id="20865">
    <literal><![CDATA[
      T(x,(y / z) * K(u,w)) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,20813,a),flip(a)].">
      <j1 rule="hyper" parents="5265 20813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20866">
    <literal><![CDATA[
      T(x,y * (z \ K(u,w * w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(18250,a,20865,a),flip(a)].">
      <j1 rule="hyper" parents="18250 20865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20867">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17333,a,20865,a)].">
      <j1 rule="hyper" parents="17333 20865"/>
    </justification>
  </clause>

  <clause id="20868">
    <literal><![CDATA[
      T(x,y / (z * K(u * u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17838,a,b,20866,a)].">
      <j1 rule="hyper" parents="60 17838 20866"/>
    </justification>
  </clause>

  <clause id="20869">
    <literal><![CDATA[
      T(x,y / (z \ T(u,w * w))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(6677(a,1),20868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6677 20868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20870">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z \ w))) = T(x,u / (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20279,a(flip),b,20867,a),flip(a)].">
      <j1 rule="hyper" parents="370 20279 20867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20871">
    <literal><![CDATA[
      T(x,y / T(z / (1 / u),u)) = T(x,y / ((u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(9989(a,1),20869(a,1,2,2))].">
      <j1 rule="para" parents="9989 20869"/>
    </justification>
  </clause>

  <clause id="20872">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,(T(y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16931,a(flip),b,20815,a)].">
      <j1 rule="hyper" parents="60 16931 20815"/>
    </justification>
  </clause>

  <clause id="20873">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,15150,a(flip),b,20872,a),flip(a)].">
      <j1 rule="hyper" parents="370 15150 20872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20874">
    <literal><![CDATA[
      K(x,(T(y,z) \ 1) \ x) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,15756,a(flip),b,20872,a),flip(a)].">
      <j1 rule="hyper" parents="60 15756 20872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20875">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(20872(a,2),15300(a,1))].">
      <j1 rule="para" parents="20872 15300"/>
    </justification>
  </clause>

  <clause id="20876">
    <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(13036,a,20873,a)].">
      <j1 rule="hyper" parents="13036 20873"/>
    </justification>
  </clause>

  <clause id="20877">
    <literal><![CDATA[
      K(x,T(y \ 1,z * u) \ w) = K(x,T(y,z / u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18480,a(flip),b,20873,a)].">
      <j1 rule="hyper" parents="60 18480 20873"/>
    </justification>
  </clause>

  <clause id="20878">
    <literal><![CDATA[
      K(x,T(1 / y,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(77(a,1),20873(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 20873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20879">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5616,a,20874,a),flip(a)].">
      <j1 rule="hyper" parents="5616 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20880">
    <literal><![CDATA[
      K(x,T(x * y,z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12622,a,20879,a)].">
      <j1 rule="hyper" parents="12622 20879"/>
    </justification>
  </clause>

  <clause id="20881">
    <literal><![CDATA[
      K(x,x * T(x \ y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),20880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 20880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20882">
    <literal><![CDATA[
      K(x,y * ((z * T(z \ u,w)) * K(z,T(u,w)))) = K(x,y * T(z * T(z \ u,w),z))
    ]]></literal>
    <justification jstring="[para(20881(a,1),19857(a,1,2,2,2))].">
      <j1 rule="para" parents="20881 19857"/>
    </justification>
  </clause>

  <clause id="20883">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (w \ (y \ v5))) = K(x,w \ (T(y,z * u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18376,a,20820,a)].">
      <j1 rule="hyper" parents="18376 20820"/>
    </justification>
  </clause>

  <clause id="20884">
    <literal><![CDATA[
      K(x,y \ (T(z,u * u) \ w)) = K(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18435,a(flip),b,20820,a),flip(a)].">
      <j1 rule="hyper" parents="60 18435 20820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20886">
    <literal><![CDATA[
      K(K(x,y) \ (z / (y * u)),w) = K(z / (T(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(17488,a,20832,a)].">
      <j1 rule="hyper" parents="17488 20832"/>
    </justification>
  </clause>

  <clause id="20887">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) \ u,w) = K(K(y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,6655,a(flip),b,20833,a),flip(a)].">
      <j1 rule="hyper" parents="60 6655 20833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20888">
    <literal><![CDATA[
      K(x,(((1 / y) * T(z,y)) \ u) * K(w,y)) = K(x,(((y * y) \ z) * T(y,w)) \ u)
    ]]></literal>
    <justification jstring="[para(1276(a,1),20835(a,1,2,1,1))].">
      <j1 rule="para" parents="1276 20835"/>
    </justification>
  </clause>

  <clause id="20889">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,u)) \ w) = K(x,K(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20465,a(flip),b,20837,a),flip(a)].">
      <j1 rule="hyper" parents="60 20465 20837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20890">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14458,a(flip),b,20837,a),flip(a)].">
      <j1 rule="hyper" parents="60 14458 20837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20891">
    <literal><![CDATA[
      K(x,(T(y,z * z) \ (z * z)) * u) = K(x,(y / (z * z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(15458,a,20890,a)].">
      <j1 rule="hyper" parents="15458 20890"/>
    </justification>
  </clause>

  <clause id="20892">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) = x * K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,20890,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 20890 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20893">
    <literal><![CDATA[
      K(x,((y * (z / y)) / y) \ u) = K(x,(T(z,y) / y) \ u)
    ]]></literal>
    <justification jstring="[para(2331(a,1),20890(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2331 20890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20894">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5749(a,2),20890(a,1,2,1))].">
      <j1 rule="para" parents="5749 20890"/>
    </justification>
  </clause>

  <clause id="20895">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = (w * K(u,(y / x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(20890(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20890 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20896">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ T(u,y)) \ w) = K(x,(u / L(y,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6495(a,1),20890(a,1,2,1,2))].">
      <j1 rule="para" parents="6495 20890"/>
    </justification>
  </clause>

  <clause id="20897">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,T(z,y) \ y)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(14580,a,20894,a),flip(a)].">
      <j1 rule="hyper" parents="14580 20894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20898">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,20892,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 20892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20899">
    <literal><![CDATA[
      T(x,(y \ T(z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(20892(a,2),5265(a,1))].">
      <j1 rule="para" parents="20892 5265"/>
    </justification>
  </clause>

  <clause id="20900">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(5749(a,2),20899(a,1,2,1))].">
      <j1 rule="para" parents="5749 20899"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      T(x,(T(y,z) * u) \ z) = T(x,(y * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(17299,a,20850,a),flip(a)].">
      <j1 rule="hyper" parents="17299 20850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20902">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * ((w / y) \ v5)) = T(x,(w / T(y,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(17781,a,20853,a)].">
      <j1 rule="hyper" parents="17781 20853"/>
    </justification>
  </clause>

  <clause id="20903">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(16774,a,20854,a)].">
      <j1 rule="hyper" parents="16774 20854"/>
    </justification>
  </clause>

  <clause id="20904">
    <literal><![CDATA[
      T(x,((y \ 1) * K(y * z,y \ 1)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4781(a,2),20856(a,1,2,1))].">
      <j1 rule="para" parents="4781 20856"/>
    </justification>
  </clause>

  <clause id="20905">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(1 / y,w * y)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[para(16232(a,1),20857(a,2,2,1,1))].">
      <j1 rule="para" parents="16232 20857"/>
    </justification>
  </clause>

  <clause id="20906">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * v5)) = K(x,(y \ (z * v5)) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18362,a(flip),b,20861,a),flip(a)].">
      <j1 rule="hyper" parents="60 18362 20861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20907">
    <literal><![CDATA[
      T(x,y / (T(z,u) \ T(u,w))) = T(x,y / (T(u,w) / z))
    ]]></literal>
    <justification jstring="[hyper(18228,a,20870,a),flip(a)].">
      <j1 rule="hyper" parents="18228 20870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20908">
    <literal><![CDATA[
      T(x,y / (T(z,u * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20870(a,1),18245(a,1))].">
      <j1 rule="para" parents="20870 18245"/>
    </justification>
  </clause>

  <clause id="20909">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),1 / z)) = T(x,y / ((z \ 1) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18736,a,b,20871,a)].">
      <j1 rule="hyper" parents="60 18736 20871"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      K(x,T(y \ 1,z * (u \ w)) \ v5) = K(x,T(y,w / ((u \ 1) * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20086,a(flip),b,20877,a)].">
      <j1 rule="hyper" parents="60 20086 20877"/>
    </justification>
  </clause>

  <clause id="20911">
    <literal><![CDATA[
      K(x / (K(y,z) \ (y * u)),w) = K(x / (T(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20829,a,b,20886,a)].">
      <j1 rule="hyper" parents="60 20829 20886"/>
    </justification>
  </clause>

  <clause id="20912">
    <literal><![CDATA[
      K(K(x,y) * ((z \ 1) * u),w) = K(K(y,x) * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20839,a(flip),b,20887,a)].">
      <j1 rule="hyper" parents="60 20839 20887"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,T(y / z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16760,a(flip),b,20893,a),flip(a)].">
      <j1 rule="hyper" parents="60 16760 20893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20914">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20913(a,2,2,1))].">
      <j1 rule="para" parents="109 20913"/>
    </justification>
  </clause>

  <clause id="20915">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5747(a,1),20914(a,1,2,1))].">
      <j1 rule="para" parents="5747 20914"/>
    </justification>
  </clause>

  <clause id="20916">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,20895,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 20895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20917">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5749(a,2),20916(a,1,1,1))].">
      <j1 rule="para" parents="5749 20916"/>
    </justification>
  </clause>

  <clause id="20918">
    <literal><![CDATA[
      K((x / y) \ T(z,x / y),u) = K(z / (T(y,x) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(16231,a,20917,a),flip(a)].">
      <j1 rule="hyper" parents="16231 20917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20919">
    <literal><![CDATA[
      K((x / y) \ z,L(u,x,y)) = K(x \ (T(y,x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19368,a(flip),b,20917,a),flip(a)].">
      <j1 rule="hyper" parents="60 19368 20917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20921">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,K(z,w) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,18233,a(flip),b,20903,a),flip(a)].">
      <j1 rule="hyper" parents="60 18233 20903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20922">
    <literal><![CDATA[
      T(x,K(y,z) * ((z \ y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20903(a,2),20899(a,1))].">
      <j1 rule="para" parents="20903 20899"/>
    </justification>
  </clause>

  <clause id="20923">
    <literal><![CDATA[
      T(x,y / (T(z,u / w) \ (w \ u))) = T(x,y / (T(u / w,w) / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),20907(a,1,2,2,2))].">
      <j1 rule="para" parents="109 20907"/>
    </justification>
  </clause>

  <clause id="20924">
    <literal><![CDATA[
      K(x / (T(y,z) * z),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(7475(a,1),20911(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7475 20911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20925">
    <literal><![CDATA[
      K(x / ((y \ z) * y),u) = K(x / (y * (z / y)),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20924(a,1,1,2,1))].">
      <j1 rule="para" parents="109 20924"/>
    </justification>
  </clause>

  <clause id="20926">
    <literal><![CDATA[
      K(x / (y * (z / y)),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14653,a(flip),b,20925,a),flip(a)].">
      <j1 rule="hyper" parents="60 14653 20925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20927">
    <literal><![CDATA[
      K(x / T(y * z,z),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(6(a,1),20926(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 20926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20928">
    <literal><![CDATA[
      K(x / T((y \ 1) * T(z,y),T(y,y \ 1)),u) = K(x / (T(y,y \ 1) * ((y * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(7241(a,1),20927(a,1,1,2,1))].">
      <j1 rule="para" parents="7241 20927"/>
    </justification>
  </clause>

  <clause id="20929">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19825,a(flip),b,20912,a)].">
      <j1 rule="hyper" parents="60 19825 20912"/>
    </justification>
  </clause>

  <clause id="20930">
    <literal><![CDATA[
      K(K(x,y) * (z \ u),T(w,z)) = K(u * (z \ K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(17958,a,20929,a),flip(a)].">
      <j1 rule="hyper" parents="17958 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20932">
    <literal><![CDATA[
      K(x / (T(y,z) \ z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(14562,a,20918,a),flip(a)].">
      <j1 rule="hyper" parents="14562 20918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20933">
    <literal><![CDATA[
      K(x / (y / (z / y)),u) = K(x / ((y \ z) \ y),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20932(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 20932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20934">
    <literal><![CDATA[
      K(x / (y \ T(z,y)),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),20932(a,1,1,2))].">
      <j1 rule="para" parents="5749 20932"/>
    </justification>
  </clause>

  <clause id="20935">
    <literal><![CDATA[
      K(x / ((y \ z) \ ((y \ z) \ z)),u) = K(x / (y / (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),20934(a,1,1,2,2))].">
      <j1 rule="para" parents="108 20934"/>
    </justification>
  </clause>

  <clause id="20937">
    <literal><![CDATA[
      K(K(x,y) * (z / (x / u)),w) = K(z / (T(x,y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(20797,a,15615,a)].">
      <j1 rule="hyper" parents="20797 15615"/>
    </justification>
  </clause>

  <clause id="20938">
    <literal><![CDATA[
      K(x / (K(y,z) * (z / u)),w) = K(x / (T(z,y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20773,a,b,20937,a)].">
      <j1 rule="hyper" parents="60 20773 20937"/>
    </justification>
  </clause>

  <clause id="20939">
    <literal><![CDATA[
      K(x / (((y * z) / y) / u),w) = K(x / (T(z,y) / u),w)
    ]]></literal>
    <justification jstring="[para(15604(a,2),20938(a,1,1,2))].">
      <j1 rule="para" parents="15604 20938"/>
    </justification>
  </clause>

  <clause id="20940">
    <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(20512(a,2),20812(a,1))].">
      <j1 rule="para" parents="20512 20812"/>
    </justification>
  </clause>

  <clause id="20941">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[para(11013(a,1),20814(a,1,2,2,1))].">
      <j1 rule="para" parents="11013 20814"/>
    </justification>
  </clause>

  <clause id="20942">
    <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(8587(a,1),20836(a,1,2,1,2))].">
      <j1 rule="para" parents="8587 20836"/>
    </justification>
  </clause>

  <clause id="20943">
    <literal><![CDATA[
      T(x,K(y,z) * ((T(z,u) \ y) \ w)) = T(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20922,a,17659,a),flip(a)].">
      <j1 rule="hyper" parents="20922 17659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20946">
    <literal><![CDATA[
      K(x,K(y,z) \ ((L(K(y,z),u,w) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,19724,a(flip),b,20941,a),flip(a)].">
      <j1 rule="hyper" parents="60 19724 20941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20948">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(L(y,u,w),z) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(6765(a,1),20946(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6765 20946"/>
    </justification>
  </clause>

  <clause id="20949">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) \ w) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20860,a(flip),b,20805,a),flip(a)].">
      <j1 rule="hyper" parents="370 20860 20805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20950">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) \ w) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(8202(a,2),20949(a,1,2,1))].">
      <j1 rule="para" parents="8202 20949"/>
    </justification>
  </clause>

  <clause id="20951">
    <literal><![CDATA[
      K(x,y \ ((z \ ((u * w) / u)) * v5)) = K(x,K(w,u) * (y \ ((z \ w) * v5)))
    ]]></literal>
    <justification jstring="[para(20259(a,2),20817(a,1,2,2,1))].">
      <j1 rule="para" parents="20259 20817"/>
    </justification>
  </clause>

  <clause id="20952">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = (x \ u) * (K(z,y) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,513,a(flip),b,20834,a),flip(a)].">
      <j1 rule="hyper" parents="370 513 20834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20953">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * u),w) = K(x * (u \ K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20930,a(flip),b,20845,a),flip(a)].">
      <j1 rule="hyper" parents="370 20930 20845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20954">
    <literal><![CDATA[
      K(x / (K(y,y \ z) * (u * z)),w) = K(x / (u * T(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20831,a(flip),b,20953,a),flip(a)].">
      <j1 rule="hyper" parents="370 20831 20953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20955">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20246,a(flip),b,20852,a)].">
      <j1 rule="hyper" parents="60 20246 20852"/>
    </justification>
  </clause>

  <clause id="20956">
    <literal><![CDATA[
      T(x,(K(y,z) / u) * w) = T(x,K(y,z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18113,a(flip),b,20852,a)].">
      <j1 rule="hyper" parents="60 18113 20852"/>
    </justification>
  </clause>

  <clause id="20957">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(w,u) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(20078,a,20955,a)].">
      <j1 rule="hyper" parents="20078 20955"/>
    </justification>
  </clause>

  <clause id="20958">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16708,a,b,20955,a),flip(a)].">
      <j1 rule="hyper" parents="370 16708 20955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20959">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (w \ z))) = T(x,u \ (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[para(15179(a,1),20957(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15179 20957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20960">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (y \ w))) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(7873(a,1),20958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7873 20958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20961">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * (K(z,y) * w)) = v5
    ]]></literal>
    <justification jstring="[para(20958(a,1),15396(a,1))].">
      <j1 rule="para" parents="20958 15396"/>
    </justification>
  </clause>

  <clause id="20962">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (w * T(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(20958(a,1),17763(a,1))].">
      <j1 rule="para" parents="20958 17763"/>
    </justification>
  </clause>

  <clause id="20963">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w \ (v5 \ u))) = T(x,w \ (v5 \ T(u,y \ z)))
    ]]></literal>
    <justification jstring="[hyper(18188,a,20959,a)].">
      <j1 rule="hyper" parents="18188 20959"/>
    </justification>
  </clause>

  <clause id="20964">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * (z \ w))) = T(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20955,a,b,20960,a)].">
      <j1 rule="hyper" parents="60 20955 20960"/>
    </justification>
  </clause>

  <clause id="20965">
    <literal><![CDATA[
      T(x,y \ (((z * u) / z) \ w)) = T(x,y \ (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[para(8209(a,2),20964(a,1,2,2))].">
      <j1 rule="para" parents="8209 20964"/>
    </justification>
  </clause>

  <clause id="20966">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u),u) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(263(a,1),20965(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="263 20965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u \ (w \ ((w * u) \ 1))),w \ (u \ (w \ 1))) \ v5)) = T(x,y \ (((u * z) / u) \ v5))
    ]]></literal>
    <justification jstring="[para(19738(a,1),20966(a,1,2,2,1,1))].">
      <j1 rule="para" parents="19738 20966"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      K(x,(T(y,y * z) * u) \ w) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20859,a(flip),b,20858,a),flip(a)].">
      <j1 rule="hyper" parents="370 20859 20858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20969">
    <literal><![CDATA[
      K(x,(T(y \ 1,y \ z) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(15252(a,1),20968(a,1,2,1,1))].">
      <j1 rule="para" parents="15252 20968"/>
    </justification>
  </clause>

  <clause id="20970">
    <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(370,a,12966,a(flip),b,20876,a),flip(a)].">
      <j1 rule="hyper" parents="370 12966 20876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20971">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20876(a,2),13036(a,1))].">
      <j1 rule="para" parents="20876 13036"/>
    </justification>
  </clause>

  <clause id="20972">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ ((z \ y) \ u))) = K(x,L(T(y,z) \ u,T(z,y),z * y))
    ]]></literal>
    <justification jstring="[hyper(19703,a,20889,a),flip(a)].">
      <j1 rule="hyper" parents="19703 20889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20973">
    <literal><![CDATA[
      K(x,(y / (z * z)) \ u) = K(x,(y \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18878,a(flip),b,20891,a),flip(a)].">
      <j1 rule="hyper" parents="60 18878 20891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20975">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) = K(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(512(a,1),20973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="512 20973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20976">
    <literal><![CDATA[
      K(x,(y \ (z * z)) * u) = K(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15151,a(flip),b,20975,a),flip(a)].">
      <j1 rule="hyper" parents="370 15151 20975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20977">
    <literal><![CDATA[
      K(x,y \ ((z * z) * u)) = K(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(15460,a,20976,a)].">
      <j1 rule="hyper" parents="15460 20976"/>
    </justification>
  </clause>

  <clause id="20978">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ T(u,z * y)))) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18313,a(flip),b,20976,a),flip(a)].">
      <j1 rule="hyper" parents="60 18313 20976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20979">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ u))) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(6928,a,20977,a),flip(a)].">
      <j1 rule="hyper" parents="6928 20977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20980">
    <literal><![CDATA[
      K(x,y * (y * ((y * z) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20977(a,1),6928(a,1))].">
      <j1 rule="para" parents="20977 6928"/>
    </justification>
  </clause>

  <clause id="20981">
    <literal><![CDATA[
      K(x,(y / z) * ((y / z) * (y \ u))) = K(x,(((y / z) \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),20979(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7 20979"/>
    </justification>
  </clause>

  <clause id="20982">
    <literal><![CDATA[
      K(x,(1 / y) * ((1 / y) * ((1 / L(y,z,z)) \ u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(11770(a,1),20979(a,1,2,2,2,1))].">
      <j1 rule="para" parents="11770 20979"/>
    </justification>
  </clause>

  <clause id="20983">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[para(16228(a,1),20897(a,1,2,2))].">
      <j1 rule="para" parents="16228 20897"/>
    </justification>
  </clause>

  <clause id="20984">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(20983(a,1),14580(a,1))].">
      <j1 rule="para" parents="20983 14580"/>
    </justification>
  </clause>

  <clause id="20985">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20984,a,20521,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20984 20521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20986">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(5749(a,1),20984(a,1,2,2))].">
      <j1 rule="para" parents="5749 20984"/>
    </justification>
  </clause>

  <clause id="20987">
    <literal><![CDATA[
      K(x,(T(y,z) * u) / (z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(20255(a,1),20984(a,1))].">
      <j1 rule="para" parents="20255 20984"/>
    </justification>
  </clause>

  <clause id="20988">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = (w * K(u,x / (z / y))) \ w
    ]]></literal>
    <justification jstring="[para(20985(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20985 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20989">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,20988,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 20988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20990">
    <literal><![CDATA[
      K(T(x,y / z) / (y / z),u) = K(T(z \ y,y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(14429,a,20989,a),flip(a)].">
      <j1 rule="hyper" parents="14429 20989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20991">
    <literal><![CDATA[
      K(x / (y / (y / z)),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(77(a,1),20989(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 20989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20992">
    <literal><![CDATA[
      K(x / T(y,y * z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(18506,a,20991,a)].">
      <j1 rule="hyper" parents="18506 20991"/>
    </justification>
  </clause>

  <clause id="20993">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18500,a(flip),b,20992,a)].">
      <j1 rule="hyper" parents="60 18500 20992"/>
    </justification>
  </clause>

  <clause id="20994">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(20990(a,1),14404(a,1))].">
      <j1 rule="para" parents="20990 14404"/>
    </justification>
  </clause>

  <clause id="20995">
    <literal><![CDATA[
      T(x,(y / T(z,T(u,w))) \ v5) = T(x,(y / T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20853,a(flip),b,20902,a)].">
      <j1 rule="hyper" parents="60 20853 20902"/>
    </justification>
  </clause>

  <clause id="20996">
    <literal><![CDATA[
      T(x,((y \ 1) * K((1 / y) \ z,1 / y)) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7734(a,2),20904(a,1,2,1,2))].">
      <j1 rule="para" parents="7734 20904"/>
    </justification>
  </clause>

  <clause id="20997">
    <literal><![CDATA[
      T(x,(K(y,z) * (T(y,u) \ z)) \ w) = T(x,(z / T(y,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20855,a,20943,a)].">
      <j1 rule="hyper" parents="20855 20943"/>
    </justification>
  </clause>

  <clause id="20998">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = (z \ u) * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10888,a,b,20952,a)].">
      <j1 rule="hyper" parents="60 10888 20952"/>
    </justification>
  </clause>

  <clause id="20999">
    <literal><![CDATA[
      ((K(x,y) * z) \ u) * (K(x,y) * K(x,y)) = ((K(x,y) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,9606,a(flip),b,20952,a),flip(a)].">
      <j1 rule="hyper" parents="60 9606 20952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21000">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,(y \ (z * v5)) * (K(u,w) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(20952(a,1),20447(a,2,2))].">
      <j1 rule="para" parents="20952 20447"/>
    </justification>
  </clause>

  <clause id="21001">
    <literal><![CDATA[
      K(x * ((y * z) \ K(u \ z,u)),w) = K(x / (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(15482,a,20954,a)].">
      <j1 rule="hyper" parents="15482 20954"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,T(y \ 1,z)),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14581,a,20970,a),flip(a)].">
      <j1 rule="hyper" parents="14581 20970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21003">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(7858(a,1),20997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7858 20997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21004">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,T(y,z))) \ w) = T(x,(u \ ((y \ z) \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(7334(a,1),21003(a,1,2,1,2))].">
      <j1 rule="para" parents="7334 21003"/>
    </justification>
  </clause>

  <clause id="21005">
    <literal><![CDATA[
      x \ (L(K(y,z),K(y,z),K(z,y) * u) * u) = (x \ (K(z,y) * u)) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20652,a,b,20998,a)].">
      <j1 rule="hyper" parents="60 20652 20998"/>
    </justification>
  </clause>

  <clause id="21006">
    <literal><![CDATA[
      K(x,y * (y * ((z \ u) * (K(y,w) * K(y,w))))) = K(x,((y \ 1) * (T(T(y,w),w) \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(20998(a,1),20979(a,1,2,2,2))].">
      <j1 rule="para" parents="20998 20979"/>
    </justification>
  </clause>

  <clause id="21007">
    <literal><![CDATA[
      K(x / ((y \ 1) * ((y \ z) * y)),u) = K(x / ((y \ 1) * T(z,y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18737,a(flip),b,21001,a)].">
      <j1 rule="hyper" parents="60 18737 21001"/>
    </justification>
  </clause>

  <clause id="21008">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,19919,a(flip),b,20737,a),flip(a)].">
      <j1 rule="hyper" parents="370 19919 20737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21009">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ (y \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(20737(a,2),19920(a,1))].">
      <j1 rule="para" parents="20737 19920"/>
    </justification>
  </clause>

  <clause id="21011">
    <literal><![CDATA[
      K(x,(K(y,z) \ (u * L(K(w,v5),v6,v7))) \ v8) = K(x,K(w,v5) \ ((K(y,z) \ u) \ v8))
    ]]></literal>
    <justification jstring="[para(19409(a,2),21008(a,1,2,1))].">
      <j1 rule="para" parents="19409 21008"/>
    </justification>
  </clause>

  <clause id="21012">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) * w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(20228,a,20777,a)].">
      <j1 rule="hyper" parents="20228 20777"/>
    </justification>
  </clause>

  <clause id="21013">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(17769,a,21012,a)].">
      <j1 rule="hyper" parents="17769 21012"/>
    </justification>
  </clause>

  <clause id="21014">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20807,a,b,21012,a)].">
      <j1 rule="hyper" parents="370 20807 21012"/>
    </justification>
  </clause>

  <clause id="21015">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(u \ K(z,y),w)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(21012(a,1),20225(a,1,1))].">
      <j1 rule="para" parents="21012 20225"/>
    </justification>
  </clause>

  <clause id="21016">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y \ u)) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(21012(a,1),20522(a,1,1))].">
      <j1 rule="para" parents="21012 20522"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(21013(a,1),15486(a,1))].">
      <j1 rule="para" parents="21013 15486"/>
    </justification>
  </clause>

  <clause id="21018">
    <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(21014(a,1),20812(a,1))].">
      <j1 rule="para" parents="21014 20812"/>
    </justification>
  </clause>

  <clause id="21022">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(17799(a,1),20795(a,2,2))].">
      <j1 rule="para" parents="17799 20795"/>
    </justification>
  </clause>

  <clause id="21023">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = a(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(370,a,19396,a,b,21022,a),flip(a)].">
      <j1 rule="hyper" parents="370 19396 21022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21024">
    <literal><![CDATA[
      K(x,L((K(y,z) * u) \ w,v5,v6)) = K(x,L(K(z,y) * (u \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(13036,a,20802,a),flip(a)].">
      <j1 rule="hyper" parents="13036 20802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21025">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,K(u,w) \ ((K(w,u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(17975,a,20816,a)].">
      <j1 rule="hyper" parents="17975 20816"/>
    </justification>
  </clause>

  <clause id="21026">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(z,y) \ u) / w)) = K(x,u / w)
    ]]></literal>
    <justification jstring="[hyper(8904,a,21025,a),flip(a)].">
      <j1 rule="hyper" parents="8904 21025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21027">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) / w) = K(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[para(7508(a,1),21026(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7508 21026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21028">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (z / u)) = K(x,(y * (z / y)) / u)
    ]]></literal>
    <justification jstring="[para(7534(a,1),21027(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7534 21027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21029">
    <literal><![CDATA[
      K(x,K(y,z) \ (y / u)) = K(x,(z * (y / z)) / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14633,a(flip),b,21028,a)].">
      <j1 rule="hyper" parents="60 14633 21028"/>
    </justification>
  </clause>

  <clause id="21030">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16740,a(flip),b,21029,a),flip(a)].">
      <j1 rule="hyper" parents="60 16740 21029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21031">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17898,a(flip),b,21030,a),flip(a)].">
      <j1 rule="hyper" parents="370 17898 21030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21032">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(263(a,1),21031(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="263 21031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21033">
    <literal><![CDATA[
      K(x,(y * z) / (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) / u,u,y)) = w
    ]]></literal>
    <justification jstring="[para(21032(a,1),16440(a,1))].">
      <j1 rule="para" parents="21032 16440"/>
    </justification>
  </clause>

  <clause id="21034">
    <literal><![CDATA[
      K(x,(y * T(z \ u,z)) \ w) = K(x,(y * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20781,a(flip),b,20819,a)].">
      <j1 rule="hyper" parents="60 20781 20819"/>
    </justification>
  </clause>

  <clause id="21035">
    <literal><![CDATA[
      K(x,(y * ((z * u) / z)) \ w) = K(x,(y * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(4(a,1),21034(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 21034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21036">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,(y * z) / y)) \ w)
    ]]></literal>
    <justification jstring="[para(1276(a,1),21035(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1276 21035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21037">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((K(u,(y * z) / y) / ((y * z) / y)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(15520(a,1),21035(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15520 21035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21038">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ (T(z * y,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16731,a,20862,a)].">
      <j1 rule="hyper" parents="16731 20862"/>
    </justification>
  </clause>

  <clause id="21039">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) \ v5)) = K(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,20820,a(flip),b,20883,a)].">
      <j1 rule="hyper" parents="60 20820 20883"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      K(x,T(y,T(z,u \ w) \ v5) \ (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) / y)
    ]]></literal>
    <justification jstring="[hyper(14575,a,21039,a),flip(a)].">
      <j1 rule="hyper" parents="14575 21039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21041">
    <literal><![CDATA[
      K(x,y \ (T(z,u * (u / w)) * v5)) = K(x,y \ (T(z,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,20861,a(flip),b,20906,a),flip(a)].">
      <j1 rule="hyper" parents="370 20861 20906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * (w * (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((w * (w / u)) * z)) = v5
    ]]></literal>
    <justification jstring="[para(21041(a,1),16874(a,1))].">
      <j1 rule="para" parents="21041 16874"/>
    </justification>
  </clause>

  <clause id="21043">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * ((u \ w) * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((u \ w) * w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(21041(a,1),16886(a,1))].">
      <j1 rule="para" parents="21041 16886"/>
    </justification>
  </clause>

  <clause id="21044">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,((y \ z) * K(w,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,20848,a,b,20921,a),flip(a)].">
      <j1 rule="hyper" parents="370 20848 20921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21045">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,w \ v5))) = T(x,y \ (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20959,a(flip),b,20963,a),flip(a)].">
      <j1 rule="hyper" parents="60 20959 20963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21046">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u * 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16679,a,b,21045,a)].">
      <j1 rule="hyper" parents="60 16679 21045"/>
    </justification>
  </clause>

  <clause id="21047">
    <literal><![CDATA[
      K(x,(T(y \ 1,z / y) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(8600(a,2),20969(a,1,2,1,1))].">
      <j1 rule="para" parents="8600 20969"/>
    </justification>
  </clause>

  <clause id="21048">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ T(u,z * y)) = K(x,u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(20980,a,20978,a)].">
      <j1 rule="hyper" parents="20980 20978"/>
    </justification>
  </clause>

  <clause id="21049">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((u \ 1) * z)) = K(x,((u \ 1) * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(16843,a,21048,a),flip(a)].">
      <j1 rule="hyper" parents="16843 21048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21051">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(((z / y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19887,a(flip),b,20981,a)].">
      <j1 rule="hyper" parents="60 19887 20981"/>
    </justification>
  </clause>

  <clause id="21052">
    <literal><![CDATA[
      T(x,T(1 / y,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16769,a(flip),b,20996,a)].">
      <j1 rule="hyper" parents="60 16769 20996"/>
    </justification>
  </clause>

  <clause id="21053">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(18260,a,21052,a)].">
      <j1 rule="hyper" parents="18260 21052"/>
    </justification>
  </clause>

  <clause id="21054">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(74(a,1),21052(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 21052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21055">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,T(y,y * z) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18960,a,b,21053,a)].">
      <j1 rule="hyper" parents="60 18960 21053"/>
    </justification>
  </clause>

  <clause id="21056">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z \ y) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,17811,a(flip),b,21053,a),flip(a)].">
      <j1 rule="hyper" parents="60 17811 21053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21057">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = u / T(u,T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(21053(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="21053 5701"/>
    </justification>
  </clause>

  <clause id="21058">
    <literal><![CDATA[
      (x * T(y,T(z,u) \ w)) / (x * y) = K(y,T(T(z \ 1,u) * w,x))
    ]]></literal>
    <justification jstring="[para(21053(a,1),8981(a,1,1,2))].">
      <j1 rule="para" parents="21053 8981"/>
    </justification>
  </clause>

  <clause id="21059">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,21057,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 21057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21060">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15646,a,21059,a),flip(a)].">
      <j1 rule="hyper" parents="15646 21059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      K(T(K(x,y) / z,u) \ w,v5) = K(T(z * K(y,x),u) * w,v5)
    ]]></literal>
    <justification jstring="[para(15284(a,1),21059(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15284 21059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      K(x / T(y \ 1,z),u) = K(T(y,z) * x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(17603,a,21060,a)].">
      <j1 rule="hyper" parents="17603 21060"/>
    </justification>
  </clause>

  <clause id="21063">
    <literal><![CDATA[
      K(x / T(y \ 1,z),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17164,a(flip),b,21062,a),flip(a)].">
      <j1 rule="hyper" parents="370 17164 21062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21064">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(77(a,1),21063(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 21063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6043,a(flip),b,21064,a)].">
      <j1 rule="hyper" parents="60 6043 21064"/>
    </justification>
  </clause>

  <clause id="21066">
    <literal><![CDATA[
      K((x / (y \ 1)) / T(x / (1 / y),z),u) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(18153,a,21065,a),flip(a)].">
      <j1 rule="hyper" parents="18153 21065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21067">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = u / T(u,x / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a(flip),b,21065,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 21065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21068">
    <literal><![CDATA[
      T(x,y * T(z \ 1,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(5733,a,21067,a)].">
      <j1 rule="hyper" parents="5733 21067"/>
    </justification>
  </clause>

  <clause id="21069">
    <literal><![CDATA[
      K(T(K(x,y) / z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * (T(z,u) * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(21061(a,2),20024(a,1))].">
      <j1 rule="para" parents="21061 20024"/>
    </justification>
  </clause>

  <clause id="21070">
    <literal><![CDATA[
      K(x,K(y * z,y * (u \ z))) = K(u,K(x,z * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,20568,a(flip),b,21066,a)].">
      <j1 rule="hyper" parents="60 20568 21066"/>
    </justification>
  </clause>

  <clause id="21071">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,L(T(x,u),u,z)) = K(y,(u * z) \ ((u * x) * z))
    ]]></literal>
    <justification jstring="[para(21070(a,1),20484(a,1,1))].">
      <j1 rule="para" parents="21070 20484"/>
    </justification>
  </clause>

  <clause id="21072">
    <literal><![CDATA[
      ((x \ y) \ (K(y,x) * z)) * (K(x,y) * K(x,y)) = ((K(x,y) \ 1) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(14015(a,1),20999(a,1,1))].">
      <j1 rule="para" parents="14015 20999"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      K(x / T((y \ 1) * z,y),u) = K(x / ((y \ 1) * T(z,y)),u)
    ]]></literal>
    <justification jstring="[para(2875(a,1),21007(a,1,1,2))].">
      <j1 rule="para" parents="2875 21007"/>
    </justification>
  </clause>

  <clause id="21074">
    <literal><![CDATA[
      K(x / T((y \ 1) * z,y),u) = K(x / (z * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18505,a(flip),b,21073,a),flip(a)].">
      <j1 rule="hyper" parents="370 18505 21073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21075">
    <literal><![CDATA[
      K(x,L((y \ K(z,u)) * w,v5,v6)) = K(x,L(K(z,u) * (y \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(18543,a,21024,a)].">
      <j1 rule="hyper" parents="18543 21024"/>
    </justification>
  </clause>

  <clause id="21076">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ (T(z * u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20863,a(flip),b,21038,a),flip(a)].">
      <j1 rule="hyper" parents="60 20863 21038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ w))) \ v5) = T(x,(y \ (z * K(w,z))) \ v5)
    ]]></literal>
    <justification jstring="[para(20258(a,2),21044(a,2,2,1))].">
      <j1 rule="para" parents="20258 21044"/>
    </justification>
  </clause>

  <clause id="21078">
    <literal><![CDATA[
      T(x,(y \ T(z,u \ (u \ (z \ w)))) \ v5) = T(x,(y \ (w / (w / z))) \ v5)
    ]]></literal>
    <justification jstring="[para(20261(a,2),21044(a,2,2,1))].">
      <j1 rule="para" parents="20261 21044"/>
    </justification>
  </clause>

  <clause id="21079">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * u) \ w) = K(x,(T(y \ 1,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(6(a,1),21047(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 21047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21080">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(y * ((y \ z) \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18562,a(flip),b,21051,a),flip(a)].">
      <j1 rule="hyper" parents="370 18562 21051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21081">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8983,a,21058,a),flip(a)].">
      <j1 rule="hyper" parents="8983 21058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      K(x,T(T(T(y \ 1,z),y) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14730,a,b,21081,a)].">
      <j1 rule="hyper" parents="60 14730 21081"/>
    </justification>
  </clause>

  <clause id="21083">
    <literal><![CDATA[
      K(x,T(T(1 / y,z) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(958(a,1),21082(a,1,2,1,1))].">
      <j1 rule="para" parents="958 21082"/>
    </justification>
  </clause>

  <clause id="21084">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z) \ u,w)) = K(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(74(a,1),21083(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 21083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21085">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,L(K(y,z) * (y \ u),y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20321,a,b,21075,a)].">
      <j1 rule="hyper" parents="60 20321 21075"/>
    </justification>
  </clause>

  <clause id="21086">
    <literal><![CDATA[
      K(x,(y \ z) * ((y \ z) * (z \ u))) = K(x,(y * (1 / (y \ z))) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5587,a,b,21080,a),flip(a)].">
      <j1 rule="hyper" parents="370 5587 21080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21087">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z)) * ((L(y,z,z) \ u) * a(y,z,z))) = K(x,(y * (1 / (y \ L(y,z,z)))) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20444,a(flip),b,21086,a)].">
      <j1 rule="hyper" parents="60 20444 21086"/>
    </justification>
  </clause>

  <clause id="21088">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19896,a,20783,a),flip(a)].">
      <j1 rule="hyper" parents="19896 20783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21090">
    <literal><![CDATA[
      K(x,(y * T((z / u) * w,K(u,u \ z))) \ v5) = K(x,K(u \ z,u) * ((y * ((u \ z) * w)) \ v5))
    ]]></literal>
    <justification jstring="[para(8566(a,2),21088(a,1,2,1,2))].">
      <j1 rule="para" parents="8566 21088"/>
    </justification>
  </clause>

  <clause id="21091">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((u * w) \ v5)) = K(x,((K(z,y) * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(12966(a,1),20806(a,1,2,1))].">
      <j1 rule="para" parents="12966 20806"/>
    </justification>
  </clause>

  <clause id="21092">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) \ v5) = K(x,K(z,y) * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19896,a,21091,a),flip(a)].">
      <j1 rule="hyper" parents="19896 21091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21094">
    <literal><![CDATA[
      K(x,K(y,z) * (((y \ u) * w) \ v5)) = K(x,((T(y,z) \ u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(7873(a,1),21092(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 21092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21095">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) \ v5)) = K(x,K(u,z) * (y \ (T(z,u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(17749,a,20810,a),flip(a)].">
      <j1 rule="hyper" parents="17749 20810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21096">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) \ w)) = K(x,y \ (T(z,K(u,v5)) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20809,a(flip),b,21095,a)].">
      <j1 rule="hyper" parents="370 20809 21095"/>
    </justification>
  </clause>

  <clause id="21097">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u),u) \ w)) = K(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,19511,a(flip),b,21096,a),flip(a)].">
      <j1 rule="hyper" parents="370 19511 21096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21099">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(109(a,1),21097(a,1,2,2,1,1))].">
      <j1 rule="para" parents="109 21097"/>
    </justification>
  </clause>

  <clause id="21100">
    <literal><![CDATA[
      K(x,y \ (T((1 / z) / u,z * z) \ w)) = K(x,y \ (((z / u) / (z * z)) \ w))
    ]]></literal>
    <justification jstring="[para(1001(a,1),21099(a,1,2,2,1,1))].">
      <j1 rule="para" parents="1001 21099"/>
    </justification>
  </clause>

  <clause id="21102">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,u \ (w * z))),v6)
    ]]></literal>
    <justification jstring="[para(11181(a,1),20844(a,2,1,2,2))].">
      <j1 rule="para" parents="11181 20844"/>
    </justification>
  </clause>

  <clause id="21103">
    <literal><![CDATA[
      K(x,T(y,z / ((u \ 1) * w)) * v5) = K(x,T(y,w * (u \ z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(20875,a,20910,a),flip(a)].">
      <j1 rule="hyper" parents="20875 20910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21104">
    <literal><![CDATA[
      K(x,T(y,((z \ 1) * u) * w) * v5) = K(x,T(y,u * (z \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18474,a(flip),b,21103,a)].">
      <j1 rule="hyper" parents="60 18474 21103"/>
    </justification>
  </clause>

  <clause id="21105">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w) * v5) = K(x,T(y,u * (z \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18856,a,21104,a)].">
      <j1 rule="hyper" parents="18856 21104"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      K(x,T(y,z * ((u \ 1) \ w)) * v5) = K(x,T(y,w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(18854,a,21105,a),flip(a)].">
      <j1 rule="hyper" parents="18854 21105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21107">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) * v5) = K(x,T(y,u * (z * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,18518,a(flip),b,21106,a)].">
      <j1 rule="hyper" parents="60 18518 21106"/>
    </justification>
  </clause>

  <clause id="21108">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ ((z * y) / z)) * w)) = K(x,y \ ((u \ y) * w))
    ]]></literal>
    <justification jstring="[para(7858(a,1),20951(a,2,2))].">
      <j1 rule="para" parents="7858 20951"/>
    </justification>
  </clause>

  <clause id="21109">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,y)) \ w) = T(x,(u \ ((y \ z) \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20995,a(flip),b,21004,a)].">
      <j1 rule="hyper" parents="60 20995 21004"/>
    </justification>
  </clause>

  <clause id="21111">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / T(u,y)) \ w) = T(x,(u \ T(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(108(a,2),21109(a,2,2,1,2))].">
      <j1 rule="para" parents="108 21109"/>
    </justification>
  </clause>

  <clause id="21112">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ ((z \ u) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21109,a(flip),b,21111,a),flip(a)].">
      <j1 rule="hyper" parents="60 21109 21111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) = T(x,((y \ z) \ 1) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20090,a(flip),b,21056,a),flip(a)].">
      <j1 rule="hyper" parents="370 20090 21056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21114">
    <literal><![CDATA[
      T(x,(y \ (z / (z / u))) \ w) = T(x,(y \ (u * K(u \ z,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21077,a(flip),b,21078,a),flip(a)].">
      <j1 rule="hyper" parents="60 21077 21078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21115">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ (u / (u / z))) \ w)
    ]]></literal>
    <justification jstring="[para(7508(a,1),21078(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7508 21078"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      K(x \ (y * T(z,T(u \ w,v5))),v6) = K(x \ (y * T(z,u * (w * z))),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,18607,a(flip),b,21102,a),flip(a)].">
      <j1 rule="hyper" parents="370 18607 21102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,z * y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(21113(a,2),15260(a,1))].">
      <j1 rule="para" parents="21113 15260"/>
    </justification>
  </clause>

  <clause id="21118">
    <literal><![CDATA[
      K(x \ (y * T(z,u * (w * z))),v5) = K(x \ (y * T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20790,a(flip),b,21116,a),flip(a)].">
      <j1 rule="hyper" parents="60 20790 21116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21119">
    <literal><![CDATA[
      K(x \ (y * T(z,u * (w * z))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y * T(z,u * w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(21118(a,2),18608(a,1))].">
      <j1 rule="para" parents="21118 18608"/>
    </justification>
  </clause>

  <clause id="21121">
    <literal><![CDATA[
      T(x,y \ (z \ T(a(u,u,u) * w,u \ 1))) = T(x,y \ (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(3(a,1),21046(a,2,2,2,2,2))].">
      <j1 rule="para" parents="3 21046"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(x,L(T(y,u),u,z)) = K(x,(u * z) \ ((u * y) * z))
    ]]></literal>
    <justification jstring="[para(8630(a,1),21071(a,1,1))].">
      <j1 rule="para" parents="8630 21071"/>
    </justification>
  </clause>

  <clause id="21123">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,(T(z,y) * y) \ (z * u))
    ]]></literal>
    <justification jstring="[para(12495(a,1),21085(a,2,2))].">
      <j1 rule="para" parents="12495 21085"/>
    </justification>
  </clause>

  <clause id="21124">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (z * ((y * y) \ u))) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,16812,a(flip),b,21123,a),flip(a)].">
      <j1 rule="hyper" parents="370 16812 21123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21125">
    <literal><![CDATA[
      K(x,(y \ z) \ ((((1 / y) \ 1) \ (y \ z)) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,20613,a,b,21124,a)].">
      <j1 rule="hyper" parents="60 20613 21124"/>
    </justification>
  </clause>

  <clause id="21126">
    <literal><![CDATA[
      K(x,(y \ z) \ ((y \ (y \ z)) * u)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(77(a,1),21125(a,1,2,2,1,1))].">
      <j1 rule="para" parents="77 21125"/>
    </justification>
  </clause>

  <clause id="21127">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) \ ((((u * z) / u) \ (((u * z) / u) \ (y * (z * K(u,z))))) * w)) = K(x,(((u * z) / u) * (y * (z * K(u,z)))) \ ((y * (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(10005(a,1),21126(a,1,2,1))].">
      <j1 rule="para" parents="10005 21126"/>
    </justification>
  </clause>

  <clause id="21128">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) = K(x,(z * u) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(20609,a,21122,a)].">
      <j1 rule="hyper" parents="20609 21122"/>
    </justification>
  </clause>

  <clause id="21129">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * u)) = K(x,(u * y) \ ((u * z) * y))
    ]]></literal>
    <justification jstring="[hyper(10031,a,21128,a)].">
      <j1 rule="hyper" parents="10031 21128"/>
    </justification>
  </clause>

  <clause id="21130">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ (((y \ z) * u) * y)) = K(x,(y * (u * (y \ z))) / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),21129(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 21129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      K(x,(y * (z * (y \ u))) / u) = K(x,u \ (((u / y) * z) * y))
    ]]></literal>
    <justification jstring="[para(12802(a,1),21130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12802 21130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21132">
    <literal><![CDATA[
      x * K(y,x \ (((x / z) * u) * z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(21131(a,1),17570(a,1,2))].">
      <j1 rule="para" parents="21131 17570"/>
    </justification>
  </clause>

  <clause id="21133">
    <literal><![CDATA[
      K(K(x,y) * ((z * y) \ u),w) = K((z * T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(6(a,1),20798(a,1,1,2))].">
      <j1 rule="para" parents="6 20798"/>
    </justification>
  </clause>

  <clause id="21134">
    <literal><![CDATA[
      K(((x * y) * T(y,x)) \ z,u) = K((y * (x * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14528,a(flip),b,21133,a),flip(a)].">
      <j1 rule="hyper" parents="60 14528 21133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      K(((x * y) * x) \ z,u) = K((x * (y * x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(1173(a,1),21134(a,1,1,1))].">
      <j1 rule="para" parents="1173 21134"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),1 / z)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[para(2104(a,1),20909(a,2,2,2))].">
      <j1 rule="para" parents="2104 20909"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,y \ 1),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17855,a,21002,a)].">
      <j1 rule="hyper" parents="17855 21002"/>
    </justification>
  </clause>

  <clause id="21139">
    <literal><![CDATA[
      K(x,L(T(y,z) * T(u,y * 1),w,v5)) = K(x,L(u / T(y \ 1,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(18406,a,21138,a)].">
      <j1 rule="hyper" parents="18406 21138"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(T(z,u) * T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(3(a,1),21139(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 21139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21141">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(K(z,u) * (y * z),w,v5))
    ]]></literal>
    <justification jstring="[para(7861(a,2),21140(a,2,2,1))].">
      <j1 rule="para" parents="7861 21140"/>
    </justification>
  </clause>

  <clause id="21142">
    <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(370,a,17852,a(flip),b,21141,a),flip(a)].">
      <j1 rule="hyper" parents="370 17852 21141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21143">
    <literal><![CDATA[
      K(x,L(y / (z \ K(u,z \ 1)),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,20365,a,b,21142,a)].">
      <j1 rule="hyper" parents="60 20365 21142"/>
    </justification>
  </clause>

  <clause id="21144">
    <literal><![CDATA[
      K(x,L(y * (K(z \ 1,u) * z),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(15725,a,21143,a)].">
      <j1 rule="hyper" parents="15725 21143"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      K(x,L(y * (z * K(z \ 1,u)),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2373(a,1),21144(a,1,2,1,2))].">
      <j1 rule="para" parents="2373 21144"/>
    </justification>
  </clause>

  <clause id="21146">
    <literal><![CDATA[
      K(x,L(y * ((z / u) * K((z / u) \ 1,u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(109(a,1),21145(a,2,2,1,2))].">
      <j1 rule="para" parents="109 21145"/>
    </justification>
  </clause>

  <clause id="21147">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(w,u * K(z,y))) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(17512(a,1),21015(a,1,2))].">
      <j1 rule="para" parents="17512 21015"/>
    </justification>
  </clause>

  <clause id="21148">
    <literal><![CDATA[
      K(x,y \ (((z / u) / (z * z)) \ w)) = K(x,y \ (((1 / z) / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20884,a(flip),b,21100,a),flip(a)].">
      <j1 rule="hyper" parents="60 20884 21100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21150">
    <literal><![CDATA[
      K(x,y \ ((z * z) * ((z / u) \ w))) = K(x,y \ (((1 / z) / u) \ w))
    ]]></literal>
    <justification jstring="[para(512(a,1),21148(a,1,2,2))].">
      <j1 rule="para" parents="512 21148"/>
    </justification>
  </clause>

  <clause id="21151">
    <literal><![CDATA[
      K(x,y * (y * (z \ ((y / u) \ w)))) = K(x,z \ (((1 / y) / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20977,a(flip),b,21150,a)].">
      <j1 rule="hyper" parents="60 20977 21150"/>
    </justification>
  </clause>

  <clause id="21152">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),z * 1)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18405,a(flip),b,21137,a)].">
      <j1 rule="hyper" parents="60 18405 21137"/>
    </justification>
  </clause>

  <clause id="21153">
    <literal><![CDATA[
      K(x,L(y * ((z / u) * K(z \ u,u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(8222(a,1),21146(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8222 21146"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      K(x,L(y * (z / T(u,z \ u)),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(5855(a,1),21153(a,1,2,1,2))].">
      <j1 rule="para" parents="5855 21153"/>
    </justification>
  </clause>

  <clause id="21155">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ w)) * K(x,K(w,u)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(17980(a,1),21147(a,1,2))].">
      <j1 rule="para" parents="17980 21147"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,K(u,w) * (z \ y)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14360(a,1),21155(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14360 21155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21158">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,21155,a(flip),b,21156,a),flip(a)].">
      <j1 rule="hyper" parents="370 21155 21156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21159">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(20326,a,21158,a)].">
      <j1 rule="hyper" parents="20326 21158"/>
    </justification>
  </clause>

  <clause id="21160">
    <literal><![CDATA[
      K(x,y / (z / T(u,u \ w))) = K(x,y * ((z / u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17836,a(flip),b,21158,a)].">
      <j1 rule="hyper" parents="60 17836 21158"/>
    </justification>
  </clause>

  <clause id="21161">
    <literal><![CDATA[
      K(x,y * (z \ K(u * w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20219,a,b,21159,a),flip(a)].">
      <j1 rule="hyper" parents="370 20219 21159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21162">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y * ((w * u) \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20309,a,b,21161,a)].">
      <j1 rule="hyper" parents="60 20309 21161"/>
    </justification>
  </clause>

  <clause id="21163">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(z * u) * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20300,a,b,21161,a)].">
      <j1 rule="hyper" parents="60 20300 21161"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y * (((u \ 1) * z) \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(15801(a,1),21161(a,1,2,2))].">
      <j1 rule="para" parents="15801 21161"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      K(x,y / (z / T(u,u \ w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17836,a(flip),b,21160,a),flip(a)].">
      <j1 rule="hyper" parents="370 17836 21160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21166">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / (w * z)) = K(x,(z * u) / (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17837,a(flip),b,21163,a),flip(a)].">
      <j1 rule="hyper" parents="370 17837 21163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      K(x,y / T((z / (z / u)) * w,u)) = K(x,y / (w * T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17837,a(flip),b,21162,a),flip(a)].">
      <j1 rule="hyper" parents="370 17837 21162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21168">
    <literal><![CDATA[
      K(x,y / (z * (u * K(u \ w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18522,a(flip),b,21167,a)].">
      <j1 rule="hyper" parents="60 18522 21167"/>
    </justification>
  </clause>

  <clause id="21169">
    <literal><![CDATA[
      K(x,y / (z * ((u \ w) \ w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20250,a,b,21168,a)].">
      <j1 rule="hyper" parents="60 20250 21168"/>
    </justification>
  </clause>

  <clause id="21170">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) \ w) = K(x,K(w,y * z)) * K(x,w / (y * T(z,u)))
    ]]></literal>
    <justification jstring="[para(21169(a,1),18012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21169 18012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y / ((u \ 1) * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20221,a(flip),b,21164,a),flip(a)].">
      <j1 rule="hyper" parents="370 20221 21164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21172">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ 1)) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18479,a(flip),b,21171,a),flip(a)].">
      <j1 rule="hyper" parents="370 18479 21171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21173">
    <literal><![CDATA[
      K(x,y / L(z / u,u,u)) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15472,a,21172,a)].">
      <j1 rule="hyper" parents="15472 21172"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      K(x,y / L(K(z,u) * (u / w),w,w)) = K(x,y / (((z * u) / z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(15604(a,1),21173(a,1,2,2,1))].">
      <j1 rule="para" parents="15604 21173"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / (((u * z) / u) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(20327,a,21174,a)].">
      <j1 rule="hyper" parents="20327 21174"/>
    </justification>
  </clause>

  <clause id="21176">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / ((u * z) / (u * u)))
    ]]></literal>
    <justification jstring="[para(1105(a,1),21175(a,2,2,2))].">
      <j1 rule="para" parents="1105 21175"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y / (u * (z / (u * u))))
    ]]></literal>
    <justification jstring="[para(1098(a,1),21176(a,2,2,2))].">
      <j1 rule="para" parents="1098 21176"/>
    </justification>
  </clause>

  <clause id="21178">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) = K(x,y * ((u * z) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18340,a(flip),b,21177,a),flip(a)].">
      <j1 rule="hyper" parents="370 18340 21177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21179">
    <literal><![CDATA[
      K(x,y * (L(z / u,u,u) \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(21178(a,2),18146(a,1))].">
      <j1 rule="para" parents="21178 18146"/>
    </justification>
  </clause>

  <clause id="21180">
    <literal><![CDATA[
      T(x,y / T(T(z \ ((z \ 1) \ u),z),z)) = T(x,y / (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[para(3(a,1),21152(a,1,2,2,2))].">
      <j1 rule="para" parents="3 21152"/>
    </justification>
  </clause>

  <clause id="21181">
    <literal><![CDATA[
      T(x,y / (z \ ((1 / z) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ ((z \ 1) \ u))) = w
    ]]></literal>
    <justification jstring="[para(21180(a,1),17464(a,1))].">
      <j1 rule="para" parents="21180 17464"/>
    </justification>
  </clause>

  <clause id="21182">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) \ w) = K(x,(y * T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,18011,a(flip),b,21170,a),flip(a)].">
      <j1 rule="hyper" parents="370 18011 21170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      K(x,(y * T(z,u * z)) \ w) = K(x,(y * T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5821(a,2),21182(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5821 21182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21184">
    <literal><![CDATA[
      K(x,(y * T(z \ 1,u * z)) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6851(a,2),21182(a,1,2,1,2))].">
      <j1 rule="para" parents="6851 21182"/>
    </justification>
  </clause>

  <clause id="21185">
    <literal><![CDATA[
      K(x,T(T(y,y * T(z \ 1,u * z)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5606(a,2),21184(a,1,2,1))].">
      <j1 rule="para" parents="5606 21184"/>
    </justification>
  </clause>

  <clause id="21186">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,T(z,y),z * y)) = K(x,z \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16734,a(flip),b,20972,a),flip(a)].">
      <j1 rule="hyper" parents="60 16734 20972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21188">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ (K(v6,v7) \ v8)) = K(x,K(z,u) \ ((K(v7,v6) \ y) \ v8))
    ]]></literal>
    <justification jstring="[hyper(60,a,19440,a(flip),b,21011,a)].">
      <j1 rule="hyper" parents="60 19440 21011"/>
    </justification>
  </clause>

  <clause id="21189">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(u,w) \ v5) \ v6)) = K(x,K(y,z) \ (v5 \ (K(w,u) \ v6)))
    ]]></literal>
    <justification jstring="[hyper(21009,a,21188,a),flip(a)].">
      <j1 rule="hyper" parents="21009 21188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21190">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (K(z,L(y,w,v5)) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,20948,a(flip),b,21189,a),flip(a)].">
      <j1 rule="hyper" parents="60 20948 21189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21191">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (L(K(z,y),w,v5) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(11013(a,1),21190(a,1,2,2,2,1))].">
      <j1 rule="para" parents="11013 21190"/>
    </justification>
  </clause>

  <clause id="21192">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (L(K(u,z),w,v5) \ v6))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,20775,a(flip),b,21191,a)].">
      <j1 rule="hyper" parents="60 20775 21191"/>
    </justification>
  </clause>

  <clause id="21193">
    <literal><![CDATA[
      K(x,y \ (a(K(z,u),w,v5) \ v6)) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(21023(a,1),21192(a,1,2,2))].">
      <j1 rule="para" parents="21023 21192"/>
    </justification>
  </clause>

  <clause id="21194">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(19395(a,1),21193(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19395 21193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21195">
    <literal><![CDATA[
      K(x,(y * (a(z,u,K(w,v5)) / v6)) \ y) = L(K(x,v6),a(z,u,K(w,v5)),y)
    ]]></literal>
    <justification jstring="[hyper(11207,a,21194,a),flip(a)].">
      <j1 rule="hyper" parents="11207 21194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21196">
    <literal><![CDATA[
      L(K(x,y),a(z,u,K(w,v5)),v6) = K(x,y / a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(9142,a,21195,a),flip(a)].">
      <j1 rule="hyper" parents="9142 21195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21197">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(21196(a,1),645(a,1)),flip(b)].">
      <j1 rule="para" parents="21196 645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21198">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(19388(a,1),21197(a,1,2))].">
      <j1 rule="para" parents="19388 21197"/>
    </justification>
  </clause>

  <clause id="21199">
    <literal><![CDATA[
      K(x,T(y * a(z,u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,v6)) = v7
    ]]></literal>
    <justification jstring="[para(20676(a,2),21198(a,1,2))].">
      <j1 rule="para" parents="20676 21198"/>
    </justification>
  </clause>

  <clause id="21200">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (v5 \ ((y * u) * w))) = K(x,v5 \ (T(R(y,u,w),z) * (u * w)))
    ]]></literal>
    <justification jstring="[para(16407(a,1),20864(a,1,2,1))].">
      <j1 rule="para" parents="16407 20864"/>
    </justification>
  </clause>

  <clause id="21201">
    <literal><![CDATA[
      K(x,y * T(z * T(z \ u,w),z)) = K(x,y * (T(z,T(u,w)) * T(z \ u,w)))
    ]]></literal>
    <justification jstring="[para(18640(a,1),20882(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18640 20882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21202">
    <literal><![CDATA[
      K(x,y * T(z * T(z \ u,w),z)) = K(x,y * (T(z,u) * T(z \ u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,19470,a(flip),b,21201,a),flip(a)].">
      <j1 rule="hyper" parents="370 19470 21201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21204">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) = K(x,y * (T(z \ u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14423,a(flip),b,21202,a),flip(a)].">
      <j1 rule="hyper" parents="60 14423 21202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21205">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(z \ u,w))) = K(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16864,a(flip),b,21204,a),flip(a)].">
      <j1 rule="hyper" parents="370 16864 21204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21206">
    <literal><![CDATA[
      K(x,y * (K(z,u * w) * T(w,u))) = K(x,y * (u * T(w / u,z)))
    ]]></literal>
    <justification jstring="[hyper(20120,a,21205,a)].">
      <j1 rule="hyper" parents="20120 21205"/>
    </justification>
  </clause>

  <clause id="21207">
    <literal><![CDATA[
      K(x,y * (T(z,u) * K(w,z * u))) = K(x,y * (u * T(z / u,w)))
    ]]></literal>
    <justification jstring="[para(17437(a,2),21206(a,1,2,2))].">
      <j1 rule="para" parents="17437 21206"/>
    </justification>
  </clause>

  <clause id="21208">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(z,u)) = K(x,y * (u * T(z / u,y)))
    ]]></literal>
    <justification jstring="[hyper(17305,a,21207,a)].">
      <j1 rule="hyper" parents="17305 21207"/>
    </justification>
  </clause>

  <clause id="21209">
    <literal><![CDATA[
      K(x,T(y / z,u * w) * T(u,w)) = K(x,(y / z) * (w * T(u / w,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17777,a(flip),b,21208,a),flip(a)].">
      <j1 rule="hyper" parents="370 17777 21208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21210">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20878,a(flip),b,21209,a)].">
      <j1 rule="hyper" parents="60 20878 21209"/>
    </justification>
  </clause>

  <clause id="21211">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y * 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18589,a(flip),b,21210,a),flip(a)].">
      <j1 rule="hyper" parents="370 18589 21210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21212">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(1 / y) * (u * T(z / u,y)))
    ]]></literal>
    <justification jstring="[para(3(a,1),21211(a,2,2,2,2,2))].">
      <j1 rule="para" parents="3 21211"/>
    </justification>
  </clause>

  <clause id="21213">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u * T(z / u,y))) = w
    ]]></literal>
    <justification jstring="[para(21212(a,2),15461(a,1))].">
      <j1 rule="para" parents="21212 15461"/>
    </justification>
  </clause>

  <clause id="21214">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(y \ 1,y * w)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12555(a,1),20905(a,1,2,2))].">
      <j1 rule="para" parents="12555 20905"/>
    </justification>
  </clause>

  <clause id="21215">
    <literal><![CDATA[
      K(x,y \ ((z * (K(u,w) * K(u,w))) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,19878,a(flip),b,21000,a),flip(a)].">
      <j1 rule="hyper" parents="370 19878 21000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21217">
    <literal><![CDATA[
      K(x,y \ (z * ((K(u,w) * K(u,w)) * v5))) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),21215(a,1,2,2))].">
      <j1 rule="para" parents="29 21215"/>
    </justification>
  </clause>

  <clause id="21218">
    <literal><![CDATA[
      K(x,y \ ((z * (u * K(w,u))) * v5)) = K(x,y \ ((z * T(u,w)) * v5))
    ]]></literal>
    <justification jstring="[para(7941(a,1),21217(a,1,2,2))].">
      <j1 rule="para" parents="7941 21217"/>
    </justification>
  </clause>

  <clause id="21219">
    <literal><![CDATA[
      K(x,T(y,T(z,u * w) \ v5) \ (T(z,u * w) \ v5)) = K(x,(T(z,u \ w) \ v5) / y)
    ]]></literal>
    <justification jstring="[para(18296(a,1),21040(a,1,2,1))].">
      <j1 rule="para" parents="18296 21040"/>
    </justification>
  </clause>

  <clause id="21220">
    <literal><![CDATA[
      K(x,y \ (T(R(z,u,w),v5) * (u * w))) = K(x,K(z,v5) * (y \ ((z * u) * w)))
    ]]></literal>
    <justification jstring="[hyper(19896,a,21200,a),flip(a)].">
      <j1 rule="hyper" parents="19896 21200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21222">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(687(a,1),21220(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="687 21220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21223">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((T(z,u) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20862,a(flip),b,21222,a)].">
      <j1 rule="hyper" parents="60 20862 21222"/>
    </justification>
  </clause>

  <clause id="21224">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20423,a(flip),b,21223,a),flip(a)].">
      <j1 rule="hyper" parents="370 20423 21223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21225">
    <literal><![CDATA[
      K(x,y \ (T(z * u,z) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21076,a(flip),b,21224,a)].">
      <j1 rule="hyper" parents="60 21076 21224"/>
    </justification>
  </clause>

  <clause id="21226">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ ((u * K(u \ z,u)) * w))
    ]]></literal>
    <justification jstring="[para(5837(a,2),21224(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5837 21224"/>
    </justification>
  </clause>

  <clause id="21227">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),21225(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 21225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21228">
    <literal><![CDATA[
      K(x,y \ (T(z / (z \ u),z) * w)) = K(x,y \ (((((u \ z) \ 1) \ 1) * z) * w))
    ]]></literal>
    <justification jstring="[para(3510(a,1),21225(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3510 21225"/>
    </justification>
  </clause>

  <clause id="21229">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z \ 1) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(1576(a,1),21227(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1576 21227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21230">
    <literal><![CDATA[
      K(x,y \ (((z \ (L(z,u,z) * u)) * z) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(5548(a,1),21227(a,2,2,2,1))].">
      <j1 rule="para" parents="5548 21227"/>
    </justification>
  </clause>

  <clause id="21231">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u \ z)) * w)) = K(x,y \ ((z / T(u \ 1,z)) * w))
    ]]></literal>
    <justification jstring="[para(18985(a,1),21227(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18985 21227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21232">
    <literal><![CDATA[
      K(x,y \ ((z * L(u,z,u)) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(10585(a,1),21230(a,1,2,2,1))].">
      <j1 rule="para" parents="10585 21230"/>
    </justification>
  </clause>

  <clause id="21233">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * z) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20425,a,b,21232,a)].">
      <j1 rule="hyper" parents="60 20425 21232"/>
    </justification>
  </clause>

  <clause id="21234">
    <literal><![CDATA[
      K(x,y \ ((T(z,z * u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(5485(a,1),21233(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5485 21233"/>
    </justification>
  </clause>

  <clause id="21235">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,T(y * (y * z),y) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16824,a(flip),b,21234,a)].">
      <j1 rule="hyper" parents="60 16824 21234"/>
    </justification>
  </clause>

  <clause id="21236">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (u * (K(u \ z,u) * w)))
    ]]></literal>
    <justification jstring="[para(7845(a,1),21226(a,2,2,2))].">
      <j1 rule="para" parents="7845 21226"/>
    </justification>
  </clause>

  <clause id="21237">
    <literal><![CDATA[
      K(x,y \ (T(z \ u,z * 1) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18696,a(flip),b,21229,a)].">
      <j1 rule="hyper" parents="60 18696 21229"/>
    </justification>
  </clause>

  <clause id="21238">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (T(u,u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16948,a(flip),b,21236,a),flip(a)].">
      <j1 rule="hyper" parents="370 16948 21236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21239">
    <literal><![CDATA[
      K(x,y \ (T(z / (z / u),u) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15730,a(flip),b,21238,a),flip(a)].">
      <j1 rule="hyper" parents="370 15730 21238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21240">
    <literal><![CDATA[
      K(x,y \ ((z / (z / u)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(418(a,1),21239(a,1,2,2,1))].">
      <j1 rule="para" parents="418 21239"/>
    </justification>
  </clause>

  <clause id="21241">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,K(w,z * u)) * K(x,w \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(21240(a,1),20404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21240 20404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21242">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z \ 1)) * w)) = K(x,y \ (T(z \ u,z) * w))
    ]]></literal>
    <justification jstring="[para(3(a,1),21237(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 21237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21243">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z \ 1)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,16950,a(flip),b,21242,a),flip(a)].">
      <j1 rule="hyper" parents="370 16950 21242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21244">
    <literal><![CDATA[
      K(x,y \ (((((z \ u) \ 1) \ 1) * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((u \ z) \ u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(21228(a,1),15732(a,1))].">
      <j1 rule="para" parents="21228 15732"/>
    </justification>
  </clause>

  <clause id="21245">
    <literal><![CDATA[
      K(x,((y / (y / z)) * u) / w) = K(x,(T(z,y) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(370,a,18014,a(flip),b,21241,a),flip(a)].">
      <j1 rule="hyper" parents="370 18014 21241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21246">
    <literal><![CDATA[
      K(x,(T(y,z) * u) / (w * y)) = K(x,(y * u) / (w * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,21166,a(flip),b,21245,a),flip(a)].">
      <j1 rule="hyper" parents="60 21166 21245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21247">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = K(x,(y * u) / (z * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(20987,a,21246,a)].">
      <j1 rule="hyper" parents="20987 21246"/>
    </justification>
  </clause>

  <clause id="21248">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (z / y)) = K(x,(y * u) / (y * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),21247(a,2,2,2))].">
      <j1 rule="para" parents="107 21247"/>
    </justification>
  </clause>

  <clause id="21249">
    <literal><![CDATA[
      K(x,(T(y,(z / y) \ 1) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,18765,a(flip),b,21248,a),flip(a)].">
      <j1 rule="hyper" parents="370 18765 21248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21250">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(y,y * w)) = K(x,(T(y \ 1,y \ w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17485,a,21214,a)].">
      <j1 rule="hyper" parents="17485 21214"/>
    </justification>
  </clause>

  <clause id="21251">
    <literal><![CDATA[
      K(x,(T(y \ 1,y \ z) * u) \ w) = K(x,(((1 / y) * u) \ w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17626,a,21250,a),flip(a)].">
      <j1 rule="hyper" parents="17626 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21252">
    <literal><![CDATA[
      K(x,(((1 / y) * z) \ u) * K(w,y)) = K(x,(T(y \ 1,w) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20969,a(flip),b,21251,a),flip(a)].">
      <j1 rule="hyper" parents="60 20969 21251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21253">
    <literal><![CDATA[
      K(x,(T(y \ 1,z) * T(u,y)) \ w) = K(x,(((y * y) \ u) * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20888,a(flip),b,21252,a),flip(a)].">
      <j1 rule="hyper" parents="60 20888 21252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21254">
    <literal><![CDATA[
      K(x,(T(y,z \ u) \ w) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z * u) \ w) / v5) = v6
    ]]></literal>
    <justification jstring="[para(21219(a,1),14575(a,1))].">
      <j1 rule="para" parents="21219 14575"/>
    </justification>
  </clause>

  <clause id="21255">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) * (K(z,y) * K(z,y)) = x \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11393(a,1),21005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11393 21005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21256">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = (x \ y) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21072,a(flip),b,21255,a)].">
      <j1 rule="hyper" parents="60 21072 21255"/>
    </justification>
  </clause>

  <clause id="21259">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(5865(a,1),21256(a,1,1,1))].">
      <j1 rule="para" parents="5865 21256"/>
    </justification>
  </clause>

  <clause id="21260">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(7873(a,1),21259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 21259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21261">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ z) \ L(K(y,z) * u,y,y)) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(21260(a,1),17048(a,2,2))].">
      <j1 rule="para" parents="21260 17048"/>
    </justification>
  </clause>

  <clause id="21262">
    <literal><![CDATA[
      K(x,K(y,z) * ((L(y,y,K(y,z) * u) \ z) \ L(u,y,y))) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20811,a(flip),b,21261,a)].">
      <j1 rule="hyper" parents="60 20811 21261"/>
    </justification>
  </clause>

  <clause id="21263">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y)) \ L(u,y,y)) = K(x,(T(y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20784,a(flip),b,21262,a)].">
      <j1 rule="hyper" parents="60 20784 21262"/>
    </justification>
  </clause>

  <clause id="21264">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ L(u,z,z)) = K(x,(T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20896,a(flip),b,21263,a)].">
      <j1 rule="hyper" parents="60 20896 21263"/>
    </justification>
  </clause>

  <clause id="21265">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ L(u,z,z)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20894,a(flip),b,21264,a),flip(a)].">
      <j1 rule="hyper" parents="370 20894 21264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21266">
    <literal><![CDATA[
      K(x / (T(y,y \ 1) * ((y * y) \ z)),u) = K(x / T((y \ 1) * T(z,y),y),u)
    ]]></literal>
    <justification jstring="[para(4437(a,1),20928(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4437 20928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21267">
    <literal><![CDATA[
      K(x / (T(y,y \ 1) * ((y * y) \ z)),u) = K(x / (T(z,y) * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21074,a(flip),b,21266,a),flip(a)].">
      <j1 rule="hyper" parents="370 21074 21266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21268">
    <literal><![CDATA[
      K(x / (T(y,z) * (z \ 1)),u) = K(x / ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(9801(a,1),21267(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9801 21267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21269">
    <literal><![CDATA[
      K(x / (T(y,z) * (z \ 1)),u) = K(x / ((z \ 1) * y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6204,a(flip),b,21268,a),flip(a)].">
      <j1 rule="hyper" parents="370 6204 21268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21270">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / ((y \ 1) * ((y \ 1) \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17061,a,b,21269,a)].">
      <j1 rule="hyper" parents="60 17061 21269"/>
    </justification>
  </clause>

  <clause id="21271">
    <literal><![CDATA[
      K(x,(y \ 1) * ((y \ 1) * ((1 / L(y,z,z)) \ u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19887,a(flip),b,20982,a)].">
      <j1 rule="hyper" parents="60 19887 20982"/>
    </justification>
  </clause>

  <clause id="21272">
    <literal><![CDATA[
      K(x,((y \ 1) * (T(T(y,z),z) \ u)) \ w) = K(x,y * (T(T(y,z),z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(18951(a,1),21006(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18951 21006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21273">
    <literal><![CDATA[
      K(x,((y \ 1) * (T(T(y,z),z) \ u)) \ w) = K(x,y * (y * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16944,a(flip),b,21272,a),flip(a)].">
      <j1 rule="hyper" parents="370 16944 21272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21275">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(16912(a,1),21016(a,1,1))].">
      <j1 rule="para" parents="16912 21016"/>
    </justification>
  </clause>

  <clause id="21276">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y * K(z,y \ 1))) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(16735(a,1),21275(a,1,1))].">
      <j1 rule="para" parents="16735 21275"/>
    </justification>
  </clause>

  <clause id="21277">
    <literal><![CDATA[
      K(x,T(y,z) \ u) * K(x,K(u,y)) = K(x,u * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(17980(a,1),21276(a,1,2))].">
      <j1 rule="para" parents="17980 21276"/>
    </justification>
  </clause>

  <clause id="21278">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(21277(a,1),17625(a,1))].">
      <j1 rule="para" parents="21277 17625"/>
    </justification>
  </clause>

  <clause id="21280">
    <literal><![CDATA[
      K(x,((a(y,z,u) \ 1) \ w) / T(a(y,z,u),v5)) = K(x,T(a(y,z,K(v5,u)) * w,a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(21278,a,20308,a)].">
      <j1 rule="hyper" parents="21278 20308"/>
    </justification>
  </clause>

  <clause id="21281">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,y \ (T(y,y * z) \ u))
    ]]></literal>
    <justification jstring="[para(1684(a,1),21055(a,2,2))].">
      <j1 rule="para" parents="1684 21055"/>
    </justification>
  </clause>

  <clause id="21282">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u \ z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20380,a(flip),b,21231,a),flip(a)].">
      <j1 rule="hyper" parents="370 20380 21231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21283">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,u * z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(17155(a,1),21282(a,1,2,2,1))].">
      <j1 rule="para" parents="17155 21282"/>
    </justification>
  </clause>

  <clause id="21284">
    <literal><![CDATA[
      K(x,y \ (T(z / (1 / u),T(u \ 1,z)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[para(7585(a,1),21283(a,1,2,2,1))].">
      <j1 rule="para" parents="7585 21283"/>
    </justification>
  </clause>

  <clause id="21285">
    <literal><![CDATA[
      K(x,y \ (T((1 / z) \ u,K(1,z)) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[para(19595(a,1),21284(a,1,2,2,1))].">
      <j1 rule="para" parents="19595 21284"/>
    </justification>
  </clause>

  <clause id="21286">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(20481,a,21285,a)].">
      <j1 rule="hyper" parents="20481 21285"/>
    </justification>
  </clause>

  <clause id="21287">
    <literal><![CDATA[
      K(x,y \ ((((z \ 1) \ 1) \ u) * w)) = K(x,y \ ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(74(a,1),21286(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 21286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21288">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ L(u,z,z)) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(581(a,1),21286(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="581 21286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21289">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((((1 / z) \ 1) \ T(u,1 / z)) * w))
    ]]></literal>
    <justification jstring="[para(9946(a,1),21286(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9946 21286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21290">
    <literal><![CDATA[
      K(x,y \ ((((z \ 1) \ 1) * u) * w)) = K(x,y \ ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(2090(a,1),21288(a,1,2,2,1))].">
      <j1 rule="para" parents="2090 21288"/>
    </justification>
  </clause>

  <clause id="21291">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ z) * w)) = K(x,y \ (((u \ z) * z) * w))
    ]]></literal>
    <justification jstring="[hyper(21244,a,21290,a)].">
      <j1 rule="hyper" parents="21244 21290"/>
    </justification>
  </clause>

  <clause id="21292">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * T(w,(u \ z) \ u))) = K(x,y \ (w * ((u \ z) \ u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),21291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 21291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21293">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * T(w,u * (u / z)))) = K(x,y \ (w * ((u \ z) \ u)))
    ]]></literal>
    <justification jstring="[para(15715(a,1),21292(a,1,2,2,2))].">
      <j1 rule="para" parents="15715 21292"/>
    </justification>
  </clause>

  <clause id="21294">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ u))) = K(x,y \ (z * ((w \ u) * u)))
    ]]></literal>
    <justification jstring="[para(14512(a,1),21293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14512 21293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21295">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,((y * z) * y) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14570,a(flip),b,21235,a),flip(a)].">
      <j1 rule="hyper" parents="370 14570 21235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21296">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ ((y \ (y * (y * z))) * u)) = K(x,(y * (z * y)) \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19677,a(flip),b,21295,a),flip(a)].">
      <j1 rule="hyper" parents="370 19677 21295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21297">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) = K(x,(y * (y * z)) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(4(a,1),21296(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 21296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21298">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ ((z * y) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19722,a(flip),b,21297,a),flip(a)].">
      <j1 rule="hyper" parents="370 19722 21297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21300">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(19681,a,21298,a)].">
      <j1 rule="hyper" parents="19681 21298"/>
    </justification>
  </clause>

  <clause id="21301">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,(z * K(u,z)) * y)) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(8857(a,1),21300(a,1,2,1,1))].">
      <j1 rule="para" parents="8857 21300"/>
    </justification>
  </clause>

  <clause id="21302">
    <literal><![CDATA[
      K(x,(T(y,z \ (y * 1)) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11094(a,1),21249(a,1,2,1,1))].">
      <j1 rule="para" parents="11094 21249"/>
    </justification>
  </clause>

  <clause id="21303">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K((((y \ 1) \ z) * (y \ 1)) / x,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),21270(a,2,1,2))].">
      <j1 rule="para" parents="5 21270"/>
    </justification>
  </clause>

  <clause id="21304">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y \ 1) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17902,a(flip),b,21303,a),flip(a)].">
      <j1 rule="hyper" parents="370 17902 21303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21305">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y * 1) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18527,a(flip),b,21304,a),flip(a)].">
      <j1 rule="hyper" parents="370 18527 21304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21306">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x * y)) = K(T(z,y) / x,u)
    ]]></literal>
    <justification jstring="[para(3(a,1),21305(a,2,1,1,2))].">
      <j1 rule="para" parents="3 21305"/>
    </justification>
  </clause>

  <clause id="21307">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,(K(x,T(y,z)) / x) * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(15351(a,2),21306(a,2,1))].">
      <j1 rule="para" parents="15351 21306"/>
    </justification>
  </clause>

  <clause id="21308">
    <literal><![CDATA[
      a(x,y,K(T(z,u) / w,v5)) = a(x,y,K(T(w,u) \ z,v5))
    ]]></literal>
    <justification jstring="[para(21306(a,1),19632(a,1,3))].">
      <j1 rule="para" parents="21306 19632"/>
    </justification>
  </clause>

  <clause id="21309">
    <literal><![CDATA[
      a(x,y,K(T(z,u) \ w,v5)) = a(x,y,K(z * T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19711,a(flip),b,21308,a),flip(a)].">
      <j1 rule="hyper" parents="60 19711 21308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21310">
    <literal><![CDATA[
      a(x,y,K(T(z,u) * w,v5)) = a(x,y,K(z * T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19710,a(flip),b,21309,a)].">
      <j1 rule="hyper" parents="60 19710 21309"/>
    </justification>
  </clause>

  <clause id="21311">
    <literal><![CDATA[
      K(x,(y \ 1) * ((y \ 1) * (L(y,z,z) * u))) = K(x,(((1 / y) \ 1) * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15719,a(flip),b,21271,a)].">
      <j1 rule="hyper" parents="60 15719 21271"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,y \ ((y \ 1) * (L(y,z,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(15233,a,21311,a),flip(a)].">
      <j1 rule="hyper" parents="15233 21311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21313">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,(y * y) \ (L(y,z,z) * u))
    ]]></literal>
    <justification jstring="[para(942(a,1),21312(a,2,2))].">
      <j1 rule="para" parents="942 21312"/>
    </justification>
  </clause>

  <clause id="21314">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,((y * y) \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[para(514(a,1),21313(a,2,2))].">
      <j1 rule="para" parents="514 21313"/>
    </justification>
  </clause>

  <clause id="21315">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,L(1 / y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(3790(a,1),21314(a,2,2,1))].">
      <j1 rule="para" parents="3790 21314"/>
    </justification>
  </clause>

  <clause id="21316">
    <literal><![CDATA[
      K(x,(((1 / y) \ 1) * a(z,z,y)) \ u) = K(x,L(y \ 1,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5618,a(flip),b,21315,a),flip(a)].">
      <j1 rule="hyper" parents="370 5618 21315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21317">
    <literal><![CDATA[
      K(x,(y * a(z,z,y)) \ u) = K(x,L(y \ 1,z,z) * u)
    ]]></literal>
    <justification jstring="[para(77(a,1),21316(a,1,2,1,1))].">
      <j1 rule="para" parents="77 21316"/>
    </justification>
  </clause>

  <clause id="21319">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (z / y)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14474,a(flip),b,21281,a),flip(a)].">
      <j1 rule="hyper" parents="370 14474 21281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21320">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,(1 / y) * (y \ z)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(11782(a,1),21319(a,1,2,2,1))].">
      <j1 rule="para" parents="11782 21319"/>
    </justification>
  </clause>

  <clause id="21321">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,y \ (y \ z)) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(15161(a,1),21320(a,1,2,2,1))].">
      <j1 rule="para" parents="15161 21320"/>
    </justification>
  </clause>

  <clause id="21322">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (K(z,y * y) * (z \ u))) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(15670(a,1),21321(a,1,2,2))].">
      <j1 rule="para" parents="15670 21321"/>
    </justification>
  </clause>

  <clause id="21323">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (T(z,y * y) \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(20077,a,21322,a)].">
      <j1 rule="hyper" parents="20077 21322"/>
    </justification>
  </clause>

  <clause id="21324">
    <literal><![CDATA[
      T(x,((1 / y) * (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18255,a(flip),b,21323,a)].">
      <j1 rule="hyper" parents="60 18255 21323"/>
    </justification>
  </clause>

  <clause id="21326">
    <literal><![CDATA[
      T(x,((y \ 1) * (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,4660,a(flip),b,21324,a)].">
      <j1 rule="hyper" parents="60 4660 21324"/>
    </justification>
  </clause>

  <clause id="21327">
    <literal><![CDATA[
      K(x,(T(y,z \ y) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(3(a,1),21302(a,1,2,1,1,2,2))].">
      <j1 rule="para" parents="3 21302"/>
    </justification>
  </clause>

  <clause id="21328">
    <literal><![CDATA[
      K(x,(T(y,z * y) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(21254,a,21327,a)].">
      <j1 rule="hyper" parents="21254 21327"/>
    </justification>
  </clause>

  <clause id="21329">
    <literal><![CDATA[
      K(x,(T(y,y * z) \ u) / (((z / y) \ 1) / y)) = K(x,(y * (((y * u) / y) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(5485(a,1),21328(a,1,2,1,1))].">
      <j1 rule="para" parents="5485 21328"/>
    </justification>
  </clause>

  <clause id="21330">
    <literal><![CDATA[
      K(x,(y * (((y * z) / y) \ 1)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) \ z) / (((u / y) \ 1) / y)) = w
    ]]></literal>
    <justification jstring="[para(21329(a,1),20470(a,1))].">
      <j1 rule="para" parents="21329 20470"/>
    </justification>
  </clause>

  <clause id="21331">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * (u * z)) \ v5)) = K(x,(w * (u * (z * K(y,z)))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(19528,a,20818,a)].">
      <j1 rule="hyper" parents="19528 20818"/>
    </justification>
  </clause>

  <clause id="21332">
    <literal><![CDATA[
      K(x,(y * (z * (u * K(w,u)))) \ v5) = K(x,(y * (z * T(u,w))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,20782,a(flip),b,21331,a),flip(a)].">
      <j1 rule="hyper" parents="60 20782 21331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21333">
    <literal><![CDATA[
      ((x * (y \ R(y,z,y))) / (K(y,z) * x)) / (K(y,z) * x) = (K(z,y) / x) * K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,18065,a(flip),b,20822,a),flip(a)].">
      <j1 rule="hyper" parents="370 18065 20822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21334">
    <literal><![CDATA[
      K(x * y,x) / (K(x,y) * z) = (K(y,x) / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(11722(a,1),21333(a,1,1))].">
      <j1 rule="para" parents="11722 21333"/>
    </justification>
  </clause>

  <clause id="21335">
    <literal><![CDATA[
      (K(x * y,x) / z) * K(y,x) = (K(y,x) / z) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,19556,a(flip),b,21334,a)].">
      <j1 rule="hyper" parents="60 19556 21334"/>
    </justification>
  </clause>

  <clause id="21337">
    <literal><![CDATA[
      a(K(x,y) * ((K(y,x) / z) * K(x * y,x)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(21335(a,1),16210(a,1,1,2))].">
      <j1 rule="para" parents="21335 16210"/>
    </justification>
  </clause>

  <clause id="21338">
    <literal><![CDATA[
      a(T(a(x,y,x) * (K(y,x) / z),K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(19732(a,1),21337(a,1,1))].">
      <j1 rule="para" parents="19732 21337"/>
    </justification>
  </clause>

  <clause id="21339">
    <literal><![CDATA[
      a(a(x,y,x) * (K(y,x) / z),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19779,a(flip),b,21338,a)].">
      <j1 rule="hyper" parents="60 19779 21338"/>
    </justification>
  </clause>

  <clause id="21340">
    <literal><![CDATA[
      a(a(x,y,x) * (z * K(x,y)),u,w) = a((1 / z) * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(15365,a,21339,a)].">
      <j1 rule="hyper" parents="15365 21339"/>
    </justification>
  </clause>

  <clause id="21342">
    <literal><![CDATA[
      a((1 / x) * K(y * z,y),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(14065,a,21340,a),flip(a)].">
      <j1 rule="hyper" parents="14065 21340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21343">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(2970,a,21342,a)].">
      <j1 rule="hyper" parents="2970 21342"/>
    </justification>
  </clause>

  <clause id="21345">
    <literal><![CDATA[
      a((x \ y) * K(z * (z \ y),z),u,w) = a(x \ (z * (y / z)),u,w)
    ]]></literal>
    <justification jstring="[para(20303(a,1),21343(a,2,1))].">
      <j1 rule="para" parents="20303 21343"/>
    </justification>
  </clause>

  <clause id="21346">
    <literal><![CDATA[
      a(x \ (y * (z / y)),u,w) = a((x \ z) * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),21345(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 21345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21347">
    <literal><![CDATA[
      a(x \ (y * (z / y)),u,w) = a(x \ T(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(15179(a,1),21346(a,2,1))].">
      <j1 rule="para" parents="15179 21346"/>
    </justification>
  </clause>

  <clause id="21348">
    <literal><![CDATA[
      a(x \ T((y * (z * y)) / y,T(y,y * z)),u,w) = a(x \ (T(y,y * z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(5547(a,1),21347(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5547 21347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21349">
    <literal><![CDATA[
      a(x \ T((y * (z * y)) / y,T(y,z)),u,w) = a(x \ (T(y,y * z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(7318(a,1),21348(a,1,1,2))].">
      <j1 rule="para" parents="7318 21348"/>
    </justification>
  </clause>

  <clause id="21350">
    <literal><![CDATA[
      a(x \ T(y * z,K(z,y)),u,w) = a(x \ (T(z,z * y) * y),u,w)
    ]]></literal>
    <justification jstring="[para(8586(a,1),21349(a,1,1,2))].">
      <j1 rule="para" parents="8586 21349"/>
    </justification>
  </clause>

  <clause id="21351">
    <literal><![CDATA[
      a(x \ (T(y,y * z) * z),u,w) = a(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(7474(a,1),21350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7474 21350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21352">
    <literal><![CDATA[
      K(x,a(y,z,z) * ((L(y,z,z) \ u) * a(y,z,z))) = K(x,(y * (1 / (y \ L(y,z,z)))) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20436,a(flip),b,21087,a)].">
      <j1 rule="hyper" parents="60 20436 21087"/>
    </justification>
  </clause>

  <clause id="21353">
    <literal><![CDATA[
      K(x,(y * T((1 / z) * u,K(z,z \ 1))) \ w) = K(x,(y * ((z \ 1) * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5571,a(flip),b,21090,a),flip(a)].">
      <j1 rule="hyper" parents="370 5571 21090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21354">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * u)) \ w) = K(x,(y * ((z \ 1) * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20836,a,21353,a)].">
      <j1 rule="hyper" parents="20836 21353"/>
    </justification>
  </clause>

  <clause id="21356">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,(y * ((y \ 1) * z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16044,a,b,21354,a)].">
      <j1 rule="hyper" parents="60 16044 21354"/>
    </justification>
  </clause>

  <clause id="21357">
    <literal><![CDATA[
      K(x,L((y * z) \ ((y \ 1) \ u),z,y)) = K(x,L(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),21356(a,2,2,1))].">
      <j1 rule="para" parents="2074 21356"/>
    </justification>
  </clause>

  <clause id="21358">
    <literal><![CDATA[
      K(x,y * (z \ ((z \ 1) \ u))) = K(x,L(y \ 1,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16583,a,21357,a)].">
      <j1 rule="hyper" parents="16583 21357"/>
    </justification>
  </clause>

  <clause id="21359">
    <literal><![CDATA[
      K(x,y \ (z \ ((z \ 1) \ u))) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16572,a(flip),b,21357,a)].">
      <j1 rule="hyper" parents="60 16572 21357"/>
    </justification>
  </clause>

  <clause id="21360">
    <literal><![CDATA[
      K(x,L(T(y,z),u,u) \ z) = K(x,(u \ ((u \ 1) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(15359,a,21359,a),flip(a)].">
      <j1 rule="hyper" parents="15359 21359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21361">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ (z \ T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1120(a,1),21359(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1120 21359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21362">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,L(y \ 1,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6661,a,b,21358,a)].">
      <j1 rule="hyper" parents="60 6661 21358"/>
    </justification>
  </clause>

  <clause id="21363">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,(z \ ((z \ 1) \ u)) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5378(a,1),21358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5378 21358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21364">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) / u) = K(x,z / L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(14579,a,21360,a),flip(a)].">
      <j1 rule="hyper" parents="14579 21360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21366">
    <literal><![CDATA[
      K(x,(y \ ((y \ 1) \ z)) * u) = K(x,z / L(u \ 1,y,y))
    ]]></literal>
    <justification jstring="[hyper(15244,a,21364,a)].">
      <j1 rule="hyper" parents="15244 21364"/>
    </justification>
  </clause>

  <clause id="21367">
    <literal><![CDATA[
      K(x,y / L(((z * z) \ u) \ 1,z,z)) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18971,a(flip),b,21366,a),flip(a)].">
      <j1 rule="hyper" parents="60 18971 21366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21368">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ T((z \ u) * z,z \ 1))
    ]]></literal>
    <justification jstring="[para(4702(a,2),21361(a,2,2,2))].">
      <j1 rule="para" parents="4702 21361"/>
    </justification>
  </clause>

  <clause id="21369">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ T((z \ u) * z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,17038,a(flip),b,21368,a),flip(a)].">
      <j1 rule="hyper" parents="370 17038 21368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21370">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ (z * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16891,a(flip),b,21369,a),flip(a)].">
      <j1 rule="hyper" parents="370 16891 21369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21371">
    <literal><![CDATA[
      K(x,L(y,z,z) \ R(u,z,z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),21370(a,2,2,2))].">
      <j1 rule="para" parents="5 21370"/>
    </justification>
  </clause>

  <clause id="21372">
    <literal><![CDATA[
      K(x,L(y,z,z) \ L(u,z,z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17042,a(flip),b,21371,a)].">
      <j1 rule="hyper" parents="60 17042 21371"/>
    </justification>
  </clause>

  <clause id="21373">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,K(x,T(y,z)) * (x \ z))) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(20956(a,1),21307(a,1,2))].">
      <j1 rule="para" parents="20956 21307"/>
    </justification>
  </clause>

  <clause id="21374">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,T(x,y) \ z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[para(17743(a,1),21373(a,1,2))].">
      <j1 rule="para" parents="17743 21373"/>
    </justification>
  </clause>

  <clause id="21375">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,T(x,y) * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[hyper(17494,a,21374,a)].">
      <j1 rule="hyper" parents="17494 21374"/>
    </justification>
  </clause>

  <clause id="21377">
    <literal><![CDATA[
      K(T(K(x,T(y,z)) / x,z) \ y,T(u,x * z)) = K(T(T(y,z),x) / (1 / x),u)
    ]]></literal>
    <justification jstring="[hyper(17976,a,21375,a)].">
      <j1 rule="hyper" parents="17976 21375"/>
    </justification>
  </clause>

  <clause id="21378">
    <literal><![CDATA[
      K(K(T(x,y),z) * (T(z,y) * x),T(u,z * y)) = K(T(T(x,y),z) / (1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(21069,a,21377,a)].">
      <j1 rule="hyper" parents="21069 21377"/>
    </justification>
  </clause>

  <clause id="21379">
    <literal><![CDATA[
      K(K(x,T(y,z)) * (T(y,z) * x),T(u,y * z)) = K(T(T(x,z),y) / (1 / y),u)
    ]]></literal>
    <justification jstring="[para(8024(a,1),21378(a,1,1,1))].">
      <j1 rule="para" parents="8024 21378"/>
    </justification>
  </clause>

  <clause id="21380">
    <literal><![CDATA[
      K(T(T(x,y),z) / (1 / z),u) = K(x * T(z,y),T(u,z * y))
    ]]></literal>
    <justification jstring="[para(7481(a,1),21379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7481 21379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21381">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y * z)) = K(T(T(x,z),y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(15422,a,21380,a),flip(a)].">
      <j1 rule="hyper" parents="15422 21380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21382">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y * z)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12598,a(flip),b,21381,a),flip(a)].">
      <j1 rule="hyper" parents="370 12598 21381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21383">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(12614,a,21382,a)].">
      <j1 rule="hyper" parents="12614 21382"/>
    </justification>
  </clause>

  <clause id="21384">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16876,a(flip),b,21383,a),flip(a)].">
      <j1 rule="hyper" parents="370 16876 21383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * z),u) = w
    ]]></literal>
    <justification jstring="[para(21383(a,2),16877(a,1))].">
      <j1 rule="para" parents="21383 16877"/>
    </justification>
  </clause>

  <clause id="21386">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = (w * K(y * (z * u),x)) \ w
    ]]></literal>
    <justification jstring="[para(21384(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="21384 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21387">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,21386,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 21386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      K(x,(y * z) * R(u,y,T(z,y))) = K(x,T(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(16973,a,21387,a)].">
      <j1 rule="hyper" parents="16973 21387"/>
    </justification>
  </clause>

  <clause id="21389">
    <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(869(a,1),21387(a,2,2))].">
      <j1 rule="para" parents="869 21387"/>
    </justification>
  </clause>

  <clause id="21390">
    <literal><![CDATA[
      K(x,(y * z) * R(u,y,z)) = K(x,T(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[para(12395(a,1),21388(a,1,2,2))].">
      <j1 rule="para" parents="12395 21388"/>
    </justification>
  </clause>

  <clause id="21391">
    <literal><![CDATA[
      K(x,R(y,z,u) * (u * z)) = K(x,L(y,z,u) * (u * z))
    ]]></literal>
    <justification jstring="[para(274(a,1),21389(a,1,2))].">
      <j1 rule="para" parents="274 21389"/>
    </justification>
  </clause>

  <clause id="21392">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * z) * T(u,z))
    ]]></literal>
    <justification jstring="[para(12402(a,1),21391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12402 21391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21393">
    <literal><![CDATA[
      K(x,L(y,z \ u,1 / z) * ((z * z) \ u)) = K(x,(y * (z \ u)) * T(1 / z,z \ u))
    ]]></literal>
    <justification jstring="[para(552(a,1),21392(a,1,2,2))].">
      <j1 rule="para" parents="552 21392"/>
    </justification>
  </clause>

  <clause id="21394">
    <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(12479(a,1),21392(a,1,2,1))].">
      <j1 rule="para" parents="12479 21392"/>
    </justification>
  </clause>

  <clause id="21395">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(u,z) * z)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19866,a(flip),b,21394,a),flip(a)].">
      <j1 rule="hyper" parents="370 19866 21394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21397">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16862,a(flip),b,21395,a)].">
      <j1 rule="hyper" parents="60 16862 21395"/>
    </justification>
  </clause>

  <clause id="21398">
    <literal><![CDATA[
      K(x,L(y,z / u,u \ 1) * (z / (u * u))) = K(x,(y * (z / u)) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(1105(a,1),21397(a,1,2,2))].">
      <j1 rule="para" parents="1105 21397"/>
    </justification>
  </clause>

  <clause id="21399">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) \ (u * z),1 / z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(10348(a,1),21397(a,1,2,2))].">
      <j1 rule="para" parents="10348 21397"/>
    </justification>
  </clause>

  <clause id="21400">
    <literal><![CDATA[
      K(x,L(y,z / u,u) * (z / (u * u))) = K(x,(y * (z / u)) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(1492(a,1),21398(a,1,2,1))].">
      <j1 rule="para" parents="1492 21398"/>
    </justification>
  </clause>

  <clause id="21401">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * (u / (z * z))) = K(x,(y * (u / z)) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(12487(a,1),21400(a,1,2,1))].">
      <j1 rule="para" parents="12487 21400"/>
    </justification>
  </clause>

  <clause id="21402">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) = K(x,(y * (u / z)) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,18318,a(flip),b,21401,a)].">
      <j1 rule="hyper" parents="60 18318 21401"/>
    </justification>
  </clause>

  <clause id="21403">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (u / z)) / z) = w
    ]]></literal>
    <justification jstring="[para(21402(a,2),15472(a,1))].">
      <j1 rule="para" parents="21402 15472"/>
    </justification>
  </clause>

  <clause id="21404">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * ((z * z) \ u)) = K(x,(y * (z \ u)) * T(1 / z,z \ u))
    ]]></literal>
    <justification jstring="[para(1488(a,1),21393(a,1,2,1))].">
      <j1 rule="para" parents="1488 21393"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      K(x,(y * (z \ u)) * T(1 / z,z \ u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(21403,a,21404,a),flip(a)].">
      <j1 rule="hyper" parents="21403 21404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21406">
    <literal><![CDATA[
      K(x,(y * (z \ u)) * T(z \ 1,u * z)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[para(7752(a,1),21405(a,1,2,2))].">
      <j1 rule="para" parents="7752 21405"/>
    </justification>
  </clause>

  <clause id="21407">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u * z)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(21278,a,21406,a)].">
      <j1 rule="hyper" parents="21278 21406"/>
    </justification>
  </clause>

  <clause id="21408">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / T(z,u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,18169,a(flip),b,21407,a)].">
      <j1 rule="hyper" parents="60 18169 21407"/>
    </justification>
  </clause>

  <clause id="21409">
    <literal><![CDATA[
      K(x,L(y / ((z \ u) \ z),z,z * u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(20348,a,21408,a)].">
      <j1 rule="hyper" parents="20348 21408"/>
    </justification>
  </clause>

  <clause id="21410">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,z * (K(u,z) * y))) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(7845(a,1),21301(a,1,2,3))].">
      <j1 rule="para" parents="7845 21301"/>
    </justification>
  </clause>

  <clause id="21411">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,(z \ ((z \ 1) \ u)) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,15155,a(flip),b,21363,a),flip(a)].">
      <j1 rule="hyper" parents="370 15155 21363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21412">
    <literal><![CDATA[
      K(x,L((y \ K(z \ ((z \ 1) \ u),y \ 1)) \ 1,z,z) \ u) = K(x,u / L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,21364,a(flip),b,21411,a),flip(a)].">
      <j1 rule="hyper" parents="370 21364 21411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21413">
    <literal><![CDATA[
      K(x,L((y \ K(z,y \ 1)) \ 1,u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(15309(a,1),21412(a,1,2,1,1,1,2))].">
      <j1 rule="para" parents="15309 21412"/>
    </justification>
  </clause>

  <clause id="21414">
    <literal><![CDATA[
      K(x,L(((y * (z \ 1)) / y) \ 1,u,u) \ y) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[para(5257(a,1),21413(a,1,2,1,1,1))].">
      <j1 rule="para" parents="5257 21413"/>
    </justification>
  </clause>

  <clause id="21416">
    <literal><![CDATA[
      K(x,L((y \ 1) \ K(y \ 1,z),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(5935(a,1),21414(a,1,2,1,1))].">
      <j1 rule="para" parents="5935 21414"/>
    </justification>
  </clause>

  <clause id="21417">
    <literal><![CDATA[
      K(x,L((y * y) * (y \ K(y \ 1,z)),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(936(a,2),21416(a,1,2,1,1))].">
      <j1 rule="para" parents="936 21416"/>
    </justification>
  </clause>

  <clause id="21418">
    <literal><![CDATA[
      K(x,L((y * y) * T(y \ 1,z),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(5260(a,1),21417(a,1,2,1,1,2))].">
      <j1 rule="para" parents="5260 21417"/>
    </justification>
  </clause>

  <clause id="21419">
    <literal><![CDATA[
      K(x,L(y * (y * T(1 / y,z)),u,u) \ z) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[para(1232(a,1),21418(a,1,2,1,1))].">
      <j1 rule="para" parents="1232 21418"/>
    </justification>
  </clause>

  <clause id="21420">
    <literal><![CDATA[
      K(x,L(T(1 / y,z),u,u) \ (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16585,a(flip),b,21419,a)].">
      <j1 rule="hyper" parents="60 16585 21419"/>
    </justification>
  </clause>

  <clause id="21421">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,u) \ (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10329,a(flip),b,21420,a)].">
      <j1 rule="hyper" parents="60 10329 21420"/>
    </justification>
  </clause>

  <clause id="21422">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,w,T(z,u) * y)) = K(x,(z * K(u,z)) \ ((y \ (z * K(u,z))) * w))
    ]]></literal>
    <justification jstring="[para(19449(a,1),21410(a,1,2))].">
      <j1 rule="para" parents="19449 21410"/>
    </justification>
  </clause>

  <clause id="21423">
    <literal><![CDATA[
      K(x,(y * K(z,y)) \ ((u \ (y * K(z,y))) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21300,a(flip),b,21422,a),flip(a)].">
      <j1 rule="hyper" parents="60 21300 21422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21424">
    <literal><![CDATA[
      K(x,(y * K(z,y)) \ (((u \ y) * K(z,y)) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(20258(a,1),21423(a,1,2,2,1))].">
      <j1 rule="para" parents="20258 21423"/>
    </justification>
  </clause>

  <clause id="21425">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ (((u \ y) * K(z,y)) * w))) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20742,a,21424,a)].">
      <j1 rule="hyper" parents="20742 21424"/>
    </justification>
  </clause>

  <clause id="21426">
    <literal><![CDATA[
      K(x,T(y,z) \ (((u \ y) * K(z,y)) * w)) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(21017,a,21425,a)].">
      <j1 rule="hyper" parents="21017 21425"/>
    </justification>
  </clause>

  <clause id="21427">
    <literal><![CDATA[
      K(x,K(y,z) * (T(y,z) \ ((u \ y) * w))) = K(x,T(y,z) \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(20940,a,21426,a)].">
      <j1 rule="hyper" parents="20940 21426"/>
    </justification>
  </clause>

  <clause id="21428">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ T(y,z)) * w)) = K(x,y \ ((u \ y) * w))
    ]]></literal>
    <justification jstring="[para(7858(a,1),21427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 21427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21430">
    <literal><![CDATA[
      T(x,y \ (T(T(z,u \ (w \ (u \ 1))),w \ (u \ ((u * w) \ 1))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(18(a,1),20967(a,1,2,2,1))].">
      <j1 rule="para" parents="18 20967"/>
    </justification>
  </clause>

  <clause id="21431">
    <literal><![CDATA[
      K(x,T(T(y,y / T(z,u * z)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(21068(a,1),21185(a,1,2,1,1,1))].">
      <j1 rule="para" parents="21068 21185"/>
    </justification>
  </clause>

  <clause id="21432">
    <literal><![CDATA[
      K(x,T(T(y,y / T(z,z * u)) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5485(a,1),21431(a,1,2,1,1,1,2,2))].">
      <j1 rule="para" parents="5485 21431"/>
    </justification>
  </clause>

  <clause id="21433">
    <literal><![CDATA[
      K(x,T(T(y,T(z,z * u) \ y) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5468(a,1),21432(a,1,2,1,1,1))].">
      <j1 rule="para" parents="5468 21432"/>
    </justification>
  </clause>

  <clause id="21434">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u) \ y) * T(z \ 1,u * z),y) \ w) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(14370(a,1),21433(a,1,2,1,1,1))].">
      <j1 rule="para" parents="14370 21433"/>
    </justification>
  </clause>

  <clause id="21435">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z) \ u)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17757,a,21434,a)].">
      <j1 rule="hyper" parents="17757 21434"/>
    </justification>
  </clause>

  <clause id="21436">
    <literal><![CDATA[
      T(x,y \ (T(z,(u * w) \ ((u * w) \ (u \ (w \ (u \ 1))))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(15671(a,1),21430(a,1,2,2,1))].">
      <j1 rule="para" parents="15671 21430"/>
    </justification>
  </clause>

  <clause id="21437">
    <literal><![CDATA[
      T(x,y \ (T(z,(u * w) * ((u * w) \ (u \ (w \ (u \ 1))))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20095,a,21436,a)].">
      <j1 rule="hyper" parents="20095 21436"/>
    </justification>
  </clause>

  <clause id="21438">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ (w \ (u \ 1))) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(5(a,1),21437(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5 21437"/>
    </justification>
  </clause>

  <clause id="21440">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (w \ u)) \ v5)) = T(x,y \ (((w * z) / w) \ v5))
    ]]></literal>
    <justification jstring="[para(16650(a,1),21438(a,1,2,2,1))].">
      <j1 rule="para" parents="16650 21438"/>
    </justification>
  </clause>

  <clause id="21441">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (w \ u)) \ v5)) = T(x,y \ (T(z,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,20965,a(flip),b,21440,a),flip(a)].">
      <j1 rule="hyper" parents="370 20965 21440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21442">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) \ (u * z),z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(1488(a,1),21399(a,1,2,1))].">
      <j1 rule="para" parents="1488 21399"/>
    </justification>
  </clause>

  <clause id="21443">
    <literal><![CDATA[
      K(x,L(y,z \ (u * z),z) * (T(u,z \ 1) * z)) = K(x,(y * ((z \ 1) \ (u * z))) * (1 / z))
    ]]></literal>
    <justification jstring="[para(3392(a,1),21442(a,1,2,1))].">
      <j1 rule="para" parents="3392 21442"/>
    </justification>
  </clause>

  <clause id="21444">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u) * (T(z,u \ 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(17(a,2),21443(a,1,2,1,2))].">
      <j1 rule="para" parents="17 21443"/>
    </justification>
  </clause>

  <clause id="21445">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u \ 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(12477(a,1),21444(a,1,2,1))].">
      <j1 rule="para" parents="12477 21444"/>
    </justification>
  </clause>

  <clause id="21446">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u * 1) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(18560,a,21445,a)].">
      <j1 rule="hyper" parents="18560 21445"/>
    </justification>
  </clause>

  <clause id="21447">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(z,u) * u)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[para(3(a,1),21446(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3 21446"/>
    </justification>
  </clause>

  <clause id="21448">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * ((u \ 1) \ (z * u))) * (1 / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16862,a(flip),b,21447,a)].">
      <j1 rule="hyper" parents="60 16862 21447"/>
    </justification>
  </clause>

  <clause id="21449">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,T(z,y))) \ w)
    ]]></literal>
    <justification jstring="[para(8855(a,1),21036(a,2,2,1,2))].">
      <j1 rule="para" parents="8855 21036"/>
    </justification>
  </clause>

  <clause id="21450">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / ((y * z) / y)) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,19514,a(flip),b,21449,a),flip(a)].">
      <j1 rule="hyper" parents="370 19514 21449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21452">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((((y * z) / y) \ 1) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5591,a(flip),b,21450,a),flip(a)].">
      <j1 rule="hyper" parents="370 5591 21450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21453">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((1 / T((y * z) / y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5720(a,1),21037(a,2,2,1,1))].">
      <j1 rule="para" parents="5720 21037"/>
    </justification>
  </clause>

  <clause id="21454">
    <literal><![CDATA[
      K(x,((T((y * z) / y,u) \ 1) * u) \ w) = K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5591,a(flip),b,21453,a)].">
      <j1 rule="hyper" parents="370 5591 21453"/>
    </justification>
  </clause>

  <clause id="21455">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(18508,a,21454,a),flip(a)].">
      <j1 rule="hyper" parents="18508 21454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21456">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (((y * z) / y) \ 1)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(21454(a,1),18508(a,1))].">
      <j1 rule="para" parents="21454 18508"/>
    </justification>
  </clause>

  <clause id="21457">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ ((((u * z) / u) * ((u * z) / u)) * w)) = K(x,(y * (((u * z) / u) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(1005(a,1),21455(a,1,2))].">
      <j1 rule="para" parents="1005 21455"/>
    </justification>
  </clause>

  <clause id="21458">
    <literal><![CDATA[
      K(x,((y * z) / y) * (((y * z) / y) * ((u * T(z,y)) \ w))) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20977,a(flip),b,21457,a)].">
      <j1 rule="hyper" parents="60 20977 21457"/>
    </justification>
  </clause>

  <clause id="21459">
    <literal><![CDATA[
      K(x,((y * z) / y) * (T(z,y) * ((u * T(z,y)) \ w))) = K(x,(u * (((y * z) / y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16942,a(flip),b,21458,a)].">
      <j1 rule="hyper" parents="60 16942 21458"/>
    </justification>
  </clause>

  <clause id="21460">
    <literal><![CDATA[
      K(x,T(y,z) * (T(y,z) * ((u * T(y,z)) \ w))) = K(x,(u * (((z * y) / z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(19909,a,21459,a)].">
      <j1 rule="hyper" parents="19909 21459"/>
    </justification>
  </clause>

  <clause id="21461">
    <literal><![CDATA[
      K(x,y * (T(T(y,z),z) * ((u * T(y,z)) \ w))) = K(x,(u * (((z * y) / z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(8262(a,1),21460(a,1,2))].">
      <j1 rule="para" parents="8262 21460"/>
    </justification>
  </clause>

  <clause id="21462">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,u * (u * ((y * T(u,z)) \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16944,a(flip),b,21461,a),flip(a)].">
      <j1 rule="hyper" parents="60 16944 21461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21464">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((z \ T(u,1 / z)) * w))
    ]]></literal>
    <justification jstring="[para(77(a,1),21289(a,2,2,2,1,1))].">
      <j1 rule="para" parents="77 21289"/>
    </justification>
  </clause>

  <clause id="21465">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((z \ T(u,z \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(4443(a,1),21464(a,2,2,2,1,2))].">
      <j1 rule="para" parents="4443 21464"/>
    </justification>
  </clause>

  <clause id="21466">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T(((1 / z) * (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,21243,a(flip),b,21465,a),flip(a)].">
      <j1 rule="hyper" parents="370 21243 21465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21467">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ (1 / z)) * u,1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(320(a,1),21466(a,1,2,2,1,2,1,1))].">
      <j1 rule="para" parents="320 21466"/>
    </justification>
  </clause>

  <clause id="21468">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ 1) * (z \ u),1 / z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(1214(a,1),21467(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1214 21467"/>
    </justification>
  </clause>

  <clause id="21469">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ T((z \ 1) * (z \ u),z \ 1)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4443(a,1),21468(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4443 21468"/>
    </justification>
  </clause>

  <clause id="21470">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ (z \ (u * (z \ 1)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(1566(a,1),21469(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1566 21469"/>
    </justification>
  </clause>

  <clause id="21471">
    <literal><![CDATA[
      K(x,y \ ((z \ ((1 / z) \ (u * (z \ 1)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(2104(a,1),21470(a,1,2,2,1))].">
      <j1 rule="para" parents="2104 21470"/>
    </justification>
  </clause>

  <clause id="21472">
    <literal><![CDATA[
      K(x,y \ ((z \ ((z \ 1) \ (u * (1 / z)))) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4479(a,1),21471(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4479 21471"/>
    </justification>
  </clause>

  <clause id="21473">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u \ 1) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[para(4706(a,1),21472(a,1,2,2,1))].">
      <j1 rule="para" parents="4706 21472"/>
    </justification>
  </clause>

  <clause id="21474">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u * 1) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18696,a(flip),b,21473,a)].">
      <j1 rule="hyper" parents="60 18696 21473"/>
    </justification>
  </clause>

  <clause id="21475">
    <literal><![CDATA[
      K(x,y \ (T(T(z,u) / u,u) * w)) = K(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[para(3(a,1),21474(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3 21474"/>
    </justification>
  </clause>

  <clause id="21476">
    <literal><![CDATA[
      K(x,y \ ((z \ T(u,z)) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(109(a,1),21475(a,1,2,2,1))].">
      <j1 rule="para" parents="109 21475"/>
    </justification>
  </clause>

  <clause id="21477">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) * w)) = K(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(5749(a,2),21476(a,1,2,2,1))].">
      <j1 rule="para" parents="5749 21476"/>
    </justification>
  </clause>

  <clause id="21478">
    <literal><![CDATA[
      (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x = ((x * y) * K(z,T(u,y))) / (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(15842(a,1),19758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15842 19758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21479">
    <literal><![CDATA[
      (((x * y) * K(z,T(u,y))) / (x * (K(z,u) * y))) * x = L(x,y,K(z,T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20209,a(flip),b,21478,a),flip(a)].">
      <j1 rule="hyper" parents="370 20209 21478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21481">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) = a(x,y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(19757(a,1),21479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19757 21479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21482">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15838,a(flip),b,21481,a),flip(a)].">
      <j1 rule="hyper" parents="370 15838 21481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21483">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(20639,a,21482,a)].">
      <j1 rule="hyper" parents="20639 21482"/>
    </justification>
  </clause>

  <clause id="21484">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(21482(a,1),20639(a,1))].">
      <j1 rule="para" parents="21482 20639"/>
    </justification>
  </clause>

  <clause id="21485">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8246,a,21483,a)].">
      <j1 rule="hyper" parents="8246 21483"/>
    </justification>
  </clause>

  <clause id="21486">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(5885,a,21483,a)].">
      <j1 rule="hyper" parents="5885 21483"/>
    </justification>
  </clause>

  <clause id="21487">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,19329,a,b,21483,a)].">
      <j1 rule="hyper" parents="370 19329 21483"/>
    </justification>
  </clause>

  <clause id="21488">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,15913,a,b,21483,a)].">
      <j1 rule="hyper" parents="370 15913 21483"/>
    </justification>
  </clause>

  <clause id="21489">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15834,a,b,21483,a)].">
      <j1 rule="hyper" parents="370 15834 21483"/>
    </justification>
  </clause>

  <clause id="21490">
    <literal><![CDATA[
      L(a(x,y,y),z,K(u,w)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,15849,a(flip),b,21483,a),flip(a)].">
      <j1 rule="hyper" parents="370 15849 21483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21491">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,21483,a,b,15913,a)].">
      <j1 rule="hyper" parents="125 21483 15913"/>
    </justification>
  </clause>

  <clause id="21492">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = L(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(15915,a,21483,a(flip))].">
      <j1 rule="hyper" parents="15915 21483"/>
    </justification>
  </clause>

  <clause id="21494">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(21483(a,2),15498(a,1,1))].">
      <j1 rule="para" parents="21483 15498"/>
    </justification>
  </clause>

  <clause id="21495">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(21483(a,2),15505(a,2,2))].">
      <j1 rule="para" parents="21483 15505"/>
    </justification>
  </clause>

  <clause id="21496">
    <literal><![CDATA[
      1 / L(x,y,K(z,u)) = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(21483(a,2),15969(a,1,2))].">
      <j1 rule="para" parents="21483 15969"/>
    </justification>
  </clause>

  <clause id="21497">
    <literal><![CDATA[
      x * L(x \ y,z,K(u,w)) = y * a(w,z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(21483(a,2),16027(a,1,2))].">
      <j1 rule="para" parents="21483 16027"/>
    </justification>
  </clause>

  <clause id="21498">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(21483(a,2),19356(a,1,2))].">
      <j1 rule="para" parents="21483 19356"/>
    </justification>
  </clause>

  <clause id="21499">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[para(21483(a,2),19460(a,2,1))].">
      <j1 rule="para" parents="21483 19460"/>
    </justification>
  </clause>

  <clause id="21500">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(21483(a,2),19798(a,1,2,2))].">
      <j1 rule="para" parents="21483 19798"/>
    </justification>
  </clause>

  <clause id="21501">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / y = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[para(21485(a,1),2130(a,1,2))].">
      <j1 rule="para" parents="21485 2130"/>
    </justification>
  </clause>

  <clause id="21502">
    <literal><![CDATA[
      T(x,a(y,y,z) \ (a(y,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(21485(a,1),15681(a,1,1))].">
      <j1 rule="para" parents="21485 15681"/>
    </justification>
  </clause>

  <clause id="21503">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15834,a,b,21486,a)].">
      <j1 rule="hyper" parents="370 15834 21486"/>
    </justification>
  </clause>

  <clause id="21504">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,15914,a(flip),b,21486,a),flip(a)].">
      <j1 rule="hyper" parents="38 15914 21486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21505">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(15915,a,21486,a(flip))].">
      <j1 rule="hyper" parents="15915 21486"/>
    </justification>
  </clause>

  <clause id="21506">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,21486,a,b,21504,a)].">
      <j1 rule="hyper" parents="60 21486 21504"/>
    </justification>
  </clause>

  <clause id="21507">
    <literal><![CDATA[
      a(K(x,y) * z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16643,a(flip),b,21490,a)].">
      <j1 rule="hyper" parents="60 16643 21490"/>
    </justification>
  </clause>

  <clause id="21509">
    <literal><![CDATA[
      a(x / y,z,z) = a(y \ x,z,z)
    ]]></literal>
    <justification jstring="[para(5232(a,1),21507(a,1,1))].">
      <j1 rule="para" parents="5232 21507"/>
    </justification>
  </clause>

  <clause id="21510">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,w) = a(L(x,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(5302(a,1),21507(a,1,1))].">
      <j1 rule="para" parents="5302 21507"/>
    </justification>
  </clause>

  <clause id="21511">
    <literal><![CDATA[
      a(x \ T(y,z),u,u) = a(x \ y,u,u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),21507(a,1,1))].">
      <j1 rule="para" parents="6128 21507"/>
    </justification>
  </clause>

  <clause id="21512">
    <literal><![CDATA[
      a((x * y) \ z,u,u) = a((y * x) \ z,u,u)
    ]]></literal>
    <justification jstring="[para(12083(a,1),21507(a,1,1))].">
      <j1 rule="para" parents="12083 21507"/>
    </justification>
  </clause>

  <clause id="21513">
    <literal><![CDATA[
      a(R(T(x,y),z,u),w,w) = a(R(x,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(16489(a,1),21507(a,1,1))].">
      <j1 rule="para" parents="16489 21507"/>
    </justification>
  </clause>

  <clause id="21514">
    <literal><![CDATA[
      (K(x,y) / z) * a(z,u,u) = R(K(x,y) / z,u,u)
    ]]></literal>
    <justification jstring="[para(21507(a,1),16515(a,1,2))].">
      <j1 rule="para" parents="21507 16515"/>
    </justification>
  </clause>

  <clause id="21515">
    <literal><![CDATA[
      K(x,y * ((K(z,u) / w) * a(w,v5,v5))) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(21507(a,1),20202(a,1,2,2,2))].">
      <j1 rule="para" parents="21507 20202"/>
    </justification>
  </clause>

  <clause id="21516">
    <literal><![CDATA[
      (x * (y \ 1)) / a(y \ x,y,y) = x / y
    ]]></literal>
    <justification jstring="[para(21509(a,1),16510(a,1,2))].">
      <j1 rule="para" parents="21509 16510"/>
    </justification>
  </clause>

  <clause id="21517">
    <literal><![CDATA[
      K(x,(y \ T(T(a(z,u,w),v5),v5)) * v6) = K(x,(a(z,u,w) / L(y,u,K(w,z))) * v6)
    ]]></literal>
    <justification jstring="[para(21487(a,1),20034(a,2,2,1,2))].">
      <j1 rule="para" parents="21487 20034"/>
    </justification>
  </clause>

  <clause id="21518">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(18143,a,21488,a)].">
      <j1 rule="hyper" parents="18143 21488"/>
    </justification>
  </clause>

  <clause id="21519">
    <literal><![CDATA[
      (T(a(x,y,z),u) * w) / T(a(x,y,z),u) = L(w,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,19637,a,b,21488,a)].">
      <j1 rule="hyper" parents="60 19637 21488"/>
    </justification>
  </clause>

  <clause id="21520">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(21488(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="21488 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21522">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) * v5) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(21488(a,1),19852(a,1,2,1))].">
      <j1 rule="para" parents="21488 19852"/>
    </justification>
  </clause>

  <clause id="21523">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(21488(a,1),21194(a,1,2,2))].">
      <j1 rule="para" parents="21488 21194"/>
    </justification>
  </clause>

  <clause id="21524">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16384,a,b,21489,a)].">
      <j1 rule="hyper" parents="60 16384 21489"/>
    </justification>
  </clause>

  <clause id="21525">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,15818,a(flip),b,21489,a)].">
      <j1 rule="hyper" parents="60 15818 21489"/>
    </justification>
  </clause>

  <clause id="21526">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(21491(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="21491 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21529">
    <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(10145(a,1),21498(a,1,2))].">
      <j1 rule="para" parents="10145 21498"/>
    </justification>
  </clause>

  <clause id="21530">
    <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(10255(a,1),21498(a,1,2))].">
      <j1 rule="para" parents="10255 21498"/>
    </justification>
  </clause>

  <clause id="21532">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(12966(a,2),21498(a,1))].">
      <j1 rule="para" parents="12966 21498"/>
    </justification>
  </clause>

  <clause id="21533">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ (K(u,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((((u * y) / u) \ 1) * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(16289(a,1),21498(a,1))].">
      <j1 rule="para" parents="16289 21498"/>
    </justification>
  </clause>

  <clause id="21535">
    <literal><![CDATA[
      a(x \ (T(y,y * z) * z),u,u) = a(x \ (y * z),u,u)
    ]]></literal>
    <justification jstring="[para(1527(a,1),21511(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1527 21511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21536">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(15480,a,21524,a)].">
      <j1 rule="hyper" parents="15480 21524"/>
    </justification>
  </clause>

  <clause id="21539">
    <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(20208(a,1),21532(a,1,1))].">
      <j1 rule="para" parents="20208 21532"/>
    </justification>
  </clause>

  <clause id="21540">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5880,a,b,21536,a),flip(a)].">
      <j1 rule="hyper" parents="370 5880 21536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21541">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(21540(a,2),5885(a,1))].">
      <j1 rule="para" parents="21540 5885"/>
    </justification>
  </clause>

  <clause id="21542">
    <literal><![CDATA[
      a(x \ y,x,x) \ (y * (x \ 1)) = y / x
    ]]></literal>
    <justification jstring="[hyper(15852,a,21516,a)].">
      <j1 rule="hyper" parents="15852 21516"/>
    </justification>
  </clause>

  <clause id="21543">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u * K(y,z))) = K(x,w * (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(17491,a,21522,a)].">
      <j1 rule="hyper" parents="17491 21522"/>
    </justification>
  </clause>

  <clause id="21544">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = 1 / L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,21483,a,b,21496,a)].">
      <j1 rule="hyper" parents="370 21483 21496"/>
    </justification>
  </clause>

  <clause id="21546">
    <literal><![CDATA[
      T(x,a(y,y,z) * (a(y,y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(64(a,1),21502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="64 21502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21547">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(L(T(z,x),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(270(a,1),21512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="270 21512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21548">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5254(a,1),21518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5254 21518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21549">
    <literal><![CDATA[
      T(x * K(y,x),L(y,y \ z,u)) = L(x,z / y,K(y,u))
    ]]></literal>
    <justification jstring="[para(12446(a,1),21518(a,1,2))].">
      <j1 rule="para" parents="12446 21518"/>
    </justification>
  </clause>

  <clause id="21550">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(20766,a,21548,a),flip(a)].">
      <j1 rule="hyper" parents="20766 21548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21551">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(21548(a,1),21500(a,1,2,2))].">
      <j1 rule="para" parents="21548 21500"/>
    </justification>
  </clause>

  <clause id="21552">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(21548(a,1),21523(a,1,2,2))].">
      <j1 rule="para" parents="21548 21523"/>
    </justification>
  </clause>

  <clause id="21554">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / w) \ 1)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20651,a(flip),b,21550,a),flip(a)].">
      <j1 rule="hyper" parents="60 20651 21550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21555">
    <literal><![CDATA[
      T(x,(L(y,z,z) / y) \ u) = T(x,(y \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17107,a(flip),b,21546,a)].">
      <j1 rule="hyper" parents="60 17107 21546"/>
    </justification>
  </clause>

  <clause id="21556">
    <literal><![CDATA[
      L(a(x,y,z) \ u,y,K(z,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(382,a,21492,a),flip(a)].">
      <j1 rule="hyper" parents="382 21492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21557">
    <literal><![CDATA[
      L(a(x,y,z) \ u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      u / a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(21492(a,1),382(a,1))].">
      <j1 rule="para" parents="21492 382"/>
    </justification>
  </clause>

  <clause id="21558">
    <literal><![CDATA[
      (x * y) / L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(21492(a,1),15841(a,1,2))].">
      <j1 rule="para" parents="21492 15841"/>
    </justification>
  </clause>

  <clause id="21559">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u) \ 1) = T(x,a(z,y,u) \ (a(z,y,u) \ 1))
    ]]></literal>
    <justification jstring="[para(21505(a,1),1794(a,1,1))].">
      <j1 rule="para" parents="21505 1794"/>
    </justification>
  </clause>

  <clause id="21560">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13020(a,2),21526(a,1))].">
      <j1 rule="para" parents="13020 21526"/>
    </justification>
  </clause>

  <clause id="21561">
    <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(6033(a,1),21529(a,1,2))].">
      <j1 rule="para" parents="6033 21529"/>
    </justification>
  </clause>

  <clause id="21563">
    <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(14003(a,1),21529(a,1,2))].">
      <j1 rule="para" parents="14003 21529"/>
    </justification>
  </clause>

  <clause id="21564">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,K(v5,v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v7
    ]]></literal>
    <justification jstring="[para(21483(a,2),21529(a,1,2,3))].">
      <j1 rule="para" parents="21483 21529"/>
    </justification>
  </clause>

  <clause id="21567">
    <literal><![CDATA[
      K(x,L(y,z,u) \ T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(21552(a,1),14580(a,1))].">
      <j1 rule="para" parents="21552 14580"/>
    </justification>
  </clause>

  <clause id="21568">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) = K(x,K(v5,y)) * K(x,v5 \ T(y,z))
    ]]></literal>
    <justification jstring="[para(21552(a,1),17277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21552 17277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21569">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = 1 / L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18844,a,b,21495,a)].">
      <j1 rule="hyper" parents="60 18844 21495"/>
    </justification>
  </clause>

  <clause id="21570">
    <literal><![CDATA[
      K(x,(y / L(z,u,K(w,v5))) * v6) = K(x,(y / z) * v6)
    ]]></literal>
    <justification jstring="[para(21495(a,1),19852(a,1,2,1))].">
      <j1 rule="para" parents="21495 19852"/>
    </justification>
  </clause>

  <clause id="21571">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(31,a,2153,a(flip),b,21499,a),flip(a)].">
      <j1 rule="hyper" parents="31 2153 21499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21572">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) * x = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(155,a,21501,a)].">
      <j1 rule="hyper" parents="155 21501"/>
    </justification>
  </clause>

  <clause id="21573">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) * K(a(y,y,y \ (y \ x)),z) = T((y \ ((1 / y) \ x)) / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(21501(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="21501 8514"/>
    </justification>
  </clause>

  <clause id="21575">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(19317,a,21571,a)].">
      <j1 rule="hyper" parents="19317 21571"/>
    </justification>
  </clause>

  <clause id="21576">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K((y \ (x \ ((1 / x) \ y))) \ 1,z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(21572(a,1),6610(a,1,1))].">
      <j1 rule="para" parents="21572 6610"/>
    </justification>
  </clause>

  <clause id="21577">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(21575(a,1),21198(a,1,2))].">
      <j1 rule="para" parents="21575 21198"/>
    </justification>
  </clause>

  <clause id="21578">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((y / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(21563,a,19709,a)].">
      <j1 rule="hyper" parents="21563 19709"/>
    </justification>
  </clause>

  <clause id="21579">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,y,z * y)) = w
    ]]></literal>
    <justification jstring="[para(19709(a,1),21563(a,1))].">
      <j1 rule="para" parents="19709 21563"/>
    </justification>
  </clause>

  <clause id="21580">
    <literal><![CDATA[
      (K(x,y) * (z * (z \ u))) / (u * a(y,z,K(x,z * u))) = R(K(x,y),z,L(z \ u,z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(21497(a,1),623(a,1,2))].">
      <j1 rule="para" parents="21497 623"/>
    </justification>
  </clause>

  <clause id="21581">
    <literal><![CDATA[
      x * a(y,z,K(u,a(y,z,u) * x)) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[para(21556(a,1),21497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21556 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21582">
    <literal><![CDATA[
      a(x \ (y * z),u,u) = a(x \ (z * y),u,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21351,a(flip),b,21535,a)].">
      <j1 rule="hyper" parents="60 21351 21535"/>
    </justification>
  </clause>

  <clause id="21583">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(880(a,1),21582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="880 21582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21584">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z / y,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,13015,a(flip),b,21549,a)].">
      <j1 rule="hyper" parents="60 13015 21549"/>
    </justification>
  </clause>

  <clause id="21585">
    <literal><![CDATA[
      L(x,y / z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(21560,a,21584,a),flip(a)].">
      <j1 rule="hyper" parents="21560 21584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21586">
    <literal><![CDATA[
      L(x,K(y,z) / u,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,20757,a(flip),b,21585,a),flip(a)].">
      <j1 rule="hyper" parents="370 20757 21585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21587">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,15172,a(flip),b,21586,a)].">
      <j1 rule="hyper" parents="60 15172 21586"/>
    </justification>
  </clause>

  <clause id="21588">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(20503,a,21587,a)].">
      <j1 rule="hyper" parents="20503 21587"/>
    </justification>
  </clause>

  <clause id="21590">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = w \ L(w,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,21588,a(flip),b,21488,a),flip(a)].">
      <j1 rule="hyper" parents="125 21588 21488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21591">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,21491,a(flip),b,21590,a),flip(a)].">
      <j1 rule="hyper" parents="370 21491 21590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21592">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(21590(a,2),21520(a,1))].">
      <j1 rule="para" parents="21590 21520"/>
    </justification>
  </clause>

  <clause id="21593">
    <literal><![CDATA[
      a(T(x,y) \ z,(x \ z) \ z,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15930,a(flip),b,21591,a),flip(a)].">
      <j1 rule="hyper" parents="60 15930 21591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21596">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(21591(a,1),15878(a,2,2))].">
      <j1 rule="para" parents="21591 15878"/>
    </justification>
  </clause>

  <clause id="21598">
    <literal><![CDATA[
      T(x,K(y,z) / (u / w)) = T(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15531,a,21554,a)].">
      <j1 rule="hyper" parents="15531 21554"/>
    </justification>
  </clause>

  <clause id="21600">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,w)) = T(x,z * (y \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17209,a,21598,a)].">
      <j1 rule="hyper" parents="17209 21598"/>
    </justification>
  </clause>

  <clause id="21602">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,(y \ L(y,z,z)) * u)
    ]]></literal>
    <justification jstring="[para(3839(a,1),21555(a,1,2,1))].">
      <j1 rule="para" parents="3839 21555"/>
    </justification>
  </clause>

  <clause id="21603">
    <literal><![CDATA[
      K(x,L(y,z * K(u,z),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,15827,a(flip),b,21596,a),flip(a)].">
      <j1 rule="hyper" parents="370 15827 21596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21605">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(5254(a,1),21603(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5254 21603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21609">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,z * y)) = K(x,z \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21186,a(flip),b,21605,a),flip(a)].">
      <j1 rule="hyper" parents="60 21186 21605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21610">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),w,L(z,u,z))) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,17062,a(flip),b,21605,a),flip(a)].">
      <j1 rule="hyper" parents="60 17062 21605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21611">
    <literal><![CDATA[
      K(x,L(y,R(z,u,u),u \ 1)) = K(x,L(y,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16043,a(flip),b,21605,a)].">
      <j1 rule="hyper" parents="60 16043 21605"/>
    </justification>
  </clause>

  <clause id="21613">
    <literal><![CDATA[
      K(x,L(y,R(z,u,u),u \ 1)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15940,a(flip),b,21611,a),flip(a)].">
      <j1 rule="hyper" parents="370 15940 21611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21614">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,R(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16484,a(flip),b,21613,a),flip(a)].">
      <j1 rule="hyper" parents="60 16484 21613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21615">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) \ u) = T(x,a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20540,a(flip),b,21602,a),flip(a)].">
      <j1 rule="hyper" parents="370 20540 21602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21616">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,15614,a(flip),b,21615,a),flip(a)].">
      <j1 rule="hyper" parents="60 15614 21615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21617">
    <literal><![CDATA[
      x / T(x,y * a(z,z,u)) = K(a(u,z,z) * y,x)
    ]]></literal>
    <justification jstring="[para(21616(a,1),5701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="21616 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21618">
    <literal><![CDATA[
      K(a(x,y,y) * z,u) = K(z * a(y,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(5734,a,21617,a),flip(a)].">
      <j1 rule="hyper" parents="5734 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21619">
    <literal><![CDATA[
      a(x,y,y) * (z * K(z * a(y,y,x),u)) = T(a(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[para(21618(a,1),15219(a,1,2,2))].">
      <j1 rule="para" parents="21618 15219"/>
    </justification>
  </clause>

  <clause id="21620">
    <literal><![CDATA[
      T(x * K(x * a(y,z,z),u),a(y,z,z)) = T(x,a(y,z,z)) * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(21618(a,1),17614(a,2,2))].">
      <j1 rule="para" parents="21618 17614"/>
    </justification>
  </clause>

  <clause id="21621">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(L(w,y,K(z,x)),T(a(x,y,z),u) \ v5)
    ]]></literal>
    <justification jstring="[para(21519(a,1),8140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21519 8140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21622">
    <literal><![CDATA[
      K((x * K(y,z)) / u,w) = K(x * (u \ K(y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(21539,a,20828,a)].">
      <j1 rule="hyper" parents="21539 20828"/>
    </justification>
  </clause>

  <clause id="21623">
    <literal><![CDATA[
      K((x / y) * (z \ K(u,y)),w) = K((x / T(y,u)) / z,w)
    ]]></literal>
    <justification jstring="[para(5855(a,1),21622(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5855 21622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21624">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) / u),w) = K((z / T(x,y)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(20797,a,21623,a)].">
      <j1 rule="hyper" parents="20797 21623"/>
    </justification>
  </clause>

  <clause id="21625">
    <literal><![CDATA[
      K((x / T(y,y * z)) / u,w) = K(K(y,z) * ((x / y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,14372,a(flip),b,21624,a),flip(a)].">
      <j1 rule="hyper" parents="60 14372 21624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21626">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(L(z,x,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21510,a(flip),b,21547,a),flip(a)].">
      <j1 rule="hyper" parents="370 21510 21547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21628">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * (y \ 1))) = K(x,z \ ((z \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(20971,a,21609,a)].">
      <j1 rule="hyper" parents="20971 21609"/>
    </justification>
  </clause>

  <clause id="21630">
    <literal><![CDATA[
      K(x,L(T((y * z) / y,y) \ u,y,T(y,z) * z)) = K(x,y \ ((y \ ((y * z) / y)) \ u))
    ]]></literal>
    <justification jstring="[para(5448(a,2),21609(a,1,2,3))].">
      <j1 rule="para" parents="5448 21609"/>
    </justification>
  </clause>

  <clause id="21631">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,L(y,z,z) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17046,a(flip),b,21614,a),flip(a)].">
      <j1 rule="hyper" parents="370 17046 21614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21632">
    <literal><![CDATA[
      K((x / ((y \ z) \ z)) / u,w) = K(K(y,z) * ((x / y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20165,a(flip),b,21625,a)].">
      <j1 rule="hyper" parents="60 20165 21625"/>
    </justification>
  </clause>

  <clause id="21633">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,(z * (z * y)) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,20391,a(flip),b,21631,a),flip(a)].">
      <j1 rule="hyper" parents="370 20391 21631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21634">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (z \ (z \ (u * z))))
    ]]></literal>
    <justification jstring="[hyper(370,a,18127,a(flip),b,21633,a),flip(a)].">
      <j1 rule="hyper" parents="370 18127 21633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21635">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (z \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(17(a,2),21634(a,2,2,2,2))].">
      <j1 rule="para" parents="17 21634"/>
    </justification>
  </clause>

  <clause id="21636">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(20986,a,21635,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20986 21635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21637">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(21635(a,2),20986(a,1))].">
      <j1 rule="para" parents="21635 20986"/>
    </justification>
  </clause>

  <clause id="21638">
    <literal><![CDATA[
      K(x,L((y * T(z,u)) / w,y,z)) = K(x,y / (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(21529,a,21636,a)].">
      <j1 rule="hyper" parents="21529 21636"/>
    </justification>
  </clause>

  <clause id="21639">
    <literal><![CDATA[
      K(L((x * y) / z,x,y),u) = (w * K(u,x / (z / y))) \ w
    ]]></literal>
    <justification jstring="[para(21636(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="21636 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21640">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z * (y / z),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (y / z)) / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(5804(a,1),21637(a,1,2,1,1))].">
      <j1 rule="para" parents="5804 21637"/>
    </justification>
  </clause>

  <clause id="21641">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) / z)) = w
    ]]></literal>
    <justification jstring="[para(15598(a,1),21637(a,1))].">
      <j1 rule="para" parents="15598 21637"/>
    </justification>
  </clause>

  <clause id="21642">
    <literal><![CDATA[
      K(x,L((y * T(z,u)) / w,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w / T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(19296(a,1),21637(a,1))].">
      <j1 rule="para" parents="19296 21637"/>
    </justification>
  </clause>

  <clause id="21643">
    <literal><![CDATA[
      K(x,L(T(y * z,K(z,u)) / w,z,y)) = K(x,z / (w / T(y,T(z,u))))
    ]]></literal>
    <justification jstring="[para(8487(a,2),21638(a,1,2,1,1))].">
      <j1 rule="para" parents="8487 21638"/>
    </justification>
  </clause>

  <clause id="21644">
    <literal><![CDATA[
      K(L((x * y) / z,x,y),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,21639,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 21639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21645">
    <literal><![CDATA[
      K((x * y) / z,L(u,x,y)) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(13036,a,21644,a)].">
      <j1 rule="hyper" parents="13036 21644"/>
    </justification>
  </clause>

  <clause id="21646">
    <literal><![CDATA[
      K((x * (y \ z)) / (z / (z / y)),L(u,x,y \ z)) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(1943(a,1),21645(a,2,1,2))].">
      <j1 rule="para" parents="1943 21645"/>
    </justification>
  </clause>

  <clause id="21647">
    <literal><![CDATA[
      K((x / ((y \ z) \ z)) / u,w) = K((x / T(y,z)) / u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,21624,a(flip),b,21632,a),flip(a)].">
      <j1 rule="hyper" parents="370 21624 21632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21648">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) = K(x,T(y,z) / v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,17277,a(flip),b,21568,a),flip(a)].">
      <j1 rule="hyper" parents="370 17277 21568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21649">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) / v5) = v6
    ]]></literal>
    <justification jstring="[para(21568(a,2),17279(a,1))].">
      <j1 rule="para" parents="21568 17279"/>
    </justification>
  </clause>

  <clause id="21650">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ w) / v5) = K(x,T(y,u \ (z * w)) / v5)
    ]]></literal>
    <justification jstring="[para(656(a,1),21648(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="656 21648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21651">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ w) / v5) = K(x,T(y,u * (z * w)) / v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,18523,a(flip),b,21650,a),flip(a)].">
      <j1 rule="hyper" parents="370 18523 21650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21652">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) / v5) = K(x,T(y,u * (z * w)) / v5)
    ]]></literal>
    <justification jstring="[hyper(18524,a,21651,a)].">
      <j1 rule="hyper" parents="18524 21651"/>
    </justification>
  </clause>

  <clause id="21653">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) / ((u \ z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u \ z) * w) \ y) = v5
    ]]></literal>
    <justification jstring="[para(21652(a,1),14407(a,1))].">
      <j1 rule="para" parents="21652 14407"/>
    </justification>
  </clause>

  <clause id="21654">
    <literal><![CDATA[
      L(x,y,z) \ T((x \ 1) * L(x,y,z),u) = L(1 / x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,21544,a,b,21569,a),flip(a)].">
      <j1 rule="hyper" parents="370 21544 21569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21655">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,u) = a(R(z,x,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21513,a(flip),b,21583,a),flip(a)].">
      <j1 rule="hyper" parents="370 21513 21583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21657">
    <literal><![CDATA[
      a(R(x,y,z),u,u) = a(L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21626,a(flip),b,21655,a),flip(a)].">
      <j1 rule="hyper" parents="60 21626 21655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21658">
    <literal><![CDATA[
      a(L(T(x,y * z),y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,16660,a(flip),b,21657,a),flip(a)].">
      <j1 rule="hyper" parents="60 16660 21657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21659">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21510,a(flip),b,21658,a)].">
      <j1 rule="hyper" parents="60 21510 21658"/>
    </justification>
  </clause>

  <clause id="21661">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (y * z) = (a(x,u,u) * y) * z
    ]]></literal>
    <justification jstring="[para(21659(a,2),103(a,1,1))].">
      <j1 rule="para" parents="21659 103"/>
    </justification>
  </clause>

  <clause id="21662">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,u)) = (a(z,u,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,16549,a(flip),b,21661,a)].">
      <j1 rule="hyper" parents="60 16549 21661"/>
    </justification>
  </clause>

  <clause id="21663">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,u)) = (y * a(z,u,u)) * x
    ]]></literal>
    <justification jstring="[para(15848(a,1),21662(a,2,1))].">
      <j1 rule="para" parents="15848 21662"/>
    </justification>
  </clause>

  <clause id="21664">
    <literal><![CDATA[
      (((a(x,y,y) * z) * u) / u) \ (u * (a(x,y,y) * z)) = T(u,z)
    ]]></literal>
    <justification jstring="[para(21662(a,1),16047(a,1,1,1))].">
      <j1 rule="para" parents="21662 16047"/>
    </justification>
  </clause>

  <clause id="21665">
    <literal><![CDATA[
      ((x * (y * a(z,u,u))) / y) \ ((y * a(z,u,u)) * x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(21663(a,1),16045(a,1,2))].">
      <j1 rule="para" parents="21663 16045"/>
    </justification>
  </clause>

  <clause id="21666">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (u * (a(x,y,y) * z)) = T(u,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),21664(a,1,1))].">
      <j1 rule="para" parents="6 21664"/>
    </justification>
  </clause>

  <clause id="21667">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(389,a,21666,a)].">
      <j1 rule="hyper" parents="389 21666"/>
    </justification>
  </clause>

  <clause id="21669">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,21616,a(flip),b,21667,a)].">
      <j1 rule="hyper" parents="60 21616 21667"/>
    </justification>
  </clause>

  <clause id="21670">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) = T(x,y * a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,21669,a,b,21669,a)].">
      <j1 rule="hyper" parents="370 21669 21669"/>
    </justification>
  </clause>

  <clause id="21672">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(19340,a,21670,a)].">
      <j1 rule="hyper" parents="19340 21670"/>
    </justification>
  </clause>

  <clause id="21675">
    <literal><![CDATA[
      T(x,y * a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(21670(a,1),14330(a,1))].">
      <j1 rule="para" parents="21670 14330"/>
    </justification>
  </clause>

  <clause id="21677">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(21616(a,2),21675(a,1))].">
      <j1 rule="para" parents="21616 21675"/>
    </justification>
  </clause>

  <clause id="21678">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,a(w,w,v5) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21616,a,b,21672,a)].">
      <j1 rule="hyper" parents="370 21616 21672"/>
    </justification>
  </clause>

  <clause id="21679">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(19341,a,21678,a),flip(a)].">
      <j1 rule="hyper" parents="19341 21678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21680">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,(w \ (v5 \ ((1 / v5) \ w))) * u)
    ]]></literal>
    <justification jstring="[para(2117(a,1),21678(a,2,2,1))].">
      <j1 rule="para" parents="2117 21678"/>
    </justification>
  </clause>

  <clause id="21681">
    <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(21678(a,2),19341(a,1))].">
      <j1 rule="para" parents="21678 19341"/>
    </justification>
  </clause>

  <clause id="21682">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,21678,a,b,21679,a)].">
      <j1 rule="hyper" parents="60 21678 21679"/>
    </justification>
  </clause>

  <clause id="21683">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(v5,v6,v6) * u) = w
    ]]></literal>
    <justification jstring="[para(21679(a,2),19340(a,1))].">
      <j1 rule="para" parents="21679 19340"/>
    </justification>
  </clause>

  <clause id="21685">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u * ((w \ ((1 / w) \ v5)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,20541,a(flip),b,21682,a),flip(a)].">
      <j1 rule="hyper" parents="370 20541 21682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21689">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * a(v5,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(21678(a,1),21681(a,1))].">
      <j1 rule="para" parents="21678 21681"/>
    </justification>
  </clause>

  <clause id="21690">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(v5,v6,v6) * u) = w
    ]]></literal>
    <justification jstring="[para(2117(a,1),21683(a,1,2,1))].">
      <j1 rule="para" parents="2117 21683"/>
    </justification>
  </clause>

  <clause id="21693">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,(w \ (v5 \ ((1 / v5) \ w))) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21678,a(flip),b,21680,a)].">
      <j1 rule="hyper" parents="60 21678 21680"/>
    </justification>
  </clause>

  <clause id="21696">
    <literal><![CDATA[
      x * K(x * a(y,z,z),u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(15748,a,21665,a)].">
      <j1 rule="hyper" parents="15748 21665"/>
    </justification>
  </clause>

  <clause id="21697">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) \ (1 / x) = K(z,(x \ 1) * L(x,y,u))
    ]]></literal>
    <justification jstring="[para(21654(a,1),18833(a,1,1))].">
      <j1 rule="para" parents="21654 18833"/>
    </justification>
  </clause>

  <clause id="21698">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,1 / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21494,a(flip),b,21697,a),flip(a)].">
      <j1 rule="hyper" parents="60 21494 21697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21699">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,y * 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,19642,a(flip),b,21698,a),flip(a)].">
      <j1 rule="hyper" parents="370 19642 21698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21700">
    <literal><![CDATA[
      K(x,(y \ 1) * L(y,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),21699(a,2,3,2))].">
      <j1 rule="para" parents="3 21699"/>
    </justification>
  </clause>

  <clause id="21701">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(15233,a,21700,a)].">
      <j1 rule="hyper" parents="15233 21700"/>
    </justification>
  </clause>

  <clause id="21702">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(y,y \ z,K(x,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(656(a,1),21701(a,1,2,2))].">
      <j1 rule="para" parents="656 21701"/>
    </justification>
  </clause>

  <clause id="21703">
    <literal><![CDATA[
      K(T(x,y * K(z,u)),w * (K(z,u) * y)) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(8896,a,21543,a),flip(a)].">
      <j1 rule="hyper" parents="8896 21543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21704">
    <literal><![CDATA[
      x * a(a(y,z,u) * x,z,K(u,y)) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15894(a,1),21581(a,1,2))].">
      <j1 rule="para" parents="15894 21581"/>
    </justification>
  </clause>

  <clause id="21706">
    <literal><![CDATA[
      a(T(x,y) \ z,T(x,z),K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15014,a(flip),b,21593,a)].">
      <j1 rule="hyper" parents="60 15014 21593"/>
    </justification>
  </clause>

  <clause id="21707">
    <literal><![CDATA[
      a(T(x,y) \ z,x,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(21592,a,21706,a)].">
      <j1 rule="hyper" parents="21592 21706"/>
    </justification>
  </clause>

  <clause id="21709">
    <literal><![CDATA[
      a(T(x,y) * z,x,K(u,w)) = a(w,z,K(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19693,a(flip),b,21707,a)].">
      <j1 rule="hyper" parents="60 19693 21707"/>
    </justification>
  </clause>

  <clause id="21710">
    <literal><![CDATA[
      K(x,T(y * (K(z,u) * w),w * K(z,u))) = K(x,K(z,u) * (w * y))
    ]]></literal>
    <justification jstring="[hyper(8181,a,21703,a)].">
      <j1 rule="hyper" parents="8181 21703"/>
    </justification>
  </clause>

  <clause id="21711">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,19695,a(flip),b,21704,a)].">
      <j1 rule="hyper" parents="60 19695 21704"/>
    </justification>
  </clause>

  <clause id="21712">
    <literal><![CDATA[
      K(K(x,K(y,z) * (u * w)) * v5,v6) = K(v5 * K(w * (K(y,z) * u),x),v6)
    ]]></literal>
    <justification jstring="[para(21710(a,1),17751(a,1,1,1))].">
      <j1 rule="para" parents="21710 17751"/>
    </justification>
  </clause>

  <clause id="21713">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * y)) = K(x,z \ ((z \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(3426(a,1),21628(a,1,2))].">
      <j1 rule="para" parents="3426 21628"/>
    </justification>
  </clause>

  <clause id="21714">
    <literal><![CDATA[
      K(x,L((y * z) / u,z,y)) = K(x,z / (u / T(y,T(z,w))))
    ]]></literal>
    <justification jstring="[hyper(17821,a,21643,a)].">
      <j1 rule="hyper" parents="17821 21643"/>
    </justification>
  </clause>

  <clause id="21716">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(y,y \ z,K(x,(y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,21702,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 21702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21717">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(x,y \ z,K(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,19655,a(flip),b,21716,a),flip(a)].">
      <j1 rule="hyper" parents="370 19655 21716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21718">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ (z \ (y * u))) = a(z * u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15927,a(flip),b,21717,a),flip(a)].">
      <j1 rule="hyper" parents="370 15927 21717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21720">
    <literal><![CDATA[
      K(x,y * R(K(z,u) / w,v5,v5)) = K(x,y * R(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[para(21514(a,1),21515(a,1,2,2))].">
      <j1 rule="para" parents="21514 21515"/>
    </justification>
  </clause>

  <clause id="21721">
    <literal><![CDATA[
      K(x,y * R(z \ K(u,w),v5,v5)) = K(x,y * L(K(u,w) / z,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,20191,a(flip),b,21720,a),flip(a)].">
      <j1 rule="hyper" parents="60 20191 21720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21722">
    <literal><![CDATA[
      K(x,y * L(K(z,u) / w,v5,v5)) = K(x,y * L(w \ K(z,u),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,20191,a(flip),b,21721,a),flip(a)].">
      <j1 rule="hyper" parents="60 20191 21721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21723">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = L(L(x,z,K(y,u)),z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(21541,a,21559,a),flip(a)].">
      <j1 rule="hyper" parents="21541 21559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21724">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,21506,a(flip),b,21723,a),flip(a)].">
      <j1 rule="hyper" parents="370 21506 21723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21725">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15680,a,21724,a)].">
      <j1 rule="hyper" parents="15680 21724"/>
    </justification>
  </clause>

  <clause id="21727">
    <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(125,a,21724,a(flip),b,1759,a(flip))].">
      <j1 rule="hyper" parents="125 21724 1759"/>
    </justification>
  </clause>

  <clause id="21728">
    <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="[para(21724(a,1),1821(a,1,1))].">
      <j1 rule="para" parents="21724 1821"/>
    </justification>
  </clause>

  <clause id="21729">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(37,a,15678,a,b,21725,a),flip(a)].">
      <j1 rule="hyper" parents="37 15678 21725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21731">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19324,a(flip),b,21729,a),flip(a)].">
      <j1 rule="hyper" parents="370 19324 21729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21732">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) / x = K(x,y / a(z,u,w))
    ]]></literal>
    <justification jstring="[para(21731(a,1),19393(a,1,1))].">
      <j1 rule="para" parents="21731 19393"/>
    </justification>
  </clause>

  <clause id="21733">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) \ x = K(y / a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(21731(a,1),19394(a,1,1))].">
      <j1 rule="para" parents="21731 19394"/>
    </justification>
  </clause>

  <clause id="21734">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) = K(x,y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5305,a,21732,a),flip(a)].">
      <j1 rule="hyper" parents="5305 21732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21735">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(19373,a,21734,a)].">
      <j1 rule="hyper" parents="19373 21734"/>
    </justification>
  </clause>

  <clause id="21736">
    <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(21734(a,1),19373(a,1))].">
      <j1 rule="para" parents="21734 19373"/>
    </justification>
  </clause>

  <clause id="21737">
    <literal><![CDATA[
      K(x,L(L(y,z,z) \ u,a(y,z,z),y)) = K(x,(y \ u) * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,17004,a,b,21735,a)].">
      <j1 rule="hyper" parents="60 17004 21735"/>
    </justification>
  </clause>

  <clause id="21738">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(19358,a,21735,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19358 21735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21739">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = (w \ K(u,a(y,y,x) * z)) \ (w \ 1)
    ]]></literal>
    <justification jstring="[para(21738(a,1),16602(a,2,1,2))].">
      <j1 rule="para" parents="21738 16602"/>
    </justification>
  </clause>

  <clause id="21740">
    <literal><![CDATA[
      K(x / a(y,z,u),w) = K(x * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(5710,a,21733,a),flip(a)].">
      <j1 rule="hyper" parents="5710 21733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21741">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u * a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(19355,a,21740,a)].">
      <j1 rule="hyper" parents="19355 21740"/>
    </justification>
  </clause>

  <clause id="21742">
    <literal><![CDATA[
      K(x,(y \ z) * a(y,u,u)) = K(x,L(y,u,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(16532,a,21737,a),flip(a)].">
      <j1 rule="hyper" parents="16532 21737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21743">
    <literal><![CDATA[
      K(L(x,y,y) * (x \ z),u) = K(a(y,y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,15194,a(flip),b,21739,a),flip(a)].">
      <j1 rule="hyper" parents="370 15194 21739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21744">
    <literal><![CDATA[
      K(a(x,x,y) \ z,u) = K(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(16624,a,21743,a)].">
      <j1 rule="hyper" parents="16624 21743"/>
    </justification>
  </clause>

  <clause id="21745">
    <literal><![CDATA[
      K((x / y) * L(y,z,z),u) = K(a(z,z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19616,a(flip),b,21743,a)].">
      <j1 rule="hyper" parents="60 19616 21743"/>
    </justification>
  </clause>

  <clause id="21746">
    <literal><![CDATA[
      K(a(x,x,y) * (z * y),u) = K(z * L(y,x,x),u)
    ]]></literal>
    <justification jstring="[para(6(a,1),21745(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 21745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21747">
    <literal><![CDATA[
      K(a(x,x,y) * (z * y),u) = u / T(u,z * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a(flip),b,21746,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 21746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21748">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * z)) = T(x,u * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(5733,a,21747,a)].">
      <j1 rule="hyper" parents="5733 21747"/>
    </justification>
  </clause>

  <clause id="21749">
    <literal><![CDATA[
      K(x * K(y * (K(z,u) * w),v5),v6) = K(K(w * y,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,18659,a(flip),b,21712,a),flip(a)].">
      <j1 rule="hyper" parents="60 18659 21712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      K(K(x * (T(y,z) * u),w) * v5,v6) = K(K((y \ x) * u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,20142,a(flip),b,21749,a),flip(a)].">
      <j1 rule="hyper" parents="60 20142 21749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21752">
    <literal><![CDATA[
      K(K((x \ y) * z,u) * w,v5) = K(K(y * (x * z),u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,19994,a(flip),b,21751,a),flip(a)].">
      <j1 rule="hyper" parents="60 19994 21751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21753">
    <literal><![CDATA[
      K(x * K(y,(z / T(u,w)) * v5),v6) = K(K(z * (u * v5),y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,19844,a,b,21752,a)].">
      <j1 rule="hyper" parents="60 19844 21752"/>
    </justification>
  </clause>

  <clause id="21754">
    <literal><![CDATA[
      K(K(x * (y * z),u * w) * w,u) = K(w,T(u,K(v5,y) * ((x / y) * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19819,a(flip),b,21753,a),flip(a)].">
      <j1 rule="hyper" parents="60 19819 21753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21755">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ 1) \ u) = (a(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(961,a,21728,a)].">
      <j1 rule="hyper" parents="961 21728"/>
    </justification>
  </clause>

  <clause id="21757">
    <literal><![CDATA[
      K(x * K(y * (z * u),x * w),w) = K(x,T(w,K(v5,z) * ((y / z) * u)))
    ]]></literal>
    <justification jstring="[para(12560(a,1),21754(a,1,1))].">
      <j1 rule="para" parents="12560 21754"/>
    </justification>
  </clause>

  <clause id="21758">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * ((w / u) * v5))) = K(x,T(y,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(20347,a,21757,a),flip(a)].">
      <j1 rule="hyper" parents="20347 21757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21759">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(8401(a,1),21758(a,1,2,2))].">
      <j1 rule="para" parents="8401 21758"/>
    </justification>
  </clause>

  <clause id="21760">
    <literal><![CDATA[
      K(x,T(y,((z * u) \ w) * (1 / u))) = K(x,T(y,w * ((z * (u \ 1)) * u)))
    ]]></literal>
    <justification jstring="[para(1288(a,2),21759(a,2,2,2,2))].">
      <j1 rule="para" parents="1288 21759"/>
    </justification>
  </clause>

  <clause id="21761">
    <literal><![CDATA[
      K(x,T(y,z * ((u * (w \ 1)) * w))) = K(x,T(y,((u * w) \ z) / w))
    ]]></literal>
    <justification jstring="[para(15400(a,1),21760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15400 21760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21762">
    <literal><![CDATA[
      K(x,T(y,z * ((u * (w \ 1)) * w))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17315,a(flip),b,21761,a),flip(a)].">
      <j1 rule="hyper" parents="370 17315 21761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21763">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) * (1 / w)))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[para(1288(a,1),21762(a,1,2,2,2))].">
      <j1 rule="para" parents="1288 21762"/>
    </justification>
  </clause>

  <clause id="21764">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) * (w \ 1)))) = K(x,T(y,w * ((u * w) \ z)))
    ]]></literal>
    <justification jstring="[para(4674(a,1),21763(a,1,2))].">
      <j1 rule="para" parents="4674 21763"/>
    </justification>
  </clause>

  <clause id="21765">
    <literal><![CDATA[
      K(x,T(y,z * ((u * z) \ w))) = K(x,T(y,w * R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1111(a,1),21764(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1111 21764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21766">
    <literal><![CDATA[
      K(x,T(y,z * ((u * z) \ w))) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,20105,a(flip),b,21765,a),flip(a)].">
      <j1 rule="hyper" parents="370 20105 21765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21767">
    <literal><![CDATA[
      K(x,T(T((y * z) * (u / (y * z)),y * z),u * L(y,z,z))) = K(x,(z * (u / T(y * z,u))) * R(y,z,u / T(y * z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14899,a(flip),b,21766,a),flip(a)].">
      <j1 rule="hyper" parents="60 14899 21766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21768">
    <literal><![CDATA[
      K((x * (y \ z)) / T(y,z),L(u,x,y \ z)) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20991,a(flip),b,21646,a)].">
      <j1 rule="hyper" parents="60 20991 21646"/>
    </justification>
  </clause>

  <clause id="21769">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K(x / (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21645,a(flip),b,21768,a)].">
      <j1 rule="hyper" parents="60 21645 21768"/>
    </justification>
  </clause>

  <clause id="21770">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K(x / ((y \ z) \ y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20933,a(flip),b,21769,a),flip(a)].">
      <j1 rule="hyper" parents="370 20933 21769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21771">
    <literal><![CDATA[
      K(x,(y \ T(T(a(z,u,w),v5),v5)) * v6) = K(x,(a(z,u,w) / y) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,21570,a(flip),b,21517,a),flip(a)].">
      <j1 rule="hyper" parents="370 21570 21517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21773">
    <literal><![CDATA[
      K(x,(a(y,z,u) / w) * v5) = K(x,(w \ a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(1336(a,1),21771(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1336 21771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21774">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * u) = K(x,(y \ a(w,v5,K(v6,v7))) * u)
    ]]></literal>
    <justification jstring="[hyper(20386,a,21773,a)].">
      <j1 rule="hyper" parents="20386 21773"/>
    </justification>
  </clause>

  <clause id="21775">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19893,a(flip),b,21774,a),flip(a)].">
      <j1 rule="hyper" parents="370 19893 21774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21776">
    <literal><![CDATA[
      K(x,((((y * z) / y) \ 1) * u) \ w) = K(x,K(z,y) * (((z \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(21533,a,20807,a)].">
      <j1 rule="hyper" parents="21533 20807"/>
    </justification>
  </clause>

  <clause id="21777">
    <literal><![CDATA[
      K(x,((((y * z) / y) \ 1) * u) \ w) = K(x,((T(z,y) \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,21094,a(flip),b,21776,a),flip(a)].">
      <j1 rule="hyper" parents="370 21094 21776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21778">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,((T(z,y) \ 1) * T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21452,a,b,21777,a)].">
      <j1 rule="hyper" parents="60 21452 21777"/>
    </justification>
  </clause>

  <clause id="21779">
    <literal><![CDATA[
      T(x * K(x * a(y,z,z),u),a(y,z,z)) = x * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(15846(a,1),21620(a,2,1))].">
      <j1 rule="para" parents="15846 21620"/>
    </justification>
  </clause>

  <clause id="21780">
    <literal><![CDATA[
      x * K(x * a(y,z,z),u) = x * K(x * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15851,a,21779,a),flip(a)].">
      <j1 rule="hyper" parents="15851 21779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21782">
    <literal><![CDATA[
      x * K(x * a(y,y,z),u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21696,a(flip),b,21780,a),flip(a)].">
      <j1 rule="hyper" parents="60 21696 21780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21784">
    <literal><![CDATA[
      K(x * a(y,y,z),u) = K(x * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(31,a,21782,a,b,21782,a)].">
      <j1 rule="hyper" parents="31 21782 21782"/>
    </justification>
  </clause>

  <clause id="21786">
    <literal><![CDATA[
      T(a(x,y,y) * z,u) = a(x,y,y) * T(z,u)
    ]]></literal>
    <justification jstring="[para(21782(a,1),21619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21782 21619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21791">
    <literal><![CDATA[
      (x * a(y,z,z)) / T(a(y,z,z) * x,u) = K(u,x)
    ]]></literal>
    <justification jstring="[para(21786(a,2),15855(a,1,2))].">
      <j1 rule="para" parents="21786 15855"/>
    </justification>
  </clause>

  <clause id="21792">
    <literal><![CDATA[
      K(x,a(y,z,z)) * K(u,a(y,z,z) * x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7492,a,21791,a)].">
      <j1 rule="hyper" parents="7492 21791"/>
    </justification>
  </clause>

  <clause id="21793">
    <literal><![CDATA[
      a(x,y,K(y,z)) * K(u,a(z,y,y) * x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(15816(a,2),21792(a,1,1))].">
      <j1 rule="para" parents="15816 21792"/>
    </justification>
  </clause>

  <clause id="21794">
    <literal><![CDATA[
      1 * K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6357(a,1),21793(a,1,1))].">
      <j1 rule="para" parents="6357 21793"/>
    </justification>
  </clause>

  <clause id="21795">
    <literal><![CDATA[
      K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,21794,a)].">
      <j1 rule="hyper" parents="131 21794"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      K(x,y * L(z,u,u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,20440,a(flip),b,21795,a)].">
      <j1 rule="hyper" parents="60 20440 21795"/>
    </justification>
  </clause>

  <clause id="21799">
    <literal><![CDATA[
      K(x,y * a(z,u,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(15848(a,1),21795(a,1,2))].">
      <j1 rule="para" parents="15848 21795"/>
    </justification>
  </clause>

  <clause id="21802">
    <literal><![CDATA[
      K(x,L(y \ z,u,T(u,y) * y)) = K(x,u \ ((u \ ((u * y) / u)) \ z))
    ]]></literal>
    <justification jstring="[para(262(a,1),21630(a,1,2,1,1))].">
      <j1 rule="para" parents="262 21630"/>
    </justification>
  </clause>

  <clause id="21803">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((u \ ((u * y) / u)) \ z))
    ]]></literal>
    <justification jstring="[para(6670(a,1),21802(a,1,2))].">
      <j1 rule="para" parents="6670 21802"/>
    </justification>
  </clause>

  <clause id="21804">
    <literal><![CDATA[
      K(x,y \ ((y \ ((y * z) / y)) \ u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21578,a(flip),b,21803,a),flip(a)].">
      <j1 rule="hyper" parents="60 21578 21803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21805">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) / y,T(z,y)) = (y \ (x \ ((1 / x) \ y))) * 1
    ]]></literal>
    <justification jstring="[para(15500(a,1),21573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15500 21573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21807">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) / y,T(z,y)) = y \ (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,21805,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 21805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21810">
    <literal><![CDATA[
      T(x \ (y \ ((1 / y) \ x)),T(z,x)) = x \ (y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(21501(a,1),21807(a,1,1))].">
      <j1 rule="para" parents="21501 21807"/>
    </justification>
  </clause>

  <clause id="21811">
    <literal><![CDATA[
      T(x \ (y \ ((1 / y) \ x)),z) = x \ (y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[hyper(9012,a,21810,a)].">
      <j1 rule="hyper" parents="9012 21810"/>
    </justification>
  </clause>

  <clause id="21812">
    <literal><![CDATA[
      x / (y \ (z \ ((1 / z) \ y))) = (y \ (z \ ((1 / z) \ y))) \ x
    ]]></literal>
    <justification jstring="[para(21811(a,1),308(a,1,2))].">
      <j1 rule="para" parents="21811 308"/>
    </justification>
  </clause>

  <clause id="21813">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ u) = T(x,u * ((z \ ((1 / z) \ y)) \ y))
    ]]></literal>
    <justification jstring="[para(21812(a,1),15407(a,1,2))].">
      <j1 rule="para" parents="21812 15407"/>
    </justification>
  </clause>

  <clause id="21814">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) \ u) = T(x,a(w,v5,v5) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21685,a,b,21813,a),flip(a)].">
      <j1 rule="hyper" parents="370 21685 21813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21816">
    <literal><![CDATA[
      T(x,a(y,z,z) * (((u \ ((1 / u) \ w)) \ w) \ v5)) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,15358,a(flip),b,21814,a),flip(a)].">
      <j1 rule="hyper" parents="60 15358 21814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21817">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) \ z) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(21677,a,21816,a)].">
      <j1 rule="hyper" parents="21677 21816"/>
    </justification>
  </clause>

  <clause id="21819">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) \ z) / u) = T(x,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(6530,a,21817,a),flip(a)].">
      <j1 rule="hyper" parents="6530 21817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21821">
    <literal><![CDATA[
      R(K(x,y),z,L(z \ u,z,K(x,y))) = (K(x,y) * u) / (u * a(y,z,K(x,z * u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),21580(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 21580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21822">
    <literal><![CDATA[
      K(x,L(y,z,L(z \ u,z,K(x,y)))) = (K(x,y) * u) / (u * a(y,z,K(x,z * u)))
    ]]></literal>
    <justification jstring="[hyper(16435,a,21821,a)].">
      <j1 rule="hyper" parents="16435 21821"/>
    </justification>
  </clause>

  <clause id="21824">
    <literal><![CDATA[
      (K(x,y) * z) / (z * a(y,u,K(x,u * z))) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[hyper(21564,a,21822,a),flip(a)].">
      <j1 rule="hyper" parents="21564 21822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21825">
    <literal><![CDATA[
      (K(x,y) * z) / (z * a(y,u,K(x,u * z))) = K(x,L(y,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19696,a(flip),b,21824,a),flip(a)].">
      <j1 rule="hyper" parents="370 19696 21824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21827">
    <literal><![CDATA[
      K(x,L((y / R(z,u,z)) \ T(w,z),w,z)) = K(x,T(y,R(z,u,z)) \ (w * R(z,u,z)))
    ]]></literal>
    <justification jstring="[para(14005(a,1),21610(a,1,2))].">
      <j1 rule="para" parents="14005 21610"/>
    </justification>
  </clause>

  <clause id="21829">
    <literal><![CDATA[
      K(x,T(y,R(z,u,z)) \ (w * R(z,u,z))) = K(x,(z * (y / R(z,u,z))) \ (w * z))
    ]]></literal>
    <justification jstring="[hyper(13075,a,21827,a),flip(a)].">
      <j1 rule="hyper" parents="13075 21827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      K(x,(y * (z / R(y,u,y))) \ (w * y)) = K(x,T(z,y) \ (w * R(y,u,y)))
    ]]></literal>
    <justification jstring="[para(7315(a,1),21829(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7315 21829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21831">
    <literal><![CDATA[
      K(x,(y * (z / R(y,u,y))) \ (w * y)) = K(x,T(z,y) \ (w * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,14418,a(flip),b,21830,a),flip(a)].">
      <j1 rule="hyper" parents="370 14418 21830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21834">
    <literal><![CDATA[
      K(x,(((((y * z) / y) * ((y * z) / y)) \ u) * T(z,y)) \ w) = K(x,(u * (T(z,y) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,19562,a(flip),b,21778,a),flip(a)].">
      <j1 rule="hyper" parents="370 19562 21778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21835">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,(y * (T(u,z) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(21456,a,21834,a)].">
      <j1 rule="hyper" parents="21456 21834"/>
    </justification>
  </clause>

  <clause id="21836">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K((x \ ((1 / x) \ y)) \ y,z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(6410(a,1),21576(a,1,2,1))].">
      <j1 rule="para" parents="6410 21576"/>
    </justification>
  </clause>

  <clause id="21837">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ (K(y \ L(y,x,x),z) * y) = T(((y \ (x \ ((1 / x) \ y))) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(16667(a,1),21836(a,1,2,1))].">
      <j1 rule="para" parents="16667 21836"/>
    </justification>
  </clause>

  <clause id="21838">
    <literal><![CDATA[
      T(((x \ (y \ ((1 / y) \ x))) * x) \ x,z) = (y \ ((1 / y) \ x)) \ (1 * x)
    ]]></literal>
    <justification jstring="[para(15116(a,1),21837(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15116 21837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21839">
    <literal><![CDATA[
      T(((x \ (y \ ((1 / y) \ x))) * x) \ x,z) = (y \ ((1 / y) \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(392,a,21838,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="392 21838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21841">
    <literal><![CDATA[
      T((x \ ((1 / x) \ y)) \ y,z) = (x \ ((1 / x) \ y)) \ y
    ]]></literal>
    <justification jstring="[para(21572(a,1),21839(a,1,1,1))].">
      <j1 rule="para" parents="21572 21839"/>
    </justification>
  </clause>

  <clause id="21842">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(L(w,y,K(z,x)),a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19935,a(flip),b,21621,a),flip(a)].">
      <j1 rule="hyper" parents="370 19935 21621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21844">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ (T(a(x,y,z),u) * w),v5 / T(a(x,y,z),u)) = K(w,a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19279,a(flip),b,21842,a),flip(a)].">
      <j1 rule="hyper" parents="370 19279 21842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21846">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / T(a(y,z,u),v6)) = v5
    ]]></literal>
    <justification jstring="[para(21844(a,1),7355(a,1))].">
      <j1 rule="para" parents="21844 7355"/>
    </justification>
  </clause>

  <clause id="21847">
    <literal><![CDATA[
      K(x,y / T(a(z,u,w),v5)) = K(x,y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(21846,a,21735,a)].">
      <j1 rule="hyper" parents="21846 21735"/>
    </justification>
  </clause>

  <clause id="21849">
    <literal><![CDATA[
      K(x,T(a(y,z,K(u,w)) * v5,a(y,z,w) \ 1)) = K(x,((a(y,z,w) \ 1) \ v5) * a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21280,a(flip),b,21847,a)].">
      <j1 rule="hyper" parents="60 21280 21847"/>
    </justification>
  </clause>

  <clause id="21851">
    <literal><![CDATA[
      K(x,T(a(y,z,K(u,w)) * v5,a(y,z,w) \ 1)) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15229,a(flip),b,21849,a),flip(a)].">
      <j1 rule="hyper" parents="370 15229 21849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21852">
    <literal><![CDATA[
      K(x,L(a(y,z,K(u,w)) * v5,z,K(w,y))) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[para(21540(a,1),21851(a,1,2))].">
      <j1 rule="para" parents="21540 21851"/>
    </justification>
  </clause>

  <clause id="21853">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,a(y,z,w) * (v5 * a(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(21498,a,21852,a)].">
      <j1 rule="hyper" parents="21498 21852"/>
    </justification>
  </clause>

  <clause id="21854">
    <literal><![CDATA[
      K(x,a(y,z,u) * (w * a(y,z,u))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(21198,a,21853,a),flip(a)].">
      <j1 rule="hyper" parents="21198 21853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21857">
    <literal><![CDATA[
      K(x,(y * (1 / (y \ L(y,z,z)))) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21352,a(flip),b,21854,a)].">
      <j1 rule="hyper" parents="60 21352 21854"/>
    </justification>
  </clause>

  <clause id="21859">
    <literal><![CDATA[
      K(x,(y * (L(y,z,z) \ y)) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(14169(a,1),21857(a,1,2,1,2))].">
      <j1 rule="para" parents="14169 21857"/>
    </justification>
  </clause>

  <clause id="21860">
    <literal><![CDATA[
      K(x,(y * a(z,z,y)) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),21859(a,1,2,1,2))].">
      <j1 rule="para" parents="1362 21859"/>
    </justification>
  </clause>

  <clause id="21861">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) * u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21317,a(flip),b,21860,a)].">
      <j1 rule="hyper" parents="60 21317 21860"/>
    </justification>
  </clause>

  <clause id="21862">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) \ u) = K(x,T(L(y,z,z),1) * u)
    ]]></literal>
    <justification jstring="[hyper(14535,a,21861,a),flip(a)].">
      <j1 rule="hyper" parents="14535 21861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21863">
    <literal><![CDATA[
      K(x,L(y \ 1,z,z) \ u) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[para(222(a,1),21862(a,2,2,1))].">
      <j1 rule="para" parents="222 21862"/>
    </justification>
  </clause>

  <clause id="21864">
    <literal><![CDATA[
      K(x,L(y,z,z) * T(u,y \ 1)) = K(x,u / L(y \ 1,z,z))
    ]]></literal>
    <justification jstring="[hyper(21567,a,21863,a),flip(a)].">
      <j1 rule="hyper" parents="21567 21863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21865">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,L(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21362,a,b,21863,a)].">
      <j1 rule="hyper" parents="60 21362 21863"/>
    </justification>
  </clause>

  <clause id="21866">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) / y,u,u) * y) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21414,a(flip),b,21863,a),flip(a)].">
      <j1 rule="hyper" parents="60 21414 21863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21867">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,y),u,u) * w) = K(x,L(R(y,z,y),u,u) \ w)
    ]]></literal>
    <justification jstring="[para(11727(a,1),21863(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11727 21863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21868">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,L(z,u,u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18314,a(flip),b,21864,a),flip(a)].">
      <j1 rule="hyper" parents="60 18314 21864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21869">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(15160(a,1),21868(a,2,2))].">
      <j1 rule="para" parents="15160 21868"/>
    </justification>
  </clause>

  <clause id="21870">
    <literal><![CDATA[
      K(x,y / L(z \ 1,u,u)) = x \ T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,21869,a),flip(a)].">
      <j1 rule="hyper" parents="370 5230 21869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21871">
    <literal><![CDATA[
      K(x,y * L((z * z) \ u,z,z)) = K(x,(z \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21367,a(flip),b,21869,a),flip(a)].">
      <j1 rule="hyper" parents="60 21367 21869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21872">
    <literal><![CDATA[
      K(x,y * (z * a(u,u,z))) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15790,a(flip),b,21869,a)].">
      <j1 rule="hyper" parents="60 15790 21869"/>
    </justification>
  </clause>

  <clause id="21873">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),v5,v5)) = K(x,y * L(K(w,u) / z,v5,v5))
    ]]></literal>
    <justification jstring="[para(15284(a,1),21869(a,1,2,2,1))].">
      <j1 rule="para" parents="15284 21869"/>
    </justification>
  </clause>

  <clause id="21874">
    <literal><![CDATA[
      K(x,y * L(z * u,z,z)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(19765(a,1),21872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19765 21872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21875">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ (z \ u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),21874(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 21874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21876">
    <literal><![CDATA[
      K(x,y * L(T(T(z,u),z \ 1) * w,T(T(z,u),z \ 1),T(T(z,u),z \ 1))) = K(x,y * ((1 / T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[para(4342(a,1),21874(a,2,2,2,1))].">
      <j1 rule="para" parents="4342 21874"/>
    </justification>
  </clause>

  <clause id="21877">
    <literal><![CDATA[
      K(x,y * (z \ ((1 / z) \ u))) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(2104(a,1),21875(a,1,2,2))].">
      <j1 rule="para" parents="2104 21875"/>
    </justification>
  </clause>

  <clause id="21878">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) = K(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21865,a(flip),b,21877,a)].">
      <j1 rule="hyper" parents="60 21865 21877"/>
    </justification>
  </clause>

  <clause id="21879">
    <literal><![CDATA[
      x \ T(x,y * L(z,u,u)) = K(x,L(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5230,a(flip),b,21878,a)].">
      <j1 rule="hyper" parents="370 5230 21878"/>
    </justification>
  </clause>

  <clause id="21880">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,u)) = K(x,a(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,20438,a(flip),b,21878,a),flip(a)].">
      <j1 rule="hyper" parents="60 20438 21878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21881">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * L(u,y,y)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(2082(a,1),21878(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2082 21878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21882">
    <literal><![CDATA[
      K(x,y * L(z \ 1,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,u) / z) = w
    ]]></literal>
    <justification jstring="[para(21878(a,1),15472(a,1))].">
      <j1 rule="para" parents="21878 15472"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,5230,a(flip),b,21879,a)].">
      <j1 rule="hyper" parents="35 5230 21879"/>
    </justification>
  </clause>

  <clause id="21884">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(21879(a,1),5290(a,1))].">
      <j1 rule="para" parents="21879 5290"/>
    </justification>
  </clause>

  <clause id="21885">
    <literal><![CDATA[
      T(x,y * L((z * z) * u,z,z)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18796,a(flip),b,21883,a),flip(a)].">
      <j1 rule="hyper" parents="60 18796 21883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21886">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (z * w))) = K(x,(y * z) * L(L(w,z,y),u,u))
    ]]></literal>
    <justification jstring="[para(13(a,2),21880(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13 21880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21887">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * L(y \ (y \ z),u,u)) = K(x,a((y \ z) \ z,u,u) * (z / y))
    ]]></literal>
    <justification jstring="[para(5608(a,1),21880(a,1,2,2,1))].">
      <j1 rule="para" parents="5608 21880"/>
    </justification>
  </clause>

  <clause id="21888">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21797,a(flip),b,21881,a)].">
      <j1 rule="hyper" parents="60 21797 21881"/>
    </justification>
  </clause>

  <clause id="21889">
    <literal><![CDATA[
      K(x,(y \ z) * (y * (y * u))) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20194,a(flip),b,21881,a)].">
      <j1 rule="hyper" parents="60 20194 21881"/>
    </justification>
  </clause>

  <clause id="21891">
    <literal><![CDATA[
      K(x,((1 / y) \ z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15734,a,b,21888,a)].">
      <j1 rule="hyper" parents="60 15734 21888"/>
    </justification>
  </clause>

  <clause id="21892">
    <literal><![CDATA[
      K(x,(y \ z) * (y * T(u,y))) = K(x,(y * z) * (u / y))
    ]]></literal>
    <justification jstring="[hyper(19984,a,21889,a)].">
      <j1 rule="hyper" parents="19984 21889"/>
    </justification>
  </clause>

  <clause id="21893">
    <literal><![CDATA[
      K(x,(y * z) * (y \ (y \ u))) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(70(a,1),21889(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="70 21889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21894">
    <literal><![CDATA[
      K(x,(y \ (y \ z)) * u) = K(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),21893(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 21893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21895">
    <literal><![CDATA[
      K(x,((y / z) / z) * u) = K(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20036,a,b,21894,a)].">
      <j1 rule="hyper" parents="60 20036 21894"/>
    </justification>
  </clause>

  <clause id="21896">
    <literal><![CDATA[
      K(x,(y * z) * (z \ (z \ u))) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),21895(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6 21895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21897">
    <literal><![CDATA[
      K(x,(y * (y / z)) * ((y / z) \ ((y / z) \ ((y / z) * u)))) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(8577(a,1),21896(a,2,2))].">
      <j1 rule="para" parents="8577 21896"/>
    </justification>
  </clause>

  <clause id="21898">
    <literal><![CDATA[
      T(x,y / L(z \ 1,u,u)) = T(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(5264,a,21870,a)].">
      <j1 rule="hyper" parents="5264 21870"/>
    </justification>
  </clause>

  <clause id="21899">
    <literal><![CDATA[
      K(x / L(y \ 1,z,z),u) = u / T(u,x * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(21898(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="21898 5701"/>
    </justification>
  </clause>

  <clause id="21900">
    <literal><![CDATA[
      K(x,(y \ z) * (u * y)) = K(x,(y * z) * (u / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),21892(a,1,2,2))].">
      <j1 rule="para" parents="107 21892"/>
    </justification>
  </clause>

  <clause id="21901">
    <literal><![CDATA[
      K(x,(y * (z * y)) * (u / y)) = K(x,T(z,y) * (u * y))
    ]]></literal>
    <justification jstring="[para(17(a,2),21900(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 21900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21902">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * ((z / y) * T(y,y \ z))) = K(x,(T(y,y \ z) * u) * ((y \ z) / y))
    ]]></literal>
    <justification jstring="[para(1913(a,1),21900(a,2,2,2))].">
      <j1 rule="para" parents="1913 21900"/>
    </justification>
  </clause>

  <clause id="21903">
    <literal><![CDATA[
      K(x / L(y \ 1,z,z),u) = K(x * L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,21899,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 21899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21904">
    <literal><![CDATA[
      K(x / L(T(y,y \ 1),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[para(108(a,2),21903(a,1,1,2,1))].">
      <j1 rule="para" parents="108 21903"/>
    </justification>
  </clause>

  <clause id="21905">
    <literal><![CDATA[
      K(x,y * L((1 / z) * u,z,z)) = K(x,(z \ (z \ y)) * (z * u))
    ]]></literal>
    <justification jstring="[para(551(a,1),21871(a,1,2,2,1))].">
      <j1 rule="para" parents="551 21871"/>
    </justification>
  </clause>

  <clause id="21906">
    <literal><![CDATA[
      T(x,(y * (y * z)) * u) = T(x,z * (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(2096(a,1),21885(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2096 21885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21907">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((1 / y) * T((1 / y) * z,y)) * u)
    ]]></literal>
    <justification jstring="[para(1066(a,1),21906(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1066 21906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21908">
    <literal><![CDATA[
      K(x,y * L(z \ 1,u,u)) = K(x,y / L(z,u,u))
    ]]></literal>
    <justification jstring="[para(875(a,1),21866(a,1,2))].">
      <j1 rule="para" parents="875 21866"/>
    </justification>
  </clause>

  <clause id="21909">
    <literal><![CDATA[
      K(x,L(y,z,z) / u) = K(x,y / L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(21882,a,21908,a)].">
      <j1 rule="hyper" parents="21882 21908"/>
    </justification>
  </clause>

  <clause id="21910">
    <literal><![CDATA[
      K(x,y / L(z * u,z,z)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18199,a(flip),b,21909,a),flip(a)].">
      <j1 rule="hyper" parents="60 18199 21909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21911">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),L(1 / z,u,z))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(11727(a,1),21910(a,2,2,2,1))].">
      <j1 rule="para" parents="11727 21910"/>
    </justification>
  </clause>

  <clause id="21912">
    <literal><![CDATA[
      K(x / L(T(y,y * 1),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18521,a(flip),b,21904,a)].">
      <j1 rule="hyper" parents="60 18521 21904"/>
    </justification>
  </clause>

  <clause id="21913">
    <literal><![CDATA[
      K(x / L(T(y,y),z,z),u) = K(x * L(y \ 1,z,z),u)
    ]]></literal>
    <justification jstring="[para(3(a,1),21912(a,1,1,2,1,2))].">
      <j1 rule="para" parents="3 21912"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      K(x * L(y \ 1,z,z),u) = K(x / L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(106(a,1),21913(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 21913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21915">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,(z \ (z \ y)) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,6748,a(flip),b,21905,a)].">
      <j1 rule="hyper" parents="60 6748 21905"/>
    </justification>
  </clause>

  <clause id="21916">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,y * (z \ (z \ (z * u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,21894,a(flip),b,21915,a),flip(a)].">
      <j1 rule="hyper" parents="370 21894 21915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21917">
    <literal><![CDATA[
      K(x,y * L((z \ 1) * u,z,z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),21916(a,2,2,2,2))].">
      <j1 rule="para" parents="4 21916"/>
    </justification>
  </clause>

  <clause id="21918">
    <literal><![CDATA[
      K(x,y * ((z \ 1) * u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21797,a(flip),b,21917,a)].">
      <j1 rule="hyper" parents="60 21797 21917"/>
    </justification>
  </clause>

  <clause id="21922">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,y),u,u) * w) = K(x,L(y,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,14394,a(flip),b,21867,a),flip(a)].">
      <j1 rule="hyper" parents="370 14394 21867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21923">
    <literal><![CDATA[
      K(x,L(1 / y,z,y) * L(u,w,w)) = K(x,L(y,w,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(21884,a,21922,a)].">
      <j1 rule="hyper" parents="21884 21922"/>
    </justification>
  </clause>

  <clause id="21925">
    <literal><![CDATA[
      K(x,L(y \ 1,z,y) * L(u,w,w)) = K(x,L(y,w,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(6555,a,21923,a)].">
      <j1 rule="hyper" parents="6555 21923"/>
    </justification>
  </clause>

  <clause id="21926">
    <literal><![CDATA[
      K(x,L(y,z,z) \ u) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21775,a(flip),b,21925,a),flip(a)].">
      <j1 rule="hyper" parents="60 21775 21925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21927">
    <literal><![CDATA[
      K(x,(y \ z) * a(y,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21742,a,b,21926,a)].">
      <j1 rule="hyper" parents="60 21742 21926"/>
    </justification>
  </clause>

  <clause id="21928">
    <literal><![CDATA[
      K(x,y \ L(L(z,u,u),u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21372,a(flip),b,21926,a),flip(a)].">
      <j1 rule="hyper" parents="60 21372 21926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21929">
    <literal><![CDATA[
      K(x,y \ L((z * y) * u,z,z)) = K(x,y \ (((z \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19781,a(flip),b,21926,a),flip(a)].">
      <j1 rule="hyper" parents="60 19781 21926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21930">
    <literal><![CDATA[
      K(x,y \ L(z,u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21799,a(flip),b,21927,a),flip(a)].">
      <j1 rule="hyper" parents="60 21799 21927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21933">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21265,a(flip),b,21930,a),flip(a)].">
      <j1 rule="hyper" parents="60 21265 21930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21935">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21930,a(flip),b,21929,a),flip(a)].">
      <j1 rule="hyper" parents="60 21930 21929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21937">
    <literal><![CDATA[
      K(x,y / L(z * K(u,w),v5,v5)) = K(x,y * L(z \ K(w,u),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,21722,a(flip),b,21873,a),flip(a)].">
      <j1 rule="hyper" parents="370 21722 21873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21938">
    <literal><![CDATA[
      K(x,y * L(z \ K(u,w),w,w)) = K(x,y * (L(z,w,w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20222,a(flip),b,21937,a),flip(a)].">
      <j1 rule="hyper" parents="60 20222 21937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21939">
    <literal><![CDATA[
      K(x,y * L((z / u) \ K(z,u),u,u)) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(21179,a,21938,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21179 21938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21940">
    <literal><![CDATA[
      K(x,T(y,L((z / u) \ K(z,u),u,u)) / ((u \ 1) * z)) = K(x,L((z / u) \ K(z,u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12637,a,21939,a),flip(a)].">
      <j1 rule="hyper" parents="12637 21939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21941">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (z * w))) = K(x,y * (z * L(w,u,u)))
    ]]></literal>
    <justification jstring="[para(528(a,1),21886(a,2,2))].">
      <j1 rule="para" parents="528 21886"/>
    </justification>
  </clause>

  <clause id="21942">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21795,a(flip),b,21941,a),flip(a)].">
      <j1 rule="hyper" parents="60 21795 21941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21943">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (w * z))) = K(x,y * (z * L(T(w,z),u,u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),21941(a,1,2,2,2))].">
      <j1 rule="para" parents="107 21941"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      K(x,y * (z * ((u * u) \ w))) = K(x,y * (z * (u \ (u \ w))))
    ]]></literal>
    <justification jstring="[para(344(a,1),21942(a,1,2,2,2))].">
      <j1 rule="para" parents="344 21942"/>
    </justification>
  </clause>

  <clause id="21946">
    <literal><![CDATA[
      K(x,y * (z * (y \ (y \ u)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18701,a(flip),b,21945,a),flip(a)].">
      <j1 rule="hyper" parents="60 18701 21945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21947">
    <literal><![CDATA[
      K(x,a(y * z,u,u) * (y * (w * z))) = K(x,y * (L(w,u,u) * z))
    ]]></literal>
    <justification jstring="[para(273(a,1),21943(a,2,2,2))].">
      <j1 rule="para" parents="273 21943"/>
    </justification>
  </clause>

  <clause id="21948">
    <literal><![CDATA[
      K(x,y * (L(z,u,u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21795,a(flip),b,21947,a),flip(a)].">
      <j1 rule="hyper" parents="60 21795 21947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21950">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15654,a,b,21948,a)].">
      <j1 rule="hyper" parents="60 15654 21948"/>
    </justification>
  </clause>

  <clause id="21952">
    <literal><![CDATA[
      K(x,T(y,z) * L(y \ (y \ z),u,u)) = K(x,a((y \ z) \ z,u,u) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(14506,a,21887,a)].">
      <j1 rule="hyper" parents="14506 21887"/>
    </justification>
  </clause>

  <clause id="21953">
    <literal><![CDATA[
      K(x,(y * (y / z)) * ((y / z) \ u)) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(4(a,1),21897(a,1,2,2,2))].">
      <j1 rule="para" parents="4 21897"/>
    </justification>
  </clause>

  <clause id="21955">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((y \ 1) * T((y \ 1) * z,y)) * u)
    ]]></literal>
    <justification jstring="[para(16048(a,1),21907(a,2,2,1))].">
      <j1 rule="para" parents="16048 21907"/>
    </justification>
  </clause>

  <clause id="21956">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((1 / y) * ((1 / y) * u))) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20153,a(flip),b,21955,a),flip(a)].">
      <j1 rule="hyper" parents="370 20153 21955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21957">
    <literal><![CDATA[
      T(x,((y \ z) * y) * ((y \ 1) * ((y \ 1) * u))) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(3745(a,1),21956(a,1,2,2))].">
      <j1 rule="para" parents="3745 21956"/>
    </justification>
  </clause>

  <clause id="21958">
    <literal><![CDATA[
      T(x,((y \ z) * (1 / y)) * L(u,y,y)) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(2089(a,1),21957(a,1,2))].">
      <j1 rule="para" parents="2089 21957"/>
    </justification>
  </clause>

  <clause id="21959">
    <literal><![CDATA[
      T(x,((y \ z) * (y \ 1)) * L(u,y,y)) = T(x,((y \ 1) * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(20314,a,21958,a)].">
      <j1 rule="hyper" parents="20314 21958"/>
    </justification>
  </clause>

  <clause id="21960">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * (y * (z / y))) = K(x,(T(y,y \ z) * u) * ((y \ z) / y))
    ]]></literal>
    <justification jstring="[para(5800(a,1),21902(a,1,2,2))].">
      <j1 rule="para" parents="5800 21902"/>
    </justification>
  </clause>

  <clause id="21961">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,y \ z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(17798,a,21960,a),flip(a)].">
      <j1 rule="hyper" parents="17798 21960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21962">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,y * z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18876,a(flip),b,21961,a),flip(a)].">
      <j1 rule="hyper" parents="370 18876 21961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21963">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * ((y \ z) / y)) = K(x,(T(y,z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,20468,a(flip),b,21962,a),flip(a)].">
      <j1 rule="hyper" parents="370 20468 21962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21964">
    <literal><![CDATA[
      K(x,(T(y,y \ z) * u) * (y \ (z / y))) = K(x,(T(y,z) \ u) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,14515,a(flip),b,21963,a)].">
      <j1 rule="hyper" parents="60 14515 21963"/>
    </justification>
  </clause>

  <clause id="21965">
    <literal><![CDATA[
      K(x,(y * z) * (T(y,y \ u) \ (u / y))) = K(x,(T(y,u) \ z) * T(u,y))
    ]]></literal>
    <justification jstring="[hyper(20021,a,21964,a)].">
      <j1 rule="hyper" parents="20021 21964"/>
    </justification>
  </clause>

  <clause id="21966">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,(y * u) * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[para(5477(a,1),21965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5477 21965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21967">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,(y \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,21893,a(flip),b,21966,a),flip(a)].">
      <j1 rule="hyper" parents="370 21893 21966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21968">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ K(z,u)) / ((u \ 1) * z)) = K(x,L((z / u) \ K(z,u),u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(21649,a,21940,a)].">
      <j1 rule="hyper" parents="21649 21940"/>
    </justification>
  </clause>

  <clause id="21970">
    <literal><![CDATA[
      K(x,T(y,z * (u \ K(u,z))) / ((z \ 1) * u)) = K(x,L((u / z) \ K(u,z),z,z) * y)
    ]]></literal>
    <justification jstring="[para(21600(a,1),21968(a,1,2,1))].">
      <j1 rule="para" parents="21600 21968"/>
    </justification>
  </clause>

  <clause id="21971">
    <literal><![CDATA[
      K(x,T(y,z / T(u,z)) / ((z \ 1) * u)) = K(x,L((u / z) \ K(u,z),z,z) * y)
    ]]></literal>
    <justification jstring="[para(16786(a,1),21970(a,1,2,1))].">
      <j1 rule="para" parents="16786 21970"/>
    </justification>
  </clause>

  <clause id="21972">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,T(u,y \ z) / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(14346(a,1),21971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14346 21971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21973">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,T(u,y * z) / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18523,a(flip),b,21972,a),flip(a)].">
      <j1 rule="hyper" parents="370 18523 21972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21974">
    <literal><![CDATA[
      K(x,L((y / z) \ K(y,z),z,z) * u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21049,a(flip),b,21973,a),flip(a)].">
      <j1 rule="hyper" parents="370 21049 21973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21975">
    <literal><![CDATA[
      K(x,((y / z) \ K(y,z)) * L(u,z,z)) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(21884,a,21974,a)].">
      <j1 rule="hyper" parents="21884 21974"/>
    </justification>
  </clause>

  <clause id="21976">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / y) \ L(u,y,y))) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(21018,a,21975,a)].">
      <j1 rule="hyper" parents="21018 21975"/>
    </justification>
  </clause>

  <clause id="21977">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ L(u,z,z)) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20780,a(flip),b,21976,a)].">
      <j1 rule="hyper" parents="60 20780 21976"/>
    </justification>
  </clause>

  <clause id="21978">
    <literal><![CDATA[
      K(x,(y \ z) \ L(u,y,y)) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20915,a(flip),b,21977,a)].">
      <j1 rule="hyper" parents="60 20915 21977"/>
    </justification>
  </clause>

  <clause id="21979">
    <literal><![CDATA[
      K(x,(L(y,y,L(z,y,y)) \ u) \ L(L(z,y,y),y,y)) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,17048,a,b,21978,a)].">
      <j1 rule="hyper" parents="60 17048 21978"/>
    </justification>
  </clause>

  <clause id="21980">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21930,a(flip),b,21978,a),flip(a)].">
      <j1 rule="hyper" parents="60 21930 21978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21982">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ L(L(z,y,y),y,y)) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[para(16041(a,1),21979(a,1,2,1,1))].">
      <j1 rule="para" parents="16041 21979"/>
    </justification>
  </clause>

  <clause id="21983">
    <literal><![CDATA[
      K(x,(L(y,y,z) \ u) \ z) = K(x,((y \ 1) * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21928,a(flip),b,21982,a)].">
      <j1 rule="hyper" parents="60 21928 21982"/>
    </justification>
  </clause>

  <clause id="21985">
    <literal><![CDATA[
      K(x,(L(y,y,K(y \ 1,z) * u) \ z) \ (K(y \ 1,z) * u)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(12471(a,1),21983(a,2,2))].">
      <j1 rule="para" parents="12471 21983"/>
    </justification>
  </clause>

  <clause id="21986">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ z) \ (K(y \ 1,z) * u)) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(20555(a,1),21985(a,1,2,1,1))].">
      <j1 rule="para" parents="20555 21985"/>
    </justification>
  </clause>

  <clause id="21987">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * ((L(z,z,K(z,y) * u) \ y) \ u)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(20812,a,21986,a)].">
      <j1 rule="hyper" parents="20812 21986"/>
    </justification>
  </clause>

  <clause id="21988">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y \ 1)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20837,a(flip),b,21987,a)].">
      <j1 rule="hyper" parents="60 20837 21987"/>
    </justification>
  </clause>

  <clause id="21989">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),L(z,u,z))) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(3804(a,1),21911(a,1,2,2))].">
      <j1 rule="para" parents="3804 21911"/>
    </justification>
  </clause>

  <clause id="21990">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(1 / z,u,z),z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(14005(a,1),21989(a,1,2,2))].">
      <j1 rule="para" parents="14005 21989"/>
    </justification>
  </clause>

  <clause id="21992">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,L(z,u,z),z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(3805(a,1),21990(a,1,2,2))].">
      <j1 rule="para" parents="3805 21990"/>
    </justification>
  </clause>

  <clause id="21993">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,z,z)) = K(x,y / (R(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(14817(a,1),21992(a,1,2,2))].">
      <j1 rule="para" parents="14817 21992"/>
    </justification>
  </clause>

  <clause id="21995">
    <literal><![CDATA[
      K(x,y / L(L(1 / z,u,z) * w,z,z)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20518,a(flip),b,21993,a),flip(a)].">
      <j1 rule="hyper" parents="370 20518 21993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21997">
    <literal><![CDATA[
      K(x,y * (T(z,u) * L(w,z,z))) = K(x,y * ((1 / T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[para(16295(a,1),21876(a,1,2,2))].">
      <j1 rule="para" parents="16295 21876"/>
    </justification>
  </clause>

  <clause id="21998">
    <literal><![CDATA[
      K(x,y * (T(z,u) * L(w,z,z))) = K(x,y * (T(z \ 1,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20177,a(flip),b,21997,a),flip(a)].">
      <j1 rule="hyper" parents="370 20177 21997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21999">
    <literal><![CDATA[
      K(x,y * (T(z \ 1,u) \ w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21942,a(flip),b,21998,a),flip(a)].">
      <j1 rule="hyper" parents="60 21942 21998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22001">
    <literal><![CDATA[
      K(x,y * (T(1 / z,u) \ w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,6164,a,b,21999,a)].">
      <j1 rule="hyper" parents="60 6164 21999"/>
    </justification>
  </clause>

  <clause id="22002">
    <literal><![CDATA[
      K(x,T(T(K(y,z) * u,w * w),v5)) = K(x,K(y,z) * T(u,w * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(10192,a,19950,a)].">
      <j1 rule="hyper" parents="10192 19950"/>
    </justification>
  </clause>

  <clause id="22003">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,w * (w * v5))) = K(x,T(K(y,z) * u,v5))
    ]]></literal>
    <justification jstring="[hyper(17132,a,22002,a),flip(a)].">
      <j1 rule="hyper" parents="17132 22002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22004">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18644,a(flip),b,22003,a),flip(a)].">
      <j1 rule="hyper" parents="60 18644 22003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22005">
    <literal><![CDATA[
      K(x,T(K(y \ z,u) * w,v5)) = K(x,K(y * z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,18359,a(flip),b,22004,a),flip(a)].">
      <j1 rule="hyper" parents="370 18359 22004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22006">
    <literal><![CDATA[
      K(x,K(y,z * u) * (z * T(u,w))) = K(x,T(K(u,w) * (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(17872,a,22004,a(flip))].">
      <j1 rule="hyper" parents="17872 22004"/>
    </justification>
  </clause>

  <clause id="22007">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(u \ w,v5)) = K(x,T(T(u,y \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),22005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7873 22005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22008">
    <literal><![CDATA[
      K(x,K(y,z * u) * (z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z * T(u,w),y)) = v5
    ]]></literal>
    <justification jstring="[para(22006(a,2),17479(a,1))].">
      <j1 rule="para" parents="22006 17479"/>
    </justification>
  </clause>

  <clause id="22009">
    <literal><![CDATA[
      K(x,T(K(y * z,u) * (u \ w),v5)) = K(x,T(T(u,y \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,22004,a,b,22007,a)].">
      <j1 rule="hyper" parents="60 22004 22007"/>
    </justification>
  </clause>

  <clause id="22010">
    <literal><![CDATA[
      K(x,T(T(y,z \ u) \ w,v5)) = K(x,T(T(y,z * u) \ w,v5))
    ]]></literal>
    <justification jstring="[para(7873(a,1),22009(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7873 22009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22011">
    <literal><![CDATA[
      K(x,L(y,y \ z,u) * (u * (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u * T(z,y),y)) = w
    ]]></literal>
    <justification jstring="[para(20445(a,2),22008(a,1))].">
      <j1 rule="para" parents="20445 22008"/>
    </justification>
  </clause>

  <clause id="22012">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T((z / (u * y)) * (u * y),z * L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,12621,a(flip),b,21767,a),flip(a)].">
      <j1 rule="hyper" parents="60 12621 21767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22013">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,z * L(u,y,y)))
    ]]></literal>
    <justification jstring="[para(7(a,1),22012(a,2,2,1))].">
      <j1 rule="para" parents="7 22012"/>
    </justification>
  </clause>

  <clause id="22014">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,7325,a(flip),b,22013,a),flip(a)].">
      <j1 rule="hyper" parents="370 7325 22013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22015">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,z / T(u * y,z))) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19413,a(flip),b,22014,a),flip(a)].">
      <j1 rule="hyper" parents="370 19413 22014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22017">
    <literal><![CDATA[
      K(x,(y * (z / T(u * y,z))) * R(u,y,(u * y) \ z)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(14743(a,1),22015(a,1,2,2))].">
      <j1 rule="para" parents="14743 22015"/>
    </justification>
  </clause>

  <clause id="22018">
    <literal><![CDATA[
      K(x,(y * ((z * y) \ u)) * R(z,y,(z * y) \ u)) = K(x,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(20332,a,22017,a)].">
      <j1 rule="hyper" parents="20332 22017"/>
    </justification>
  </clause>

  <clause id="22019">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z) * (z * y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21390,a(flip),b,22018,a)].">
      <j1 rule="hyper" parents="60 21390 22018"/>
    </justification>
  </clause>

  <clause id="22020">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ w,z * u) * ((z \ u) * y)) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,18454,a(flip),b,22019,a)].">
      <j1 rule="hyper" parents="60 18454 22019"/>
    </justification>
  </clause>

  <clause id="22021">
    <literal><![CDATA[
      K(x,T((a(y,z,u) * (w / a(y,z,u))) \ v5,a(y,z,u)) * (a(y,z,u) * (a(y,z,u) \ w))) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(21711(a,1),22019(a,1,2,1,1,1))].">
      <j1 rule="para" parents="21711 22019"/>
    </justification>
  </clause>

  <clause id="22022">
    <literal><![CDATA[
      K(x,T((y * (z \ 1)) \ u,z) * ((z \ 1) * y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),22020(a,1,2,1,2))].">
      <j1 rule="para" parents="3 22020"/>
    </justification>
  </clause>

  <clause id="22023">
    <literal><![CDATA[
      K(x,T((y * (z \ 1)) \ u,z) * (z \ y)) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21918,a(flip),b,22022,a)].">
      <j1 rule="hyper" parents="60 21918 22022"/>
    </justification>
  </clause>

  <clause id="22024">
    <literal><![CDATA[
      K(x,L((a(y,z,u) * (w / a(y,z,u))) \ v5,z,K(u,y)) * (a(y,z,u) * (a(y,z,u) \ w))) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(21483(a,2),22021(a,1,2,1))].">
      <j1 rule="para" parents="21483 22021"/>
    </justification>
  </clause>

  <clause id="22025">
    <literal><![CDATA[
      K(x,L((a(y,z,u) * (w / a(y,z,u))) \ v5,z,K(u,y)) * w) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),22024(a,1,2,2))].">
      <j1 rule="para" parents="5 22024"/>
    </justification>
  </clause>

  <clause id="22026">
    <literal><![CDATA[
      K(x,((a(y,z,u) * (w / a(y,z,u))) \ v5) * w) = K(x,T(v5,a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(21577,a,22025,a)].">
      <j1 rule="hyper" parents="21577 22025"/>
    </justification>
  </clause>

  <clause id="22029">
    <literal><![CDATA[
      K(x,T(y * K(z,a(u,w,v5)),z)) = K(x,T(y,a(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20527,a(flip),b,22026,a)].">
      <j1 rule="hyper" parents="60 20527 22026"/>
    </justification>
  </clause>

  <clause id="22030">
    <literal><![CDATA[
      K(x,T(y * a(z,u,K(w,v5)),z)) = K(x,T(y,a(v5,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(15816(a,2),22029(a,1,2,1,2))].">
      <j1 rule="para" parents="15816 22029"/>
    </justification>
  </clause>

  <clause id="22031">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(21199,a,22030,a),flip(a)].">
      <j1 rule="hyper" parents="21199 22030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22033">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(17494,a,22031,a)].">
      <j1 rule="hyper" parents="17494 22031"/>
    </justification>
  </clause>

  <clause id="22034">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17493,a,22031,a)].">
      <j1 rule="hyper" parents="17493 22031"/>
    </justification>
  </clause>

  <clause id="22035">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,a(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[para(22033(a,1),8749(a,1,1,2))].">
      <j1 rule="para" parents="22033 8749"/>
    </justification>
  </clause>

  <clause id="22036">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,T(v5,u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w / (a(x,y,z) * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(22033(a,1),8906(a,1))].">
      <j1 rule="para" parents="22033 8906"/>
    </justification>
  </clause>

  <clause id="22037">
    <literal><![CDATA[
      T(x,a(y,z,u)) * K(w,T(v5,x)) = T(K(w,v5) * x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(22033(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="22033 17920"/>
    </justification>
  </clause>

  <clause id="22038">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(19665(a,1),22033(a,1,2,2))].">
      <j1 rule="para" parents="19665 22033"/>
    </justification>
  </clause>

  <clause id="22039">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,w))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(21748(a,1),22033(a,1,2))].">
      <j1 rule="para" parents="21748 22033"/>
    </justification>
  </clause>

  <clause id="22040">
    <literal><![CDATA[
      T(K(x,y),z * a(u,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8021,a,22034,a)].">
      <j1 rule="hyper" parents="8021 22034"/>
    </justification>
  </clause>

  <clause id="22043">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * (u * w))) = K(x,K(y,(z * u) * w))
    ]]></literal>
    <justification jstring="[para(22038(a,1),8649(a,1,2))].">
      <j1 rule="para" parents="22038 8649"/>
    </justification>
  </clause>

  <clause id="22044">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) * v5)) = T(x,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(9102,a,22035,a),flip(a)].">
      <j1 rule="hyper" parents="9102 22035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22045">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u / a(w,v5,v6),z)) = T(y,K(z,a(w,v5,v6) \ u) * x)
    ]]></literal>
    <justification jstring="[para(22044(a,1),18164(a,1,2,1,2))].">
      <j1 rule="para" parents="22044 18164"/>
    </justification>
  </clause>

  <clause id="22046">
    <literal><![CDATA[
      L(x,y,K(z,u)) * K(w,T(v5,x)) = T(K(w,v5) * x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(21483(a,2),22037(a,1,1))].">
      <j1 rule="para" parents="21483 22037"/>
    </justification>
  </clause>

  <clause id="22047">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(8887,a,22043,a),flip(a)].">
      <j1 rule="hyper" parents="8887 22043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22048">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(19523,a,22047,a)].">
      <j1 rule="hyper" parents="19523 22047"/>
    </justification>
  </clause>

  <clause id="22049">
    <literal><![CDATA[
      K(x,K(y * z,y * (z * u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8888,a,22047,a),flip(a)].">
      <j1 rule="hyper" parents="8888 22047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22051">
    <literal><![CDATA[
      K(x,K(y,z * ((u \ z) * w))) = K(x,K(y,z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,20454,a(flip),b,22048,a),flip(a)].">
      <j1 rule="hyper" parents="60 20454 22048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22054">
    <literal><![CDATA[
      T(K(x,y) * z,a(u,w,v5)) = K(x,y) * L(z,w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19419,a,22046,a),flip(a)].">
      <j1 rule="hyper" parents="19419 22046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22055">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(21484,a,22054,a)].">
      <j1 rule="hyper" parents="21484 22054"/>
    </justification>
  </clause>

  <clause id="22056">
    <literal><![CDATA[
      (x \ K(y,z)) \ L(x \ K(y,z),u,K(w,v5)) = x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(22055(a,2),3823(a,2,2))].">
      <j1 rule="para" parents="22055 3823"/>
    </justification>
  </clause>

  <clause id="22057">
    <literal><![CDATA[
      K(x,K(y,z * (u * (z \ w)))) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19499,a(flip),b,22051,a),flip(a)].">
      <j1 rule="hyper" parents="60 19499 22051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22059">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y,L(T(z,u \ x),u \ x,u)) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(22057(a,1),9365(a,1,1))].">
      <j1 rule="para" parents="22057 9365"/>
    </justification>
  </clause>

  <clause id="22060">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z / a(w,v5,v6),u)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(8700(a,1),22045(a,1,2,1,2))].">
      <j1 rule="para" parents="8700 22045"/>
    </justification>
  </clause>

  <clause id="22061">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,a(w,v5,v6) \ z)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(17667(a,1),22060(a,1,2))].">
      <j1 rule="para" parents="17667 22060"/>
    </justification>
  </clause>

  <clause id="22062">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,a(w,v5,v6) * z)) = T(y,K(u,a(w,v5,v6) \ z) * x)
    ]]></literal>
    <justification jstring="[para(17528(a,1),22061(a,1,2))].">
      <j1 rule="para" parents="17528 22061"/>
    </justification>
  </clause>

  <clause id="22063">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) \ v5) * v6) = v6 \ T(x * T(v6,K(v5,y)),K(y,v5))
    ]]></literal>
    <justification jstring="[para(22044(a,1),22062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22044 22062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22064">
    <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(8700(a,1),22063(a,2,2))].">
      <j1 rule="para" parents="8700 22063"/>
    </justification>
  </clause>

  <clause id="22066">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) \ v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,16700,a(flip),b,22064,a),flip(a)].">
      <j1 rule="hyper" parents="370 16700 22064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22067">
    <literal><![CDATA[
      T(x,y * K(z,a(u,w,v5) * v6)) = T(x,K(z,v6) * y)
    ]]></literal>
    <justification jstring="[hyper(18265,a,22066,a)].">
      <j1 rule="hyper" parents="18265 22066"/>
    </justification>
  </clause>

  <clause id="22068">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (a(w,v5,v6) * z))) = T(x,u \ T(a(w,v5,v6) * z,y))
    ]]></literal>
    <justification jstring="[hyper(17618,a,22067,a),flip(a)].">
      <j1 rule="hyper" parents="17618 22067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22069">
    <literal><![CDATA[
      T(x,y \ T(a(z,u,w) * v5,v6)) = T(x,y \ (a(z,u,w) * T(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(20962,a,22068,a),flip(a)].">
      <j1 rule="hyper" parents="20962 22068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22070">
    <literal><![CDATA[
      T(x,y \ T(a(z,u,u) * w,v5)) = T(x,y \ (T(w,v5) * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(16881,a,22069,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16881 22069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22071">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u \ x),u \ x,u)) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(8863(a,1),22059(a,1,1))].">
      <j1 rule="para" parents="8863 22059"/>
    </justification>
  </clause>

  <clause id="22073">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (z * (u \ x)))) = K(y,(u * (z * (u \ x))) / x)
    ]]></literal>
    <justification jstring="[para(1032(a,1),22071(a,1,2,2))].">
      <j1 rule="para" parents="1032 22071"/>
    </justification>
  </clause>

  <clause id="22074">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x \ (u * (z * (u \ x)))) = K(y,x \ (((x / u) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,21131,a(flip),b,22073,a),flip(a)].">
      <j1 rule="hyper" parents="370 21131 22073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22075">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,L(T(z,u * x),x,u)) = K(y,x \ (((x / u) * z) * u))
    ]]></literal>
    <justification jstring="[para(17870(a,1),22074(a,1,2))].">
      <j1 rule="para" parents="17870 22074"/>
    </justification>
  </clause>

  <clause id="22076">
    <literal><![CDATA[
      K(x,L(T(T(y,z),u * z),z,u)) = K(x,z \ (((z / u) * y) * u))
    ]]></literal>
    <justification jstring="[hyper(20501,a,22075,a)].">
      <j1 rule="hyper" parents="20501 22075"/>
    </justification>
  </clause>

  <clause id="22077">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = K(x,z \ (((z / y) * u) * y))
    ]]></literal>
    <justification jstring="[hyper(12951,a,22076,a)].">
      <j1 rule="hyper" parents="12951 22076"/>
    </justification>
  </clause>

  <clause id="22078">
    <literal><![CDATA[
      x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5)) = a(v5,u,K(w,x \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(21520,a,22056,a),flip(a)].">
      <j1 rule="hyper" parents="21520 22056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22079">
    <literal><![CDATA[
      x \ L(K(y,z) * (K(y,z) \ x),u,K(w,v5)) = a(v5,u,K(w,x * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15958,a(flip),b,22078,a),flip(a)].">
      <j1 rule="hyper" parents="370 15958 22078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22080">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = u \ L(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),22079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 22079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22081">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,21491,a(flip),b,22080,a),flip(a)].">
      <j1 rule="hyper" parents="370 21491 22080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22082">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(v5,u,K(w,z))
    ]]></literal>
    <justification jstring="[hyper(17405,a,22081,a)].">
      <j1 rule="hyper" parents="17405 22081"/>
    </justification>
  </clause>

  <clause id="22083">
    <literal><![CDATA[
      a(x,y,K(z,u * T(w,v5))) = a(u * w,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,20362,a(flip),b,22082,a),flip(a)].">
      <j1 rule="hyper" parents="60 20362 22082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22085">
    <literal><![CDATA[
      K(x,((y * T(z,u \ w)) \ (v5 * ((y * T(z,u \ w)) \ 1))) * (y * T(z,u * w))) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,14353,a(flip),b,20318,a),flip(a)].">
      <j1 rule="hyper" parents="370 14353 20318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22086">
    <literal><![CDATA[
      K(x,(((y * T(z,u \ w)) \ v5) * ((y * T(z,u \ w)) \ 1)) * (y * T(z,u * w))) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,14491,a(flip),b,22085,a)].">
      <j1 rule="hyper" parents="60 14491 22085"/>
    </justification>
  </clause>

  <clause id="22087">
    <literal><![CDATA[
      K(x,(y * T(z,u \ w)) \ v5) = K(x,(y * T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,19088,a(flip),b,22086,a)].">
      <j1 rule="hyper" parents="60 19088 22086"/>
    </justification>
  </clause>

  <clause id="22089">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z) * u)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21435,a(flip),b,22087,a),flip(a)].">
      <j1 rule="hyper" parents="60 21435 22087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      K(x,((1 / y) * T(y \ ((y \ 1) \ z),u * w)) \ v5) = K(x,(y \ T(z,u \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(15656(a,1),22087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15656 22087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22091">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,T(y,z))) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21183,a(flip),b,22089,a)].">
      <j1 rule="hyper" parents="60 21183 22089"/>
    </justification>
  </clause>

  <clause id="22092">
    <literal><![CDATA[
      K(x,(T(y \ 1,z * y) * T(u,y)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(20942,a,22091,a)].">
      <j1 rule="hyper" parents="20942 22091"/>
    </justification>
  </clause>

  <clause id="22094">
    <literal><![CDATA[
      K(x,(T(y \ 1,z) * T(u,y)) \ w) = K(x,(u * T(y \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21079,a(flip),b,22092,a)].">
      <j1 rule="hyper" parents="60 21079 22092"/>
    </justification>
  </clause>

  <clause id="22095">
    <literal><![CDATA[
      K(x,(((y * y) \ z) * T(y,u)) \ w) = K(x,(z * T(y \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21253,a(flip),b,22094,a)].">
      <j1 rule="hyper" parents="60 21253 22094"/>
    </justification>
  </clause>

  <clause id="22096">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ ((z * z) * w)) = K(x,(y * T(z \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[para(1005(a,1),22095(a,1,2))].">
      <j1 rule="para" parents="1005 22095"/>
    </justification>
  </clause>

  <clause id="22097">
    <literal><![CDATA[
      K(x,y * (y * ((z * T(y,u)) \ w))) = K(x,(z * T(y \ 1,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20977,a(flip),b,22096,a)].">
      <j1 rule="hyper" parents="60 20977 22096"/>
    </justification>
  </clause>

  <clause id="22098">
    <literal><![CDATA[
      K(x,(y * (((z * u) / z) \ 1)) \ w) = K(x,(y * T(u \ 1,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21462,a,b,22097,a)].">
      <j1 rule="hyper" parents="60 21462 22097"/>
    </justification>
  </clause>

  <clause id="22099">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (((z / y) \ 1) / y)) = K(x,(y * T(u \ 1,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(21330,a,22098,a)].">
      <j1 rule="hyper" parents="21330 22098"/>
    </justification>
  </clause>

  <clause id="22100">
    <literal><![CDATA[
      K(x,(y * T(z \ 1,u)) \ w) = K(x,(y * (T(z,u) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21835,a(flip),b,22098,a),flip(a)].">
      <j1 rule="hyper" parents="60 21835 22098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22101">
    <literal><![CDATA[
      K(x,((T(y \ 1,z) \ L(T(y \ 1,z),u,w)) * (T(y,z) \ 1)) \ v5) = K(x,L(T(y \ 1,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(3838(a,1),22100(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3838 22100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22102">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) / (((z / y) \ 1) / y)) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),22099(a,2,2,1))].">
      <j1 rule="para" parents="107 22099"/>
    </justification>
  </clause>

  <clause id="22103">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) \ v5) = K(x,(y \ T(z,u * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(15656(a,1),22090(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15656 22090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22104">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y * 1)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21988,a(flip),b,22103,a),flip(a)].">
      <j1 rule="hyper" parents="60 21988 22103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22105">
    <literal><![CDATA[
      K(x,(L(y,y,K(y,z) * u) \ T(z,y)) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3(a,1),22104(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3 22104"/>
    </justification>
  </clause>

  <clause id="22106">
    <literal><![CDATA[
      K(x,(y / L(z,z,K(z,y) * u)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20896,a(flip),b,22105,a)].">
      <j1 rule="hyper" parents="60 20896 22105"/>
    </justification>
  </clause>

  <clause id="22107">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21933,a(flip),b,22106,a),flip(a)].">
      <j1 rule="hyper" parents="60 21933 22106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22108">
    <literal><![CDATA[
      K(x,(T((y \ 1) \ L(y \ 1,z,u),w) * (T(y,w) \ 1)) \ v5) = K(x,L(T(y \ 1,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(4205(a,1),22101(a,1,2,1,1))].">
      <j1 rule="para" parents="4205 22101"/>
    </justification>
  </clause>

  <clause id="22109">
    <literal><![CDATA[
      K(x,(T(y \ L(y,z,u),w) * (T(y,w) \ 1)) \ v5) = K(x,L(T(y \ 1,w),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(3820(a,1),22108(a,1,2,1,1,1))].">
      <j1 rule="para" parents="3820 22108"/>
    </justification>
  </clause>

  <clause id="22110">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ v5) = K(x,L(T(y,z) \ 1,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(4207(a,1),22109(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4207 22109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22111">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,u) \ w) = K(x,L(T(y,z),u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,21863,a(flip),b,22110,a),flip(a)].">
      <j1 rule="hyper" parents="370 21863 22110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22112">
    <literal><![CDATA[
      K(x,L(T(y,z),u,u) * (y \ (y \ z))) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21421,a(flip),b,22111,a),flip(a)].">
      <j1 rule="hyper" parents="60 21421 22111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22113">
    <literal><![CDATA[
      K(x,T(y,z) * L(y \ (y \ z),u,u)) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(21884,a,22112,a)].">
      <j1 rule="hyper" parents="21884 22112"/>
    </justification>
  </clause>

  <clause id="22114">
    <literal><![CDATA[
      K(x,a((y \ z) \ z,u,u) * (z / y)) = K(x,z / L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21952,a(flip),b,22113,a)].">
      <j1 rule="hyper" parents="60 21952 22113"/>
    </justification>
  </clause>

  <clause id="22115">
    <literal><![CDATA[
      K(x,y / L(z,u,u)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21795,a(flip),b,22114,a),flip(a)].">
      <j1 rule="hyper" parents="60 21795 22114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22117">
    <literal><![CDATA[
      K(x,y / (L(1 / z,u,z) * w)) = K(x,y / (z \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21995,a(flip),b,22115,a),flip(a)].">
      <j1 rule="hyper" parents="60 21995 22115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22119">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(1229(a,1),22117(a,1,2,2,1))].">
      <j1 rule="para" parents="1229 22117"/>
    </justification>
  </clause>

  <clause id="22122">
    <literal><![CDATA[
      L(x / L(T(y,y \ 1),y * z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(12726(a,1),20341(a,1,1,2))].">
      <j1 rule="para" parents="12726 20341"/>
    </justification>
  </clause>

  <clause id="22129">
    <literal><![CDATA[
      L(x / R(T(y,y * 1),z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(18920(a,1),22122(a,1,1,2))].">
      <j1 rule="para" parents="18920 22122"/>
    </justification>
  </clause>

  <clause id="22132">
    <literal><![CDATA[
      L(x / R(T(y,y),z,y),L(y,y * z,y),L(y,y * z,y)) = L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y))
    ]]></literal>
    <justification jstring="[para(3(a,1),22129(a,1,1,2,1,2))].">
      <j1 rule="para" parents="3 22129"/>
    </justification>
  </clause>

  <clause id="22137">
    <literal><![CDATA[
      L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y)) = L(x / R(y,z,y),L(y,y * z,y),L(y,y * z,y))
    ]]></literal>
    <justification jstring="[para(106(a,1),22132(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 22132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22142">
    <literal><![CDATA[
      L(x,L(y,y * z,y),L(y,y * z,y)) / (z / (T(z,y) / y)) = L(x / R(y,z,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14818,a(flip),b,22137,a),flip(a)].">
      <j1 rule="hyper" parents="370 14818 22137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22147">
    <literal><![CDATA[
      L(x,y,y) / (z / (T(z,y) / y)) = L(x / R(y,z,y),y,y)
    ]]></literal>
    <justification jstring="[para(14818(a,1),22142(a,1,1))].">
      <j1 rule="para" parents="14818 22142"/>
    </justification>
  </clause>

  <clause id="22150">
    <literal><![CDATA[
      K(x,T((y / (T(y,z) / z)) \ L(u,z,z),L(u,z,z)) * w) = K(x,L(u / R(z,y,z),z,z) * w)
    ]]></literal>
    <justification jstring="[para(22147(a,1),19891(a,2,2,1))].">
      <j1 rule="para" parents="22147 19891"/>
    </justification>
  </clause>

  <clause id="22151">
    <literal><![CDATA[
      K(x,T(L(1 / y,z,y) * u,L(u,y,y)) * w) = K(x,L(u / R(y,z,y),y,y) * w)
    ]]></literal>
    <justification jstring="[para(17634(a,1),22150(a,1,2,1,1))].">
      <j1 rule="para" parents="17634 22150"/>
    </justification>
  </clause>

  <clause id="22152">
    <literal><![CDATA[
      K(x,T(L(1 / y,z,y) * u,u) * w) = K(x,L(u / R(y,z,y),y,y) * w)
    ]]></literal>
    <justification jstring="[para(15156(a,1),22151(a,1,2,1))].">
      <j1 rule="para" parents="15156 22151"/>
    </justification>
  </clause>

  <clause id="22153">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) = K(x,(y * L(1 / z,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16971,a(flip),b,22152,a),flip(a)].">
      <j1 rule="hyper" parents="60 16971 22152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22155">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) = K(x,(y * L(z \ 1,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,14477,a(flip),b,22153,a),flip(a)].">
      <j1 rule="hyper" parents="370 14477 22153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22156">
    <literal><![CDATA[
      K(x,L(y / R(z,u,z),z,z) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * w) = v5
    ]]></literal>
    <justification jstring="[para(22155(a,2),14584(a,1))].">
      <j1 rule="para" parents="22155 14584"/>
    </justification>
  </clause>

  <clause id="22157">
    <literal><![CDATA[
      K(x,(y / R(z,u,z)) * L(w,z,z)) = K(x,(y * (z \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(22156,a,21878,a),flip(a)].">
      <j1 rule="hyper" parents="22156 21878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22158">
    <literal><![CDATA[
      K(x,(y / z) * L(u,z,z)) = K(x,(y * (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14422,a(flip),b,22157,a)].">
      <j1 rule="hyper" parents="60 14422 22157"/>
    </justification>
  </clause>

  <clause id="22159">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u / (z \ 1))) = K(x,(y / z) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,19972,a(flip),b,22158,a),flip(a)].">
      <j1 rule="hyper" parents="60 19972 22158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22160">
    <literal><![CDATA[
      K(x,(y / z) * (u * z)) = K(x,(y * z) * (u / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20159,a(flip),b,22159,a),flip(a)].">
      <j1 rule="hyper" parents="60 20159 22159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22161">
    <literal><![CDATA[
      K(x,(y * (z \ y)) * (u / (z \ y))) = K(x,z * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(74(a,1),22160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 22160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22162">
    <literal><![CDATA[
      K(x,(y * L(y,z,z)) * (u / (a(z,z,y) \ y))) = K(x,a(z,z,y) * (u * (a(z,z,y) \ y)))
    ]]></literal>
    <justification jstring="[para(3943(a,1),22161(a,1,2,1,2))].">
      <j1 rule="para" parents="3943 22161"/>
    </justification>
  </clause>

  <clause id="22163">
    <literal><![CDATA[
      K(x,(y * L(y,z,z)) * (u / L(y,z,z))) = K(x,a(z,z,y) * (u * (a(z,z,y) \ y)))
    ]]></literal>
    <justification jstring="[para(3943(a,1),22162(a,1,2,2,2))].">
      <j1 rule="para" parents="3943 22162"/>
    </justification>
  </clause>

  <clause id="22164">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * (z * K(y,z))) * w)) = K(x,T(u,T(z,y)) \ ((((y * z) / y) \ T(u,T(z,y))) * w))
    ]]></literal>
    <justification jstring="[para(10005(a,1),21127(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10005 21127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22165">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * (z * K(y,z))) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,21428,a(flip),b,22164,a),flip(a)].">
      <j1 rule="hyper" parents="370 21428 22164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22167">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * (z * K(y,z)))) \ ((u * T(z,y)) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21218,a(flip),b,22165,a)].">
      <j1 rule="hyper" parents="60 21218 22165"/>
    </justification>
  </clause>

  <clause id="22168">
    <literal><![CDATA[
      K(x,(((y * z) / y) * (u * T(z,y))) \ ((u * T(z,y)) * w)) = K(x,u \ ((((y * z) / y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21332,a(flip),b,22167,a)].">
      <j1 rule="hyper" parents="60 21332 22167"/>
    </justification>
  </clause>

  <clause id="22169">
    <literal><![CDATA[
      K(x,(T(y,z) * (u * T(y,z))) \ ((u * T(y,z)) * w)) = K(x,u \ ((((z * y) / z) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20950,a(flip),b,22168,a)].">
      <j1 rule="hyper" parents="60 20950 22168"/>
    </justification>
  </clause>

  <clause id="22170">
    <literal><![CDATA[
      K(x,y \ ((((z * u) / z) \ y) * w)) = K(x,y \ ((T(u,z) \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,21298,a(flip),b,22169,a),flip(a)].">
      <j1 rule="hyper" parents="60 21298 22169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22171">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,K(z,u) * z),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(18651(a,1),17800(a,1,1,2))].">
      <j1 rule="para" parents="18651 17800"/>
    </justification>
  </clause>

  <clause id="22172">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) * T(w,T(z,u)),T(v5,w * (z * K(z * K(y,x),u)))) = K((w * (z * K(z * K(y,x),u))) * R(K(x,y),z * K(z * K(y,x),u),w),v5)
    ]]></literal>
    <justification jstring="[para(5275(a,2),22171(a,1,1,2,2))].">
      <j1 rule="para" parents="5275 22171"/>
    </justification>
  </clause>

  <clause id="22174">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(T(K(u,z) * y,w) * T(x,T(y,w)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(19908,a,22172,a),flip(a)].">
      <j1 rule="hyper" parents="19908 22172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22175">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(T(K(u,z) * y,w) * T(x,y),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,17710,a(flip),b,22174,a),flip(a)].">
      <j1 rule="hyper" parents="370 17710 22174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22177">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(u,z) * (T(y,w) * T(x,y)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,19835,a(flip),b,22175,a),flip(a)].">
      <j1 rule="hyper" parents="370 19835 22175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22178">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(u,z) * (K(y,w) * (x * y)),T(v5,x * y))
    ]]></literal>
    <justification jstring="[para(7861(a,2),22177(a,2,1,2))].">
      <j1 rule="para" parents="7861 22177"/>
    </justification>
  </clause>

  <clause id="22179">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(K(y,w) * ((x * y) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19840,a(flip),b,22178,a),flip(a)].">
      <j1 rule="hyper" parents="370 19840 22178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22180">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K((x * T(y,w)) * K(u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19824,a(flip),b,22179,a),flip(a)].">
      <j1 rule="hyper" parents="370 19824 22179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22181">
    <literal><![CDATA[
      K((x * (y * K(y * K(z,u),w))) * R(K(u,z),y * K(y * K(z,u),w),x),v5) = K(x * (T(y,w) * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,19812,a(flip),b,22180,a),flip(a)].">
      <j1 rule="hyper" parents="370 19812 22180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22182">
    <literal><![CDATA[
      K(x * ((y * K(y * K(z,u),w)) * K(u,z)),v5) = K(x * (T(y,w) * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(21385,a,22181,a)].">
      <j1 rule="hyper" parents="21385 22181"/>
    </justification>
  </clause>

  <clause id="22183">
    <literal><![CDATA[
      K(x * (y * (K(z,u) * K(y * K(u,z),w))),v5) = K(x * (T(y,w) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(20753(a,1),22182(a,1,1,2))].">
      <j1 rule="para" parents="20753 22182"/>
    </justification>
  </clause>

  <clause id="22184">
    <literal><![CDATA[
      K(x * T(y * K(z,u),w),v5) = K(x * (T(y,w) * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(17418(a,1),22183(a,1,1,2))].">
      <j1 rule="para" parents="17418 22183"/>
    </justification>
  </clause>

  <clause id="22185">
    <literal><![CDATA[
      K(x * T(y * K(z,u),w),T(v5,y)) = K(K(u,z) * (T(y,w) * x),v5)
    ]]></literal>
    <justification jstring="[hyper(19841,a,22184,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19841 22184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22186">
    <literal><![CDATA[
      K(K(x,y) * (T(y,z) * u),w) = K(u * T(T(y,x),z),T(w,y))
    ]]></literal>
    <justification jstring="[para(5256(a,2),22185(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5256 22185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22187">
    <literal><![CDATA[
      K(K(x,y) * (T(y,z) * u),w) = K(T(T(y,x),z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17434,a(flip),b,22186,a),flip(a)].">
      <j1 rule="hyper" parents="370 17434 22186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22188">
    <literal><![CDATA[
      a(x,y,K(T(T(z,u * w),v5) * w,u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[para(22187(a,1),20115(a,1,3))].">
      <j1 rule="para" parents="22187 20115"/>
    </justification>
  </clause>

  <clause id="22189">
    <literal><![CDATA[
      a(x,y,K(T(z,u * w) * T(w,v5),u)) = a(x,y,K(u,w * T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,21310,a(flip),b,22188,a)].">
      <j1 rule="hyper" parents="60 21310 22188"/>
    </justification>
  </clause>

  <clause id="22190">
    <literal><![CDATA[
      a(x,y,K(z * T(T(u,w),v5 * u),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,21310,a(flip),b,22189,a)].">
      <j1 rule="hyper" parents="60 21310 22189"/>
    </justification>
  </clause>

  <clause id="22191">
    <literal><![CDATA[
      a(x,y,K(z * T(T(u,w),v5),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[para(18547(a,1),22190(a,1,3))].">
      <j1 rule="para" parents="18547 22190"/>
    </justification>
  </clause>

  <clause id="22192">
    <literal><![CDATA[
      a(x,y,K(z * T(u,w),v5)) = a(x,y,K(v5,u * T(z,w)))
    ]]></literal>
    <justification jstring="[para(9232(a,1),22191(a,1,3))].">
      <j1 rule="para" parents="9232 22191"/>
    </justification>
  </clause>

  <clause id="22193">
    <literal><![CDATA[
      a(x,y,K(z * T(u,w),v5)) = a(u * z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,22083,a(flip),b,22192,a),flip(a)].">
      <j1 rule="hyper" parents="370 22083 22192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22195">
    <literal><![CDATA[
      a(x,y,K(T(z,u) * w,v5)) = a(w * z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,21310,a,b,22193,a)].">
      <j1 rule="hyper" parents="60 21310 22193"/>
    </justification>
  </clause>

  <clause id="22196">
    <literal><![CDATA[
      K(x,L(y,z,u \ T(w,v5))) = K(x,y) * a(w * u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(22193(a,1),19698(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22193 19698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22197">
    <literal><![CDATA[
      a(T(x,y) * z,u,K(w,v5)) = a(z * x,u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(15903,a,22195,a)].">
      <j1 rule="hyper" parents="15903 22195"/>
    </justification>
  </clause>

  <clause id="22199">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(z,x,K(T(y,w) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21709,a(flip),b,22197,a),flip(a)].">
      <j1 rule="hyper" parents="60 21709 22197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22200">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(z,x,K(T(y,w) * x,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19710,a(flip),b,22199,a),flip(a)].">
      <j1 rule="hyper" parents="370 19710 22199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22202">
    <literal><![CDATA[
      a(x * y,y,K(z,u)) = a(x * y,x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22195,a(flip),b,22200,a),flip(a)].">
      <j1 rule="hyper" parents="370 22195 22200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22203">
    <literal><![CDATA[
      a(x * y,x,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(22202(a,1),19657(a,1))].">
      <j1 rule="para" parents="22202 19657"/>
    </justification>
  </clause>

  <clause id="22204">
    <literal><![CDATA[
      K(x,L(y,z,u \ T(w,v5))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15907,a(flip),b,22196,a),flip(a)].">
      <j1 rule="hyper" parents="370 15907 22196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22205">
    <literal><![CDATA[
      K(x,L(y,z,u * T(w,v5))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(19697,a,22204,a)].">
      <j1 rule="hyper" parents="19697 22204"/>
    </justification>
  </clause>

  <clause id="22206">
    <literal><![CDATA[
      K(x,L(((y \ ((z * u) / z)) \ ((z * u) / z)) \ w,y,u * y)) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20272,a(flip),b,22204,a),flip(a)].">
      <j1 rule="hyper" parents="60 20272 22204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22207">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) * v5)) = K(x,L(y,z,u * v5))
    ]]></literal>
    <justification jstring="[hyper(21563,a,22205,a)].">
      <j1 rule="hyper" parents="21563 22205"/>
    </justification>
  </clause>

  <clause id="22208">
    <literal><![CDATA[
      K(x,L((y * (z / y)) / u,w,z * w)) = K(x,w / (u * ((y * (z / y)) \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19706,a(flip),b,22207,a),flip(a)].">
      <j1 rule="hyper" parents="60 19706 22207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22210">
    <literal><![CDATA[
      K(x,L(T(y / z,z),u,y * u)) = K(x,u / (z * ((z * (y / z)) \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,9124,a(flip),b,22208,a)].">
      <j1 rule="hyper" parents="60 9124 22208"/>
    </justification>
  </clause>

  <clause id="22211">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,u / (y * ((y * (z / y)) \ u)))
    ]]></literal>
    <justification jstring="[para(109(a,1),22210(a,1,2,1))].">
      <j1 rule="para" parents="109 22210"/>
    </justification>
  </clause>

  <clause id="22212">
    <literal><![CDATA[
      K(x,L(T(y / z,z),u,z * u)) = K(x,L(z \ y,u,y * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,20151,a(flip),b,22211,a)].">
      <j1 rule="hyper" parents="370 20151 22211"/>
    </justification>
  </clause>

  <clause id="22213">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,L(y \ z,u,y * u))
    ]]></literal>
    <justification jstring="[para(109(a,1),22212(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 22212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22214">
    <literal><![CDATA[
      K(x,L(T(y,(z * u) / z) \ w,y,u * y)) = K(x,T(u,z) \ ((y \ ((z * u) / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(14746,a,22206,a)].">
      <j1 rule="hyper" parents="14746 22206"/>
    </justification>
  </clause>

  <clause id="22216">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,y,z * y)) = K(x,T(z,u) \ ((y \ ((u * z) / u)) * w))
    ]]></literal>
    <justification jstring="[para(8855(a,1),22214(a,1,2,1,1))].">
      <j1 rule="para" parents="8855 22214"/>
    </justification>
  </clause>

  <clause id="22217">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z * y)) = K(x,T(z,w) \ ((y \ ((w * z) / w)) * u))
    ]]></literal>
    <justification jstring="[hyper(17877,a,22216,a)].">
      <j1 rule="hyper" parents="17877 22216"/>
    </justification>
  </clause>

  <clause id="22218">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,21108,a(flip),b,22217,a),flip(a)].">
      <j1 rule="hyper" parents="370 21108 22217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22219">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y \ (z * y),z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19749,a,b,22218,a)].">
      <j1 rule="hyper" parents="60 19749 22218"/>
    </justification>
  </clause>

  <clause id="22220">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,T(z,y),z * y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(17(a,2),22219(a,1,2,2))].">
      <j1 rule="para" parents="17 22219"/>
    </justification>
  </clause>

  <clause id="22221">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21186,a(flip),b,22220,a)].">
      <j1 rule="hyper" parents="60 21186 22220"/>
    </justification>
  </clause>

  <clause id="22222">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,z * y)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21713,a,b,22221,a)].">
      <j1 rule="hyper" parents="60 21713 22221"/>
    </justification>
  </clause>

  <clause id="22223">
    <literal><![CDATA[
      K(x,y \ ((((y * z) / y) \ y) * u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21804,a(flip),b,22221,a),flip(a)].">
      <j1 rule="hyper" parents="60 21804 22221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22224">
    <literal><![CDATA[
      K(x,y \ (((y * z) \ y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),22221(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 22221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22225">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) \ y) * u)) = K(x,y \ ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22170,a(flip),b,22223,a)].">
      <j1 rule="hyper" parents="60 22170 22223"/>
    </justification>
  </clause>

  <clause id="22226">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21477,a(flip),b,22225,a),flip(a)].">
      <j1 rule="hyper" parents="60 21477 22225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22227">
    <literal><![CDATA[
      K(x,L(y \ z,u,y * u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(21579,a,22226,a)].">
      <j1 rule="hyper" parents="21579 22226"/>
    </justification>
  </clause>

  <clause id="22228">
    <literal><![CDATA[
      K(x,L(y \ z,u,z * u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22213,a,b,22227,a)].">
      <j1 rule="hyper" parents="60 22213 22227"/>
    </justification>
  </clause>

  <clause id="22229">
    <literal><![CDATA[
      K(x,L(y \ z,u,u * z)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(21563,a,22228,a)].">
      <j1 rule="hyper" parents="21563 22228"/>
    </justification>
  </clause>

  <clause id="22230">
    <literal><![CDATA[
      K(x,y \ ((y / (z \ 1)) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z * u,y,u * y)) = w
    ]]></literal>
    <justification jstring="[para(22228(a,1),15590(a,1))].">
      <j1 rule="para" parents="22228 15590"/>
    </justification>
  </clause>

  <clause id="22231">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,19707,a(flip),b,22229,a)].">
      <j1 rule="hyper" parents="60 19707 22229"/>
    </justification>
  </clause>

  <clause id="22232">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(21563,a,22222,a)].">
      <j1 rule="hyper" parents="21563 22222"/>
    </justification>
  </clause>

  <clause id="22233">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z \ 1,R(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(1111(a,1),22232(a,1,2,3))].">
      <j1 rule="para" parents="1111 22232"/>
    </justification>
  </clause>

  <clause id="22234">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z \ 1,L(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(16039(a,1),22233(a,1,2))].">
      <j1 rule="para" parents="16039 22233"/>
    </justification>
  </clause>

  <clause id="22235">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z,L(y,z,z))) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19401,a(flip),b,22234,a)].">
      <j1 rule="hyper" parents="60 19401 22234"/>
    </justification>
  </clause>

  <clause id="22236">
    <literal><![CDATA[
      K(x,L(T(y * z,z \ 1) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19701,a(flip),b,22235,a)].">
      <j1 rule="hyper" parents="60 19701 22235"/>
    </justification>
  </clause>

  <clause id="22237">
    <literal><![CDATA[
      K(x,L(T(y * z,z * 1) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(18517,a,22236,a)].">
      <j1 rule="hyper" parents="18517 22236"/>
    </justification>
  </clause>

  <clause id="22239">
    <literal><![CDATA[
      K(x,L(T(y * z,z) * u,z,y)) = K(x,(z \ 1) \ ((((y * z) \ 1) \ (z \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(3(a,1),22237(a,1,2,1,1,2))].">
      <j1 rule="para" parents="3 22237"/>
    </justification>
  </clause>

  <clause id="22240">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) = K(x,(y \ 1) \ ((((z * y) \ 1) \ (y \ 1)) * u))
    ]]></literal>
    <justification jstring="[hyper(18813,a,22239,a)].">
      <j1 rule="hyper" parents="18813 22239"/>
    </justification>
  </clause>

  <clause id="22241">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z)) = K(x,y \ ((((z * y) \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,18703,a(flip),b,22240,a),flip(a)].">
      <j1 rule="hyper" parents="370 18703 22240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22242">
    <literal><![CDATA[
      K(x,y \ ((((z * y) \ 1) \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) / z)) = w
    ]]></literal>
    <justification jstring="[para(22241(a,1),21641(a,1))].">
      <j1 rule="para" parents="22241 21641"/>
    </justification>
  </clause>

  <clause id="22243">
    <literal><![CDATA[
      K(x,y \ (((z * y) * y) * u)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(22242,a,21935,a),flip(a)].">
      <j1 rule="hyper" parents="22242 21935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22244">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * ((((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * K((z \ 1) \ (x / z),y))
    ]]></literal>
    <justification jstring="[para(13700(a,1),12718(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13700 12718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22245">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * ((x / z) * K((z \ 1) \ (x / z),y))
    ]]></literal>
    <justification jstring="[para(77(a,1),22244(a,2,2,1))].">
      <j1 rule="para" parents="77 22244"/>
    </justification>
  </clause>

  <clause id="22248">
    <literal><![CDATA[
      (((T(x,y) / z) / (x / z)) \ (T(x,y) / z)) * T(T((T(x,y) / z) / (x / z),T(x,y) / z),u) = K(x,K(y,u)) * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),22245(a,2,2))].">
      <j1 rule="para" parents="6519 22245"/>
    </justification>
  </clause>

  <clause id="22249">
    <literal><![CDATA[
      (x / y) * T(T((T(x,z) / y) / (x / y),T(x,z) / y),u) = K(x,K(z,u)) * (T(x,z) / y)
    ]]></literal>
    <justification jstring="[hyper(841,a,22248,a)].">
      <j1 rule="hyper" parents="841 22248"/>
    </justification>
  </clause>

  <clause id="22251">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = (x / u) * T(K((u \ 1) \ (x / u),y),z)
    ]]></literal>
    <justification jstring="[para(7465(a,1),22249(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7465 22249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22252">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = (x / u) * K((u \ 1) \ (x / u),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8034,a,b,22251,a),flip(a)].">
      <j1 rule="hyper" parents="370 8034 22251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22253">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = T(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[hyper(370,a,6519,a(flip),b,22252,a),flip(a)].">
      <j1 rule="hyper" parents="370 6519 22252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22254">
    <literal><![CDATA[
      K(T(x,T(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(22253(a,1),17690(a,1,1))].">
      <j1 rule="para" parents="22253 17690"/>
    </justification>
  </clause>

  <clause id="22255">
    <literal><![CDATA[
      L(x \ y,y / x,y / x) = T(y / x,(y / x) * y)
    ]]></literal>
    <justification jstring="[para(888(a,1),15438(a,1,1))].">
      <j1 rule="para" parents="888 15438"/>
    </justification>
  </clause>

  <clause id="22256">
    <literal><![CDATA[
      L(x \ y,y / x,x \ y) = T(y / x,(y / x) * y)
    ]]></literal>
    <justification jstring="[hyper(12505,a,22255,a)].">
      <j1 rule="hyper" parents="12505 22255"/>
    </justification>
  </clause>

  <clause id="22257">
    <literal><![CDATA[
      T(x / y,(x / y) * x) = T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(14626,a,22256,a),flip(a)].">
      <j1 rule="hyper" parents="14626 22256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22258">
    <literal><![CDATA[
      L(x / y,x,x / y) * x = x * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(22257(a,1),895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22257 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22259">
    <literal><![CDATA[
      T(x * T(y \ x,x \ y),x / y) = x * (x / y)
    ]]></literal>
    <justification jstring="[para(22258(a,1),5548(a,1,1))].">
      <j1 rule="para" parents="22258 5548"/>
    </justification>
  </clause>

  <clause id="22260">
    <literal><![CDATA[
      T(x / (x \ y),x / y) = x * (x / y)
    ]]></literal>
    <justification jstring="[para(3422(a,1),22259(a,1,1))].">
      <j1 rule="para" parents="3422 22259"/>
    </justification>
  </clause>

  <clause id="22261">
    <literal><![CDATA[
      T(x / (x \ y),y \ x) = x * (x / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,17641,a(flip),b,22260,a)].">
      <j1 rule="hyper" parents="60 17641 22260"/>
    </justification>
  </clause>

  <clause id="22262">
    <literal><![CDATA[
      (x / (x \ y)) * (y \ x) = (y \ x) * (x * (x / y))
    ]]></literal>
    <justification jstring="[hyper(129,a,22261,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22261 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22263">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),(u / (u \ w)) * (w \ u)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(22261(a,1),14475(a,2,2,2,2))].">
      <j1 rule="para" parents="22261 14475"/>
    </justification>
  </clause>

  <clause id="22264">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),(w \ u) * (u * (u / w))))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(22262(a,1),22263(a,1,2,2,2,2))].">
      <j1 rule="para" parents="22262 22263"/>
    </justification>
  </clause>

  <clause id="22265">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),u * (u * (w \ (u / w)))))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(20592(a,1),22264(a,1,2,2,2))].">
      <j1 rule="para" parents="20592 22264"/>
    </justification>
  </clause>

  <clause id="22266">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),w \ (u / w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,18600,a(flip),b,22265,a)].">
      <j1 rule="hyper" parents="60 18600 22265"/>
    </justification>
  </clause>

  <clause id="22267">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),w * (u / w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(18599,a,22266,a)].">
      <j1 rule="hyper" parents="18599 22266"/>
    </justification>
  </clause>

  <clause id="22269">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),T(u,w)))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[para(12547(a,1),22267(a,1,2,2,2))].">
      <j1 rule="para" parents="12547 22267"/>
    </justification>
  </clause>

  <clause id="22270">
    <literal><![CDATA[
      K(x,y \ (z * T(u / (u \ w),u))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(60,a,19515,a(flip),b,22269,a)].">
      <j1 rule="hyper" parents="60 19515 22269"/>
    </justification>
  </clause>

  <clause id="22271">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ u))) = K(x,y \ (z * (u * (u / w))))
    ]]></literal>
    <justification jstring="[hyper(15729,a,22270,a)].">
      <j1 rule="hyper" parents="15729 22270"/>
    </justification>
  </clause>

  <clause id="22273">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * w))) = K(x,y \ (z * (w * (w / u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,21294,a(flip),b,22271,a)].">
      <j1 rule="hyper" parents="60 21294 22271"/>
    </justification>
  </clause>

  <clause id="22274">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * (w * (w / u)))) = K(x,y \ (((u \ w) * w) * z))
    ]]></literal>
    <justification jstring="[hyper(21043,a,22273,a),flip(a)].">
      <j1 rule="hyper" parents="21043 22273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22275">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * u) * w)) = K(x,y \ ((u * (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(21042,a,22274,a),flip(a)].">
      <j1 rule="hyper" parents="21042 22274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22276">
    <literal><![CDATA[
      K(x,y \ (((T(z,u) \ (z * u)) * (z * u)) * w)) = K(x,y \ (((z * u) * u) * w))
    ]]></literal>
    <justification jstring="[para(214(a,1),22275(a,2,2,2,1,2))].">
      <j1 rule="para" parents="214 22275"/>
    </justification>
  </clause>

  <clause id="22277">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * (u * z)) * w)) = K(x,y \ (((u * z) * z) * w))
    ]]></literal>
    <justification jstring="[para(5808(a,1),22276(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5808 22276"/>
    </justification>
  </clause>

  <clause id="22278">
    <literal><![CDATA[
      K(x,y \ (((z * u) * u) * w)) = K(x,y \ ((u * (u * z)) * w))
    ]]></literal>
    <justification jstring="[para(5818(a,1),22277(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5818 22277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22279">
    <literal><![CDATA[
      K(x,y \ ((y * (y * z)) * u)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22243,a(flip),b,22278,a),flip(a)].">
      <j1 rule="hyper" parents="60 22243 22278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22280">
    <literal><![CDATA[
      K(x,y / ((z \ 1) / u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21950,a(flip),b,22279,a),flip(a)].">
      <j1 rule="hyper" parents="60 21950 22279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22281">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (y * (z / y))) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,22102,a(flip),b,22280,a),flip(a)].">
      <j1 rule="hyper" parents="60 22102 22280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22282">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * T(z,y)) = K(x,((u \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(17798,a,22281,a)].">
      <j1 rule="hyper" parents="17798 22281"/>
    </justification>
  </clause>

  <clause id="22283">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21967,a(flip),b,22282,a),flip(a)].">
      <j1 rule="hyper" parents="60 21967 22282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22284">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(T(y,z) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(18478,a,22283,a)].">
      <j1 rule="hyper" parents="18478 22283"/>
    </justification>
  </clause>

  <clause id="22285">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21980,a(flip),b,22283,a)].">
      <j1 rule="hyper" parents="60 21980 22283"/>
    </justification>
  </clause>

  <clause id="22286">
    <literal><![CDATA[
      K(x,((T(T(y,z),z) \ u) \ y) * w) = K(x,y * (y * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,21273,a(flip),b,22283,a),flip(a)].">
      <j1 rule="hyper" parents="60 21273 22283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22287">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21048,a(flip),b,22283,a),flip(a)].">
      <j1 rule="hyper" parents="60 21048 22283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22288">
    <literal><![CDATA[
      K(x,y \ ((y / z) * u)) = K(x,(z \ (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22231,a(flip),b,22285,a)].">
      <j1 rule="hyper" parents="60 22231 22285"/>
    </justification>
  </clause>

  <clause id="22289">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) * (u \ (z * y))) = a(u * y,u,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,21718,a(flip),b,22285,a),flip(a)].">
      <j1 rule="hyper" parents="60 21718 22285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22292">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20037,a(flip),b,22284,a),flip(a)].">
      <j1 rule="hyper" parents="370 20037 22284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22293">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),u,z)) = K(x,(y / z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(15980,a,22292,a)].">
      <j1 rule="hyper" parents="15980 22292"/>
    </justification>
  </clause>

  <clause id="22294">
    <literal><![CDATA[
      K(x,(y / z) \ u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22107,a(flip),b,22292,a)].">
      <j1 rule="hyper" parents="60 22107 22292"/>
    </justification>
  </clause>

  <clause id="22295">
    <literal><![CDATA[
      K(R(x,y,z) * K(u,x),(w / v5) * v6) = K(x,L(T((v5 / w) \ v6,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(19941,a,22294,a),flip(a)].">
      <j1 rule="hyper" parents="19941 22294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22296">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(w / y) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,20726,a,b,22294,a)].">
      <j1 rule="hyper" parents="370 20726 22294"/>
    </justification>
  </clause>

  <clause id="22298">
    <literal><![CDATA[
      x * K(x,(y / z) * u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,22294,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22294 5230"/>
    </justification>
  </clause>

  <clause id="22300">
    <literal><![CDATA[
      T(x,(y / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(22298(a,1),5265(a,1))].">
      <j1 rule="para" parents="22298 5265"/>
    </justification>
  </clause>

  <clause id="22301">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(22300,a,21003,a)].">
      <j1 rule="hyper" parents="22300 21003"/>
    </justification>
  </clause>

  <clause id="22302">
    <literal><![CDATA[
      T(x,(y / z) * (z / y)) = x
    ]]></literal>
    <justification jstring="[hyper(22300,a,227,a)].">
      <j1 rule="hyper" parents="22300 227"/>
    </justification>
  </clause>

  <clause id="22304">
    <literal><![CDATA[
      T(x,(y / (z * y)) * z) = x
    ]]></literal>
    <justification jstring="[para(6(a,1),22302(a,1,2,2))].">
      <j1 rule="para" parents="6 22302"/>
    </justification>
  </clause>

  <clause id="22305">
    <literal><![CDATA[
      T(x,y * ((y \ z) / z)) = x
    ]]></literal>
    <justification jstring="[para(74(a,1),22302(a,1,2,1))].">
      <j1 rule="para" parents="74 22302"/>
    </justification>
  </clause>

  <clause id="22306">
    <literal><![CDATA[
      L(x,y,z / (y * z)) * ((z / (y * z)) * y) = (z / (y * z)) * (y * x)
    ]]></literal>
    <justification jstring="[para(22304(a,1),869(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22304 869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22307">
    <literal><![CDATA[
      L(x,(y \ z) / z,y) * (y * ((y \ z) / z)) = y * (((y \ z) / z) * x)
    ]]></literal>
    <justification jstring="[para(22305(a,1),869(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22305 869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22308">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(17916,a,22301,a),flip(a)].">
      <j1 rule="hyper" parents="17916 22301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22309">
    <literal><![CDATA[
      T(x,(y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(22301(a,1),17916(a,1))].">
      <j1 rule="para" parents="22301 17916"/>
    </justification>
  </clause>

  <clause id="22311">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) / ((u \ z) \ w)) = K(x,((u \ z) \ w) \ y)
    ]]></literal>
    <justification jstring="[para(22308(a,1),14353(a,1,2,1))].">
      <j1 rule="para" parents="22308 14353"/>
    </justification>
  </clause>

  <clause id="22314">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,((y \ 1) \ (z / u)) * u)
    ]]></literal>
    <justification jstring="[hyper(22230,a,22288,a)].">
      <j1 rule="hyper" parents="22230 22288"/>
    </justification>
  </clause>

  <clause id="22315">
    <literal><![CDATA[
      K(x,((y / (z \ 1)) / u) \ K(z,z \ 1)) = K(x,u / (y / (1 / z)))
    ]]></literal>
    <justification jstring="[para(4402(a,1),22296(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4402 22296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22317">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,18316,a(flip),b,22287,a),flip(a)].">
      <j1 rule="hyper" parents="60 18316 22287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22318">
    <literal><![CDATA[
      K(x,L((y / z) * u,y,z)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(16486,a,22317,a)].">
      <j1 rule="hyper" parents="16486 22317"/>
    </justification>
  </clause>

  <clause id="22319">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22119,a(flip),b,22317,a)].">
      <j1 rule="hyper" parents="60 22119 22317"/>
    </justification>
  </clause>

  <clause id="22320">
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = K(x,(y \ z) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(18675,a,22319,a)].">
      <j1 rule="hyper" parents="18675 22319"/>
    </justification>
  </clause>

  <clause id="22321">
    <literal><![CDATA[
      K(x,y \ (((y / z) * u) * z)) = K(x,(z \ y) * ((u \ y) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22077,a(flip),b,22320,a)].">
      <j1 rule="hyper" parents="60 22077 22320"/>
    </justification>
  </clause>

  <clause id="22322">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,(y * (z / u)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21888,a(flip),b,22314,a),flip(a)].">
      <j1 rule="hyper" parents="370 21888 22314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22323">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[para(1336(a,1),22286(a,1,2,1,1,1))].">
      <j1 rule="para" parents="1336 22286"/>
    </justification>
  </clause>

  <clause id="22324">
    <literal><![CDATA[
      K(x,(y * (y / z)) * u) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16980,a(flip),b,22323,a)].">
      <j1 rule="hyper" parents="60 16980 22323"/>
    </justification>
  </clause>

  <clause id="22325">
    <literal><![CDATA[
      K(x,y * (y * (z \ ((y / z) \ u)))) = K(x,z * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21953,a(flip),b,22324,a),flip(a)].">
      <j1 rule="hyper" parents="60 21953 22324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22326">
    <literal><![CDATA[
      x * K(y,(z \ x) * ((u \ x) \ z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(22321(a,1),21132(a,1,2))].">
      <j1 rule="para" parents="22321 21132"/>
    </justification>
  </clause>

  <clause id="22327">
    <literal><![CDATA[
      K(x,y \ (((1 / z) / y) \ u)) = K(x,y * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21151,a(flip),b,22325,a)].">
      <j1 rule="hyper" parents="60 21151 22325"/>
    </justification>
  </clause>

  <clause id="22328">
    <literal><![CDATA[
      K(x,y \ ((y / (1 / z)) * u)) = K(x,y * ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22226,a(flip),b,22327,a)].">
      <j1 rule="hyper" parents="60 22226 22327"/>
    </justification>
  </clause>

  <clause id="22329">
    <literal><![CDATA[
      K(x,((1 / y) \ (z / u)) * u) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22288,a(flip),b,22328,a)].">
      <j1 rule="hyper" parents="60 22288 22328"/>
    </justification>
  </clause>

  <clause id="22330">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21891,a(flip),b,22329,a)].">
      <j1 rule="hyper" parents="60 21891 22329"/>
    </justification>
  </clause>

  <clause id="22331">
    <literal><![CDATA[
      K(x,L(y * z,u,z * u)) = K(x,u * ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22322,a,b,22330,a)].">
      <j1 rule="hyper" parents="60 22322 22330"/>
    </justification>
  </clause>

  <clause id="22332">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),(z \ 1) \ 1,z \ T(u,z))) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(15658(a,1),22331(a,1,2,3))].">
      <j1 rule="para" parents="15658 22331"/>
    </justification>
  </clause>

  <clause id="22333">
    <literal><![CDATA[
      x * K(y,(z \ x) * (T(1 / (u / x),u) \ z)) = ((x / z) * K(y,(1 / (u / x)) \ x)) * z
    ]]></literal>
    <justification jstring="[para(7722(a,2),22326(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7722 22326"/>
    </justification>
  </clause>

  <clause id="22334">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) * (w \ (u \ z))) = K(x,((u \ z) \ w) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22319,a(flip),b,22311,a)].">
      <j1 rule="hyper" parents="60 22319 22311"/>
    </justification>
  </clause>

  <clause id="22335">
    <literal><![CDATA[
      K(x,((y / (z \ 1)) / u) \ 1) = K(x,u / (y / (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(6061,a,22315,a)].">
      <j1 rule="hyper" parents="6061 22315"/>
    </justification>
  </clause>

  <clause id="22336">
    <literal><![CDATA[
      K(x,y / (z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(22335(a,1),9140(a,1))].">
      <j1 rule="para" parents="22335 9140"/>
    </justification>
  </clause>

  <clause id="22337">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,((z \ u) \ w) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,21107,a(flip),b,22334,a)].">
      <j1 rule="hyper" parents="60 21107 22334"/>
    </justification>
  </clause>

  <clause id="22338">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,(w \ (z \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,22285,a(flip),b,22337,a),flip(a)].">
      <j1 rule="hyper" parents="370 22285 22337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22339">
    <literal><![CDATA[
      K(x,L(T((y / z) \ u,w),v5,v6)) = K(x,L(T((z / y) * u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19941,a,22295,a),flip(a)].">
      <j1 rule="hyper" parents="19941 22295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22340">
    <literal><![CDATA[
      K(x,L(T((y / z) * u,y * z),w,v5)) = K(x,L(u / (z / y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(17829,a,22339,a),flip(a)].">
      <j1 rule="hyper" parents="17829 22339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22341">
    <literal><![CDATA[
      K(x,L(y / (z / u),w,v5)) = K(x,L(y * (u / z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(18647,a,22340,a),flip(a)].">
      <j1 rule="hyper" parents="18647 22340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22342">
    <literal><![CDATA[
      K(x,L(y * (z / T(u,z \ u)),w,v5)) = K(x,L(y / (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(20367,a,22341,a),flip(a)].">
      <j1 rule="hyper" parents="20367 22341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22343">
    <literal><![CDATA[
      K(x,L(y / (z \ u),w,v5)) = K(x,L(y * (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,21154,a(flip),b,22342,a),flip(a)].">
      <j1 rule="hyper" parents="60 21154 22342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22344">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,(y * (u / z)) / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21409,a(flip),b,22343,a),flip(a)].">
      <j1 rule="hyper" parents="60 21409 22343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22345">
    <literal><![CDATA[
      K(x,L((y / z) * (u \ w),y,z)) = K(x,y / ((w \ 1) * (w \ (((1 / w) \ u) * z))))
    ]]></literal>
    <justification jstring="[hyper(60,a,16485,a(flip),b,22343,a),flip(a)].">
      <j1 rule="hyper" parents="60 16485 22343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22346">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (z \ (((1 / z) \ u) * w)))) = K(x,y * (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22318,a(flip),b,22345,a),flip(a)].">
      <j1 rule="hyper" parents="60 22318 22345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22347">
    <literal><![CDATA[
      K(x,y / ((z \ u) * w)) = K(x,y * (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(2102(a,1),22346(a,1,2,2))].">
      <j1 rule="para" parents="2102 22346"/>
    </justification>
  </clause>

  <clause id="22348">
    <literal><![CDATA[
      K(x,T(y,z * (u * w)) * (w \ (z \ u))) = K(x,((u \ z) * w) \ y)
    ]]></literal>
    <justification jstring="[hyper(21653,a,22347,a),flip(a)].">
      <j1 rule="hyper" parents="21653 22347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22349">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ w) = K(x,(u \ (z \ y)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,22338,a(flip),b,22348,a),flip(a)].">
      <j1 rule="hyper" parents="60 22338 22348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22351">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) * (u \ (z * y))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,16655,a(flip),b,22349,a),flip(a)].">
      <j1 rule="hyper" parents="60 16655 22349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22352">
    <literal><![CDATA[
      a(x * y,x,K(z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22289,a(flip),b,22351,a)].">
      <j1 rule="hyper" parents="60 22289 22351"/>
    </justification>
  </clause>

  <clause id="22353">
    <literal><![CDATA[
      a(x,y,K(z,y * u)) = a(y,x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(22203,a,22352,a)].">
      <j1 rule="hyper" parents="22203 22352"/>
    </justification>
  </clause>

  <clause id="22354">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = (K(x,y) * u) / (u * a(z,y,K(u,x)))
    ]]></literal>
    <justification jstring="[para(22353(a,1),21825(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22353 21825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22355">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = (K(x,y) * u) / L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(21525(a,1),22354(a,2,2))].">
      <j1 rule="para" parents="21525 22354"/>
    </justification>
  </clause>

  <clause id="22356">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) = K(x,y) * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,21558,a(flip),b,22355,a),flip(a)].">
      <j1 rule="hyper" parents="370 21558 22355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22357">
    <literal><![CDATA[
      K(x,y) * a(z * u,y,K(x,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19700,a(flip),b,22356,a),flip(a)].">
      <j1 rule="hyper" parents="60 19700 22356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22358">
    <literal><![CDATA[
      K(x,y) * a(z,y,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19643(a,1),22357(a,1,2))].">
      <j1 rule="para" parents="19643 22357"/>
    </justification>
  </clause>

  <clause id="22359">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22357,a(flip),b,22358,a),flip(a)].">
      <j1 rule="hyper" parents="60 22357 22358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22360">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(31,a,12932,a,b,22358,a),flip(a)].">
      <j1 rule="hyper" parents="31 12932 22358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22361">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(15867,a,22360,a)].">
      <j1 rule="hyper" parents="15867 22360"/>
    </justification>
  </clause>

  <clause id="22363">
    <literal><![CDATA[
      K(x,y) * a(z,x,K(u,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(22360(a,1),15909(a,1,2))].">
      <j1 rule="para" parents="22360 15909"/>
    </justification>
  </clause>

  <clause id="22364">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z,y / z)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(21640,a,22359,a),flip(a)].">
      <j1 rule="hyper" parents="21640 22359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22365">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,15934,a(flip),b,22359,a)].">
      <j1 rule="hyper" parents="60 15934 22359"/>
    </justification>
  </clause>

  <clause id="22366">
    <literal><![CDATA[
      K((x * y) \ ((1 / x) \ z),L(u,x,y)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13053,a(flip),b,22359,a),flip(a)].">
      <j1 rule="hyper" parents="60 13053 22359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22367">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),22359(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 22359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22368">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(14828(a,2),22359(a,1,2))].">
      <j1 rule="para" parents="14828 22359"/>
    </justification>
  </clause>

  <clause id="22369">
    <literal><![CDATA[
      K(x,L((y * z) / u,z,y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(21637,a,22365,a),flip(a)].">
      <j1 rule="hyper" parents="21637 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22370">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,w,z))
    ]]></literal>
    <justification jstring="[hyper(21529,a,22365,a),flip(a)].">
      <j1 rule="hyper" parents="21529 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22371">
    <literal><![CDATA[
      K(x,L(y,z \ u,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,19749,a,b,22365,a)].">
      <j1 rule="hyper" parents="370 19749 22365"/>
    </justification>
  </clause>

  <clause id="22372">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,16572,a(flip),b,22365,a),flip(a)].">
      <j1 rule="hyper" parents="370 16572 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22373">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x,y)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,15933,a(flip),b,22365,a),flip(a)].">
      <j1 rule="hyper" parents="370 15933 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22374">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,y)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,12534,a(flip),b,22365,a),flip(a)].">
      <j1 rule="hyper" parents="370 12534 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22375">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(22365(a,1),15944(a,1))].">
      <j1 rule="para" parents="22365 15944"/>
    </justification>
  </clause>

  <clause id="22376">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * u) * z
    ]]></literal>
    <justification jstring="[para(22365(a,1),16420(a,1,1))].">
      <j1 rule="para" parents="22365 16420"/>
    </justification>
  </clause>

  <clause id="22377">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,L(u,y,x)) = K(x \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16571,a(flip),b,22367,a),flip(a)].">
      <j1 rule="hyper" parents="60 16571 22367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22378">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,z,y)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14583,a(flip),b,22367,a),flip(a)].">
      <j1 rule="hyper" parents="60 14583 22367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22379">
    <literal><![CDATA[
      K(x,L((y * (z \ 1)) \ (z * u),z,y)) = K(x,T(y * (z \ (1 / z)),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16677,a(flip),b,22368,a),flip(a)].">
      <j1 rule="hyper" parents="60 16677 22368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22380">
    <literal><![CDATA[
      K(((x * (y / x)) * x) \ z,L(u,y,x)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16578,a(flip),b,22370,a),flip(a)].">
      <j1 rule="hyper" parents="60 16578 22370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22381">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(22370(a,1),21530(a,1))].">
      <j1 rule="para" parents="22370 21530"/>
    </justification>
  </clause>

  <clause id="22382">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22365,a,b,22371,a)].">
      <j1 rule="hyper" parents="60 22365 22371"/>
    </justification>
  </clause>

  <clause id="22383">
    <literal><![CDATA[
      K((x \ y) \ (y \ T(z,x)),L(u,y,x)) = K(z / (y * (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18534,a(flip),b,22371,a),flip(a)].">
      <j1 rule="hyper" parents="60 18534 22371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22384">
    <literal><![CDATA[
      K(x,L(y,z / u,z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14832(a,2),22371(a,1,2))].">
      <j1 rule="para" parents="14832 22371"/>
    </justification>
  </clause>

  <clause id="22385">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15941,a(flip),b,22382,a),flip(a)].">
      <j1 rule="hyper" parents="60 15941 22382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22386">
    <literal><![CDATA[
      K((x / y) \ (T(x,z) \ u),L(w,x,y)) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,19369,a(flip),b,22384,a),flip(a)].">
      <j1 rule="hyper" parents="60 19369 22384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22390">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(22370(a,2),22381(a,1))].">
      <j1 rule="para" parents="22370 22381"/>
    </justification>
  </clause>

  <clause id="22391">
    <literal><![CDATA[
      K(x,y / (z / T(u,T(y,w)))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21714,a(flip),b,22369,a)].">
      <j1 rule="hyper" parents="60 21714 22369"/>
    </justification>
  </clause>

  <clause id="22392">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16611,a(flip),b,22372,a)].">
      <j1 rule="hyper" parents="60 16611 22372"/>
    </justification>
  </clause>

  <clause id="22393">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ T(z,u)) = K(x,(z \ u) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(20299,a,22392,a)].">
      <j1 rule="hyper" parents="20299 22392"/>
    </justification>
  </clause>

  <clause id="22394">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ u)) = K(x,z \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16759,a(flip),b,22392,a)].">
      <j1 rule="hyper" parents="60 16759 22392"/>
    </justification>
  </clause>

  <clause id="22395">
    <literal><![CDATA[
      K(x,y \ (T(z,y) \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16758,a(flip),b,22392,a),flip(a)].">
      <j1 rule="hyper" parents="60 16758 22392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22396">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = x * K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(129,a,22392,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22392 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      K(x,(y \ (y \ 1)) \ ((z \ (y \ 1)) \ ((y * y) \ u))) = K(x,(z \ y) \ ((y \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(1760(a,1),22395(a,1,2,2))].">
      <j1 rule="para" parents="1760 22395"/>
    </justification>
  </clause>

  <clause id="22399">
    <literal><![CDATA[
      K(x,L(y,z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(19696(a,1),22375(a,1))].">
      <j1 rule="para" parents="19696 22375"/>
    </justification>
  </clause>

  <clause id="22400">
    <literal><![CDATA[
      (K(x,y) * z) * T(u,z) = (K(x,y) * u) * z
    ]]></literal>
    <justification jstring="[hyper(16493,a,22376,a)].">
      <j1 rule="hyper" parents="16493 22376"/>
    </justification>
  </clause>

  <clause id="22401">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(22376(a,1),41(a,1))].">
      <j1 rule="para" parents="22376 41"/>
    </justification>
  </clause>

  <clause id="22403">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,y)) = z * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(22400(a,1),19771(a,1,1))].">
      <j1 rule="para" parents="22400 19771"/>
    </justification>
  </clause>

  <clause id="22407">
    <literal><![CDATA[
      K(x,y / (z / T(u,y))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,19620,a(flip),b,22391,a)].">
      <j1 rule="hyper" parents="60 19620 22391"/>
    </justification>
  </clause>

  <clause id="22408">
    <literal><![CDATA[
      K(x,(1 / (y / z)) / (1 / T(u,1 / (y / z)))) = K(x,u / ((y / z) * K(y \ z,z \ y)))
    ]]></literal>
    <justification jstring="[para(4640(a,2),22407(a,2,2,2))].">
      <j1 rule="para" parents="4640 22407"/>
    </justification>
  </clause>

  <clause id="22409">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,22221,a(flip),b,22394,a),flip(a)].">
      <j1 rule="hyper" parents="370 22221 22394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22410">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22396,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22411">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(22396(a,2),5265(a,1))].">
      <j1 rule="para" parents="22396 5265"/>
    </justification>
  </clause>

  <clause id="22412">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,z * y) \ w)) = T(x,u \ ((y \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(21117,a,22410,a)].">
      <j1 rule="hyper" parents="21117 22410"/>
    </justification>
  </clause>

  <clause id="22413">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21054,a(flip),b,22410,a),flip(a)].">
      <j1 rule="hyper" parents="60 21054 22410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22414">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16767,a(flip),b,22410,a),flip(a)].">
      <j1 rule="hyper" parents="60 16767 22410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22415">
    <literal><![CDATA[
      T(x,L(y \ z,u,w) \ (y \ v5)) = T(x,y \ (L(z / y,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(285(a,1),22410(a,1,2,1))].">
      <j1 rule="para" parents="285 22410"/>
    </justification>
  </clause>

  <clause id="22416">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,L(y,z,z)) \ y)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[para(1362(a,1),22414(a,2,2,2))].">
      <j1 rule="para" parents="1362 22414"/>
    </justification>
  </clause>

  <clause id="22417">
    <literal><![CDATA[
      T((K(x,y) * z) * K(x,y),K(x,y)) \ u = (K(x,y) * K(x,y)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(22403(a,2),517(a,1,1))].">
      <j1 rule="para" parents="22403 517"/>
    </justification>
  </clause>

  <clause id="22418">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (y * u))) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),22409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 22409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22419">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ (u * ((1 / y) \ y)))) = K(x,z \ T(((1 / y) \ z) * u,y * y))
    ]]></literal>
    <justification jstring="[para(15322(a,2),22409(a,2,2,2))].">
      <j1 rule="para" parents="15322 22409"/>
    </justification>
  </clause>

  <clause id="22420">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ (((y \ z) \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20093,a(flip),b,22413,a)].">
      <j1 rule="hyper" parents="370 20093 22413"/>
    </justification>
  </clause>

  <clause id="22421">
    <literal><![CDATA[
      T(x,(y \ z) \ ((y \ 1) \ u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,16765,a(flip),b,22413,a),flip(a)].">
      <j1 rule="hyper" parents="370 16765 22413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22422">
    <literal><![CDATA[
      K(x,(y * z) \ (z * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22374,a(flip),b,22378,a)].">
      <j1 rule="hyper" parents="60 22374 22378"/>
    </justification>
  </clause>

  <clause id="22423">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) \ y) * u)) = K(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16812,a(flip),b,22422,a),flip(a)].">
      <j1 rule="hyper" parents="60 16812 22422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22424">
    <literal><![CDATA[
      x * K(x,y \ ((z \ y) * u)) = T(x,(z * y) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,22422,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22422 5230"/>
    </justification>
  </clause>

  <clause id="22425">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (y \ u))) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),22422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 22422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22426">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (z * ((1 / z) * u))) = K(x,(z \ 1) \ ((y \ (z \ 1)) * (z * u)))
    ]]></literal>
    <justification jstring="[para(951(a,1),22422(a,1,2,2))].">
      <j1 rule="para" parents="951 22422"/>
    </justification>
  </clause>

  <clause id="22427">
    <literal><![CDATA[
      K(x,((y * z) * y) \ u) = K(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22224,a(flip),b,22425,a),flip(a)].">
      <j1 rule="hyper" parents="60 22224 22425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22428">
    <literal><![CDATA[
      K(x,(y * (z * y)) \ u) = K(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19677,a(flip),b,22427,a)].">
      <j1 rule="hyper" parents="60 19677 22427"/>
    </justification>
  </clause>

  <clause id="22429">
    <literal><![CDATA[
      x * K(x,y \ (z \ (y \ u))) = T(x,(y * (z * y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,22428,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22428 5230"/>
    </justification>
  </clause>

  <clause id="22431">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((z / y) \ u)) = w
    ]]></literal>
    <justification jstring="[para(109(a,1),22411(a,1,2,1))].">
      <j1 rule="para" parents="109 22411"/>
    </justification>
  </clause>

  <clause id="22432">
    <literal><![CDATA[
      T(x,(y / z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ ((z \ y) \ u)) = w
    ]]></literal>
    <justification jstring="[para(16754(a,1),22411(a,1))].">
      <j1 rule="para" parents="16754 22411"/>
    </justification>
  </clause>

  <clause id="22433">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(16755(a,1),22411(a,1))].">
      <j1 rule="para" parents="16755 22411"/>
    </justification>
  </clause>

  <clause id="22435">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,y * z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y \ z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20094(a,1),22433(a,1))].">
      <j1 rule="para" parents="20094 22433"/>
    </justification>
  </clause>

  <clause id="22436">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ (T(u,z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y * (z \ y)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(21441(a,1),22433(a,1))].">
      <j1 rule="para" parents="21441 22433"/>
    </justification>
  </clause>

  <clause id="22437">
    <literal><![CDATA[
      K(x,T(y,z * u) \ T(z,u)) = K(x,(z \ u) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18452,a(flip),b,22393,a)].">
      <j1 rule="hyper" parents="60 18452 22393"/>
    </justification>
  </clause>

  <clause id="22438">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y * u)) = T(x,y * ((z / y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16615,a,b,22421,a)].">
      <j1 rule="hyper" parents="60 16615 22421"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      T(x,y * ((z / y) \ ((y \ 1) * u))) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),22421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 22421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22440">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21477,a(flip),b,22423,a),flip(a)].">
      <j1 rule="hyper" parents="60 21477 22423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22441">
    <literal><![CDATA[
      x * K(x,y \ ((y / z) * u)) = T(x,(y * z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,22440,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22440 5230"/>
    </justification>
  </clause>

  <clause id="22442">
    <literal><![CDATA[
      (x * K(y,z \ ((z / u) * w))) \ x = K((z * u) \ (z * w),y)
    ]]></literal>
    <justification jstring="[para(22440(a,1),6294(a,1,1,2))].">
      <j1 rule="para" parents="22440 6294"/>
    </justification>
  </clause>

  <clause id="22443">
    <literal><![CDATA[
      T(x,(y * z) \ (z * u)) = T(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(5265,a,22424,a),flip(a)].">
      <j1 rule="hyper" parents="5265 22424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22444">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,y \ ((z \ y) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,16621,a,b,22443,a)].">
      <j1 rule="hyper" parents="60 16621 22443"/>
    </justification>
  </clause>

  <clause id="22445">
    <literal><![CDATA[
      T(x,(y * (z * y)) \ u) = T(x,y \ (z \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,22429,a),flip(a)].">
      <j1 rule="hyper" parents="5265 22429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22446">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,((y \ 1) * (z * (y \ 1))) \ (u * (1 / y)))
    ]]></literal>
    <justification jstring="[para(4694(a,2),22445(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4694 22445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22447">
    <literal><![CDATA[
      K(x,y \ (z * T(u / z,y))) = K(x,(u \ z) \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(21213,a,22437,a)].">
      <j1 rule="hyper" parents="21213 22437"/>
    </justification>
  </clause>

  <clause id="22448">
    <literal><![CDATA[
      T(x,y * ((z / y) \ ((y \ 1) * u))) = T(x,((y \ 1) * z) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(2074(a,1),22438(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2074 22438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22449">
    <literal><![CDATA[
      T(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((y / z) * u)) = w
    ]]></literal>
    <justification jstring="[para(22441(a,1),5265(a,1))].">
      <j1 rule="para" parents="22441 5265"/>
    </justification>
  </clause>

  <clause id="22450">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ u) = w
    ]]></literal>
    <justification jstring="[para(22444(a,1),20900(a,1))].">
      <j1 rule="para" parents="22444 20900"/>
    </justification>
  </clause>

  <clause id="22451">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (y * T(z * K(y,z),u)))
    ]]></literal>
    <justification jstring="[para(5233(a,1),22447(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5233 22447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22452">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K(y \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16826,a(flip),b,22377,a)].">
      <j1 rule="hyper" parents="60 16826 22377"/>
    </justification>
  </clause>

  <clause id="22453">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14559,a(flip),b,22385,a)].">
      <j1 rule="hyper" parents="60 14559 22385"/>
    </justification>
  </clause>

  <clause id="22454">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(22381,a,22453,a)].">
      <j1 rule="hyper" parents="22381 22453"/>
    </justification>
  </clause>

  <clause id="22455">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),u) = K(x \ ((y \ x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22452,a(flip),b,22454,a)].">
      <j1 rule="hyper" parents="60 22452 22454"/>
    </justification>
  </clause>

  <clause id="22456">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16772,a(flip),b,22454,a)].">
      <j1 rule="hyper" parents="60 16772 22454"/>
    </justification>
  </clause>

  <clause id="22457">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12982,a(flip),b,22454,a)].">
      <j1 rule="hyper" parents="60 12982 22454"/>
    </justification>
  </clause>

  <clause id="22458">
    <literal><![CDATA[
      K(x \ (((K(y,x) * z) \ x) * u),w) = K(x \ ((T(x,y) \ z) \ u),w)
    ]]></literal>
    <justification jstring="[para(7890(a,1),22455(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7890 22455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22460">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(5(a,1),22450(a,1,2,2,2))].">
      <j1 rule="para" parents="5 22450"/>
    </justification>
  </clause>

  <clause id="22461">
    <literal><![CDATA[
      T(x,(y / z) \ (z \ u)) = T(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(22460,a,xx)].">
      <j1 rule="hyper" parents="22460"/>
    </justification>
  </clause>

  <clause id="22462">
    <literal><![CDATA[
      T(x,y \ ((y \ z) \ u)) = T(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(22432,a,22461,a)].">
      <j1 rule="hyper" parents="22432 22461"/>
    </justification>
  </clause>

  <clause id="22464">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((u \ y) * z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20182,a(flip),b,22462,a),flip(a)].">
      <j1 rule="hyper" parents="60 20182 22462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22465">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,T(y * z,y) * z) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(5536(a,1),22412(a,1,2,1))].">
      <j1 rule="para" parents="5536 22412"/>
    </justification>
  </clause>

  <clause id="22466">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ (T(w,u * K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(7506(a,1),22412(a,1,2,1))].">
      <j1 rule="para" parents="7506 22412"/>
    </justification>
  </clause>

  <clause id="22467">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,T(y * z,K(u,w)) * T(z,K(u,w))) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(17081(a,1),22412(a,1,2,1))].">
      <j1 rule="para" parents="17081 22412"/>
    </justification>
  </clause>

  <clause id="22468">
    <literal><![CDATA[
      K((x * y) \ (x * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(19552,a,22442,a),flip(a)].">
      <j1 rule="hyper" parents="19552 22442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22469">
    <literal><![CDATA[
      K((x * y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((x / y) * z),u) = w
    ]]></literal>
    <justification jstring="[para(22442(a,1),6305(a,1))].">
      <j1 rule="para" parents="22442 6305"/>
    </justification>
  </clause>

  <clause id="22470">
    <literal><![CDATA[
      K((T(x,y) * y) \ (y * z),u) = K(y \ ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16832,a,b,22468,a)].">
      <j1 rule="hyper" parents="60 16832 22468"/>
    </justification>
  </clause>

  <clause id="22471">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / y) * z),u) = K((x * y) \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(1273(a,1),22468(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1273 22468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22472">
    <literal><![CDATA[
      K(x \ ((T(y,x) \ x) * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22457,a(flip),b,22470,a)].">
      <j1 rule="hyper" parents="60 22457 22470"/>
    </justification>
  </clause>

  <clause id="22473">
    <literal><![CDATA[
      K(x \ ((y \ T(x,y)) * z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),22472(a,1,1,2,1))].">
      <j1 rule="para" parents="5749 22472"/>
    </justification>
  </clause>

  <clause id="22474">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / (y * (z * z))) * u),w) = K((z * z) \ ((x * y) \ (x * u)),w)
    ]]></literal>
    <justification jstring="[para(968(a,1),22471(a,2,1))].">
      <j1 rule="para" parents="968 22471"/>
    </justification>
  </clause>

  <clause id="22475">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((x / y) * z),u) = w
    ]]></literal>
    <justification jstring="[para(22471(a,2),22469(a,1))].">
      <j1 rule="para" parents="22471 22469"/>
    </justification>
  </clause>

  <clause id="22476">
    <literal><![CDATA[
      K(x \ (y * (x \ T(z,y))),u) = K(z / (x * (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15933,a(flip),b,22383,a)].">
      <j1 rule="hyper" parents="60 15933 22383"/>
    </justification>
  </clause>

  <clause id="22477">
    <literal><![CDATA[
      K(x \ (L(x,y,y) * (x \ T(z,L(x,y,y)))),u) = K(z / (x * a(y,y,x)),u)
    ]]></literal>
    <justification jstring="[para(1362(a,1),22476(a,2,1,2,2))].">
      <j1 rule="para" parents="1362 22476"/>
    </justification>
  </clause>

  <clause id="22478">
    <literal><![CDATA[
      K((x * K(y,x)) / (z * (y \ z)),u) = K(z \ (y * (z \ x)),u)
    ]]></literal>
    <justification jstring="[para(5280(a,1),22476(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5280 22476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22479">
    <literal><![CDATA[
      K(T(x,y) / (z * (y \ z)),u) = K(z \ (y * (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(17017,a,22478,a)].">
      <j1 rule="hyper" parents="17017 22478"/>
    </justification>
  </clause>

  <clause id="22480">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,u) = K(x \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(18531,a,22479,a)].">
      <j1 rule="hyper" parents="18531 22479"/>
    </justification>
  </clause>

  <clause id="22481">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (y \ x)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(22479(a,1),18531(a,1))].">
      <j1 rule="para" parents="22479 18531"/>
    </justification>
  </clause>

  <clause id="22482">
    <literal><![CDATA[
      (x * y) / (K(z \ (u * (z \ w)),x) * y) = T(x,(z * (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(22480(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="22480 7934"/>
    </justification>
  </clause>

  <clause id="22483">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (x * (y \ x)),u) = w
    ]]></literal>
    <justification jstring="[para(22480(a,1),17429(a,1))].">
      <j1 rule="para" parents="22480 17429"/>
    </justification>
  </clause>

  <clause id="22484">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,y) \ y)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[para(15156(a,1),22416(a,1,2,2,1))].">
      <j1 rule="para" parents="15156 22416"/>
    </justification>
  </clause>

  <clause id="22485">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (y / u)) = T(x,u \ a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(16816,a,22484,a)].">
      <j1 rule="hyper" parents="16816 22484"/>
    </justification>
  </clause>

  <clause id="22487">
    <literal><![CDATA[
      T(1 / L(x \ y,z,u),x \ (L(y / x,z,u) \ w)) = T(L(x \ y,z,u) \ 1,L(x \ y,z,u) * (x \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,7751,a(flip),b,22415,a),flip(a)].">
      <j1 rule="hyper" parents="60 7751 22415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22488">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (y * T(T(z,y),u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,16984,a(flip),b,22451,a),flip(a)].">
      <j1 rule="hyper" parents="370 16984 22451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22489">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ (u \ y)) = K(x,u \ (T(z,u) * y))
    ]]></literal>
    <justification jstring="[para(272(a,1),22488(a,2,2,2))].">
      <j1 rule="para" parents="272 22488"/>
    </justification>
  </clause>

  <clause id="22490">
    <literal><![CDATA[
      K(x \ ((T(x,y) \ z) \ u),w) = K(x \ ((z \ T(x,y)) * u),w)
    ]]></literal>
    <justification jstring="[para(15339(a,1),22458(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15339 22458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22491">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ u) = T(x,y \ (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(7939,a,22482,a),flip(a)].">
      <j1 rule="hyper" parents="7939 22482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22492">
    <literal><![CDATA[
      T(x,(y * (z \ y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(22482(a,1),7939(a,1))].">
      <j1 rule="para" parents="22482 7939"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (z * (u \ y))) = w
    ]]></literal>
    <justification jstring="[para(17552(a,2),22492(a,1))].">
      <j1 rule="para" parents="17552 22492"/>
    </justification>
  </clause>

  <clause id="22494">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) \ z),L(u,x,y)) = K((x * ((x \ 1) * y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6892,a,22366,a)].">
      <j1 rule="hyper" parents="6892 22366"/>
    </justification>
  </clause>

  <clause id="22496">
    <literal><![CDATA[
      K((x * ((y / x) * x)) \ z,L(u,y,x)) = K(T(x,x \ y) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21136,a(flip),b,22380,a)].">
      <j1 rule="hyper" parents="60 21136 22380"/>
    </justification>
  </clause>

  <clause id="22497">
    <literal><![CDATA[
      K(x \ (T(y,x) * (T(x,z) \ u)),w) = K((x * (T(x,z) / y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20919,a(flip),b,22386,a)].">
      <j1 rule="hyper" parents="60 20919 22386"/>
    </justification>
  </clause>

  <clause id="22498">
    <literal><![CDATA[
      T(x,((y / z) \ z) \ (T(u,y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (((y / z) \ z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(7(a,1),22435(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7 22435"/>
    </justification>
  </clause>

  <clause id="22499">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((z \ y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(22308(a,1),22435(a,1))].">
      <j1 rule="para" parents="22308 22435"/>
    </justification>
  </clause>

  <clause id="22500">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ L(u,y,y)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22439,a(flip),b,22448,a),flip(a)].">
      <j1 rule="hyper" parents="60 22439 22448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22501">
    <literal><![CDATA[
      T(x,(y \ ((y \ 1) \ z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),22500(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 22500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22502">
    <literal><![CDATA[
      T(x,y \ L(T(z,y),u,u)) = T(x,z / (u \ ((u \ 1) \ y)))
    ]]></literal>
    <justification jstring="[hyper(17503,a,22501,a),flip(a)].">
      <j1 rule="hyper" parents="17503 22501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22503">
    <literal><![CDATA[
      T(x,y / (z \ ((z \ 1) \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,z) / u) = w
    ]]></literal>
    <justification jstring="[para(22502(a,1),17500(a,1))].">
      <j1 rule="para" parents="22502 17500"/>
    </justification>
  </clause>

  <clause id="22504">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) \ z),L(u,x,y)) = K(L(y,x,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),22494(a,2,1,1))].">
      <j1 rule="para" parents="2074 22494"/>
    </justification>
  </clause>

  <clause id="22505">
    <literal><![CDATA[
      K(x \ (T(y,x) \ ((x \ 1) \ z)),u) = K(L(y,x,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19570,a(flip),b,22504,a)].">
      <j1 rule="hyper" parents="60 19570 22504"/>
    </justification>
  </clause>

  <clause id="22506">
    <literal><![CDATA[
      K(T(x,x \ y) \ (y \ z),u) = K((x * y) \ z,L(u,y,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),22496(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 22496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22507">
    <literal><![CDATA[
      K(T(x,x \ y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16571,a(flip),b,22506,a),flip(a)].">
      <j1 rule="hyper" parents="370 16571 22506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22508">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14559,a(flip),b,22507,a)].">
      <j1 rule="hyper" parents="60 14559 22507"/>
    </justification>
  </clause>

  <clause id="22509">
    <literal><![CDATA[
      K((x / y) \ (x \ z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(20994,a,22508,a)].">
      <j1 rule="hyper" parents="20994 22508"/>
    </justification>
  </clause>

  <clause id="22510">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16773,a(flip),b,22508,a),flip(a)].">
      <j1 rule="hyper" parents="60 16773 22508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22511">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),u) = K(x \ ((y / x) \ z),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),22508(a,1,1,1))].">
      <j1 rule="para" parents="109 22508"/>
    </justification>
  </clause>

  <clause id="22512">
    <literal><![CDATA[
      K(x \ (y \ ((y \ 1) \ z)),u) = K(L(x,y,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22505,a(flip),b,22510,a),flip(a)].">
      <j1 rule="hyper" parents="60 22505 22510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22513">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((T(y,x) \ x) \ z),u)
    ]]></literal>
    <justification jstring="[para(5482(a,1),22510(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5482 22510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22514">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,(y \ x) \ z)),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[para(5472(a,1),22509(a,2,1,2))].">
      <j1 rule="para" parents="5472 22509"/>
    </justification>
  </clause>

  <clause id="22515">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((x \ T(y,x)) * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22490,a(flip),b,22513,a),flip(a)].">
      <j1 rule="hyper" parents="370 22490 22513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22516">
    <literal><![CDATA[
      K((x / T(y,x)) \ (y \ z),u) = K(y \ ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22473,a(flip),b,22515,a),flip(a)].">
      <j1 rule="hyper" parents="370 22473 22515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22517">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20842,a(flip),b,22516,a)].">
      <j1 rule="hyper" parents="60 20842 22516"/>
    </justification>
  </clause>

  <clause id="22518">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),u) = K(x \ ((x / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22511,a(flip),b,22517,a)].">
      <j1 rule="hyper" parents="60 22511 22517"/>
    </justification>
  </clause>

  <clause id="22519">
    <literal><![CDATA[
      (x * y) / (K(z \ ((z / u) * w),x) * y) = T(x,(z \ u) \ (z \ w))
    ]]></literal>
    <justification jstring="[para(22517(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="22517 7934"/>
    </justification>
  </clause>

  <clause id="22520">
    <literal><![CDATA[
      (K(x \ ((x / y) * z),u) * w) \ w = K(u,T((x \ y) \ (x \ z),w))
    ]]></literal>
    <justification jstring="[para(22517(a,1),8017(a,1,1,1))].">
      <j1 rule="para" parents="22517 8017"/>
    </justification>
  </clause>

  <clause id="22521">
    <literal><![CDATA[
      K(x \ ((x \ (y \ ((1 / y) \ x))) \ z),u) = K(x \ ((x / (y \ ((1 / y) \ x))) * z),u)
    ]]></literal>
    <justification jstring="[para(21501(a,1),22518(a,1,1,2,1))].">
      <j1 rule="para" parents="21501 22518"/>
    </justification>
  </clause>

  <clause id="22522">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) = T(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(7939,a,22519,a),flip(a)].">
      <j1 rule="hyper" parents="7939 22519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22523">
    <literal><![CDATA[
      T(x,y \ ((z / y) \ u)) = T(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(22431,a,22522,a)].">
      <j1 rule="hyper" parents="22431 22522"/>
    </justification>
  </clause>

  <clause id="22524">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ ((y / 1) * z))
    ]]></literal>
    <justification jstring="[para(22523(a,1),16111(a,2,2))].">
      <j1 rule="para" parents="22523 16111"/>
    </justification>
  </clause>

  <clause id="22525">
    <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(22520(a,1),8018(a,1))].">
      <j1 rule="para" parents="22520 8018"/>
    </justification>
  </clause>

  <clause id="22526">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = (K(x,y) * K(x,y)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(8704(a,1),22417(a,1,1))].">
      <j1 rule="para" parents="8704 22417"/>
    </justification>
  </clause>

  <clause id="22527">
    <literal><![CDATA[
      (K(x,y) * (K(x,y) * z)) \ u = K(y,x) * (K(y,x) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,20765,a(flip),b,22526,a),flip(a)].">
      <j1 rule="hyper" parents="370 20765 22526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22528">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = K(x,y) * (K(x,y) * (z \ u))
    ]]></literal>
    <justification jstring="[para(9604(a,1),22527(a,1,1))].">
      <j1 rule="para" parents="9604 22527"/>
    </justification>
  </clause>

  <clause id="22529">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) \ u = y * (T(T(y,x),x) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,9604,a(flip),b,22528,a),flip(a)].">
      <j1 rule="hyper" parents="370 9604 22528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22530">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = y * (T(T(y,z),z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10888,a(flip),b,22529,a)].">
      <j1 rule="hyper" parents="60 10888 22529"/>
    </justification>
  </clause>

  <clause id="22531">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((K(y,x) * z) \ u)) = ((K(y,x) \ 1) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,9606,a(flip),b,22530,a),flip(a)].">
      <j1 rule="hyper" parents="60 9606 22530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (K(x,y) * ((y \ x) \ z))) = ((K(y,x) \ 1) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(13934(a,1),22531(a,1,2,2))].">
      <j1 rule="para" parents="13934 22531"/>
    </justification>
  </clause>

  <clause id="22533">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,z,z \ y)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(21561,a,22364,a)].">
      <j1 rule="hyper" parents="21561 22364"/>
    </justification>
  </clause>

  <clause id="22534">
    <literal><![CDATA[
      K(x,T(y * (z \ (1 / z)),z) \ u) = K(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(16623,a,22379,a),flip(a)].">
      <j1 rule="hyper" parents="16623 22379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22535">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) \ u) = K(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1217(a,1),22534(a,1,2,1))].">
      <j1 rule="para" parents="1217 22534"/>
    </justification>
  </clause>

  <clause id="22536">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (T(u,z) \ w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y * (z \ y)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(22491(a,1),22436(a,1))].">
      <j1 rule="para" parents="22491 22436"/>
    </justification>
  </clause>

  <clause id="22537">
    <literal><![CDATA[
      K(x \ (L(x,y,y) * (x \ T(z,x))),u) = K(z / (x * a(y,y,x)),u)
    ]]></literal>
    <justification jstring="[para(15156(a,1),22477(a,1,1,2,2,2))].">
      <j1 rule="para" parents="15156 22477"/>
    </justification>
  </clause>

  <clause id="22539">
    <literal><![CDATA[
      K(x \ (x \ (y * L(x,z,z))),u) = K(y / (x * a(z,z,x)),u)
    ]]></literal>
    <justification jstring="[para(15384(a,1),22537(a,1,1,2))].">
      <j1 rule="para" parents="15384 22537"/>
    </justification>
  </clause>

  <clause id="22540">
    <literal><![CDATA[
      K(x * ((y * y) \ L(y,z,z)),u) = K(x / (y * a(z,z,y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18635,a(flip),b,22539,a)].">
      <j1 rule="hyper" parents="60 18635 22539"/>
    </justification>
  </clause>

  <clause id="22541">
    <literal><![CDATA[
      K(x / (y * a(z,z,y)),u) = K(x * L(1 / y,z,z),u)
    ]]></literal>
    <justification jstring="[para(3790(a,1),22540(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3790 22540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22542">
    <literal><![CDATA[
      K(x / (y * a(z,z,y)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * L(y \ 1,z,z),u) = w
    ]]></literal>
    <justification jstring="[para(22541(a,2),6735(a,1))].">
      <j1 rule="para" parents="22541 6735"/>
    </justification>
  </clause>

  <clause id="22543">
    <literal><![CDATA[
      K(x,L((y * T(z,z \ y)) / u,y,z)) = K(x,(z * (y / z)) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(22375,a,22533,a)].">
      <j1 rule="hyper" parents="22375 22533"/>
    </justification>
  </clause>

  <clause id="22544">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,z / (u / T(y,y \ z)))
    ]]></literal>
    <justification jstring="[hyper(21642,a,22543,a),flip(a)].">
      <j1 rule="hyper" parents="21642 22543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22545">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,z / (u / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,21165,a(flip),b,22544,a),flip(a)].">
      <j1 rule="hyper" parents="370 21165 22544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22546">
    <literal><![CDATA[
      K(x,(y * (z / y)) / (u / y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22407,a(flip),b,22545,a),flip(a)].">
      <j1 rule="hyper" parents="370 22407 22545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22547">
    <literal><![CDATA[
      K(x,T(y,z) / (u / z)) = K(x,z / (u / y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21030,a(flip),b,22546,a)].">
      <j1 rule="hyper" parents="60 21030 22546"/>
    </justification>
  </clause>

  <clause id="22548">
    <literal><![CDATA[
      T(x,T(y,z) / (u / z)) = x * K(x,z / (u / y))
    ]]></literal>
    <justification jstring="[hyper(129,a,22547,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22547 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22549">
    <literal><![CDATA[
      T(x,T(y,z) / (u / z)) = T(x,z / (u / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22548,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22550">
    <literal><![CDATA[
      T(x,(y \ z) / (u / z)) = T(x,z / (u / (z / y)))
    ]]></literal>
    <justification jstring="[hyper(15612,a,22549,a)].">
      <j1 rule="hyper" parents="15612 22549"/>
    </justification>
  </clause>

  <clause id="22551">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (z \ u)))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ ((y * (z \ y)) \ u)) = w
    ]]></literal>
    <justification jstring="[para(106(a,1),22536(a,1,2,2,2,2,1))].">
      <j1 rule="para" parents="106 22536"/>
    </justification>
  </clause>

  <clause id="22552">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u \ K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[para(15133(a,1),22466(a,1,2,2,1,2))].">
      <j1 rule="para" parents="15133 22466"/>
    </justification>
  </clause>

  <clause id="22553">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,x \ (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[para(11181(a,1),22514(a,1,1,2,2))].">
      <j1 rule="para" parents="11181 22514"/>
    </justification>
  </clause>

  <clause id="22554">
    <literal><![CDATA[
      x * (T(x,T(y,y)) \ ((y \ x) \ z)) = ((K(y,x) \ 1) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(10219(a,1),22532(a,1,2))].">
      <j1 rule="para" parents="10219 22532"/>
    </justification>
  </clause>

  <clause id="22555">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = y * (T(y,x) \ ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),22554(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="106 22554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22556">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (x \ y)) \ z = K(x,y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,7932,a(flip),b,22555,a),flip(a)].">
      <j1 rule="hyper" parents="370 7932 22555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22557">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = K(y,x) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(5865(a,1),22556(a,1,1,1))].">
      <j1 rule="para" parents="5865 22556"/>
    </justification>
  </clause>

  <clause id="22558">
    <literal><![CDATA[
      K(x,y) * ((x \ y) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(7873(a,1),22557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 22557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22559">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ w) * K(u,z))) = T(x,y * ((T(z,u) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(22558(a,1),20074(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22558 20074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22560">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,20354,a(flip),b,22559,a),flip(a)].">
      <j1 rule="hyper" parents="60 20354 22559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22561">
    <literal><![CDATA[
      T(x,y * ((z \ T(u,z)) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(5749(a,1),22560(a,1,2,2,1))].">
      <j1 rule="para" parents="5749 22560"/>
    </justification>
  </clause>

  <clause id="22562">
    <literal><![CDATA[
      T(x,y * (((((z \ u) \ 1) \ 1) \ T(z,((z \ u) \ 1) \ 1)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[para(3492(a,1),22561(a,2,2,2,1))].">
      <j1 rule="para" parents="3492 22561"/>
    </justification>
  </clause>

  <clause id="22563">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ T(L(u,z,z),z \ 1)) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(20597(a,2),22561(a,2,2,2,1))].">
      <j1 rule="para" parents="20597 22561"/>
    </justification>
  </clause>

  <clause id="22564">
    <literal><![CDATA[
      K((x / y) \ (x \ T(z,x * (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18420,a(flip),b,22553,a)].">
      <j1 rule="hyper" parents="60 18420 22553"/>
    </justification>
  </clause>

  <clause id="22565">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ ((z * ((y \ x) \ z)) / z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22509,a(flip),b,22564,a)].">
      <j1 rule="hyper" parents="60 22509 22564"/>
    </justification>
  </clause>

  <clause id="22566">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ T((y \ x) \ z,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16836,a(flip),b,22565,a),flip(a)].">
      <j1 rule="hyper" parents="370 16836 22565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22567">
    <literal><![CDATA[
      K(x \ ((y \ x) \ T(z,x * (y * z))),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18337,a(flip),b,22566,a),flip(a)].">
      <j1 rule="hyper" parents="370 18337 22566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22568">
    <literal><![CDATA[
      K(x,(y / z) \ ((z \ u) * ((1 / y) \ y))) = K(x,z \ T(((1 / y) \ z) * u,y * y))
    ]]></literal>
    <justification jstring="[para(4187(a,1),22419(a,1,2,2))].">
      <j1 rule="para" parents="4187 22419"/>
    </justification>
  </clause>

  <clause id="22569">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z \ (y \ 1)) * (y * u))) = K(x,(z * (y \ 1)) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,6166,a(flip),b,22426,a),flip(a)].">
      <j1 rule="hyper" parents="60 6166 22426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22570">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z)) = K(x,z \ ((y \ z) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18703,a(flip),b,22569,a),flip(a)].">
      <j1 rule="hyper" parents="60 18703 22569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22571">
    <literal><![CDATA[
      x * K(x,y \ ((z \ y) * (y * u))) = T(x,(z * (y \ 1)) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,22570,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22570 5230"/>
    </justification>
  </clause>

  <clause id="22572">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ L(u,z,z)) = T(x,z \ ((y \ z) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(5265,a,22571,a),flip(a)].">
      <j1 rule="hyper" parents="5265 22571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22573">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ L(u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(22572(a,2),22450(a,1))].">
      <j1 rule="para" parents="22572 22450"/>
    </justification>
  </clause>

  <clause id="22574">
    <literal><![CDATA[
      K((1 / x) \ (((1 / x) / (y * (z * z))) * u),w) = K(z \ (z \ ((x * y) \ (x * u))),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,15130,a(flip),b,22474,a),flip(a)].">
      <j1 rule="hyper" parents="370 15130 22474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22575">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) \ y) * u,z * z)) = K(x,((z / y) \ (y \ u)) * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[para(4187(a,1),22568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4187 22568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22576">
    <literal><![CDATA[
      K(x \ (x \ ((y * z) \ (y * u))),w) = K(y \ ((y / (z * (x * x))) * u),w)
    ]]></literal>
    <justification jstring="[hyper(22475,a,22574,a),flip(a)].">
      <j1 rule="hyper" parents="22475 22574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22577">
    <literal><![CDATA[
      K(x \ (x \ ((x * y) \ (x * z))),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[para(977(a,1),22576(a,2,1,2,1))].">
      <j1 rule="para" parents="977 22576"/>
    </justification>
  </clause>

  <clause id="22578">
    <literal><![CDATA[
      K((x * y) \ ((x \ 1) * z),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18344,a(flip),b,22577,a)].">
      <j1 rule="hyper" parents="60 18344 22577"/>
    </justification>
  </clause>

  <clause id="22579">
    <literal><![CDATA[
      K(x \ (x \ (y \ z)),L(u,y,x)) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18400,a,b,22578,a)].">
      <j1 rule="hyper" parents="60 18400 22578"/>
    </justification>
  </clause>

  <clause id="22580">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ (x \ z),u) = K(x \ (((x \ 1) / y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18342,a(flip),b,22579,a)].">
      <j1 rule="hyper" parents="60 18342 22579"/>
    </justification>
  </clause>

  <clause id="22581">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) \ y) * u,z * z)) = K(x,((z / y) \ (y \ u)) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,6621,a(flip),b,22575,a),flip(a)].">
      <j1 rule="hyper" parents="370 6621 22575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22582">
    <literal><![CDATA[
      K(x,((y / z) \ (z \ u)) * (y * y)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(18447,a,22581,a),flip(a)].">
      <j1 rule="hyper" parents="18447 22581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22584">
    <literal><![CDATA[
      K(x,((y / z) \ (z \ u)) * (y * y)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,21286,a(flip),b,22582,a),flip(a)].">
      <j1 rule="hyper" parents="370 21286 22582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22585">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,(z * y) * z) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(20055(a,1),22465(a,1,2,2,1))].">
      <j1 rule="para" parents="20055 22465"/>
    </justification>
  </clause>

  <clause id="22586">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (T(u,z * (y * z)) \ w)) = T(x,u \ ((z \ T(y * z,y)) \ w))
    ]]></literal>
    <justification jstring="[para(14333(a,1),22585(a,1,2,2,1))].">
      <j1 rule="para" parents="14333 22585"/>
    </justification>
  </clause>

  <clause id="22587">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (y * u)) \ w)) = T(x,z \ ((u \ T(y * u,y)) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14337,a(flip),b,22586,a)].">
      <j1 rule="hyper" parents="60 14337 22586"/>
    </justification>
  </clause>

  <clause id="22588">
    <literal><![CDATA[
      T(x,y \ (T(z,u * (y * u)) \ w)) = T(x,z \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,14473,a(flip),b,22587,a),flip(a)].">
      <j1 rule="hyper" parents="370 14473 22587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22591">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(u,z * (z * y)) \ w)) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(16853(a,1),22588(a,1,2,2,1))].">
      <j1 rule="para" parents="16853 22588"/>
    </justification>
  </clause>

  <clause id="22592">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y \ x) * (T(u / x,u) * y))
    ]]></literal>
    <justification jstring="[para(22001(a,1),22333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22001 22333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22593">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y \ x) * ((x \ u) * y))
    ]]></literal>
    <justification jstring="[para(14481(a,1),22592(a,2,2))].">
      <j1 rule="para" parents="14481 22592"/>
    </justification>
  </clause>

  <clause id="22594">
    <literal><![CDATA[
      ((x / y) * K(z,(1 / (u / x)) \ x)) * y = x * K(z,(y * x) * ((x \ u) / y))
    ]]></literal>
    <justification jstring="[para(21900(a,1),22593(a,2,2))].">
      <j1 rule="para" parents="21900 22593"/>
    </justification>
  </clause>

  <clause id="22595">
    <literal><![CDATA[
      ((x / y) * K(z,(u / x) * x)) * y = x * K(z,(y * x) * ((x \ u) / y))
    ]]></literal>
    <justification jstring="[para(15226(a,1),22594(a,1,1,2))].">
      <j1 rule="para" parents="15226 22594"/>
    </justification>
  </clause>

  <clause id="22596">
    <literal><![CDATA[
      x * K(y,(z * x) * ((x \ u) / z)) = ((x / z) * K(y,u)) * z
    ]]></literal>
    <justification jstring="[para(7(a,1),22595(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 22595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22597">
    <literal><![CDATA[
      (x * y) * K(z,(y * (x * y)) * (((x * y) \ u) / y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(6(a,1),22596(a,2,1,1))].">
      <j1 rule="para" parents="6 22596"/>
    </justification>
  </clause>

  <clause id="22598">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y) * (((x * y) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(21901(a,1),22597(a,1,2))].">
      <j1 rule="para" parents="21901 22597"/>
    </justification>
  </clause>

  <clause id="22599">
    <literal><![CDATA[
      (x * y) * K(z,x * (((y * x) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(12101(a,1),22598(a,1,2,2))].">
      <j1 rule="para" parents="12101 22598"/>
    </justification>
  </clause>

  <clause id="22600">
    <literal><![CDATA[
      ((x \ 1) * ((x * x) * y)) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,1418,a(flip),b,22599,a),flip(a)].">
      <j1 rule="hyper" parents="370 1418 22599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22601">
    <literal><![CDATA[
      K(x,(y * y) * ((z \ (y \ 1)) \ ((y * y) \ u))) = K(x,(z \ y) \ ((y \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(605(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="605 22398"/>
    </justification>
  </clause>

  <clause id="22602">
    <literal><![CDATA[
      K(x,T(y \ (z \ 1),z \ (z \ 1)) \ u) = K(x,(y \ z) \ ((z \ (z \ 1)) \ u))
    ]]></literal>
    <justification jstring="[para(1763(a,1),22601(a,1,2))].">
      <j1 rule="para" parents="1763 22601"/>
    </justification>
  </clause>

  <clause id="22603">
    <literal><![CDATA[
      K(x,T(y \ (z \ 1),z * (z \ 1)) \ u) = K(x,(y \ z) \ ((z \ (z \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18452,a(flip),b,22602,a)].">
      <j1 rule="hyper" parents="60 18452 22602"/>
    </justification>
  </clause>

  <clause id="22604">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z \ (z \ 1)) \ u)) = K(x,T(y \ (z \ 1),1) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),22603(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 22603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22606">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z \ (z \ 1)) \ u)) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(222(a,1),22604(a,2,2,1))].">
      <j1 rule="para" parents="222 22604"/>
    </justification>
  </clause>

  <clause id="22607">
    <literal><![CDATA[
      K(x,(y \ z) \ ((z * z) * u)) = K(x,(y \ (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(605(a,1),22606(a,1,2,2))].">
      <j1 rule="para" parents="605 22606"/>
    </justification>
  </clause>

  <clause id="22608">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ (y \ 1)) \ w) = K(x,L(y,z,u) * ((1 / y) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16600,a(flip),b,22607,a),flip(a)].">
      <j1 rule="hyper" parents="60 16600 22607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22609">
    <literal><![CDATA[
      K(x,L(y,z,u) * ((1 / y) \ w)) = K(x,y * (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(18546,a,22608,a),flip(a)].">
      <j1 rule="hyper" parents="18546 22608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22610">
    <literal><![CDATA[
      K(x,(y * L(y,z,u)) * w) = K(x,y * (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,16629,a(flip),b,22609,a)].">
      <j1 rule="hyper" parents="60 16629 22609"/>
    </justification>
  </clause>

  <clause id="22611">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * (L(z,y,y) * (u / L(z,y,y))))
    ]]></literal>
    <justification jstring="[hyper(60,a,22163,a(flip),b,22610,a)].">
      <j1 rule="hyper" parents="60 22163 22610"/>
    </justification>
  </clause>

  <clause id="22612">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * T(u,L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,17797,a(flip),b,22611,a),flip(a)].">
      <j1 rule="hyper" parents="370 17797 22611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22613">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,z * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,21551,a(flip),b,22612,a),flip(a)].">
      <j1 rule="hyper" parents="370 21551 22612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22615">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * (a(y,y,z) \ z))) = K(x,u * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),22613(a,2,2))].">
      <j1 rule="para" parents="107 22613"/>
    </justification>
  </clause>

  <clause id="22616">
    <literal><![CDATA[
      K(x,a(y,y,z) * (u * L(z,y,y))) = K(x,u * z)
    ]]></literal>
    <justification jstring="[para(3943(a,1),22615(a,1,2,2,2))].">
      <j1 rule="para" parents="3943 22615"/>
    </justification>
  </clause>

  <clause id="22617">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * L(z,y,y))) = x * K(x,u * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,22616,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22616 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22618">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * L(z,y,y))) = T(x,u * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22617,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22619">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * (u * L(w,v5,v5))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21693,a(flip),b,22618,a)].">
      <j1 rule="hyper" parents="60 21693 22618"/>
    </justification>
  </clause>

  <clause id="22620">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((1 / y) * z))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(586(a,1),22618(a,1,2,2,2))].">
      <j1 rule="para" parents="586 22618"/>
    </justification>
  </clause>

  <clause id="22621">
    <literal><![CDATA[
      T(x,a(y,y,(1 / T(y,y)) \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(12486(a,2),22618(a,1,2,2,2))].">
      <j1 rule="para" parents="12486 22618"/>
    </justification>
  </clause>

  <clause id="22623">
    <literal><![CDATA[
      T(x,(y \ (z \ ((1 / z) \ y))) * (u * ((w * w) \ v5))) = T(x,u * (w \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(344(a,1),22619(a,1,2,2,2))].">
      <j1 rule="para" parents="344 22619"/>
    </justification>
  </clause>

  <clause id="22624">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((y \ 1) * z))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16049,a(flip),b,22620,a)].">
      <j1 rule="hyper" parents="60 16049 22620"/>
    </justification>
  </clause>

  <clause id="22625">
    <literal><![CDATA[
      T(x,(y * ((y * ((z \ 1) * u)) / y)) * T(a(z,z,z \ u),((z \ 1) * u) * y)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[para(12644(a,2),22624(a,1,2))].">
      <j1 rule="para" parents="12644 22624"/>
    </justification>
  </clause>

  <clause id="22626">
    <literal><![CDATA[
      T(x,a(y,z,z) * (u * ((w * w) \ v5))) = T(x,u * (w \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(21690,a,22623,a)].">
      <j1 rule="hyper" parents="21690 22623"/>
    </justification>
  </clause>

  <clause id="22627">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(21677,a,22626,a)].">
      <j1 rule="hyper" parents="21677 22626"/>
    </justification>
  </clause>

  <clause id="22628">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(22627(a,1),18277(a,1,1))].">
      <j1 rule="para" parents="22627 18277"/>
    </justification>
  </clause>

  <clause id="22629">
    <literal><![CDATA[
      K(x,(1 / (y / z)) / (1 / T(u,(y / z) \ 1))) = K(x,u / ((y / z) * K(y \ z,z \ y)))
    ]]></literal>
    <justification jstring="[para(4443(a,1),22408(a,1,2,2,2))].">
      <j1 rule="para" parents="4443 22408"/>
    </justification>
  </clause>

  <clause id="22630">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u * K(z,y)) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20095,a,22552,a)].">
      <j1 rule="hyper" parents="20095 22552"/>
    </justification>
  </clause>

  <clause id="22631">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ (z * (u * (z \ 1)))) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(2119(a,1),22563(a,1,2,2,1,2))].">
      <j1 rule="para" parents="2119 22563"/>
    </justification>
  </clause>

  <clause id="22632">
    <literal><![CDATA[
      T(x,y * (((z * z) * (u * (z \ 1))) \ w)) = T(x,y * (L(u / (1 / z),z,z) \ w))
    ]]></literal>
    <justification jstring="[para(939(a,1),22631(a,1,2,2,1))].">
      <j1 rule="para" parents="939 22631"/>
    </justification>
  </clause>

  <clause id="22633">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) \ ((u * u) \ w))) = T(x,y * (L(z / (1 / u),u,u) \ w))
    ]]></literal>
    <justification jstring="[para(518(a,1),22632(a,1,2,2))].">
      <j1 rule="para" parents="518 22632"/>
    </justification>
  </clause>

  <clause id="22634">
    <literal><![CDATA[
      T(x,y * (L(z / (1 / u),u,u) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18295,a(flip),b,22633,a),flip(a)].">
      <j1 rule="hyper" parents="60 18295 22633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22635">
    <literal><![CDATA[
      K(x,(1 / (y / z)) / (1 / T(u,z / y))) = K(x,u / ((y / z) * K(y \ z,z \ y)))
    ]]></literal>
    <justification jstring="[para(9704(a,1),22629(a,1,2,2,2))].">
      <j1 rule="para" parents="9704 22629"/>
    </justification>
  </clause>

  <clause id="22636">
    <literal><![CDATA[
      K(x,y / ((z / u) * K(z \ u,u \ z))) = K(x,(1 / (z / u)) * T(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(15463,a,22635,a),flip(a)].">
      <j1 rule="hyper" parents="15463 22635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22637">
    <literal><![CDATA[
      K(x,y / ((z / u) * K(z \ u,u \ z))) = K(x,(z / u) \ T(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,15148,a(flip),b,22636,a),flip(a)].">
      <j1 rule="hyper" parents="370 15148 22636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22638">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,z / y)) = K(x,u / (1 / (1 / (y / z))))
    ]]></literal>
    <justification jstring="[para(4640(a,1),22637(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4640 22637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22639">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (y / z)) = w
    ]]></literal>
    <justification jstring="[para(22638(a,2),6057(a,1))].">
      <j1 rule="para" parents="22638 6057"/>
    </justification>
  </clause>

  <clause id="22640">
    <literal><![CDATA[
      K(x,(y / z) * T(u,y / z)) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(22639,a,22294,a),flip(a)].">
      <j1 rule="hyper" parents="22639 22294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22641">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(107(a,1),22640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 22640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22642">
    <literal><![CDATA[
      T(x,y * (((((z \ u) \ 1) \ 1) \ T(z,z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[para(4441(a,1),22562(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4441 22562"/>
    </justification>
  </clause>

  <clause id="22643">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ T(z,z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,10300,a(flip),b,22642,a)].">
      <j1 rule="hyper" parents="60 10300 22642"/>
    </justification>
  </clause>

  <clause id="22644">
    <literal><![CDATA[
      T(x,y * ((z / (z \ u)) \ w)) = T(x,y * ((z * (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,22561,a(flip),b,22643,a)].">
      <j1 rule="hyper" parents="60 22561 22643"/>
    </justification>
  </clause>

  <clause id="22645">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,((y \ 1) * (z * (y \ 1))) \ (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,18584,a(flip),b,22446,a),flip(a)].">
      <j1 rule="hyper" parents="370 18584 22446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22646">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,y \ (y * z))
    ]]></literal>
    <justification jstring="[para(72(a,1),22524(a,2,2,2,2,1))].">
      <j1 rule="para" parents="72 22524"/>
    </justification>
  </clause>

  <clause id="22647">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(y \ ((1 / y) \ z),z)) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),22646(a,2,2,2))].">
      <j1 rule="para" parents="4 22646"/>
    </justification>
  </clause>

  <clause id="22648">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),K(z,z)) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(15212(a,1),22647(a,1,2))].">
      <j1 rule="para" parents="15212 22647"/>
    </justification>
  </clause>

  <clause id="22649">
    <literal><![CDATA[
      T(x * (y \ ((1 / y) \ z)),1) = (y \ ((1 / y) \ z)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(193(a,1),22648(a,1,2))].">
      <j1 rule="para" parents="193 22648"/>
    </justification>
  </clause>

  <clause id="22651">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * T(z,y) = z * (x \ ((1 / x) \ y))
    ]]></literal>
    <justification jstring="[hyper(226,a,22649,a),flip(a)].">
      <j1 rule="hyper" parents="226 22649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22653">
    <literal><![CDATA[
      T(x,a(y,y,(1 / y) \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),22621(a,1,2,1,3,1,2))].">
      <j1 rule="para" parents="106 22621"/>
    </justification>
  </clause>

  <clause id="22654">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((T(y,y) * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(3083(a,1),22653(a,1,2,1))].">
      <j1 rule="para" parents="3083 22653"/>
    </justification>
  </clause>

  <clause id="22655">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * ((y * (1 / y)) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),22654(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="106 22654"/>
    </justification>
  </clause>

  <clause id="22656">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y,y \ 1) \ (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(1709(a,2),22655(a,1,2,2,2,1))].">
      <j1 rule="para" parents="1709 22655"/>
    </justification>
  </clause>

  <clause id="22657">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y \ 1,y) * (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(3617(a,1),22656(a,1,2,2,2))].">
      <j1 rule="para" parents="3617 22656"/>
    </justification>
  </clause>

  <clause id="22658">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (K(y,y \ 1) * (y * z)))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(1716(a,1),22657(a,1,2,2,2,1))].">
      <j1 rule="para" parents="1716 22657"/>
    </justification>
  </clause>

  <clause id="22659">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (T(y,y \ 1) * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(3555(a,1),22658(a,1,2,2,2))].">
      <j1 rule="para" parents="3555 22658"/>
    </justification>
  </clause>

  <clause id="22660">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (T(y,1) * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20457,a(flip),b,22659,a)].">
      <j1 rule="hyper" parents="60 20457 22659"/>
    </justification>
  </clause>

  <clause id="22661">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((1 / T(y,y)) \ z))
    ]]></literal>
    <justification jstring="[para(222(a,1),22660(a,1,2,2,2,1))].">
      <j1 rule="para" parents="222 22660"/>
    </justification>
  </clause>

  <clause id="22662">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(106(a,1),22661(a,2,2,2,1,2))].">
      <j1 rule="para" parents="106 22661"/>
    </justification>
  </clause>

  <clause id="22663">
    <literal><![CDATA[
      T(x,a(y,y,y \ z) * (u * (y * z))) = T(x,u * ((y \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,4671,a(flip),b,22662,a),flip(a)].">
      <j1 rule="hyper" parents="370 4671 22662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22664">
    <literal><![CDATA[
      T(x,a(y,y,T(z * (1 / y),y)) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(2061(a,2),22663(a,1,2,1,3))].">
      <j1 rule="para" parents="2061 22663"/>
    </justification>
  </clause>

  <clause id="22665">
    <literal><![CDATA[
      T(x,a(y,y,z * (1 / y)) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(15514(a,1),22664(a,1,2,1))].">
      <j1 rule="para" parents="15514 22664"/>
    </justification>
  </clause>

  <clause id="22667">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * R(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[para(15773(a,1),22665(a,1,2,1))].">
      <j1 rule="para" parents="15773 22665"/>
    </justification>
  </clause>

  <clause id="22668">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * ((y \ 1) \ R(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,20542,a(flip),b,22667,a)].">
      <j1 rule="hyper" parents="60 20542 22667"/>
    </justification>
  </clause>

  <clause id="22669">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * T(z * y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1120(a,1),22668(a,2,2,2))].">
      <j1 rule="para" parents="1120 22668"/>
    </justification>
  </clause>

  <clause id="22670">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * T(z * y,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18271,a(flip),b,22669,a),flip(a)].">
      <j1 rule="hyper" parents="370 18271 22669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22671">
    <literal><![CDATA[
      T(x,a(y,y,z * y) * (u * (y * L(z,y,y)))) = T(x,u * (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,16869,a(flip),b,22670,a),flip(a)].">
      <j1 rule="hyper" parents="370 16869 22670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22672">
    <literal><![CDATA[
      T(x,(y * (z * L(u,z,z))) * a(w,w,v5)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(21689,a,22671,a)].">
      <j1 rule="hyper" parents="21689 22671"/>
    </justification>
  </clause>

  <clause id="22673">
    <literal><![CDATA[
      T(x,y * (z * L(u,z,z))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(21675,a,22672,a)].">
      <j1 rule="hyper" parents="21675 22672"/>
    </justification>
  </clause>

  <clause id="22675">
    <literal><![CDATA[
      T(L(1 / x,y,z) \ 1,x \ (L(1 / x,y,z) \ u)) = T(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(5071(a,1),22487(a,1,1))].">
      <j1 rule="para" parents="5071 22487"/>
    </justification>
  </clause>

  <clause id="22676">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),(z \ 1) \ 1,u / z)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(19452(a,1),22332(a,1,2))].">
      <j1 rule="para" parents="19452 22332"/>
    </justification>
  </clause>

  <clause id="22677">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,u / z)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[para(3406(a,1),22676(a,1,2))].">
      <j1 rule="para" parents="3406 22676"/>
    </justification>
  </clause>

  <clause id="22678">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,((z \ 1) \ 1) * ((((z \ 1) \ 1) \ y) * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(19704,a,22677,a)].">
      <j1 rule="hyper" parents="19704 22677"/>
    </justification>
  </clause>

  <clause id="22679">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * ((((y \ 1) \ 1) \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22344,a(flip),b,22678,a),flip(a)].">
      <j1 rule="hyper" parents="60 22344 22678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22680">
    <literal><![CDATA[
      K(x,(y \ 1) * (((y \ 1) \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[para(1251(a,1),22679(a,1,2))].">
      <j1 rule="para" parents="1251 22679"/>
    </justification>
  </clause>

  <clause id="22681">
    <literal><![CDATA[
      K(x,y * ((y \ z) * (y \ (y \ u)))) = K(x,(z * (u / y)) / y)
    ]]></literal>
    <justification jstring="[para(1251(a,1),22680(a,1,2))].">
      <j1 rule="para" parents="1251 22680"/>
    </justification>
  </clause>

  <clause id="22682">
    <literal><![CDATA[
      K(x,(y * (z / u)) / u) = K(x,u \ ((u \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21946,a(flip),b,22681,a),flip(a)].">
      <j1 rule="hyper" parents="60 21946 22681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22683">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),z,z * u)) = K(x,z \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22344,a,b,22682,a)].">
      <j1 rule="hyper" parents="60 22344 22682"/>
    </justification>
  </clause>

  <clause id="22684">
    <literal><![CDATA[
      K(x,L(y * (z \ (z \ u)),u,z)) = K(x,z \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(22399,a,22683,a)].">
      <j1 rule="hyper" parents="22399 22683"/>
    </justification>
  </clause>

  <clause id="22685">
    <literal><![CDATA[
      K(x,y \ ((y \ z) * u)) = K(x,(z / y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22293,a(flip),b,22684,a),flip(a)].">
      <j1 rule="hyper" parents="60 22293 22684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22686">
    <literal><![CDATA[
      K(x,((y * z) / y) * (y \ u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(4(a,1),22685(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 22685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22687">
    <literal><![CDATA[
      K(x,T(y,z) * (z \ u)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(19909,a,22686,a)].">
      <j1 rule="hyper" parents="19909 22686"/>
    </justification>
  </clause>

  <clause id="22688">
    <literal><![CDATA[
      K(x,T(y,z) / (u \ z)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22319,a,b,22687,a)].">
      <j1 rule="hyper" parents="60 22319 22687"/>
    </justification>
  </clause>

  <clause id="22689">
    <literal><![CDATA[
      K(x,y \ (((z * (y \ 1)) \ u) * z)) = K(x,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22023,a(flip),b,22687,a),flip(a)].">
      <j1 rule="hyper" parents="60 22023 22687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22690">
    <literal><![CDATA[
      K(x,y \ (z * (y / u))) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(77(a,1),22688(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 22688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22691">
    <literal><![CDATA[
      T(x,(y * ((y * ((z \ 1) * u)) / y)) * a(z,z,z \ u)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(19583,a,22625,a)].">
      <j1 rule="hyper" parents="19583 22625"/>
    </justification>
  </clause>

  <clause id="22693">
    <literal><![CDATA[
      T(x,T(y * ((z \ 1) * u),y) * a(z,z,z \ u)) = T(x,T(y,(z \ 1) * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,20053,a(flip),b,22691,a)].">
      <j1 rule="hyper" parents="60 20053 22691"/>
    </justification>
  </clause>

  <clause id="22694">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,T(u,(y \ 1) * z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(20056,a,22693,a)].">
      <j1 rule="hyper" parents="20056 22693"/>
    </justification>
  </clause>

  <clause id="22697">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,T(u,y \ z) * (y \ z))
    ]]></literal>
    <justification jstring="[para(15252(a,1),22694(a,2,2,1))].">
      <j1 rule="para" parents="15252 22694"/>
    </justification>
  </clause>

  <clause id="22698">
    <literal><![CDATA[
      T(x,(((y \ 1) * z) * u) * a(y,y,y \ z)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,12600,a(flip),b,22697,a),flip(a)].">
      <j1 rule="hyper" parents="370 12600 22697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22700">
    <literal><![CDATA[
      T(x,((y \ 1) * z) * u) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(21675,a,22698,a)].">
      <j1 rule="hyper" parents="21675 22698"/>
    </justification>
  </clause>

  <clause id="22703">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * (z \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,21326,a(flip),b,22700,a),flip(a)].">
      <j1 rule="hyper" parents="60 21326 22700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22704">
    <literal><![CDATA[
      (x * (((1 / x) * x) * y)) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(1254(a,1),22600(a,1,1))].">
      <j1 rule="para" parents="1254 22600"/>
    </justification>
  </clause>

  <clause id="22705">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((((x * x) * y) * (x \ 1)) \ u) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),22704(a,1,1,2))].">
      <j1 rule="para" parents="75 22704"/>
    </justification>
  </clause>

  <clause id="22706">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ ((x * x) \ u)) * ((x * x) * y))) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(971(a,1),22705(a,1,2,2,2,1))].">
      <j1 rule="para" parents="971 22705"/>
    </justification>
  </clause>

  <clause id="22707">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ T(u,x * x)) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(20477(a,1),22706(a,1,2,2,2))].">
      <j1 rule="para" parents="20477 22706"/>
    </justification>
  </clause>

  <clause id="22708">
    <literal><![CDATA[
      (x * y) * K(z,(x \ 1) * (((y * (x \ 1)) \ u) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(20514(a,1),22707(a,1,2))].">
      <j1 rule="para" parents="20514 22707"/>
    </justification>
  </clause>

  <clause id="22709">
    <literal><![CDATA[
      (x * y) * K(z,x \ (((y * (x \ 1)) \ u) * y)) = (x * T(K(z,u),x * x)) * y
    ]]></literal>
    <justification jstring="[para(15200(a,1),22708(a,1,2))].">
      <j1 rule="para" parents="15200 22708"/>
    </justification>
  </clause>

  <clause id="22711">
    <literal><![CDATA[
      (x * y) * K(z,x \ (((y * (x \ 1)) \ u) * y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(17129(a,1),22709(a,2,1,2))].">
      <j1 rule="para" parents="17129 22709"/>
    </justification>
  </clause>

  <clause id="22713">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(22689(a,1),22711(a,1,2))].">
      <j1 rule="para" parents="22689 22711"/>
    </justification>
  </clause>

  <clause id="22715">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(z,u) * y) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,20273,a,b,22713,a)].">
      <j1 rule="hyper" parents="60 20273 22713"/>
    </justification>
  </clause>

  <clause id="22716">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,u) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,8934,a,b,22713,a)].">
      <j1 rule="hyper" parents="60 8934 22713"/>
    </justification>
  </clause>

  <clause id="22717">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(x \ z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(31,a,7086,a,b,22713,a)].">
      <j1 rule="hyper" parents="31 7086 22713"/>
    </justification>
  </clause>

  <clause id="22718">
    <literal><![CDATA[
      ((x * K(y,z)) * u) \ (x * u) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(22713(a,1),8061(a,1,1))].">
      <j1 rule="para" parents="22713 8061"/>
    </justification>
  </clause>

  <clause id="22721">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,v5) = (x * a(u,w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(19328(a,1),22713(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19328 22713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22722">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / (x * (K(y,z) * u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(22713(a,1),19757(a,1,1))].">
      <j1 rule="para" parents="22713 19757"/>
    </justification>
  </clause>

  <clause id="22724">
    <literal><![CDATA[
      K(x \ (y / z),T(u,z)) = K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),22717(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 22717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22726">
    <literal><![CDATA[
      K(x \ (y * z),T(u,(y \ x) * y)) = K(z / (y \ x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16680,a(flip),b,22718,a)].">
      <j1 rule="hyper" parents="60 16680 22718"/>
    </justification>
  </clause>

  <clause id="22727">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(8847,a,22724,a),flip(a)].">
      <j1 rule="hyper" parents="8847 22724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22728">
    <literal><![CDATA[
      K(x / (a(y,z,u) * w),v5) = K(a(y,z,u) \ (x / w),v5)
    ]]></literal>
    <justification jstring="[hyper(22036,a,22727,a)].">
      <j1 rule="hyper" parents="22036 22727"/>
    </justification>
  </clause>

  <clause id="22729">
    <literal><![CDATA[
      K((x * y) \ z,T(u,x * z)) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(17911,a,22727,a)].">
      <j1 rule="hyper" parents="17911 22727"/>
    </justification>
  </clause>

  <clause id="22730">
    <literal><![CDATA[
      K(T(x,y) / (z * y),u) = K(y \ (x / z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17903,a(flip),b,22727,a)].">
      <j1 rule="hyper" parents="60 17903 22727"/>
    </justification>
  </clause>

  <clause id="22731">
    <literal><![CDATA[
      K(T(x,y) / (z * y),u) = (w * K(u,y \ (x / z))) \ w
    ]]></literal>
    <justification jstring="[hyper(370,a,6294,a,b,22730,a),flip(a)].">
      <j1 rule="hyper" parents="370 6294 22730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22732">
    <literal><![CDATA[
      (x * K(y,z)) * T(u,K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8706(a,1),22716(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8706 22716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22733">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,20638,a,b,22732,a)].">
      <j1 rule="hyper" parents="60 20638 22732"/>
    </justification>
  </clause>

  <clause id="22734">
    <literal><![CDATA[
      (x * K(y,z)) * u != w * (K(y,z) * u)
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(22715(a,1),41(a,1))].">
      <j1 rule="para" parents="22715 41"/>
    </justification>
  </clause>

  <clause id="22735">
    <literal><![CDATA[
      L(x,K(y,z),u) * (u * K(z,y)) = (x * u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,5950,a,b,22733,a)].">
      <j1 rule="hyper" parents="60 5950 22733"/>
    </justification>
  </clause>

  <clause id="22736">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(32,a,20211,a,b,22735,a),flip(a)].">
      <j1 rule="hyper" parents="32 20211 22735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22737">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,22736,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 22736 13"/>
    </justification>
  </clause>

  <clause id="22738">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12675,a(flip),b,22737,a)].">
      <j1 rule="hyper" parents="60 12675 22737"/>
    </justification>
  </clause>

  <clause id="22739">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,172,a(flip),b,22738,a),flip(a)].">
      <j1 rule="hyper" parents="125 172 22738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22741">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8763(a,1),22738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8763 22738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22742">
    <literal><![CDATA[
      T(x,y) * (K(z,T(u,x)) * w) = K(z,u) * (T(x,y) * w)
    ]]></literal>
    <justification jstring="[para(17162(a,1),22738(a,1,2,1))].">
      <j1 rule="para" parents="17162 22738"/>
    </justification>
  </clause>

  <clause id="22743">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * v5) = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(19328(a,1),22739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19328 22739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22744">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / (x * u) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(147,a,22741,a)].">
      <j1 rule="hyper" parents="147 22741"/>
    </justification>
  </clause>

  <clause id="22745">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,T(y,x)) = T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(22741(a,1),17773(a,1,1))].">
      <j1 rule="para" parents="22741 17773"/>
    </justification>
  </clause>

  <clause id="22746">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = K(z,T(T(u,y),x))
    ]]></literal>
    <justification jstring="[para(8758(a,1),22744(a,1,1,2))].">
      <j1 rule="para" parents="8758 22744"/>
    </justification>
  </clause>

  <clause id="22747">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(13034,a,22746,a)].">
      <j1 rule="hyper" parents="13034 22746"/>
    </justification>
  </clause>

  <clause id="22748">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(22381,a,22747,a)].">
      <j1 rule="hyper" parents="22381 22747"/>
    </justification>
  </clause>

  <clause id="22749">
    <literal><![CDATA[
      K(x,T(T(y \ z,y),u)) = K(x,(u * z) / (u * y))
    ]]></literal>
    <justification jstring="[hyper(9023,a,22747,a),flip(a)].">
      <j1 rule="hyper" parents="9023 22747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22750">
    <literal><![CDATA[
      K(L(x,y,z),T(u,y * z)) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(13048,a,22748,a)].">
      <j1 rule="hyper" parents="13048 22748"/>
    </justification>
  </clause>

  <clause id="22751">
    <literal><![CDATA[
      K(L(x,y,z),T(u,z * y)) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(17421,a,22750,a)].">
      <j1 rule="hyper" parents="17421 22750"/>
    </justification>
  </clause>

  <clause id="22752">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * (y * z)) = K(z,T(T(u,x),y))
    ]]></literal>
    <justification jstring="[hyper(60,a,10270,a,b,22751,a)].">
      <j1 rule="hyper" parents="60 10270 22751"/>
    </justification>
  </clause>

  <clause id="22753">
    <literal><![CDATA[
      K(x,(y * z) / (y * u)) = K(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[hyper(9157,a,22749,a),flip(a)].">
      <j1 rule="hyper" parents="9157 22749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22754">
    <literal><![CDATA[
      K(x,T(y,z) / (z * u)) = K(x,T((y / z) / u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21030,a(flip),b,22753,a)].">
      <j1 rule="hyper" parents="60 21030 22753"/>
    </justification>
  </clause>

  <clause id="22755">
    <literal><![CDATA[
      K(x,T((y * z) / u,y)) = K(x,z / (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18128,a(flip),b,22753,a),flip(a)].">
      <j1 rule="hyper" parents="60 18128 22753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22756">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) = x * K(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,22753,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22753 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22757">
    <literal><![CDATA[
      K(x,(y * z) / (u * y)) = K(x,T(z / T(u,y),y))
    ]]></literal>
    <justification jstring="[para(107(a,1),22753(a,1,2,2))].">
      <j1 rule="para" parents="107 22753"/>
    </justification>
  </clause>

  <clause id="22758">
    <literal><![CDATA[
      K(x,T((y * z) / y,u)) * K(x,K(u * (y * z),u * y)) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(22753(a,1),9371(a,1,1))].">
      <j1 rule="para" parents="22753 9371"/>
    </justification>
  </clause>

  <clause id="22759">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) = T(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22756,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22760">
    <literal><![CDATA[
      T(x,(y * z) / (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z / u,y)) = w
    ]]></literal>
    <justification jstring="[para(22756(a,2),5265(a,1))].">
      <j1 rule="para" parents="22756 5265"/>
    </justification>
  </clause>

  <clause id="22761">
    <literal><![CDATA[
      T(x,T(y / L(z,u,u),a(u,u,z))) = T(x,(a(u,u,z) * y) / z)
    ]]></literal>
    <justification jstring="[para(3942(a,1),22759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3942 22759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22762">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,T(y / T(u,z),z))
    ]]></literal>
    <justification jstring="[hyper(21033,a,22757,a)].">
      <j1 rule="hyper" parents="21033 22757"/>
    </justification>
  </clause>

  <clause id="22763">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,T(z,u)),u) / z,z,u))
    ]]></literal>
    <justification jstring="[para(5747(a,1),22762(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5747 22762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22764">
    <literal><![CDATA[
      K(x / (y * a(z,u,w)),v5) = K(a(z,u,w) \ (x / y),v5)
    ]]></literal>
    <justification jstring="[hyper(19806,a,22728,a)].">
      <j1 rule="hyper" parents="19806 22728"/>
    </justification>
  </clause>

  <clause id="22765">
    <literal><![CDATA[
      T(x,T(y,z) / (u * z)) = x * K(x,z \ (y / u))
    ]]></literal>
    <justification jstring="[hyper(5708,a,22731,a)].">
      <j1 rule="hyper" parents="5708 22731"/>
    </justification>
  </clause>

  <clause id="22766">
    <literal><![CDATA[
      K(x,T(y,z) / (u * z)) = K(x,z \ (y / u))
    ]]></literal>
    <justification jstring="[hyper(5289,a,22765,a)].">
      <j1 rule="hyper" parents="5289 22765"/>
    </justification>
  </clause>

  <clause id="22767">
    <literal><![CDATA[
      K(x,T(y,z) / (z * u)) = K(x,z \ (y / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(20257,a,22766,a)].">
      <j1 rule="hyper" parents="20257 22766"/>
    </justification>
  </clause>

  <clause id="22768">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) = K(x,z \ ((z * y) / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17898,a(flip),b,22766,a)].">
      <j1 rule="hyper" parents="60 17898 22766"/>
    </justification>
  </clause>

  <clause id="22769">
    <literal><![CDATA[
      K(x,T((y / z) / u,z)) = K(x,z \ (y / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22754,a(flip),b,22767,a)].">
      <j1 rule="hyper" parents="60 22754 22767"/>
    </justification>
  </clause>

  <clause id="22770">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(16440,a,22768,a)].">
      <j1 rule="hyper" parents="16440 22768"/>
    </justification>
  </clause>

  <clause id="22771">
    <literal><![CDATA[
      K(x,L(y / T(z,u),z,w)) = K(x,w \ ((w * y) / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(22390,a,22770,a)].">
      <j1 rule="hyper" parents="22390 22770"/>
    </justification>
  </clause>

  <clause id="22774">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,8265,a(flip),b,22742,a),flip(a)].">
      <j1 rule="hyper" parents="60 8265 22742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22775">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = T(z,K(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(7518,a,22774,a)].">
      <j1 rule="hyper" parents="7518 22774"/>
    </justification>
  </clause>

  <clause id="22777">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(8706(a,1),22774(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8706 22774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22778">
    <literal><![CDATA[
      T(x,(T(y,K(z,u)) * w) * (v5 \ K(z,u))) = T(x,(y * (K(z,u) * w)) / v5)
    ]]></literal>
    <justification jstring="[para(22774(a,1),20244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22774 20244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22779">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(8700(a,1),22775(a,2,1))].">
      <j1 rule="para" parents="8700 22775"/>
    </justification>
  </clause>

  <clause id="22780">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u,K(y,z)) = K(y,z) * (x * (u * K(z,y)))
    ]]></literal>
    <justification jstring="[para(8703(a,1),22777(a,1,2))].">
      <j1 rule="para" parents="8703 22777"/>
    </justification>
  </clause>

  <clause id="22781">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ (1 / v5)) = a(z,u,w) \ (K(x,y) / v5)
    ]]></literal>
    <justification jstring="[para(15121(a,1),22743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15121 22743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22782">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (K(z,u) * y)) = K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(22745(a,1),8061(a,1,1))].">
      <j1 rule="para" parents="22745 8061"/>
    </justification>
  </clause>

  <clause id="22783">
    <literal><![CDATA[
      K(x,T(T(y,z * L(u,w,w)),w * w)) = K(x,T(y,z * (w * (w * u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,18976,a(flip),b,22752,a),flip(a)].">
      <j1 rule="hyper" parents="60 18976 22752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22784">
    <literal><![CDATA[
      K(a(x,x,y) \ (z / y),u) = K(z * L(y \ 1,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(22542,a,22764,a),flip(a)].">
      <j1 rule="hyper" parents="22542 22764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22785">
    <literal><![CDATA[
      T(K(x,y),z * a(u,w,v5)) = T(z * v6,K(x,y)) \ (z * (K(x,y) * v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,22040,a,b,22782,a)].">
      <j1 rule="hyper" parents="370 22040 22782"/>
    </justification>
  </clause>

  <clause id="22786">
    <literal><![CDATA[
      K(a(x,x,y) * (z / y),u) = K(z * L(y \ 1,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21744,a(flip),b,22784,a)].">
      <j1 rule="hyper" parents="60 21744 22784"/>
    </justification>
  </clause>

  <clause id="22787">
    <literal><![CDATA[
      K(a(x,x,y) * (z / y),u) = K(z / L(y,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21914,a(flip),b,22786,a),flip(a)].">
      <j1 rule="hyper" parents="370 21914 22786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22788">
    <literal><![CDATA[
      K((x / y) * a(z,z,y),u) = K(x / L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(19357,a,22787,a)].">
      <j1 rule="hyper" parents="19357 22787"/>
    </justification>
  </clause>

  <clause id="22790">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19674,a,22722,a)].">
      <j1 rule="hyper" parents="19674 22722"/>
    </justification>
  </clause>

  <clause id="22791">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22361,a,b,22790,a),flip(a)].">
      <j1 rule="hyper" parents="370 22361 22790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22792">
    <literal><![CDATA[
      (K(x,y) * a(z,u,K(w,v5))) \ y = K(y,x) * (a(z,K(u,v5),w) \ y)
    ]]></literal>
    <justification jstring="[para(22791(a,1),19399(a,1,1,2))].">
      <j1 rule="para" parents="22791 19399"/>
    </justification>
  </clause>

  <clause id="22793">
    <literal><![CDATA[
      K(x,T(((y * z) / y) / u,y)) = K(x,L(z / T(u,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,22769,a,b,22771,a)].">
      <j1 rule="hyper" parents="370 22769 22771"/>
    </justification>
  </clause>

  <clause id="22794">
    <literal><![CDATA[
      K(x,L(y / T(z,u),z,u)) = K(x,T(T(y,u) / z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,20122,a(flip),b,22793,a),flip(a)].">
      <j1 rule="hyper" parents="60 20122 22793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22795">
    <literal><![CDATA[
      K(L(x / T(y,z),y,z),u) = (w * K(u,T(T(x,z) / y,z))) \ w
    ]]></literal>
    <justification jstring="[para(22794(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22794 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22797">
    <literal><![CDATA[
      K(x \ (y * z),T(u,T(x,y))) = K(z / (y \ x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,12686,a(flip),b,22726,a)].">
      <j1 rule="hyper" parents="60 12686 22726"/>
    </justification>
  </clause>

  <clause id="22798">
    <literal><![CDATA[
      K(x / (y \ z),T(u,y)) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(17177,a,22797,a),flip(a)].">
      <j1 rule="hyper" parents="17177 22797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22799">
    <literal><![CDATA[
      K((x * y) / (x * z),u) = K(y / z,T(u,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),22798(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 22798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22800">
    <literal><![CDATA[
      K((x * y) / (y * z),u) = K(T(x,y) / z,T(u,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),22799(a,1,1,1))].">
      <j1 rule="para" parents="107 22799"/>
    </justification>
  </clause>

  <clause id="22801">
    <literal><![CDATA[
      K(T(x,y / z) / z,T(u,y / z)) = K((x * (y / z)) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),22800(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 22800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22802">
    <literal><![CDATA[
      K(T(x,y / z) / z,T(u,z * y)) = K((x * (y / z)) / y,u)
    ]]></literal>
    <justification jstring="[hyper(17507,a,22801,a)].">
      <j1 rule="hyper" parents="17507 22801"/>
    </justification>
  </clause>

  <clause id="22803">
    <literal><![CDATA[
      K(T(x,y * z) / y,T(u,y * z)) = K((x * (z / y)) / z,u)
    ]]></literal>
    <justification jstring="[hyper(18532,a,22802,a)].">
      <j1 rule="hyper" parents="18532 22802"/>
    </justification>
  </clause>

  <clause id="22804">
    <literal><![CDATA[
      T(x,(a(y,y,z) * u) / z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / L(z,y,y)) = w
    ]]></literal>
    <justification jstring="[para(22761(a,1),19335(a,1))].">
      <j1 rule="para" parents="22761 19335"/>
    </justification>
  </clause>

  <clause id="22805">
    <literal><![CDATA[
      K(L(x / T(y,z),y,z),u) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,8061,a(flip),b,22795,a),flip(a)].">
      <j1 rule="hyper" parents="370 8061 22795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22806">
    <literal><![CDATA[
      K(x / T(y,z),L(u,y,z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(13036,a,22805,a)].">
      <j1 rule="hyper" parents="13036 22805"/>
    </justification>
  </clause>

  <clause id="22807">
    <literal><![CDATA[
      K(x / T(y,z),L(u,z,y)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(22381,a,22806,a)].">
      <j1 rule="hyper" parents="22381 22806"/>
    </justification>
  </clause>

  <clause id="22808">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),L(u,y,y \ z)) = K(T(x,y \ z) / y,T(u,y \ z))
    ]]></literal>
    <justification jstring="[para(108(a,1),22806(a,1,1,2))].">
      <j1 rule="para" parents="108 22806"/>
    </justification>
  </clause>

  <clause id="22809">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(y,L(x,u,z)) \ x
    ]]></literal>
    <justification jstring="[para(22363(a,1),22792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22363 22792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22810">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(L(x,u,z),y) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,22809,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 22809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22811">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = K(x,L(y,u,z)) * x
    ]]></literal>
    <justification jstring="[para(12966(a,1),22810(a,2,1))].">
      <j1 rule="para" parents="12966 22810"/>
    </justification>
  </clause>

  <clause id="22812">
    <literal><![CDATA[
      K(x,y) * (a(z,K(y,x),u) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,5275,a,b,22811,a),flip(a)].">
      <j1 rule="hyper" parents="370 5275 22811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22813">
    <literal><![CDATA[
      K(x,y) * (a(z,y,K(u,x)) \ x) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(22791(a,1),22812(a,1,2,1))].">
      <j1 rule="para" parents="22791 22812"/>
    </justification>
  </clause>

  <clause id="22814">
    <literal><![CDATA[
      K(x,y) * (x * a(x,y,K(z,u))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19389(a,1),22813(a,1,2))].">
      <j1 rule="para" parents="19389 22813"/>
    </justification>
  </clause>

  <clause id="22815">
    <literal><![CDATA[
      K(x,y) * L(x,y,K(z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(21503(a,1),22814(a,1,2))].">
      <j1 rule="para" parents="21503 22814"/>
    </justification>
  </clause>

  <clause id="22816">
    <literal><![CDATA[
      L(T(x,y),y,K(z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12351,a(flip),b,22815,a)].">
      <j1 rule="hyper" parents="60 12351 22815"/>
    </justification>
  </clause>

  <clause id="22817">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,u),T(z,u)) / z,z,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),22763(a,2,2,1,1))].">
      <j1 rule="para" parents="18 22763"/>
    </justification>
  </clause>

  <clause id="22818">
    <literal><![CDATA[
      K(x,T(y,z * (u * (u * w)))) = K(x,T(y,z * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(17131,a,22783,a),flip(a)].">
      <j1 rule="hyper" parents="17131 22783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22819">
    <literal><![CDATA[
      K(x,T(y,(z * (z * u)) * w)) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(17421,a,22818,a)].">
      <j1 rule="hyper" parents="17421 22818"/>
    </justification>
  </clause>

  <clause id="22821">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,w * L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(19484,a,22819,a)].">
      <j1 rule="hyper" parents="19484 22819"/>
    </justification>
  </clause>

  <clause id="22822">
    <literal><![CDATA[
      K(x,T(y,z * (u \ (u \ w)))) = K(x,T(y,w * L(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(19484,a,22821,a)].">
      <j1 rule="hyper" parents="19484 22821"/>
    </justification>
  </clause>

  <clause id="22823">
    <literal><![CDATA[
      (x * a(y,z,u)) * K(w,v5) = x * (K(w,v5) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5826,a,22785,a(flip))].">
      <j1 rule="hyper" parents="5826 22785"/>
    </justification>
  </clause>

  <clause id="22824">
    <literal><![CDATA[
      (x * K(y,z)) * a(u,w,v5) = x * (K(y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,22721,a,b,22823,a)].">
      <j1 rule="hyper" parents="60 22721 22823"/>
    </justification>
  </clause>

  <clause id="22825">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(22734,a,22824,a)].">
      <j1 rule="hyper" parents="22734 22824"/>
    </justification>
  </clause>

  <clause id="22829">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) * v5 = K(x,y) * (a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1838,a,22825,a),flip(a)].">
      <j1 rule="hyper" parents="1838 22825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22830">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(22401,a,22829,a)].">
      <j1 rule="hyper" parents="22401 22829"/>
    </justification>
  </clause>

  <clause id="22831">
    <literal><![CDATA[
      K((x \ a(y,z,u)) \ w,v5) = K(a(y,z,u) \ (x * w),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,22373,a(flip),b,22830,a),flip(a)].">
      <j1 rule="hyper" parents="60 22373 22830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22832">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(T(T(y,u),z) / z,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17827,a(flip),b,22817,a),flip(a)].">
      <j1 rule="hyper" parents="370 17827 22817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22834">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,L(z \ T(y,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14523,a(flip),b,22832,a),flip(a)].">
      <j1 rule="hyper" parents="370 14523 22832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22835">
    <literal><![CDATA[
      K(x,T(y / T(T(z,u),y),u)) = K(x,(u * z) \ (y * u))
    ]]></literal>
    <justification jstring="[para(653(a,1),22834(a,2,2))].">
      <j1 rule="para" parents="653 22834"/>
    </justification>
  </clause>

  <clause id="22836">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z)) = K(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14554,a(flip),b,22835,a)].">
      <j1 rule="hyper" parents="60 14554 22835"/>
    </justification>
  </clause>

  <clause id="22837">
    <literal><![CDATA[
      K(x,T(T(y / R(z,u,z),z) \ w,z)) = K(x,T(y,z) \ (w * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,21831,a(flip),b,22836,a),flip(a)].">
      <j1 rule="hyper" parents="370 21831 22836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22838">
    <literal><![CDATA[
      x * K(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(129,a,22836,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 22836 5230"/>
    </justification>
  </clause>

  <clause id="22839">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,(z / (y * y)) \ (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(1105(a,1),22836(a,2,2,1))].">
      <j1 rule="para" parents="1105 22836"/>
    </justification>
  </clause>

  <clause id="22840">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(5265,a,22838,a)].">
      <j1 rule="hyper" parents="5265 22838"/>
    </justification>
  </clause>

  <clause id="22841">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y \ 1) \ u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,22645,a,b,22840,a)].">
      <j1 rule="hyper" parents="370 22645 22840"/>
    </justification>
  </clause>

  <clause id="22842">
    <literal><![CDATA[
      K(x,T((R(y,z,y) \ u) \ w,y)) = K(x,T(u,y) \ (w * y))
    ]]></literal>
    <justification jstring="[para(7316(a,1),22837(a,1,2,1,1))].">
      <j1 rule="para" parents="7316 22837"/>
    </justification>
  </clause>

  <clause id="22843">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y)) = K(x,T(z,y) \ (u * y))
    ]]></literal>
    <justification jstring="[para(682(a,1),22842(a,1,2,1,1,1))].">
      <j1 rule="para" parents="682 22842"/>
    </justification>
  </clause>

  <clause id="22844">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ u,y)) = K(x,(y / z) \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,16797,a(flip),b,22843,a),flip(a)].">
      <j1 rule="hyper" parents="370 16797 22843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22845">
    <literal><![CDATA[
      K(x,T(T(y,z \ 1),z * z) \ (u * (z * z))) = K(x,T((z \ (y * (z \ 1))) \ u,z * z))
    ]]></literal>
    <justification jstring="[para(941(a,1),22843(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="941 22843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22846">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,T(z,y) \ (u * ((1 / y) \ y)))
    ]]></literal>
    <justification jstring="[para(1663(a,1),22843(a,2,2,2))].">
      <j1 rule="para" parents="1663 22843"/>
    </justification>
  </clause>

  <clause id="22847">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ (u / (1 / y)),y)) = K(x,(y / z) \ (u * ((1 / y) \ y)))
    ]]></literal>
    <justification jstring="[para(1663(a,1),22844(a,2,2,2))].">
      <j1 rule="para" parents="1663 22844"/>
    </justification>
  </clause>

  <clause id="22848">
    <literal><![CDATA[
      K(x,T((y \ (z \ y)) \ (y \ ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[para(2874(a,1),22844(a,2,2,2))].">
      <j1 rule="para" parents="2874 22844"/>
    </justification>
  </clause>

  <clause id="22849">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * w)) / v5) = T(x,(y * w) * (v5 \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(17722,a,22778,a),flip(a)].">
      <j1 rule="hyper" parents="17722 22778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22850">
    <literal><![CDATA[
      T(x,(y * z) * (u \ K(z,w))) = T(x,(y * T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(5275(a,2),22849(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5275 22849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22851">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(22850(a,1),15533(a,1))].">
      <j1 rule="para" parents="22850 15533"/>
    </justification>
  </clause>

  <clause id="22852">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,(T(z,y) \ u) * ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[para(4187(a,1),22846(a,2,2))].">
      <j1 rule="para" parents="4187 22846"/>
    </justification>
  </clause>

  <clause id="22853">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,6621,a(flip),b,22852,a),flip(a)].">
      <j1 rule="hyper" parents="370 6621 22852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22854">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(u * (z * y),u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9108(a,1),22758(a,1,1))].">
      <j1 rule="para" parents="9108 22758"/>
    </justification>
  </clause>

  <clause id="22855">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(u * z,u * (z * y))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8648(a,1),22854(a,1,2))].">
      <j1 rule="para" parents="8648 22854"/>
    </justification>
  </clause>

  <clause id="22856">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * K(x,K(y,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(22049(a,1),22855(a,1,2))].">
      <j1 rule="para" parents="22049 22855"/>
    </justification>
  </clause>

  <clause id="22857">
    <literal><![CDATA[
      T(K(x,T(y,z)) * K(x,K(y,u * z)),u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,17815,a,b,22856,a)].">
      <j1 rule="hyper" parents="60 17815 22856"/>
    </justification>
  </clause>

  <clause id="22858">
    <literal><![CDATA[
      T(K(x,T(T(y,z),u * z)),u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(17286(a,1),22857(a,1,1))].">
      <j1 rule="para" parents="17286 22857"/>
    </justification>
  </clause>

  <clause id="22859">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8966,a,22858,a)].">
      <j1 rule="hyper" parents="8966 22858"/>
    </justification>
  </clause>

  <clause id="22860">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(8175,a,22858,a),flip(a)].">
      <j1 rule="hyper" parents="8175 22858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22861">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),u * z)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,15932,a,b,22859,a),flip(a)].">
      <j1 rule="hyper" parents="370 15932 22859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22862">
    <literal><![CDATA[
      T(K(x,T(T(y,z),u)),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(8021,a,22861,a)].">
      <j1 rule="hyper" parents="8021 22861"/>
    </justification>
  </clause>

  <clause id="22863">
    <literal><![CDATA[
      T(T(K(x,T(y,z)),u),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(8019(a,1),22862(a,1,1))].">
      <j1 rule="para" parents="8019 22862"/>
    </justification>
  </clause>

  <clause id="22864">
    <literal><![CDATA[
      T(T(K(x,y) * K(x,K(z,y)),u),u * z) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(8667(a,2),22863(a,1,1,1))].">
      <j1 rule="para" parents="8667 22863"/>
    </justification>
  </clause>

  <clause id="22865">
    <literal><![CDATA[
      T(K(x,T(y,z)) * K(x,K(u,y)),z * u) = K(x,L(y,z \ u,z))
    ]]></literal>
    <justification jstring="[para(17815(a,1),22864(a,1,1))].">
      <j1 rule="para" parents="17815 22864"/>
    </justification>
  </clause>

  <clause id="22866">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(T(z,u),u * y)) = K(x,L(z,u \ y,u))
    ]]></literal>
    <justification jstring="[hyper(17858,a,22865,a)].">
      <j1 rule="hyper" parents="17858 22865"/>
    </justification>
  </clause>

  <clause id="22867">
    <literal><![CDATA[
      K(x,L(T(y,z),u \ z,u)) = K(x,T(T(y,u),u * z))
    ]]></literal>
    <justification jstring="[hyper(31,a,20499,a,b,22866,a)].">
      <j1 rule="hyper" parents="31 20499 22866"/>
    </justification>
  </clause>

  <clause id="22868">
    <literal><![CDATA[
      K(x,T(T(y,z),z * u)) = K(x,L(T(y,u),u,z))
    ]]></literal>
    <justification jstring="[hyper(15944,a,22867,a),flip(a)].">
      <j1 rule="hyper" parents="15944 22867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22869">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),u * (w \ (w \ y)))) = K(x,L(T(z,w \ (w \ 1)),w \ (w \ y),u))
    ]]></literal>
    <justification jstring="[para(15663(a,1),22868(a,2,2,1))].">
      <j1 rule="para" parents="15663 22868"/>
    </justification>
  </clause>

  <clause id="22870">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(x / ((y \ z) \ z),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(22375,a,22808,a),flip(a)].">
      <j1 rule="hyper" parents="22375 22808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22871">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(x / T(y,z),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,20993,a(flip),b,22870,a),flip(a)].">
      <j1 rule="hyper" parents="370 20993 22870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22872">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y \ z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22807,a(flip),b,22871,a),flip(a)].">
      <j1 rule="hyper" parents="370 22807 22871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22873">
    <literal><![CDATA[
      K(T(x,y \ z) / y,T(u,y * z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17494,a,22872,a)].">
      <j1 rule="hyper" parents="17494 22872"/>
    </justification>
  </clause>

  <clause id="22874">
    <literal><![CDATA[
      K(T(x,y * z) / y,T(u,y * z)) = K(T(x,z) / y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(18528,a,22873,a)].">
      <j1 rule="hyper" parents="18528 22873"/>
    </justification>
  </clause>

  <clause id="22875">
    <literal><![CDATA[
      K((x * (y / z)) / y,u) = K(T(x,y) / z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,22803,a(flip),b,22874,a)].">
      <j1 rule="hyper" parents="60 22803 22874"/>
    </justification>
  </clause>

  <clause id="22876">
    <literal><![CDATA[
      K(T(x,y) / (z \ y),T(u,y)) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(74(a,1),22875(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 22875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22877">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,(y * y) * (z \ (u * (z / y))))
    ]]></literal>
    <justification jstring="[para(512(a,1),22839(a,2,2))].">
      <j1 rule="para" parents="512 22839"/>
    </justification>
  </clause>

  <clause id="22878">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,y * (y * (z \ (u * (z / y)))))
    ]]></literal>
    <justification jstring="[hyper(370,a,15151,a(flip),b,22877,a),flip(a)].">
      <j1 rule="hyper" parents="370 15151 22877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22879">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,z \ (u * (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(370,a,15436,a(flip),b,22878,a),flip(a)].">
      <j1 rule="hyper" parents="370 15436 22878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22880">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,T(u,z) / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,22690,a(flip),b,22879,a),flip(a)].">
      <j1 rule="hyper" parents="370 22690 22879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22881">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z / y) \ u,z / y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,15241,a(flip),b,22880,a),flip(a)].">
      <j1 rule="hyper" parents="370 15241 22880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22882">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y \ z) \ u,z / y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[para(8600(a,1),22881(a,1,2,1,1))].">
      <j1 rule="para" parents="8600 22881"/>
    </justification>
  </clause>

  <clause id="22883">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y \ z) \ u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(17507,a,22882,a)].">
      <j1 rule="hyper" parents="17507 22882"/>
    </justification>
  </clause>

  <clause id="22884">
    <literal><![CDATA[
      K(x,T(T(y \ 1,y * z) \ u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22010,a(flip),b,22883,a)].">
      <j1 rule="hyper" parents="60 22010 22883"/>
    </justification>
  </clause>

  <clause id="22885">
    <literal><![CDATA[
      K(x,T(T(y,y * z) * u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,21084,a(flip),b,22884,a)].">
      <j1 rule="hyper" parents="60 21084 22884"/>
    </justification>
  </clause>

  <clause id="22886">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y * z)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,14636,a(flip),b,22885,a)].">
      <j1 rule="hyper" parents="60 14636 22885"/>
    </justification>
  </clause>

  <clause id="22887">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,z * y)) = K(x,T(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(17421,a,22886,a)].">
      <j1 rule="hyper" parents="17421 22886"/>
    </justification>
  </clause>

  <clause id="22888">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,(y * z) * T(y,z))) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,21208,a(flip),b,22887,a),flip(a)].">
      <j1 rule="hyper" parents="370 21208 22887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22889">
    <literal><![CDATA[
      K(x,T(y * (z * u),z * y)) = K(x,T(T(z,y) * u,z) * y)
    ]]></literal>
    <justification jstring="[para(7946(a,1),22887(a,1,2,1))].">
      <j1 rule="para" parents="7946 22887"/>
    </justification>
  </clause>

  <clause id="22890">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y) * z) = K(x,L(u,y,z) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(17159,a,22889,a),flip(a)].">
      <j1 rule="hyper" parents="17159 22889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22891">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * T(z,u)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17782,a(flip),b,22890,a),flip(a)].">
      <j1 rule="hyper" parents="60 17782 22890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22892">
    <literal><![CDATA[
      K(x,(y * T(y \ z,u)) * u) = K(x,T(u * T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(22011,a,22891,a),flip(a)].">
      <j1 rule="hyper" parents="22011 22891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22893">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ (u * z))) * (1 / z)) = K(x,(y * T(u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,21448,a(flip),b,22891,a)].">
      <j1 rule="hyper" parents="60 21448 22891"/>
    </justification>
  </clause>

  <clause id="22895">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ (u * z))) / z) = K(x,(y * T(u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(15319,a,22893,a)].">
      <j1 rule="hyper" parents="15319 22893"/>
    </justification>
  </clause>

  <clause id="22896">
    <literal><![CDATA[
      K(x,T(y \ ((y / (z \ y)) * ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(22525,a,22848,a)].">
      <j1 rule="hyper" parents="22525 22848"/>
    </justification>
  </clause>

  <clause id="22897">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,y * (y * z))) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(17974,a,22888,a)].">
      <j1 rule="hyper" parents="17974 22888"/>
    </justification>
  </clause>

  <clause id="22898">
    <literal><![CDATA[
      K(x,T(T(T(y,z),y * z) * u,z)) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(17148,a,22897,a)].">
      <j1 rule="hyper" parents="17148 22897"/>
    </justification>
  </clause>

  <clause id="22900">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z) * u,z)) = K(x,u * (z * T(y / z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14728,a(flip),b,22898,a)].">
      <j1 rule="hyper" parents="60 14728 22898"/>
    </justification>
  </clause>

  <clause id="22901">
    <literal><![CDATA[
      K(x,y * (z * T(u / z,y))) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(19932,a,22900,a),flip(a)].">
      <j1 rule="hyper" parents="19932 22900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22902">
    <literal><![CDATA[
      K(x,(y / z) * (u * T(w / u,z * y))) = K(x,T(w * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(18610,a,22901,a)].">
      <j1 rule="hyper" parents="18610 22901"/>
    </justification>
  </clause>

  <clause id="22903">
    <literal><![CDATA[
      K(x,(1 / y) * (z * T(u / z,y))) = K(x,T(u * (1 / y),z))
    ]]></literal>
    <justification jstring="[para(3(a,1),22902(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3 22902"/>
    </justification>
  </clause>

  <clause id="22904">
    <literal><![CDATA[
      K(x,y \ (z * T(u / z,y))) = K(x,T(u * (1 / y),z))
    ]]></literal>
    <justification jstring="[hyper(15461,a,22903,a)].">
      <j1 rule="hyper" parents="15461 22903"/>
    </justification>
  </clause>

  <clause id="22905">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,(y \ u) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22447,a(flip),b,22904,a),flip(a)].">
      <j1 rule="hyper" parents="60 22447 22904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22906">
    <literal><![CDATA[
      K(x,(y \ z) \ (u \ z)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[hyper(16053,a,22905,a),flip(a)].">
      <j1 rule="hyper" parents="16053 22905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22907">
    <literal><![CDATA[
      K(x,T((y * z) / u,y)) = K(x,u \ (T(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,22489,a(flip),b,22906,a),flip(a)].">
      <j1 rule="hyper" parents="60 22489 22906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22908">
    <literal><![CDATA[
      K(x,y \ (T(z,y) * u)) = K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,22755,a(flip),b,22907,a),flip(a)].">
      <j1 rule="hyper" parents="60 22755 22907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22909">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(u,(y \ z) \ z) * w)) = K(x,u / (w \ ((y \ z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(14555,a,22908,a)].">
      <j1 rule="hyper" parents="14555 22908"/>
    </justification>
  </clause>

  <clause id="22910">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * u)) = K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(7965(a,2),22908(a,1,2))].">
      <j1 rule="para" parents="7965 22908"/>
    </justification>
  </clause>

  <clause id="22911">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = x * K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(129,a,22910,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22910 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22912">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) = (w * K(u,y / (z \ x))) \ w
    ]]></literal>
    <justification jstring="[para(22910(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22910 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22913">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22911,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22914">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (u \ y)) = w
    ]]></literal>
    <justification jstring="[para(22911(a,2),5265(a,1))].">
      <j1 rule="para" parents="22911 5265"/>
    </justification>
  </clause>

  <clause id="22915">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * (u * w))) = T(x,z / (T(w * u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(20065,a,22913,a)].">
      <j1 rule="hyper" parents="20065 22913"/>
    </justification>
  </clause>

  <clause id="22916">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ (y * u)) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(16901,a,22913,a)].">
      <j1 rule="hyper" parents="16901 22913"/>
    </justification>
  </clause>

  <clause id="22917">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(7965(a,1),22913(a,1,2))].">
      <j1 rule="para" parents="7965 22913"/>
    </justification>
  </clause>

  <clause id="22918">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,T(u,y) \ R(y,z,z))
    ]]></literal>
    <justification jstring="[para(16504(a,1),22913(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16504 22913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22919">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,y * z) * w)) = T(x,u / (w \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(18694,a,22917,a)].">
      <j1 rule="hyper" parents="18694 22917"/>
    </justification>
  </clause>

  <clause id="22920">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) \ (T(u,z \ y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[para(6446(a,1),22917(a,1,2,2,1))].">
      <j1 rule="para" parents="6446 22917"/>
    </justification>
  </clause>

  <clause id="22921">
    <literal><![CDATA[
      T(x,((y / z) \ 1) \ (T(u,z / y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(9704(a,1),22917(a,1,2,2,1))].">
      <j1 rule="para" parents="9704 22917"/>
    </justification>
  </clause>

  <clause id="22922">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ (T(u,y * (z \ 1)) * a(z \ y,z,z))) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[para(21542(a,1),22917(a,2,2,2))].">
      <j1 rule="para" parents="21542 22917"/>
    </justification>
  </clause>

  <clause id="22923">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (u \ y)) = w
    ]]></literal>
    <justification jstring="[para(7965(a,1),22914(a,1,2))].">
      <j1 rule="para" parents="7965 22914"/>
    </justification>
  </clause>

  <clause id="22924">
    <literal><![CDATA[
      T(x,L(y,z,z) \ (T(u,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (w \ L(y,z,z))) = v5
    ]]></literal>
    <justification jstring="[para(15156(a,1),22923(a,1,2,2,1))].">
      <j1 rule="para" parents="15156 22923"/>
    </justification>
  </clause>

  <clause id="22925">
    <literal><![CDATA[
      K(T(x,y) \ (y * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,22912,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 22912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22926">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(8276,a,22925,a)].">
      <j1 rule="hyper" parents="8276 22925"/>
    </justification>
  </clause>

  <clause id="22927">
    <literal><![CDATA[
      K(x / ((x \ y) \ z),u) = K(T(z,x) \ y,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),22925(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 22925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22928">
    <literal><![CDATA[
      K(x / ((T(y,z) \ u) \ y),w) = K((y * (T(y,z) / x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,22497,a(flip),b,22926,a),flip(a)].">
      <j1 rule="hyper" parents="60 22497 22926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22929">
    <literal><![CDATA[
      K(T(x,y) \ (T(z,x) * u),w) = K(z / (u \ T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20752,a(flip),b,22926,a)].">
      <j1 rule="hyper" parents="60 20752 22926"/>
    </justification>
  </clause>

  <clause id="22930">
    <literal><![CDATA[
      K((x / y) / (z \ y),u) = K(y \ ((y \ x) * z),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),22926(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 22926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22931">
    <literal><![CDATA[
      K(((x \ y) \ y) \ (T(z,T(x,y)) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[para(7334(a,1),22926(a,1,1,2,1))].">
      <j1 rule="para" parents="7334 22926"/>
    </justification>
  </clause>

  <clause id="22932">
    <literal><![CDATA[
      K(((x \ y) \ z) \ x,u) = K(T(z,x) \ y,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(8461,a,22927,a)].">
      <j1 rule="hyper" parents="8461 22927"/>
    </justification>
  </clause>

  <clause id="22933">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(((u \ w) \ a(x,y,z)) \ u,v5)
    ]]></literal>
    <justification jstring="[para(15499(a,2),22932(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15499 22932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22934">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,T(u,y) \ L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,18618,a(flip),b,22918,a),flip(a)].">
      <j1 rule="hyper" parents="370 18618 22918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22935">
    <literal><![CDATA[
      T(x,y / (a(y,z,z) \ u)) = T(x,L(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19936,a(flip),b,22934,a),flip(a)].">
      <j1 rule="hyper" parents="370 19936 22934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22936">
    <literal><![CDATA[
      T(x,y / (T(z * u,z) \ w)) = T(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(22914,a,22915,a),flip(a)].">
      <j1 rule="hyper" parents="22914 22915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22937">
    <literal><![CDATA[
      T(x,y / (((z \ u) * z) \ w)) = T(x,y / (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),22936(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 22936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22938">
    <literal><![CDATA[
      T(x,y / ((z * (u / z)) \ w)) = T(x,y / (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18975,a(flip),b,22937,a)].">
      <j1 rule="hyper" parents="60 18975 22937"/>
    </justification>
  </clause>

  <clause id="22939">
    <literal><![CDATA[
      T(x,y / (((z * u) * ((u \ 1) * (u \ (w / (z * (1 / u)))))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(2051(a,2),22938(a,1,2,2,1))].">
      <j1 rule="para" parents="2051 22938"/>
    </justification>
  </clause>

  <clause id="22940">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) * w)) = T(x,u / (w \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(22309,a,22919,a)].">
      <j1 rule="hyper" parents="22309 22919"/>
    </justification>
  </clause>

  <clause id="22941">
    <literal><![CDATA[
      K(x / ((y \ z) \ T(y,u)),w) = K((y * (T(y,u) / x)) \ z,w)
    ]]></literal>
    <justification jstring="[para(15361(a,1),22928(a,1,1,2))].">
      <j1 rule="para" parents="15361 22928"/>
    </justification>
  </clause>

  <clause id="22942">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(u,T(y,z)) * w)) = K(x,u / (w \ ((y \ z) \ z)))
    ]]></literal>
    <justification jstring="[para(7334(a,1),22909(a,1,2,2,1))].">
      <j1 rule="para" parents="7334 22909"/>
    </justification>
  </clause>

  <clause id="22943">
    <literal><![CDATA[
      K(x,y / (z \ ((u \ w) \ w))) = K(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22908,a(flip),b,22942,a),flip(a)].">
      <j1 rule="hyper" parents="60 22908 22942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22944">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ w))) = x * K(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,22943,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 22943 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22945">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ w))) = T(x,y / (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,22944,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 22944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22946">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (u \ T(z,w))) = T(x,(u \ ((z \ w) \ w)) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,18055,a(flip),b,22945,a),flip(a)].">
      <j1 rule="hyper" parents="60 18055 22945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22947">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) \ (T(u,z * y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18694,a,22920,a)].">
      <j1 rule="hyper" parents="18694 22920"/>
    </justification>
  </clause>

  <clause id="22948">
    <literal><![CDATA[
      T(x,((y / z) \ 1) \ (T(u,z * y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18698,a(flip),b,22921,a)].">
      <j1 rule="hyper" parents="60 18698 22921"/>
    </justification>
  </clause>

  <clause id="22949">
    <literal><![CDATA[
      K(((x \ y) \ y) \ (T(z,x) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,20752,a(flip),b,22931,a)].">
      <j1 rule="hyper" parents="60 20752 22931"/>
    </justification>
  </clause>

  <clause id="22951">
    <literal><![CDATA[
      K(T(x,y) \ (T(z,x) * u),w) = K(z / (u \ ((x \ y) \ y)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,14558,a(flip),b,22949,a)].">
      <j1 rule="hyper" parents="60 14558 22949"/>
    </justification>
  </clause>

  <clause id="22952">
    <literal><![CDATA[
      K(x / (y \ ((z \ u) \ u)),w) = K(x / (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,22929,a(flip),b,22951,a),flip(a)].">
      <j1 rule="hyper" parents="60 22929 22951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22953">
    <literal><![CDATA[
      K(x / ((y \ z) \ T(y,z)),u) = K(x / (y / (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20935,a(flip),b,22952,a),flip(a)].">
      <j1 rule="hyper" parents="60 20935 22952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22954">
    <literal><![CDATA[
      K((x * (T(x,y) / z)) \ y,u) = K(z / (x / (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22941,a(flip),b,22953,a)].">
      <j1 rule="hyper" parents="60 22941 22953"/>
    </justification>
  </clause>

  <clause id="22955">
    <literal><![CDATA[
      K((((x * y) / x) * (T((x * y) / x,T(x,y)) / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(2269(a,1),22954(a,2,1,2,2))].">
      <j1 rule="para" parents="2269 22954"/>
    </justification>
  </clause>

  <clause id="22956">
    <literal><![CDATA[
      T(x,(y \ ((z \ u) \ u)) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,18033,a(flip),b,22946,a),flip(a)].">
      <j1 rule="hyper" parents="60 18033 22946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22957">
    <literal><![CDATA[
      T(x,(y \ T(z,z \ u)) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21112,a,b,22956,a)].">
      <j1 rule="hyper" parents="60 21112 22956"/>
    </justification>
  </clause>

  <clause id="22958">
    <literal><![CDATA[
      T(x,(y \ (z / (z / u))) \ w) = T(x,(y \ T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21115,a(flip),b,22957,a)].">
      <j1 rule="hyper" parents="60 21115 22957"/>
    </justification>
  </clause>

  <clause id="22959">
    <literal><![CDATA[
      T(x,(y \ (z * K(z \ u,z))) \ w) = T(x,(y \ T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21114,a(flip),b,22958,a)].">
      <j1 rule="hyper" parents="60 21114 22958"/>
    </justification>
  </clause>

  <clause id="22960">
    <literal><![CDATA[
      T(x,(y \ (z * K(z \ y,z))) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20898,a(flip),b,22959,a),flip(a)].">
      <j1 rule="hyper" parents="370 20898 22959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22961">
    <literal><![CDATA[
      T(x,((y * (z / y)) \ y) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5684(a,1),22960(a,1,2,1))].">
      <j1 rule="para" parents="5684 22960"/>
    </justification>
  </clause>

  <clause id="22962">
    <literal><![CDATA[
      T(x,(y \ (y / (z / y))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(14485,a,22961,a)].">
      <j1 rule="hyper" parents="14485 22961"/>
    </justification>
  </clause>

  <clause id="22963">
    <literal><![CDATA[
      T(x,((1 / y) \ ((1 / y) / (z / y))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(1002(a,2),22962(a,1,2,1))].">
      <j1 rule="para" parents="1002 22962"/>
    </justification>
  </clause>

  <clause id="22964">
    <literal><![CDATA[
      T(x,((1 / y) \ (y / (z / (y \ 1)))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(16129(a,1),22963(a,1,2,1,2))].">
      <j1 rule="para" parents="16129 22963"/>
    </justification>
  </clause>

  <clause id="22965">
    <literal><![CDATA[
      T(x,((y \ 1) \ (y / (z / (y \ 1)))) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4676,a(flip),b,22964,a)].">
      <j1 rule="hyper" parents="60 4676 22964"/>
    </justification>
  </clause>

  <clause id="22966">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ z,u) = u / T(u,(x / y) \ z)
    ]]></literal>
    <justification jstring="[para(22965(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="22965 5701"/>
    </justification>
  </clause>

  <clause id="22967">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ z,u) = K((x / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,22966,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 22966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22968">
    <literal><![CDATA[
      K(((x \ 1) \ (x / (y / (x \ 1)))) \ (x \ z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22509,a(flip),b,22967,a),flip(a)].">
      <j1 rule="hyper" parents="370 22509 22967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22969">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) * w)) = T(x,u / (w \ ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15396,a,22947,a)].">
      <j1 rule="hyper" parents="15396 22947"/>
    </justification>
  </clause>

  <clause id="22970">
    <literal><![CDATA[
      T(x,y / (z \ ((u \ w) \ 1))) = T(x,y / (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22940,a(flip),b,22969,a),flip(a)].">
      <j1 rule="hyper" parents="60 22940 22969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22971">
    <literal><![CDATA[
      T(x,(y / z) * (T(u,z * y) * w)) = T(x,u / (w \ ((y / z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15396,a,22948,a)].">
      <j1 rule="hyper" parents="15396 22948"/>
    </justification>
  </clause>

  <clause id="22972">
    <literal><![CDATA[
      K(x \ (((x \ 1) / (x / (y / (x \ 1)))) * z),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22580,a(flip),b,22968,a)].">
      <j1 rule="hyper" parents="60 22580 22968"/>
    </justification>
  </clause>

  <clause id="22973">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ (T(u,y / z) * a(z \ y,z,z))) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[para(15398(a,1),22922(a,1,2,2,1))].">
      <j1 rule="para" parents="15398 22922"/>
    </justification>
  </clause>

  <clause id="22974">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ T(a(z \ y,z,z) * u,y / z)) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22070,a,b,22973,a)].">
      <j1 rule="hyper" parents="60 22070 22973"/>
    </justification>
  </clause>

  <clause id="22975">
    <literal><![CDATA[
      T(x,(a(y \ z,y,y) * u) / (z * (y \ 1))) = T(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(17504,a,22974,a)].">
      <j1 rule="hyper" parents="17504 22974"/>
    </justification>
  </clause>

  <clause id="22976">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(a(x,y,z) \ ((u \ w) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,22831,a(flip),b,22933,a),flip(a)].">
      <j1 rule="hyper" parents="370 22831 22933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22977">
    <literal><![CDATA[
      K((a(x,y,z) * a(x,y,K(z,u))) \ w,T(v5,u)) = K(a(x,y,z) \ T(w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,17905,a(flip),b,22976,a),flip(a)].">
      <j1 rule="hyper" parents="370 17905 22976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22978">
    <literal><![CDATA[
      K(T(a(x,y,z),u) \ w,T(v5,u)) = K(a(x,y,z) \ T(w,u),v5)
    ]]></literal>
    <justification jstring="[para(15499(a,1),22977(a,1,1,1))].">
      <j1 rule="para" parents="15499 22977"/>
    </justification>
  </clause>

  <clause id="22979">
    <literal><![CDATA[
      K(a(x,y,z) \ T(u,w),v5) = K(a(x,y,z) \ u,T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,19800,a(flip),b,22978,a),flip(a)].">
      <j1 rule="hyper" parents="60 19800 22978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22981">
    <literal><![CDATA[
      K(T(x,y) * a(z,u,w),v5) = K(a(z,u,w) \ x,T(v5,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,21741,a(flip),b,22979,a)].">
      <j1 rule="hyper" parents="60 21741 22979"/>
    </justification>
  </clause>

  <clause id="22982">
    <literal><![CDATA[
      K(T(x,y) * a(z,u,w),v5) = K(x * a(z,u,w),T(v5,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,21741,a(flip),b,22981,a),flip(a)].">
      <j1 rule="hyper" parents="370 21741 22981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22983">
    <literal><![CDATA[
      K(x,T(y \ (z * ((y \ 1) \ u)),y)) = K(x,(y / z) \ ((y \ 1) \ T(u,y)))
    ]]></literal>
    <justification jstring="[para(74(a,1),22896(a,1,2,1,2,1))].">
      <j1 rule="para" parents="74 22896"/>
    </justification>
  </clause>

  <clause id="22985">
    <literal><![CDATA[
      K(x,(y / z) \ ((y \ 1) \ T(u,y))) = K(x,(z * ((y \ 1) \ u)) / y)
    ]]></literal>
    <justification jstring="[hyper(8904,a,22983,a),flip(a)].">
      <j1 rule="hyper" parents="8904 22983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22986">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) \ u)) / z) = K(x,(z / y) \ (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(18401,a,22985,a),flip(a)].">
      <j1 rule="hyper" parents="18401 22985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22987">
    <literal><![CDATA[
      K(x,(y / z) \ ((u * y) / (y \ 1))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22895,a(flip),b,22986,a),flip(a)].">
      <j1 rule="hyper" parents="60 22895 22986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22988">
    <literal><![CDATA[
      K(x,(y / z) \ (u * ((1 / y) \ y))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[para(2851(a,1),22987(a,1,2,2))].">
      <j1 rule="para" parents="2851 22987"/>
    </justification>
  </clause>

  <clause id="22989">
    <literal><![CDATA[
      K(x,T(y,z * (z * (z \ 1))) \ (u * (z * z))) = K(x,T((z \ (y * (z \ 1))) \ u,z * z))
    ]]></literal>
    <justification jstring="[para(15429(a,1),22845(a,1,2,1))].">
      <j1 rule="para" parents="15429 22845"/>
    </justification>
  </clause>

  <clause id="22990">
    <literal><![CDATA[
      K(x,T((y \ (z * (y \ 1))) \ u,y * y)) = K(x,T(z,y) \ (u * (y * y)))
    ]]></literal>
    <justification jstring="[para(67(a,1),22989(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="67 22989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22991">
    <literal><![CDATA[
      K(x,T((y \ (z * (y \ 1))) \ u,y * y)) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[para(513(a,1),22990(a,2,2))].">
      <j1 rule="para" parents="513 22990"/>
    </justification>
  </clause>

  <clause id="22992">
    <literal><![CDATA[
      K(x,(y \ (z * (y \ 1))) \ u) = K(x,(T(z,y) \ u) * (y * y))
    ]]></literal>
    <justification jstring="[hyper(17131,a,22991,a)].">
      <j1 rule="hyper" parents="17131 22991"/>
    </justification>
  </clause>

  <clause id="22994">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (z * z)) = K(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22535,a(flip),b,22992,a),flip(a)].">
      <j1 rule="hyper" parents="60 22535 22992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22995">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / (1 / y)),y)) = K(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22853,a,b,22994,a)].">
      <j1 rule="hyper" parents="60 22853 22994"/>
    </justification>
  </clause>

  <clause id="22996">
    <literal><![CDATA[
      K(x,(y / z) \ (u * ((1 / y) \ y))) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22847,a(flip),b,22995,a)].">
      <j1 rule="hyper" parents="60 22847 22995"/>
    </justification>
  </clause>

  <clause id="22997">
    <literal><![CDATA[
      K(x,y * ((z \ y) \ (y * u))) = K(x,(z * T(u,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22988,a(flip),b,22996,a),flip(a)].">
      <j1 rule="hyper" parents="60 22988 22996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22998">
    <literal><![CDATA[
      K(x,((y / z) \ u) * ((1 / y) \ y)) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[para(4187(a,1),22996(a,1,2))].">
      <j1 rule="para" parents="4187 22996"/>
    </justification>
  </clause>

  <clause id="22999">
    <literal><![CDATA[
      K(x,((y / z) \ u) * (y * y)) = K(x,y * ((z \ y) \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,6621,a(flip),b,22998,a)].">
      <j1 rule="hyper" parents="60 6621 22998"/>
    </justification>
  </clause>

  <clause id="23000">
    <literal><![CDATA[
      K(x,y * ((z \ y) \ (y * (z \ u)))) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22584,a(flip),b,22999,a),flip(a)].">
      <j1 rule="hyper" parents="60 22584 22999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23001">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,(y * T(y \ u,z)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,22997,a(flip),b,23000,a),flip(a)].">
      <j1 rule="hyper" parents="60 22997 23000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23002">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,T(z * T(u,y),y))
    ]]></literal>
    <justification jstring="[hyper(370,a,22892,a(flip),b,23001,a),flip(a)].">
      <j1 rule="hyper" parents="370 22892 23001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23003">
    <literal><![CDATA[
      K(x,T((y \ 1) * T(z,u),u)) = K(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,21287,a(flip),b,23002,a),flip(a)].">
      <j1 rule="hyper" parents="60 21287 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23004">
    <literal><![CDATA[
      K(x,T(y \ T(z,u),u)) = K(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(15596,a,23003,a)].">
      <j1 rule="hyper" parents="15596 23003"/>
    </justification>
  </clause>

  <clause id="23005">
    <literal><![CDATA[
      K(x,T(y \ T(z * u,z),z)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22418,a(flip),b,23004,a),flip(a)].">
      <j1 rule="hyper" parents="370 22418 23004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23006">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[hyper(18748,a,23005,a)].">
      <j1 rule="hyper" parents="18748 23005"/>
    </justification>
  </clause>

  <clause id="23007">
    <literal><![CDATA[
      K(T(x \ (y * z),z),u) = (w * K(u,(x / z) \ y)) \ w
    ]]></literal>
    <justification jstring="[para(23006(a,1),6294(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23006 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23010">
    <literal><![CDATA[
      K(T(x \ (y * z),z),u) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,19551,a(flip),b,23007,a),flip(a)].">
      <j1 rule="hyper" parents="370 19551 23007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23011">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(8181,a,23010,a)].">
      <j1 rule="hyper" parents="8181 23010"/>
    </justification>
  </clause>

  <clause id="23012">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,x \ z)) = K((x / (x \ z)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(22481,a,23011,a)].">
      <j1 rule="hyper" parents="22481 23011"/>
    </justification>
  </clause>

  <clause id="23013">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(x \ T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,17905,a(flip),b,23011,a),flip(a)].">
      <j1 rule="hyper" parents="60 17905 23011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23014">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,22456,a(flip),b,23013,a)].">
      <j1 rule="hyper" parents="60 22456 23013"/>
    </justification>
  </clause>

  <clause id="23015">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),T(u,z)) = K(T(z,x) / y,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,17435,a(flip),b,23014,a),flip(a)].">
      <j1 rule="hyper" parents="370 17435 23014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23016">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,22455,a,b,23014,a)].">
      <j1 rule="hyper" parents="60 22455 23014"/>
    </justification>
  </clause>

  <clause id="23017">
    <literal><![CDATA[
      (x * y) / (K(z \ T(u,w),T(x,w)) * y) = T(x,w \ ((z \ w) * u))
    ]]></literal>
    <justification jstring="[para(23014(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="23014 7934"/>
    </justification>
  </clause>

  <clause id="23018">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K((y \ ((1 / y) \ x)) \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,22521,a(flip),b,23016,a)].">
      <j1 rule="hyper" parents="60 22521 23016"/>
    </justification>
  </clause>

  <clause id="23019">
    <literal><![CDATA[
      K((x / y) \ (z \ x),u) = K(T(y,x) / z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,23011,a(flip),b,23015,a)].">
      <j1 rule="hyper" parents="60 23011 23015"/>
    </justification>
  </clause>

  <clause id="23020">
    <literal><![CDATA[
      K((T(x,y) / z) \ R(y,y * x,y),u) = K(T(z,T(x,y)) / (y \ x),T(u,T(x,y)))
    ]]></literal>
    <justification jstring="[para(14547(a,2),23019(a,1,1,2))].">
      <j1 rule="para" parents="14547 23019"/>
    </justification>
  </clause>

  <clause id="23021">
    <literal><![CDATA[
      K((x * (y \ x)) \ z,T(u,x * z)) = K((x / (x \ z)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(17494,a,23012,a)].">
      <j1 rule="hyper" parents="17494 23012"/>
    </justification>
  </clause>

  <clause id="23022">
    <literal><![CDATA[
      K((x / (x \ y)) \ z,u) = K(x \ (y / (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22729,a(flip),b,23021,a),flip(a)].">
      <j1 rule="hyper" parents="60 22729 23021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23023">
    <literal><![CDATA[
      K(((x / y) \ y) \ z,u) = K(y \ (x / (z \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20843,a(flip),b,23022,a)].">
      <j1 rule="hyper" parents="60 20843 23022"/>
    </justification>
  </clause>

  <clause id="23024">
    <literal><![CDATA[
      K(x \ (y / (z \ x)),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / ((y / x) \ x),u) = w
    ]]></literal>
    <justification jstring="[para(23023(a,1),17430(a,1))].">
      <j1 rule="para" parents="23023 17430"/>
    </justification>
  </clause>

  <clause id="23025">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(8444,a,23017,a)].">
      <j1 rule="hyper" parents="8444 23017"/>
    </justification>
  </clause>

  <clause id="23026">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,u \ ((u \ y) \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22462,a,b,23025,a),flip(a)].">
      <j1 rule="hyper" parents="370 22462 23025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23027">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(y / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22461,a,b,23025,a),flip(a)].">
      <j1 rule="hyper" parents="370 22461 23025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23028">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(y * u) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22443,a,b,23025,a),flip(a)].">
      <j1 rule="hyper" parents="370 22443 23025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23029">
    <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(370,a,22464,a(flip),b,23025,a),flip(a)].">
      <j1 rule="hyper" parents="370 22464 23025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23030">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(z \ T(u,y),y)) = T(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,19772,a(flip),b,23025,a),flip(a)].">
      <j1 rule="hyper" parents="370 19772 23025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23031">
    <literal><![CDATA[
      T(x,T(((y \ z) * (y \ z)) \ T(u,y),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,20368,a(flip),b,23026,a),flip(a)].">
      <j1 rule="hyper" parents="370 20368 23026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23032">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u)) = T(x,(u / y) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(22300,a,23027,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22300 23027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23033">
    <literal><![CDATA[
      T(x,T((y \ z) \ T(u,y),y)) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,22916,a(flip),b,23028,a),flip(a)].">
      <j1 rule="hyper" parents="370 22916 23028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23034">
    <literal><![CDATA[
      T(x,y / (z \ (y * u))) = T(x,T(u \ T(z,y),y))
    ]]></literal>
    <justification jstring="[para(4(a,1),23033(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 23033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23035">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ T(u,y),y)) = T(x,y / (u \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[para(2072(a,1),23033(a,1,2,1,1))].">
      <j1 rule="para" parents="2072 23033"/>
    </justification>
  </clause>

  <clause id="23036">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(z \ T(u,y),y)) = T(x,(u \ (y * z)) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20181,a(flip),b,23034,a),flip(a)].">
      <j1 rule="hyper" parents="60 20181 23034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23037">
    <literal><![CDATA[
      T(x,((y \ z) \ u) / y) = T(x,z \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,18118,a(flip),b,23029,a),flip(a)].">
      <j1 rule="hyper" parents="60 18118 23029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23039">
    <literal><![CDATA[
      T(x,(y * z) \ T(u,y)) = T(x,(z \ u) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),23037(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 23037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23040">
    <literal><![CDATA[
      T(x,(y \ T(z,y \ 1)) \ T(u,z)) = T(x,(((y \ z) / z) \ u) / z)
    ]]></literal>
    <justification jstring="[para(6152(a,1),23037(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6152 23037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23041">
    <literal><![CDATA[
      T(x,(T(y,z) * u) \ z) = T(x,(u \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,20901,a,b,23039,a)].">
      <j1 rule="hyper" parents="60 20901 23039"/>
    </justification>
  </clause>

  <clause id="23042">
    <literal><![CDATA[
      T(x,(y * z) \ L(T(u,y),w,v5)) = T(x,(z \ L(u,w,v5)) / y)
    ]]></literal>
    <justification jstring="[para(20(a,2),23039(a,1,2,2))].">
      <j1 rule="para" parents="20 23039"/>
    </justification>
  </clause>

  <clause id="23043">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,(L(z,u,w) * y) \ z)
    ]]></literal>
    <justification jstring="[para(201(a,1),23039(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="201 23039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23044">
    <literal><![CDATA[
      T(x,(y * z) \ T(R(z,u,u),y)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(16509(a,1),23039(a,2,2,1))].">
      <j1 rule="para" parents="16509 23039"/>
    </justification>
  </clause>

  <clause id="23045">
    <literal><![CDATA[
      T(x,(T(y,L(z,u,u)) * (1 / u)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[para(581(a,1),23041(a,2,2,1))].">
      <j1 rule="para" parents="581 23041"/>
    </justification>
  </clause>

  <clause id="23046">
    <literal><![CDATA[
      T(x,(y \ T(T(z,u),y \ 1)) \ u) = T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z)
    ]]></literal>
    <justification jstring="[para(6149(a,2),23041(a,1,2,1))].">
      <j1 rule="para" parents="6149 23041"/>
    </justification>
  </clause>

  <clause id="23047">
    <literal><![CDATA[
      T(x,(y \ z) / (u \ ((1 / u) \ z))) = T(x,((u \ ((1 / u) \ z)) * y) \ z)
    ]]></literal>
    <justification jstring="[para(16110(a,1),23041(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="16110 23041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23048">
    <literal><![CDATA[
      T(x,(y * z) \ R(T(z,y),u,u)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[para(22(a,2),23044(a,1,2,2))].">
      <j1 rule="para" parents="22 23044"/>
    </justification>
  </clause>

  <clause id="23049">
    <literal><![CDATA[
      T(x,(y * z) \ L(T(z,y),u,u)) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,18618,a(flip),b,23048,a)].">
      <j1 rule="hyper" parents="60 18618 23048"/>
    </justification>
  </clause>

  <clause id="23050">
    <literal><![CDATA[
      T(x,(y \ L(y,z,z)) / u) = T(x,a(y,z,z) / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,23049,a(flip),b,23042,a),flip(a)].">
      <j1 rule="hyper" parents="60 23049 23042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23051">
    <literal><![CDATA[
      T(x,y \ (z \ L(z,u,u))) = T(x,a(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(19363,a,23050,a)].">
      <j1 rule="hyper" parents="19363 23050"/>
    </justification>
  </clause>

  <clause id="23052">
    <literal><![CDATA[
      T(x,y \ (z \ L(z,u,u))) = T(x,y \ a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,19326,a(flip),b,23051,a),flip(a)].">
      <j1 rule="hyper" parents="370 19326 23051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23054">
    <literal><![CDATA[
      T(x,((y \ z) * u) / z) = T(x,(u \ (z * y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,23030,a(flip),b,23036,a)].">
      <j1 rule="hyper" parents="60 23030 23036"/>
    </justification>
  </clause>

  <clause id="23055">
    <literal><![CDATA[
      T(x,(((y \ z) / z) \ u) / z) = T(x,(z / y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,19737,a(flip),b,23040,a),flip(a)].">
      <j1 rule="hyper" parents="60 19737 23040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23056">
    <literal><![CDATA[
      T(x,(T(y,z) * (1 / u)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[para(15156(a,1),23045(a,1,2,1,1))].">
      <j1 rule="para" parents="15156 23045"/>
    </justification>
  </clause>

  <clause id="23057">
    <literal><![CDATA[
      T(x,(T(y,z) * (u \ 1)) \ L(z,u,u)) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4661,a(flip),b,23056,a)].">
      <j1 rule="hyper" parents="60 4661 23056"/>
    </justification>
  </clause>

  <clause id="23059">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ z) = T(x,(u * z) / y)
    ]]></literal>
    <justification jstring="[hyper(22573,a,23057,a)].">
      <j1 rule="hyper" parents="22573 23057"/>
    </justification>
  </clause>

  <clause id="23060">
    <literal><![CDATA[
      T(x,(y \ z) / (u \ ((u \ 1) \ z))) = T(x,((u \ ((1 / u) \ z)) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(21181,a,23047,a)].">
      <j1 rule="hyper" parents="21181 23047"/>
    </justification>
  </clause>

  <clause id="23061">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,L(u \ z,y,y) / z)
    ]]></literal>
    <justification jstring="[hyper(22503,a,23060,a),flip(a)].">
      <j1 rule="hyper" parents="22503 23060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23062">
    <literal><![CDATA[
      T(x,T((y \ z) \ ((y \ z) \ T(u,y)),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(15249,a,23031,a)].">
      <j1 rule="hyper" parents="15249 23031"/>
    </justification>
  </clause>

  <clause id="23063">
    <literal><![CDATA[
      T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z) = T(x,(T(z,u) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,19737,a(flip),b,23046,a),flip(a)].">
      <j1 rule="hyper" parents="60 19737 23046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23064">
    <literal><![CDATA[
      T(x,(((y \ T(z,u)) / T(z,u)) \ u) / z) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(370,a,23059,a(flip),b,23063,a),flip(a)].">
      <j1 rule="hyper" parents="370 23059 23063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23065">
    <literal><![CDATA[
      T(x,(((y \ z) / z) \ u) / z) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(15277(a,1),23064(a,1,2,1,1))].">
      <j1 rule="para" parents="15277 23064"/>
    </justification>
  </clause>

  <clause id="23066">
    <literal><![CDATA[
      T(x,(y / z) \ T(u,y)) = T(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,23055,a(flip),b,23065,a)].">
      <j1 rule="hyper" parents="60 23055 23065"/>
    </justification>
  </clause>

  <clause id="23068">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / u) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(16779,a,23066,a),flip(a)].">
      <j1 rule="hyper" parents="16779 23066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23069">
    <literal><![CDATA[
      T(x,((y \ z) * u) / z) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(74(a,1),23066(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 23066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23070">
    <literal><![CDATA[
      T(x,(y * z) / T(u,z)) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(22851,a,23068,a)].">
      <j1 rule="hyper" parents="22851 23068"/>
    </justification>
  </clause>

  <clause id="23071">
    <literal><![CDATA[
      T(x,(y \ (z * u)) \ z) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23054,a(flip),b,23069,a)].">
      <j1 rule="hyper" parents="60 23054 23069"/>
    </justification>
  </clause>

  <clause id="23072">
    <literal><![CDATA[
      T(x,(y * a(z,u,w)) / v5) = T(x,(v5 / y) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(19582,a,23070,a)].">
      <j1 rule="hyper" parents="19582 23070"/>
    </justification>
  </clause>

  <clause id="23076">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) / v5) = T(x,(v5 / w) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19585,a,b,23072,a)].">
      <j1 rule="hyper" parents="60 19585 23072"/>
    </justification>
  </clause>

  <clause id="23077">
    <literal><![CDATA[
      T(x,((y * (z \ 1)) / u) \ a(z \ y,z,z)) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22975,a(flip),b,23076,a),flip(a)].">
      <j1 rule="hyper" parents="60 22975 23076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23078">
    <literal><![CDATA[
      T(x,(y / z) \ a(u,u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / L(y,u,u)) = w
    ]]></literal>
    <justification jstring="[para(23076(a,1),22804(a,1))].">
      <j1 rule="para" parents="23076 22804"/>
    </justification>
  </clause>

  <clause id="23079">
    <literal><![CDATA[
      T(x,T(T((y \ z) \ ((y \ z) \ u),y),y)) = T(x,y * ((z / (1 / (y \ z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,18418,a,b,23062,a)].">
      <j1 rule="hyper" parents="60 18418 23062"/>
    </justification>
  </clause>

  <clause id="23080">
    <literal><![CDATA[
      T(x,y * ((z / (1 / (y \ z))) \ u)) = T(x,(y \ z) \ ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(9012,a,23079,a),flip(a)].">
      <j1 rule="hyper" parents="9012 23079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23082">
    <literal><![CDATA[
      T(x,y * ((z / (1 / (y \ z))) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(23080(a,2),17095(a,1))].">
      <j1 rule="para" parents="23080 17095"/>
    </justification>
  </clause>

  <clause id="23083">
    <literal><![CDATA[
      K(T(x,T(y,z)) / (z \ y),T(u,T(y,z))) = K((T(y,z) / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14377,a(flip),b,23020,a),flip(a)].">
      <j1 rule="hyper" parents="60 14377 23020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23084">
    <literal><![CDATA[
      K(T(x,T(y,z)) / (z \ y),T(u,y)) = K((T(y,z) / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(17183,a,23083,a)].">
      <j1 rule="hyper" parents="17183 23083"/>
    </justification>
  </clause>

  <clause id="23086">
    <literal><![CDATA[
      K((T(x,y) / z) \ y,u) = K(T(z,x) / (y \ x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(22254,a,23084,a),flip(a)].">
      <j1 rule="hyper" parents="22254 23084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23088">
    <literal><![CDATA[
      K((T(x,y) / z) \ y,u) = K((z * y) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22876,a(flip),b,23086,a),flip(a)].">
      <j1 rule="hyper" parents="370 22876 23086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23089">
    <literal><![CDATA[
      K((x * y) / (K(y,z \ 1) / z),u) = K(((1 / z) / x) \ y,u)
    ]]></literal>
    <justification jstring="[para(6133(a,1),23088(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6133 23088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23090">
    <literal><![CDATA[
      K((x * y) / (K(y,z \ 1) / z),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,6201,a(flip),b,23089,a),flip(a)].">
      <j1 rule="hyper" parents="370 6201 23089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23091">
    <literal><![CDATA[
      K((x * y) * (z * K(z \ 1,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(15483,a,23090,a)].">
      <j1 rule="hyper" parents="15483 23090"/>
    </justification>
  </clause>

  <clause id="23092">
    <literal><![CDATA[
      K((x * y) * (z * K(z * 1,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(18557,a,23091,a)].">
      <j1 rule="hyper" parents="18557 23091"/>
    </justification>
  </clause>

  <clause id="23093">
    <literal><![CDATA[
      K((x * y) * (z * K(z,y)),u) = K(((z \ 1) / x) \ y,u)
    ]]></literal>
    <justification jstring="[para(3(a,1),23092(a,1,1,2,2,1))].">
      <j1 rule="para" parents="3 23092"/>
    </justification>
  </clause>

  <clause id="23094">
    <literal><![CDATA[
      K(((x \ 1) / y) \ z,u) = K((y * z) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5256(a,2),23093(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5256 23093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23095">
    <literal><![CDATA[
      K(((x \ 1) / (y \ (z \ ((1 / z) \ y)))) \ y,u) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[para(21572(a,1),23094(a,2,1,1))].">
      <j1 rule="para" parents="21572 23094"/>
    </justification>
  </clause>

  <clause id="23096">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(x \ L(T(z,x),y,y),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,16667,a(flip),b,23018,a),flip(a)].">
      <j1 rule="hyper" parents="370 16667 23018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23097">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(L(T(z,x),y,y) / x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8783,a(flip),b,23096,a),flip(a)].">
      <j1 rule="hyper" parents="370 8783 23096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23098">
    <literal><![CDATA[
      K(x \ ((x / (y \ ((1 / y) \ x))) * z),u) = K(x \ L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14381,a(flip),b,23097,a),flip(a)].">
      <j1 rule="hyper" parents="370 14381 23097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23100">
    <literal><![CDATA[
      K(((x \ (y \ ((1 / y) \ x))) \ (z \ 1)) \ x,u) = K((y \ ((1 / y) \ x)) * T(z,x),u)
    ]]></literal>
    <justification jstring="[para(21812(a,1),23095(a,1,1,1))].">
      <j1 rule="para" parents="21812 23095"/>
    </justification>
  </clause>

  <clause id="23101">
    <literal><![CDATA[
      K(T(x \ 1,y) \ (z \ ((1 / z) \ y)),T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22932,a(flip),b,23100,a)].">
      <j1 rule="hyper" parents="60 22932 23100"/>
    </justification>
  </clause>

  <clause id="23102">
    <literal><![CDATA[
      K(T(x \ 1,y) \ (z \ ((z \ 1) \ y)),T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16625,a(flip),b,23101,a)].">
      <j1 rule="hyper" parents="60 16625 23101"/>
    </justification>
  </clause>

  <clause id="23103">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,z) \ y,T(u,y)) = K((z \ ((1 / z) \ y)) * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22512,a(flip),b,23102,a)].">
      <j1 rule="hyper" parents="60 22512 23102"/>
    </justification>
  </clause>

  <clause id="23104">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(y / L(T(z \ 1,y),x,x),u)
    ]]></literal>
    <justification jstring="[hyper(8897,a,23103,a),flip(a)].">
      <j1 rule="hyper" parents="8897 23103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23105">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(L(z \ 1,x,x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,14383,a(flip),b,23104,a),flip(a)].">
      <j1 rule="hyper" parents="370 14383 23104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23106">
    <literal><![CDATA[
      K(x,T(T((y * z) / y,u),y * L(u,w,w))) = K(x,L(T(z,w \ (w \ 1)),w \ (w \ y),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22822,a(flip),b,22869,a)].">
      <j1 rule="hyper" parents="60 22822 22869"/>
    </justification>
  </clause>

  <clause id="23107">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,w \ (w \ 1)),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9937,a(flip),b,23106,a)].">
      <j1 rule="hyper" parents="60 9937 23106"/>
    </justification>
  </clause>

  <clause id="23108">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,w * (w \ 1)),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,17638,a(flip),b,23107,a),flip(a)].">
      <j1 rule="hyper" parents="370 17638 23107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23109">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(T(y,1),w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[para(5(a,1),23108(a,2,2,1,2))].">
      <j1 rule="para" parents="5 23108"/>
    </justification>
  </clause>

  <clause id="23111">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * L(u,w,w))) = K(x,L(y,w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[para(222(a,1),23109(a,2,2,1))].">
      <j1 rule="para" parents="222 23109"/>
    </justification>
  </clause>

  <clause id="23112">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z * u)) = K(x,L(y,w \ (w \ z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22039,a(flip),b,23111,a)].">
      <j1 rule="hyper" parents="60 22039 23111"/>
    </justification>
  </clause>

  <clause id="23114">
    <literal><![CDATA[
      K(x,L(y,z \ (z \ u),w)) = K(x,L(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22860,a(flip),b,23112,a),flip(a)].">
      <j1 rule="hyper" parents="60 22860 23112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23115">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ z))) \ u,L(w,x,z)) = K((y \ ((1 / y) \ z)) \ (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15942,a(flip),b,23114,a),flip(a)].">
      <j1 rule="hyper" parents="60 15942 23114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23116">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K((y \ ((1 / y) \ x)) \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(16444,a,23115,a)].">
      <j1 rule="hyper" parents="16444 23115"/>
    </justification>
  </clause>

  <clause id="23117">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K(x \ L(x * z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16667,a(flip),b,23116,a),flip(a)].">
      <j1 rule="hyper" parents="370 16667 23116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23118">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ z,u) = K(x * L(x \ z,y,y),u)
    ]]></literal>
    <justification jstring="[para(3916(a,1),23117(a,2,1))].">
      <j1 rule="para" parents="3916 23117"/>
    </justification>
  </clause>

  <clause id="23119">
    <literal><![CDATA[
      K(a(x,x,x \ (x \ y)) \ z,u) = K(y * L(y \ z,x,x),u)
    ]]></literal>
    <justification jstring="[para(2117(a,2),23118(a,1,1,1))].">
      <j1 rule="para" parents="2117 23118"/>
    </justification>
  </clause>

  <clause id="23120">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ (z / (z / (z / x))),u) = K(x * L((z / (z / x)) \ (z / x),y,y),u)
    ]]></literal>
    <justification jstring="[para(9033(a,2),23118(a,2,1,2,1))].">
      <j1 rule="para" parents="9033 23118"/>
    </justification>
  </clause>

  <clause id="23121">
    <literal><![CDATA[
      K(x * L(x \ y,z,z),u) = K(y * a(z,z,z \ (z \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21741,a(flip),b,23119,a),flip(a)].">
      <j1 rule="hyper" parents="60 21741 23119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23122">
    <literal><![CDATA[
      K(x * L(x \ y,z,z),u) = K(y * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,21784,a,b,23121,a),flip(a)].">
      <j1 rule="hyper" parents="370 21784 23121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23124">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y \ 1) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,9495,a(flip),b,22841,a),flip(a)].">
      <j1 rule="hyper" parents="370 9495 22841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23125">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y * 1) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18679,a(flip),b,23124,a),flip(a)].">
      <j1 rule="hyper" parents="370 18679 23124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23126">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(T(z * (y \ 1),y) \ u,y))
    ]]></literal>
    <justification jstring="[para(3(a,1),23125(a,2,2,1,1,2))].">
      <j1 rule="para" parents="3 23125"/>
    </justification>
  </clause>

  <clause id="23127">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z \ T(a(y,y,y) * u,y \ 1))) = T(x,T(((y \ 1) * z) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,20200,a(flip),b,23126,a),flip(a)].">
      <j1 rule="hyper" parents="370 20200 23126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23128">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ u,y)) = T(x,(y \ 1) \ (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,21121,a(flip),b,23127,a),flip(a)].">
      <j1 rule="hyper" parents="60 21121 23127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23129">
    <literal><![CDATA[
      T(x,T(((y \ 1) * z) \ u,y)) = T(x,y * (z \ T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15165,a(flip),b,23128,a),flip(a)].">
      <j1 rule="hyper" parents="370 15165 23128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23130">
    <literal><![CDATA[
      T(x,y * (z \ T(T(u,y),y))) = T(x,y / (u \ L(z,y,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,23035,a(flip),b,23129,a),flip(a)].">
      <j1 rule="hyper" parents="60 23035 23129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23131">
    <literal><![CDATA[
      T(x,y / (z \ L(u,y,y))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16788,a(flip),b,23130,a),flip(a)].">
      <j1 rule="hyper" parents="60 16788 23130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23133">
    <literal><![CDATA[
      K((x \ (y \ ((1 / y) \ x))) \ T(z / x,z),u) = K(x * L((z / (z / x)) \ (z / x),y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18335,a(flip),b,23120,a)].">
      <j1 rule="hyper" parents="60 18335 23120"/>
    </justification>
  </clause>

  <clause id="23134">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K((x \ (z \ ((1 / z) \ x))) \ (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14447,a(flip),b,23133,a),flip(a)].">
      <j1 rule="hyper" parents="60 14447 23133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23135">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K(x \ ((x / (z \ ((1 / z) \ x))) * y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22517,a(flip),b,23134,a),flip(a)].">
      <j1 rule="hyper" parents="370 22517 23134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23136">
    <literal><![CDATA[
      K(x * L((y / (y / x)) \ (y / x),z,z),u) = K(x \ L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,23098,a(flip),b,23135,a),flip(a)].">
      <j1 rule="hyper" parents="370 23098 23135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23137">
    <literal><![CDATA[
      K(x * L(x \ (y / (y / (y / x))),z,z),u) = K(x \ L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(9033(a,1),23136(a,1,1,2,1))].">
      <j1 rule="para" parents="9033 23136"/>
    </justification>
  </clause>

  <clause id="23138">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K((y / (y / (y / x))) * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,23122,a(flip),b,23137,a),flip(a)].">
      <j1 rule="hyper" parents="60 23122 23137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23140">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K(T(y / x,y) * a(w,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16795,a(flip),b,23138,a),flip(a)].">
      <j1 rule="hyper" parents="370 16795 23138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23141">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K((y / x) * a(w,w,v5),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,22982,a(flip),b,23140,a),flip(a)].">
      <j1 rule="hyper" parents="370 22982 23140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23142">
    <literal><![CDATA[
      K(x \ L(y,z,z),u) = K(y / L(x,w,w),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,22788,a(flip),b,23141,a),flip(a)].">
      <j1 rule="hyper" parents="370 22788 23141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23143">
    <literal><![CDATA[
      K(L(x,y,y) \ z,u) = K(x \ L(z,w,w),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,8031,a(flip),b,23142,a)].">
      <j1 rule="hyper" parents="370 8031 23142"/>
    </justification>
  </clause>

  <clause id="23144">
    <literal><![CDATA[
      T(x,L(y,z,z) \ u) = (x * w) / (K(y \ L(u,v5,v5),x) * w)
    ]]></literal>
    <justification jstring="[para(23143(a,1),7934(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23143 7934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23145">
    <literal><![CDATA[
      T(x,L(y,z,z) \ u) = T(x,y \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,7934,a(flip),b,23144,a),flip(a)].">
      <j1 rule="hyper" parents="370 7934 23144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23146">
    <literal><![CDATA[
      T(x,y \ L(T(z,y) * u,w,w)) = T(x,z / (u \ L(y,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(22924,a,23145,a),flip(a)].">
      <j1 rule="hyper" parents="22924 23145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23147">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(14403,a,23145,a),flip(a)].">
      <j1 rule="hyper" parents="14403 23145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23148">
    <literal><![CDATA[
      T(x,y \ L(y / z,u,u)) = T(x,z \ a(w,w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,22485,a(flip),b,23145,a),flip(a)].">
      <j1 rule="hyper" parents="60 22485 23145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23149">
    <literal><![CDATA[
      T(x,y \ L(z * u,w,w)) = T(x,y \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16622,a(flip),b,23145,a),flip(a)].">
      <j1 rule="hyper" parents="60 16622 23145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23150">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(23145(a,1),14403(a,1))].">
      <j1 rule="para" parents="23145 14403"/>
    </justification>
  </clause>

  <clause id="23151">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(22573,a,23147,a),flip(a)].">
      <j1 rule="hyper" parents="22573 23147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23153">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2082(a,1),23147(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2082 23147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23155">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z / u) \ y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18957,a(flip),b,23151,a),flip(a)].">
      <j1 rule="hyper" parents="60 18957 23151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23157">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ (y \ 1))) = T(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18555,a(flip),b,23153,a),flip(a)].">
      <j1 rule="hyper" parents="370 18555 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23158">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,22420,a,b,23153,a)].">
      <j1 rule="hyper" parents="60 22420 23153"/>
    </justification>
  </clause>

  <clause id="23160">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(z * (1 / x)) \ ((z * (1 / x)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(19613,a,23157,a),flip(a)].">
      <j1 rule="hyper" parents="19613 23157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23162">
    <literal><![CDATA[
      T(x,y \ L(T(z,u) * w,v5,v5)) = T(x,y \ ((z \ K(u,z)) \ w))
    ]]></literal>
    <justification jstring="[para(5721(a,1),23149(a,2,2,2,1))].">
      <j1 rule="para" parents="5721 23149"/>
    </justification>
  </clause>

  <clause id="23163">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ L(y,w,w)))
    ]]></literal>
    <justification jstring="[hyper(23150,a,23146,a)].">
      <j1 rule="hyper" parents="23150 23146"/>
    </justification>
  </clause>

  <clause id="23164">
    <literal><![CDATA[
      T(x,y / (z \ L(u,w,w))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(22923,a,23163,a),flip(a)].">
      <j1 rule="hyper" parents="22923 23163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23165">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23131,a(flip),b,23164,a),flip(a)].">
      <j1 rule="hyper" parents="60 23131 23164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23166">
    <literal><![CDATA[
      T(x,y / (z \ L(u,w,w))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23164,a,b,23165,a)].">
      <j1 rule="hyper" parents="60 23164 23165"/>
    </justification>
  </clause>

  <clause id="23167">
    <literal><![CDATA[
      T(x,y * (((z \ u) \ 1) \ w)) = T(x,y / (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,22970,a(flip),b,23165,a),flip(a)].">
      <j1 rule="hyper" parents="60 22970 23165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23169">
    <literal><![CDATA[
      T(x,y * (L(z,u,u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23165,a(flip),b,23166,a)].">
      <j1 rule="hyper" parents="60 23165 23166"/>
    </justification>
  </clause>

  <clause id="23170">
    <literal><![CDATA[
      T(x,y * ((z / (1 / u)) \ w)) = T(x,y * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,22634,a(flip),b,23169,a),flip(a)].">
      <j1 rule="hyper" parents="60 22634 23169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23172">
    <literal><![CDATA[
      T(x,y * ((z * (y \ z)) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((z \ y) * u)) = w
    ]]></literal>
    <justification jstring="[para(23170(a,1),23082(a,1))].">
      <j1 rule="para" parents="23170 23082"/>
    </justification>
  </clause>

  <clause id="23173">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u / z) * y) = T(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(22300,a,23155,a)].">
      <j1 rule="hyper" parents="22300 23155"/>
    </justification>
  </clause>

  <clause id="23174">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ w)) = T(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(22499,a,23158,a)].">
      <j1 rule="hyper" parents="22499 23158"/>
    </justification>
  </clause>

  <clause id="23179">
    <literal><![CDATA[
      T(x,y / (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(23173(a,1),17716(a,1))].">
      <j1 rule="para" parents="23173 17716"/>
    </justification>
  </clause>

  <clause id="23180">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(1 / x) \ (z \ ((z * (1 / x)) \ 1)))
    ]]></literal>
    <justification jstring="[para(1284(a,1),23160(a,2,2))].">
      <j1 rule="para" parents="1284 23160"/>
    </justification>
  </clause>

  <clause id="23181">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,x * (z \ ((z * (1 / x)) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15251,a(flip),b,23180,a),flip(a)].">
      <j1 rule="hyper" parents="370 15251 23180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23182">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),z \ (x / z)) = T(y,(z \ x) * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,18899,a(flip),b,23181,a),flip(a)].">
      <j1 rule="hyper" parents="370 18899 23181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23183">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),x \ (L(x,y,z) / x)) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3837(a,2),23182(a,2,2,1))].">
      <j1 rule="para" parents="3837 23182"/>
    </justification>
  </clause>

  <clause id="23184">
    <literal><![CDATA[
      T(x,y / (((z * u) * (T(w,u * u) / (z * u))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(15324(a,1),22939(a,1,2,2,1,2))].">
      <j1 rule="para" parents="15324 22939"/>
    </justification>
  </clause>

  <clause id="23185">
    <literal><![CDATA[
      T(x,y / (T((z * u) * (w / (z * u)),u * u) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[para(4804(a,2),23184(a,1,2,2,1))].">
      <j1 rule="para" parents="4804 23184"/>
    </justification>
  </clause>

  <clause id="23186">
    <literal><![CDATA[
      T(x,y / (((z * u) * (w / (z * u))) \ v5)) = T(x,y / (T(w,z * (1 / u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20908,a,23185,a)].">
      <j1 rule="hyper" parents="20908 23185"/>
    </justification>
  </clause>

  <clause id="23187">
    <literal><![CDATA[
      T(x,y / (T(z,u * (1 / w)) \ v5)) = T(x,y / (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,22938,a(flip),b,23186,a),flip(a)].">
      <j1 rule="hyper" parents="60 22938 23186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23188">
    <literal><![CDATA[
      T(x,y / (T(z,u / w) \ v5)) = T(x,y / (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(15400(a,1),23187(a,1,2,2,1))].">
      <j1 rule="para" parents="15400 23187"/>
    </justification>
  </clause>

  <clause id="23189">
    <literal><![CDATA[
      T(x,y / (T(z,u * w) \ (w \ u))) = T(x,y / (T(u / w,w) / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,20923,a(flip),b,23188,a),flip(a)].">
      <j1 rule="hyper" parents="60 20923 23188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23190">
    <literal><![CDATA[
      T(x,y / (T(z,u * w) \ (w \ u))) = T(x,y / ((w \ u) / z))
    ]]></literal>
    <justification jstring="[para(109(a,1),23189(a,2,2,2,1))].">
      <j1 rule="para" parents="109 23189"/>
    </justification>
  </clause>

  <clause id="23191">
    <literal><![CDATA[
      K((((x * y) / x) * (T(y,K(x,y)) / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(8586(a,1),22955(a,1,1,1,2,1))].">
      <j1 rule="para" parents="8586 22955"/>
    </justification>
  </clause>

  <clause id="23192">
    <literal><![CDATA[
      K((((x * y) / x) * (y / z)) \ T(x,y),u) = K(z / (((x * y) / x) / (y \ x)),u)
    ]]></literal>
    <justification jstring="[para(4745(a,1),23191(a,1,1,1,2,1))].">
      <j1 rule="para" parents="4745 23191"/>
    </justification>
  </clause>

  <clause id="23193">
    <literal><![CDATA[
      K(x / (((y * z) / y) / (z \ y)),u) = K((z * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[para(15363(a,1),23192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15363 23192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23194">
    <literal><![CDATA[
      K(x / (T(y,z) / (y \ z)),u) = K((y * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20939,a(flip),b,23193,a)].">
      <j1 rule="hyper" parents="60 20939 23193"/>
    </justification>
  </clause>

  <clause id="23195">
    <literal><![CDATA[
      K(x / ((y \ z) \ y),u) = K((y * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21770,a(flip),b,23194,a)].">
      <j1 rule="hyper" parents="60 21770 23194"/>
    </justification>
  </clause>

  <clause id="23196">
    <literal><![CDATA[
      K(x / (((y \ 1) * (y \ z)) \ y),u) = K((y * (y / x)) \ ((1 / y) * z),u)
    ]]></literal>
    <justification jstring="[para(2073(a,1),23195(a,1,1,2,1))].">
      <j1 rule="para" parents="2073 23195"/>
    </justification>
  </clause>

  <clause id="23197">
    <literal><![CDATA[
      (x * y) / (K((z * (z / u)) \ w,x) * y) = T(x,u / ((z \ w) \ z))
    ]]></literal>
    <justification jstring="[para(23195(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="23195 7934"/>
    </justification>
  </clause>

  <clause id="23198">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ z)) = T(x,(z * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7939,a,23197,a),flip(a)].">
      <j1 rule="hyper" parents="7939 23197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23199">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u * (u / y)) \ z) = T(x,((u \ z) \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,17802,a(flip),b,23198,a),flip(a)].">
      <j1 rule="hyper" parents="60 17802 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23200">
    <literal><![CDATA[
      T(x,(y * (y / z)) \ (y * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(4(a,1),23198(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23201">
    <literal><![CDATA[
      T(x,y \ ((y / (y / z)) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(22449,a,23200,a)].">
      <j1 rule="hyper" parents="22449 23200"/>
    </justification>
  </clause>

  <clause id="23202">
    <literal><![CDATA[
      T(x,y / (a(z / (z / y),u,u) \ z)) = T(x,z \ R(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[para(16504(a,1),23201(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16504 23201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23203">
    <literal><![CDATA[
      T(x,y / (z * (z / u))) = T(x,((z \ y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,17851,a(flip),b,23199,a)].">
      <j1 rule="hyper" parents="60 17851 23199"/>
    </justification>
  </clause>

  <clause id="23204">
    <literal><![CDATA[
      T(x,((y \ (y * z)) \ y) \ u) = T(x,T(z / (y / u),y))
    ]]></literal>
    <justification jstring="[hyper(22760,a,23203,a),flip(a)].">
      <j1 rule="hyper" parents="22760 23203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23205">
    <literal><![CDATA[
      T(x,T(y / (z / u),z)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),23204(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 23204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23206">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),z * (z * u))) = T(x,(y \ (z * (z * u))) \ z)
    ]]></literal>
    <justification jstring="[para(5463(a,1),23205(a,1,2,1,2))].">
      <j1 rule="para" parents="5463 23205"/>
    </justification>
  </clause>

  <clause id="23207">
    <literal><![CDATA[
      K(x / (y \ (z * ((z \ 1) \ z))),u) = K((z * (z / x)) \ ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[para(1511(a,1),23196(a,1,1,2))].">
      <j1 rule="para" parents="1511 23196"/>
    </justification>
  </clause>

  <clause id="23208">
    <literal><![CDATA[
      T(x,y / (a(z / (z / y),u,u) \ z)) = T(x,z \ L(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,18618,a(flip),b,23202,a),flip(a)].">
      <j1 rule="hyper" parents="370 18618 23202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23209">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(y / (z \ (x * (x * x))),u)
    ]]></literal>
    <justification jstring="[para(311(a,1),23207(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="311 23207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23210">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(y / ((z \ x) * (x * x)),u)
    ]]></literal>
    <justification jstring="[para(513(a,1),23209(a,2,1,2))].">
      <j1 rule="para" parents="513 23209"/>
    </justification>
  </clause>

  <clause id="23211">
    <literal><![CDATA[
      K((x * (x / y)) \ ((1 / x) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,18503,a(flip),b,23210,a),flip(a)].">
      <j1 rule="hyper" parents="370 18503 23210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23212">
    <literal><![CDATA[
      K((x * (x / y)) \ ((x \ 1) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(18387,a,23211,a)].">
      <j1 rule="hyper" parents="18387 23211"/>
    </justification>
  </clause>

  <clause id="23213">
    <literal><![CDATA[
      K(x \ (((x \ 1) / (x / y)) * z),u) = K(x \ (x \ (y / (z \ x))),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22578,a(flip),b,23212,a)].">
      <j1 rule="hyper" parents="60 22578 23212"/>
    </justification>
  </clause>

  <clause id="23214">
    <literal><![CDATA[
      K(x \ (x \ ((y / (x \ 1)) / (z \ x))),u) = K(x \ ((y \ x) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22972,a(flip),b,23213,a),flip(a)].">
      <j1 rule="hyper" parents="60 22972 23213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23215">
    <literal><![CDATA[
      K((x / ((y \ 1) \ 1)) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20173,a(flip),b,23214,a)].">
      <j1 rule="hyper" parents="60 20173 23214"/>
    </justification>
  </clause>

  <clause id="23216">
    <literal><![CDATA[
      K((x / T(y,1)) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21647,a(flip),b,23215,a)].">
      <j1 rule="hyper" parents="60 21647 23215"/>
    </justification>
  </clause>

  <clause id="23217">
    <literal><![CDATA[
      K((x / y) / (z \ y),u) = K(y \ ((x \ y) \ z),u)
    ]]></literal>
    <justification jstring="[para(222(a,1),23216(a,1,1,1,2))].">
      <j1 rule="para" parents="222 23216"/>
    </justification>
  </clause>

  <clause id="23218">
    <literal><![CDATA[
      K(x \ ((y \ x) \ z),u) = K(x \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22930,a(flip),b,23217,a),flip(a)].">
      <j1 rule="hyper" parents="60 22930 23217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23219">
    <literal><![CDATA[
      K(x \ ((x \ y) * T(z,x * (y * z))),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22567,a(flip),b,23218,a),flip(a)].">
      <j1 rule="hyper" parents="60 22567 23218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23220">
    <literal><![CDATA[
      K(x \ ((x \ y) * T(z,x * y)),u) = K(x \ (z / (y \ x)),u)
    ]]></literal>
    <justification jstring="[hyper(21119,a,23219,a)].">
      <j1 rule="hyper" parents="21119 23219"/>
    </justification>
  </clause>

  <clause id="23221">
    <literal><![CDATA[
      K(x \ (y / (z \ x)),u) = K(x \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,18609,a(flip),b,23220,a),flip(a)].">
      <j1 rule="hyper" parents="60 18609 23220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23222">
    <literal><![CDATA[
      K(x \ (y * (x \ z)),T(u,y)) = K(z / ((y / x) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(23024,a,23221,a),flip(a)].">
      <j1 rule="hyper" parents="23024 23221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23223">
    <literal><![CDATA[
      K(x / ((y / z) \ z),u) = K(x / (z * (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(22483,a,23222,a),flip(a)].">
      <j1 rule="hyper" parents="22483 23222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23224">
    <literal><![CDATA[
      (x * y) / (K(z / (u * (w \ u)),x) * y) = T(x,z / ((w / u) \ u))
    ]]></literal>
    <justification jstring="[para(23223(a,1),7934(a,1,2,1))].">
      <j1 rule="para" parents="23223 7934"/>
    </justification>
  </clause>

  <clause id="23225">
    <literal><![CDATA[
      T(x,y / ((z / u) \ u)) = T(x,y / (u * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(7939,a,23224,a),flip(a)].">
      <j1 rule="hyper" parents="7939 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23226">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u * (z \ u))) = T(x,((z / u) \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,17801,a(flip),b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="60 17801 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23227">
    <literal><![CDATA[
      T(x,((y / z) \ z) \ u) = T(x,z \ (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(22493,a,23226,a),flip(a)].">
      <j1 rule="hyper" parents="22493 23226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23228">
    <literal><![CDATA[
      T(x,y \ (z * (y \ (T(u,z) \ w)))) = T(x,u \ (((z / y) \ y) \ w))
    ]]></literal>
    <justification jstring="[hyper(22498,a,23227,a),flip(a)].">
      <j1 rule="hyper" parents="22498 23227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23229">
    <literal><![CDATA[
      T(x,y \ (z * (y \ u))) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(22309,a,23227,a),flip(a)].">
      <j1 rule="hyper" parents="22309 23227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23231">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ z)) \ u)) = T(x,(z \ (y / z)) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(22551,a,23229,a)].">
      <j1 rule="hyper" parents="22551 23229"/>
    </justification>
  </clause>

  <clause id="23232">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ z)) \ u)) = T(x,z \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,22703,a(flip),b,23231,a),flip(a)].">
      <j1 rule="hyper" parents="370 22703 23231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23233">
    <literal><![CDATA[
      T(x,y \ (((z / u) \ u) \ w)) = T(x,y \ ((u * (z \ u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(22536,a,23228,a),flip(a)].">
      <j1 rule="hyper" parents="22536 23228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23234">
    <literal><![CDATA[
      T(x,y \ ((z * (u \ z)) \ w)) = T(x,y \ ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23174,a(flip),b,23233,a),flip(a)].">
      <j1 rule="hyper" parents="60 23174 23233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23235">
    <literal><![CDATA[
      T(x,y \ ((z \ (y / z)) * u)) = T(x,z \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,23232,a(flip),b,23234,a),flip(a)].">
      <j1 rule="hyper" parents="60 23232 23234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23236">
    <literal><![CDATA[
      T(x,y / (a((z / y) \ z,u,u) \ z)) = T(x,z \ L(z / (z / y),u,u))
    ]]></literal>
    <justification jstring="[para(21509(a,1),23208(a,1,2,2,1))].">
      <j1 rule="para" parents="21509 23208"/>
    </justification>
  </clause>

  <clause id="23237">
    <literal><![CDATA[
      T(x,y \ L(y / (y / z),u,u)) = T(x,z / (a(z,u,u) \ y))
    ]]></literal>
    <justification jstring="[para(77(a,1),23236(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 23236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23238">
    <literal><![CDATA[
      T(x,y \ L(y / (y / z),u,u)) = T(x,L(z,u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,22935,a(flip),b,23237,a),flip(a)].">
      <j1 rule="hyper" parents="370 22935 23237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23239">
    <literal><![CDATA[
      T(x,(y / z) \ a(u,u,y)) = T(x,L(z,w,w) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,23148,a(flip),b,23238,a)].">
      <j1 rule="hyper" parents="60 23148 23238"/>
    </justification>
  </clause>

  <clause id="23240">
    <literal><![CDATA[
      T(x,L(y,z,z) / u) = T(x,y / L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(23078,a,23239,a),flip(a)].">
      <j1 rule="hyper" parents="23078 23239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23242">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,(u \ z) / L(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23061,a,b,23240,a)].">
      <j1 rule="hyper" parents="60 23061 23240"/>
    </justification>
  </clause>

  <clause id="23244">
    <literal><![CDATA[
      T(x,T(y / (T(z,z * u) * u),u)) = T(x,(y \ (z * (z * u))) \ z)
    ]]></literal>
    <justification jstring="[hyper(17150,a,23206,a)].">
      <j1 rule="hyper" parents="17150 23206"/>
    </justification>
  </clause>

  <clause id="23246">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(y \ (u * (u * z))) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,20578,a(flip),b,23244,a)].">
      <j1 rule="hyper" parents="60 20578 23244"/>
    </justification>
  </clause>

  <clause id="23247">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(u * z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,23071,a(flip),b,23246,a),flip(a)].">
      <j1 rule="hyper" parents="370 23071 23246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23248">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(370,a,23039,a(flip),b,23247,a),flip(a)].">
      <j1 rule="hyper" parents="370 23039 23247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23249">
    <literal><![CDATA[
      T(x,T(y / (L(y,z,u) * w),L(y,z,u))) = T(x,(y / L(y,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(3938(a,2),23248(a,2,2,1))].">
      <j1 rule="para" parents="3938 23248"/>
    </justification>
  </clause>

  <clause id="23250">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ ((1 / z) \ y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(21841(a,2),23248(a,2,2,1))].">
      <j1 rule="para" parents="21841 23248"/>
    </justification>
  </clause>

  <clause id="23251">
    <literal><![CDATA[
      T(x,T(y / (L(y,z,u) * w),y)) = T(x,(y / L(y,z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(19424,a,23249,a)].">
      <j1 rule="hyper" parents="19424 23249"/>
    </justification>
  </clause>

  <clause id="23252">
    <literal><![CDATA[
      T(x,(y / L(y,z,u)) / w) = T(x,(L(y,z,u) * w) \ y)
    ]]></literal>
    <justification jstring="[hyper(7333,a,23251,a),flip(a)].">
      <j1 rule="hyper" parents="7333 23251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23253">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) / w) = T(x,(L(y,z,u) * w) \ y)
    ]]></literal>
    <justification jstring="[para(3938(a,1),23252(a,1,2,1))].">
      <j1 rule="para" parents="3938 23252"/>
    </justification>
  </clause>

  <clause id="23254">
    <literal><![CDATA[
      T(x,(L(y,z,u) * w) \ y) = T(x,w \ (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(19361,a,23253,a),flip(a)].">
      <j1 rule="hyper" parents="19361 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23255">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,y \ (L(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23043,a,b,23254,a)].">
      <j1 rule="hyper" parents="60 23043 23254"/>
    </justification>
  </clause>

  <clause id="23256">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ ((z / 1) * y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(22523(a,1),23250(a,1,2))].">
      <j1 rule="para" parents="22523 23250"/>
    </justification>
  </clause>

  <clause id="23257">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),z \ (z * y))) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(72(a,1),23256(a,1,2,2,2,1))].">
      <j1 rule="para" parents="72 23256"/>
    </justification>
  </clause>

  <clause id="23258">
    <literal><![CDATA[
      T(x,T(y / ((z \ ((1 / z) \ y)) * u),y)) = T(x,T((z \ ((1 / z) \ y)) \ y,w) / u)
    ]]></literal>
    <justification jstring="[para(4(a,1),23257(a,1,2,2))].">
      <j1 rule="para" parents="4 23257"/>
    </justification>
  </clause>

  <clause id="23259">
    <literal><![CDATA[
      T(x,T((y \ ((1 / y) \ z)) \ z,u) / w) = T(x,((y \ ((1 / y) \ z)) * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(7333,a,23258,a),flip(a)].">
      <j1 rule="hyper" parents="7333 23258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23260">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),x \ (x \ L(x,y,z))) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3839(a,1),23183(a,1,2,2))].">
      <j1 rule="para" parents="3839 23183"/>
    </justification>
  </clause>

  <clause id="23261">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) * u) / (L(x,y,z) \ 1),L(x \ 1,y,z)) = T(u,T(x \ L(x,y,z),x) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15355,a(flip),b,23260,a)].">
      <j1 rule="hyper" parents="60 15355 23260"/>
    </justification>
  </clause>

  <clause id="23262">
    <literal><![CDATA[
      T(x,T(y \ L(y,z,u),y) * (y \ L(y,z,u))) = (L(y,z,u) \ 1) \ ((L(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(13056,a,23261,a),flip(a)].">
      <j1 rule="hyper" parents="13056 23261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23263">
    <literal><![CDATA[
      T(x,T(y \ L(y,z,u),y) * (y \ L(y,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a(flip),b,23262,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 23262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23265">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * (y \ L(y,z,u))) = x
    ]]></literal>
    <justification jstring="[para(3837(a,1),23263(a,1,2,1))].">
      <j1 rule="para" parents="3837 23263"/>
    </justification>
  </clause>

  <clause id="23266">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ (y \ L(y,z,u)))) = x
    ]]></literal>
    <justification jstring="[hyper(16619,a,23265,a)].">
      <j1 rule="hyper" parents="16619 23265"/>
    </justification>
  </clause>

  <clause id="23267">
    <literal><![CDATA[
      T(T(x,(L(y,z,u) \ y) \ w),1) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18953,a(flip),b,23266,a)].">
      <j1 rule="hyper" parents="60 18953 23266"/>
    </justification>
  </clause>

  <clause id="23269">
    <literal><![CDATA[
      T(T(x,L(y,z,u) * (y \ w)),1) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(16617(a,1),23267(a,1,1))].">
      <j1 rule="para" parents="16617 23267"/>
    </justification>
  </clause>

  <clause id="23270">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(226,a,23269,a)].">
      <j1 rule="hyper" parents="226 23269"/>
    </justification>
  </clause>

  <clause id="23271">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (w \ 1))) = T(x,w \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,19596,a(flip),b,23270,a),flip(a)].">
      <j1 rule="hyper" parents="60 19596 23270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23272">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (y \ w))) = T(x,L(y \ 1,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15991,a(flip),b,23270,a),flip(a)].">
      <j1 rule="hyper" parents="60 15991 23270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23273">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) \ z)) = T(x,y \ (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19617,a,23271,a)].">
      <j1 rule="hyper" parents="19617 23271"/>
    </justification>
  </clause>

  <clause id="23274">
    <literal><![CDATA[
      T(x,(y \ z) / L(z,u,w)) = T(x,y \ (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,23255,a,b,23273,a)].">
      <j1 rule="hyper" parents="60 23255 23273"/>
    </justification>
  </clause>

  <clause id="23275">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,u \ (z \ L(z,w,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,23242,a,b,23274,a)].">
      <j1 rule="hyper" parents="60 23242 23274"/>
    </justification>
  </clause>

  <clause id="23276">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) * w) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,14639,a(flip),b,23272,a),flip(a)].">
      <j1 rule="hyper" parents="60 14639 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23277">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) * w) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15572,a,23276,a)].">
      <j1 rule="hyper" parents="15572 23276"/>
    </justification>
  </clause>

  <clause id="23278">
    <literal><![CDATA[
      T(x,L(1 / y,z,u) \ w) = T(x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(77(a,1),23276(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="77 23276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23280">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),L(1 / y,z,u) \ (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(23277(a,1),15683(a,1,1))].">
      <j1 rule="para" parents="23277 15683"/>
    </justification>
  </clause>

  <clause id="23281">
    <literal><![CDATA[
      T(x,((y \ ((1 / y) \ z)) * u) \ z) = T(x,u \ a(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,23052,a(flip),b,23275,a),flip(a)].">
      <j1 rule="hyper" parents="370 23052 23275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23282">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,T((w \ ((1 / w) \ z)) \ z,v5) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,23259,a,b,23281,a),flip(a)].">
      <j1 rule="hyper" parents="60 23259 23281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23284">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,((w \ ((1 / w) \ z)) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,18241,a(flip),b,23282,a),flip(a)].">
      <j1 rule="hyper" parents="370 18241 23282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23286">
    <literal><![CDATA[
      T(x,y \ a(z,u,u)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,21819,a(flip),b,23284,a),flip(a)].">
      <j1 rule="hyper" parents="370 21819 23284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23288">
    <literal><![CDATA[
      T(x,((y * (z \ 1)) / u) \ 1) = T(x,u / (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23077,a(flip),b,23286,a),flip(a)].">
      <j1 rule="hyper" parents="60 23077 23286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23290">
    <literal><![CDATA[
      T(x,y / (z * (u \ 1))) = T(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,9704,a(flip),b,23288,a)].">
      <j1 rule="hyper" parents="60 9704 23288"/>
    </justification>
  </clause>

  <clause id="23291">
    <literal><![CDATA[
      T(x,y / (z / u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(23179,a,23290,a),flip(a)].">
      <j1 rule="hyper" parents="23179 23290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23292">
    <literal><![CDATA[
      T(x,y / (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u / z)) = w
    ]]></literal>
    <justification jstring="[para(23290(a,1),23179(a,1))].">
      <j1 rule="para" parents="23290 23179"/>
    </justification>
  </clause>

  <clause id="23293">
    <literal><![CDATA[
      T(x,(y \ z) / (u / w)) = T(x,(z \ y) \ (w / u))
    ]]></literal>
    <justification jstring="[hyper(370,a,22308,a,b,23291,a),flip(a)].">
      <j1 rule="hyper" parents="370 22308 23291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23294">
    <literal><![CDATA[
      T(x,y / (z / (y / u))) = T(x,(y \ u) \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22550,a(flip),b,23293,a)].">
      <j1 rule="hyper" parents="60 22550 23293"/>
    </justification>
  </clause>

  <clause id="23295">
    <literal><![CDATA[
      T(x,(y \ z) \ (y / u)) = T(x,y * ((y / z) / u))
    ]]></literal>
    <justification jstring="[hyper(23292,a,23294,a),flip(a)].">
      <j1 rule="hyper" parents="23292 23294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23296">
    <literal><![CDATA[
      T(x,(y \ z) * (z / u)) = T(x,z * ((z / y) / u))
    ]]></literal>
    <justification jstring="[hyper(22309,a,23295,a)].">
      <j1 rule="hyper" parents="22309 23295"/>
    </justification>
  </clause>

  <clause id="23297">
    <literal><![CDATA[
      T(T(x,y * ((y / z) / z)),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(23296(a,1),16329(a,1,1))].">
      <j1 rule="para" parents="23296 16329"/>
    </justification>
  </clause>

  <clause id="23298">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),L(y,z,u) * (y * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[hyper(60,a,23278,a(flip),b,23280,a)].">
      <j1 rule="hyper" parents="60 23278 23280"/>
    </justification>
  </clause>

  <clause id="23299">
    <literal><![CDATA[
      T(T(x,L(y,z,u) \ w),y * (L(y,z,u) * (L(y,z,u) \ y))) = T(T(x,L(1 / y,z,u) \ w),1)
    ]]></literal>
    <justification jstring="[para(2153(a,1),23298(a,1,2))].">
      <j1 rule="para" parents="2153 23298"/>
    </justification>
  </clause>

  <clause id="23300">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) \ w),1) = T(T(x,L(y,z,u) \ w),y * y)
    ]]></literal>
    <justification jstring="[para(5(a,1),23299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 23299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23301">
    <literal><![CDATA[
      T(T(x,L(1 / y,z,u) \ w),1) = T(x,y * (y * (L(y,z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,15429,a(flip),b,23300,a),flip(a)].">
      <j1 rule="hyper" parents="370 15429 23300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23303">
    <literal><![CDATA[
      T(x,y * (y * (L(y,z,u) \ w))) = T(T(x,L(y,z,u) * w),1)
    ]]></literal>
    <justification jstring="[para(23278(a,1),23301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23278 23301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23304">
    <literal><![CDATA[
      T(x,y * (y * (L(y,z,u) \ w))) = T(x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,222,a(flip),b,23303,a),flip(a)].">
      <j1 rule="hyper" parents="370 222 23303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23305">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = w / T(w,L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(23304(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="23304 5701"/>
    </justification>
  </clause>

  <clause id="23306">
    <literal><![CDATA[
      K(x * (x * (L(x,y,z) \ u)),w) = K(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,23305,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 23305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23307">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ u,w) = K(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15146,a(flip),b,23306,a)].">
      <j1 rule="hyper" parents="60 15146 23306"/>
    </justification>
  </clause>

  <clause id="23308">
    <literal><![CDATA[
      K((x \ ((1 / x) \ y)) * T(z,y),u) = K(L(z,x,x) * y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,23105,a,b,23307,a)].">
      <j1 rule="hyper" parents="60 23105 23307"/>
    </justification>
  </clause>

  <clause id="23309">
    <literal><![CDATA[
      K(x * (y \ ((1 / y) \ z)),u) = K(L(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[para(22651(a,1),23308(a,1,1))].">
      <j1 rule="para" parents="22651 23308"/>
    </justification>
  </clause>

  <clause id="23310">
    <literal><![CDATA[
      K(x * (y \ ((y \ 1) \ z)),u) = K(L(x,y,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(16628,a,23309,a)].">
      <j1 rule="hyper" parents="16628 23309"/>
    </justification>
  </clause>

  <clause id="23311">
    <literal><![CDATA[
      K(L(T(x,y),z,z) * y,u) = K((z \ ((z \ 1) \ y)) * x,u)
    ]]></literal>
    <justification jstring="[hyper(15356,a,23310,a),flip(a)].">
      <j1 rule="hyper" parents="15356 23310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23312">
    <literal><![CDATA[
      K((x \ ((x \ 1) \ y)) * z,u) = K(y * L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(12619,a,23311,a),flip(a)].">
      <j1 rule="hyper" parents="12619 23311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23313">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y \ 1)) * z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),23312(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17 23312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23314">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y * 1)) * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20371,a(flip),b,23313,a),flip(a)].">
      <j1 rule="hyper" parents="370 20371 23313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23315">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((y \ T(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(3(a,1),23314(a,2,1,1,2,2))].">
      <j1 rule="para" parents="3 23314"/>
    </justification>
  </clause>

  <clause id="23316">
    <literal><![CDATA[
      K((x * (y \ 1)) * L(z,y,y),u) = K((x / y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,20045,a(flip),b,23315,a),flip(a)].">
      <j1 rule="hyper" parents="370 20045 23315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23317">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = (x * w) / (K((y / z) * u,x) * w)
    ]]></literal>
    <justification jstring="[para(23316(a,1),7934(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23316 7934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23318">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * L(u,z,z)) = T(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,7934,a(flip),b,23317,a),flip(a)].">
      <j1 rule="hyper" parents="370 7934 23317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23319">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * (y \ 1))) * u) = T(x,((y \ z) / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21959,a(flip),b,23318,a)].">
      <j1 rule="hyper" parents="60 21959 23318"/>
    </justification>
  </clause>

  <clause id="23320">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * (y \ 1))) * u) = T(x,(y \ (z / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,17917,a(flip),b,23319,a),flip(a)].">
      <j1 rule="hyper" parents="370 17917 23319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23321">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * T(u,y \ (z * (y \ 1)))) = T(x,u * ((y \ 1) * (z * (y \ 1))))
    ]]></literal>
    <justification jstring="[para(15329(a,1),23320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15329 23320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23322">
    <literal><![CDATA[
      T(x,(y \ (z / y)) * T(u,y \ (z / y))) = T(x,u * ((y \ 1) * (z * (y \ 1))))
    ]]></literal>
    <justification jstring="[para(18555(a,1),23321(a,1,2,2))].">
      <j1 rule="para" parents="18555 23321"/>
    </justification>
  </clause>

  <clause id="23323">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * (z \ 1)))) = T(x,y * (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),23322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 23322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23324">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * (((z \ 1) \ 1) * R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(1515(a,1),23323(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1515 23323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23325">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * R(z * u,z,z))
    ]]></literal>
    <justification jstring="[para(4484(a,1),23324(a,2,2,2))].">
      <j1 rule="para" parents="4484 23324"/>
    </justification>
  </clause>

  <clause id="23326">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ ((u * (z \ 1)) / (z \ 1)))) = T(x,y * L(z * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,20103,a(flip),b,23325,a),flip(a)].">
      <j1 rule="hyper" parents="370 20103 23325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23327">
    <literal><![CDATA[
      T(x,y * L(z * u,z,z)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(6(a,1),23326(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 23326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23328">
    <literal><![CDATA[
      T(x,y * (z * L(u,z,z))) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16940,a(flip),b,23327,a)].">
      <j1 rule="hyper" parents="60 16940 23327"/>
    </justification>
  </clause>

  <clause id="23329">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ u)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22673,a(flip),b,23328,a),flip(a)].">
      <j1 rule="hyper" parents="60 22673 23328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23330">
    <literal><![CDATA[
      T(x,y / (z \ (u \ w))) = T(x,y * ((w \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,23167,a(flip),b,23329,a)].">
      <j1 rule="hyper" parents="60 23167 23329"/>
    </justification>
  </clause>

  <clause id="23331">
    <literal><![CDATA[
      T(x,y * ((z \ u) * T(w,z * u))) = T(x,y / ((u \ z) / w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23190,a(flip),b,23330,a),flip(a)].">
      <j1 rule="hyper" parents="60 23190 23330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23332">
    <literal><![CDATA[
      T(x,y / ((z \ u) / w)) = T(x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,18579,a(flip),b,23331,a),flip(a)].">
      <j1 rule="hyper" parents="60 18579 23331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23333">
    <literal><![CDATA[
      T(x,y * (z / (u \ w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(23292,a,23332,a)].">
      <j1 rule="hyper" parents="23292 23332"/>
    </justification>
  </clause>

  <clause id="23335">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),T(z \ y,y \ z) \ (T(z \ y,y \ z) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(20047(a,1),23297(a,1,1))].">
      <j1 rule="para" parents="20047 23297"/>
    </justification>
  </clause>

  <clause id="23336">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),(z \ y) \ ((z \ y) \ u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(16821,a,23335,a)].">
      <j1 rule="hyper" parents="16821 23335"/>
    </justification>
  </clause>

  <clause id="23337">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),(y \ z) * ((y \ z) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(17095,a,23336,a)].">
      <j1 rule="hyper" parents="17095 23336"/>
    </justification>
  </clause>

  <clause id="23339">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,K(u,w) * ((y * z) * (z * K(w,u)))) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(22780(a,1),22467(a,1,2,2,1,2))].">
      <j1 rule="para" parents="22780 22467"/>
    </justification>
  </clause>

  <clause id="23340">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,(y * z) * z) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(19903(a,1),23339(a,1,2,2,1))].">
      <j1 rule="para" parents="19903 23339"/>
    </justification>
  </clause>

  <clause id="23341">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) \ (T(v5,z * (z * y)) \ v6)) = T(x,v5 \ ((T(z,K(u,w)) \ T(y * z,K(u,w))) \ v6))
    ]]></literal>
    <justification jstring="[para(16871(a,1),23340(a,1,2,2,1))].">
      <j1 rule="para" parents="16871 23340"/>
    </justification>
  </clause>

  <clause id="23343">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(u,z * (z * y)) \ w)) = T(x,u \ ((T(z,K(v5,v6)) \ T(y * z,K(v5,v6))) \ w))
    ]]></literal>
    <justification jstring="[hyper(18668,a,23341,a)].">
      <j1 rule="hyper" parents="18668 23341"/>
    </justification>
  </clause>

  <clause id="23344">
    <literal><![CDATA[
      T(x,y \ ((T(z,K(u,w)) \ T(v5 * z,K(u,w))) \ v6)) = T(x,y \ (T(v5,z) \ v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,22591,a(flip),b,23343,a),flip(a)].">
      <j1 rule="hyper" parents="60 22591 23343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23345">
    <literal><![CDATA[
      T(x,y \ (T(z,u * K(w,v5)) \ v6)) = T(x,y \ (T(z,u) \ v6))
    ]]></literal>
    <justification jstring="[para(17081(a,1),23344(a,1,2,2,1))].">
      <j1 rule="para" parents="17081 23344"/>
    </justification>
  </clause>

  <clause id="23346">
    <literal><![CDATA[
      T(x,(K(y,z) * (u \ 1)) \ (T(w,u) \ v5)) = T(x,w \ ((K(z,y) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,22630,a(flip),b,23345,a),flip(a)].">
      <j1 rule="hyper" parents="60 22630 23345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23347">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ 1) \ (T(w,u) \ v5))) = T(x,w \ ((K(y,z) \ (u \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20847,a,23346,a)].">
      <j1 rule="hyper" parents="20847 23346"/>
    </justification>
  </clause>

  <clause id="23349">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) \ (w \ 1)) \ v5)) = T(x,w * (K(u,z) * (T(y,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(20961,a,23347,a),flip(a)].">
      <j1 rule="hyper" parents="20961 23347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23350">
    <literal><![CDATA[
      T(x,y \ ((K(z,u) * (w \ 1)) \ v5)) = T(x,w * (K(z,u) * (T(y,w) \ v5)))
    ]]></literal>
    <justification jstring="[para(7506(a,1),23349(a,1,2,2,1))].">
      <j1 rule="para" parents="7506 23349"/>
    </justification>
  </clause>

  <clause id="23351">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (T(w,y) \ v5))) = T(x,w \ ((y \ K(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,19516,a(flip),b,23350,a),flip(a)].">
      <j1 rule="hyper" parents="60 19516 23350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23352">
    <literal><![CDATA[
      T(x,y \ ((z \ K(u,z)) \ w)) = T(x,T(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(16814,a,23351,a),flip(a)].">
      <j1 rule="hyper" parents="16814 23351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23353">
    <literal><![CDATA[
      T(x,y \ L(T(z,u) * w,v5,v5)) = T(x,T(z,u) * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23162,a,b,23352,a)].">
      <j1 rule="hyper" parents="60 23162 23352"/>
    </justification>
  </clause>

  <clause id="23354">
    <literal><![CDATA[
      T(x,T(y,z) * (T(u,y) \ w)) = T(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(23150,a,23353,a),flip(a)].">
      <j1 rule="hyper" parents="23150 23353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23355">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,y * z) * w)) = T(x,u * ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,18993,a(flip),b,23354,a),flip(a)].">
      <j1 rule="hyper" parents="60 18993 23354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23356">
    <literal><![CDATA[
      T(x,(y / z) * (T(u,z * y) * w)) = T(x,u * ((z / y) \ w))
    ]]></literal>
    <justification jstring="[hyper(22300,a,23355,a)].">
      <j1 rule="hyper" parents="22300 23355"/>
    </justification>
  </clause>

  <clause id="23357">
    <literal><![CDATA[
      T(x,y / (z \ ((u / w) \ 1))) = T(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,22971,a(flip),b,23356,a)].">
      <j1 rule="hyper" parents="60 22971 23356"/>
    </justification>
  </clause>

  <clause id="23358">
    <literal><![CDATA[
      T(x,y * (((z / u) \ 1) \ w)) = T(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23165,a(flip),b,23357,a)].">
      <j1 rule="hyper" parents="60 23165 23357"/>
    </justification>
  </clause>

  <clause id="23359">
    <literal><![CDATA[
      T(x,y * ((z / u) \ w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,23329,a(flip),b,23358,a),flip(a)].">
      <j1 rule="hyper" parents="60 23329 23358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23360">
    <literal><![CDATA[
      T(x,y * ((z * (u \ z)) \ w)) = T(x,y * (((z \ u) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,22644,a(flip),b,23359,a)].">
      <j1 rule="hyper" parents="60 22644 23359"/>
    </justification>
  </clause>

  <clause id="23361">
    <literal><![CDATA[
      T(x,y * ((z * (u \ z)) \ w)) = T(x,y * ((z \ (u / z)) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,20312,a(flip),b,23360,a),flip(a)].">
      <j1 rule="hyper" parents="370 20312 23360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23362">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * u)) = T(x,z * ((y \ (z / y)) * u))
    ]]></literal>
    <justification jstring="[hyper(23172,a,23361,a)].">
      <j1 rule="hyper" parents="23172 23361"/>
    </justification>
  </clause>

  <clause id="23363">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ y))),z * ((y \ (z / y)) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,23337,a(flip),b,23362,a),flip(a)].">
      <j1 rule="hyper" parents="60 23337 23362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23364">
    <literal><![CDATA[
      T(T(x,y * y),z \ (z \ (z * ((y \ (z / y)) * u)))) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,22628,a(flip),b,23363,a)].">
      <j1 rule="hyper" parents="60 22628 23363"/>
    </justification>
  </clause>

  <clause id="23365">
    <literal><![CDATA[
      T(T(x,y * y),z \ ((y \ (z / y)) * u)) = T(T(x,(y / z) * (1 / (z \ y))),u)
    ]]></literal>
    <justification jstring="[para(4(a,1),23364(a,1,2,2))].">
      <j1 rule="para" parents="4 23364"/>
    </justification>
  </clause>

  <clause id="23366">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(T(x,y * y),y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,23235,a(flip),b,23365,a),flip(a)].">
      <j1 rule="hyper" parents="60 23235 23365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23368">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,y * (y * (y \ (T(y,z) \ u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,15388,a(flip),b,23366,a),flip(a)].">
      <j1 rule="hyper" parents="370 15388 23366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23369">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,y * (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[para(5(a,1),23368(a,2,2,2))].">
      <j1 rule="para" parents="5 23368"/>
    </justification>
  </clause>

  <clause id="23371">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 / (z \ y))),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7932(a,1),23369(a,2,2))].">
      <j1 rule="para" parents="7932 23369"/>
    </justification>
  </clause>

  <clause id="23372">
    <literal><![CDATA[
      T(T(x,(y / z) * (1 * (y \ z))),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(23333(a,1),23371(a,1,1))].">
      <j1 rule="para" parents="23333 23371"/>
    </justification>
  </clause>

  <clause id="23373">
    <literal><![CDATA[
      T(T(x,(y / z) * (y \ z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2(a,1),23372(a,1,1,2,2))].">
      <j1 rule="para" parents="2 23372"/>
    </justification>
  </clause>

  <clause id="23374">
    <literal><![CDATA[
      T(T(x,T(y \ T(y,z),z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(23032(a,2),23373(a,1,1))].">
      <j1 rule="para" parents="23032 23373"/>
    </justification>
  </clause>

  <clause id="23375">
    <literal><![CDATA[
      T(T(x,T(K(y,z),z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5230(a,2),23374(a,1,1,2,1))].">
      <j1 rule="para" parents="5230 23374"/>
    </justification>
  </clause>

  <clause id="23376">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4743(a,1),23375(a,1,1,2))].">
      <j1 rule="para" parents="4743 23375"/>
    </justification>
  </clause>

  <clause id="23381">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16708,a,b,23376,a),flip(a)].">
      <j1 rule="hyper" parents="370 16708 23376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23385">
    <literal><![CDATA[
      x * T(y,K(z,u) * x) = T(y,K(u,z)) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,23381,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 23381 17"/>
    </justification>
  </clause>

  <clause id="23388">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = u * T(z,K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,22779,a,b,23385,a)].">
      <j1 rule="hyper" parents="370 22779 23385"/>
    </justification>
  </clause>

  <clause id="23389">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(32,a,16550,a,b,23388,a)].">
      <j1 rule="hyper" parents="32 16550 23388"/>
    </justification>
  </clause>

  <clause id="23390">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(13047,a,23389,a)].">
      <j1 rule="hyper" parents="13047 23389"/>
    </justification>
  </clause>

  <clause id="23391">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13033,a,23389,a)].">
      <j1 rule="hyper" parents="13033 23389"/>
    </justification>
  </clause>

  <clause id="23393">
    <literal><![CDATA[
      K(x,(y * z) \ u) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(11363,a,23389,a)].">
      <j1 rule="hyper" parents="11363 23389"/>
    </justification>
  </clause>

  <clause id="23443">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,23389,a,b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="126 23389 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23445">
    <literal><![CDATA[
      (x * y) \ (x * (y * K(z,u))) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9147,a,b,23389,a)].">
      <j1 rule="hyper" parents="60 9147 23389"/>
    </justification>
  </clause>

  <clause id="23451">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,6754,a(flip),b,23389,a),flip(a)].">
      <j1 rule="hyper" parents="60 6754 23389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23453">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(129,a,23389,a(flip),b,11130,a)].">
      <j1 rule="hyper" parents="129 23389 11130"/>
    </justification>
  </clause>

  <clause id="23454">
    <literal><![CDATA[
      (x * y) * K(z,u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,23389,a(flip),b,9147,a)].">
      <j1 rule="hyper" parents="129 23389 9147"/>
    </justification>
  </clause>

  <clause id="23455">
    <literal><![CDATA[
      x * ((x \ y) * K(z,u)) = y * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,23389,a(flip),b,8573,a),flip(a)].">
      <j1 rule="hyper" parents="129 23389 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23456">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = (x * (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,23389,a(flip),b,620,a),flip(a)].">
      <j1 rule="hyper" parents="129 23389 620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23460">
    <literal><![CDATA[
      x \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(23389(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="23389 617"/>
    </justification>
  </clause>

  <clause id="23461">
    <literal><![CDATA[
      (x * y) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(23389(a,1),336(a,1,2))].">
      <j1 rule="para" parents="23389 336"/>
    </justification>
  </clause>

  <clause id="23481">
    <literal><![CDATA[
      (K(x,y) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(23389(a,1),16431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23389 16431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23489">
    <literal><![CDATA[
      K(a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(15509,a,23443,a)].">
      <j1 rule="hyper" parents="15509 23443"/>
    </justification>
  </clause>

  <clause id="23492">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,23443,a,b,63,a)].">
      <j1 rule="hyper" parents="129 23443 63"/>
    </justification>
  </clause>

  <clause id="23493">
    <literal><![CDATA[
      a(x,K(y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,22791,a,b,23443,a)].">
      <j1 rule="hyper" parents="60 22791 23443"/>
    </justification>
  </clause>

  <clause id="23495">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,15892,a,b,23443,a)].">
      <j1 rule="hyper" parents="60 15892 23443"/>
    </justification>
  </clause>

  <clause id="23496">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,12999,a,b,23443,a)].">
      <j1 rule="hyper" parents="60 12999 23443"/>
    </justification>
  </clause>

  <clause id="23497">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,15816,a(flip),b,23443,a)].">
      <j1 rule="hyper" parents="60 15816 23443"/>
    </justification>
  </clause>

  <clause id="23499">
    <literal><![CDATA[
      K(L(x,y,z),u) = 1 / K(u,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,23443,a(flip),b,12969,a),flip(a)].">
      <j1 rule="hyper" parents="128 23443 12969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23515">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,23489,a,b,63,a)].">
      <j1 rule="hyper" parents="129 23489 63"/>
    </justification>
  </clause>

  <clause id="23516">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,14956,a,b,23489,a)].">
      <j1 rule="hyper" parents="60 14956 23489"/>
    </justification>
  </clause>

  <clause id="23517">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = 1 * w
    ]]></literal>
    <justification jstring="[hyper(54,a,23489,a)].">
      <j1 rule="hyper" parents="54 23489"/>
    </justification>
  </clause>

  <clause id="23518">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,23489,a)].">
      <j1 rule="hyper" parents="53 23489"/>
    </justification>
  </clause>

  <clause id="23519">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = w
    ]]></literal>
    <justification jstring="[para(23489(a,2),2(a,1,1))].">
      <j1 rule="para" parents="23489 2"/>
    </justification>
  </clause>

  <clause id="23520">
    <literal><![CDATA[
      K(a(x,y,z),u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(23489(a,2),131(a,1,1))].">
      <j1 rule="para" parents="23489 131"/>
    </justification>
  </clause>

  <clause id="23523">
    <literal><![CDATA[
      L(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,23493,a)].">
      <j1 rule="hyper" parents="49 23493"/>
    </justification>
  </clause>

  <clause id="23525">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(15062,a,23495,a)].">
      <j1 rule="hyper" parents="15062 23495"/>
    </justification>
  </clause>

  <clause id="23532">
    <literal><![CDATA[
      L(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,23495,a)].">
      <j1 rule="hyper" parents="49 23495"/>
    </justification>
  </clause>

  <clause id="23539">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,14959,a,b,23497,a)].">
      <j1 rule="hyper" parents="60 14959 23497"/>
    </justification>
  </clause>

  <clause id="23540">
    <literal><![CDATA[
      T(x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,23497,a)].">
      <j1 rule="hyper" parents="53 23497"/>
    </justification>
  </clause>

  <clause id="23541">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w
    ]]></literal>
    <justification jstring="[para(23497(a,2),2(a,1,1))].">
      <j1 rule="para" parents="23497 2"/>
    </justification>
  </clause>

  <clause id="23542">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(23497(a,2),131(a,1,1))].">
      <j1 rule="para" parents="23497 131"/>
    </justification>
  </clause>

  <clause id="23543">
    <literal><![CDATA[
      x * K(y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(23497(a,2),143(a,1,2))].">
      <j1 rule="para" parents="23497 143"/>
    </justification>
  </clause>

  <clause id="23546">
    <literal><![CDATA[
      x / (K(y,z) * u) = (x / u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(20636,a,23523,a)].">
      <j1 rule="hyper" parents="20636 23523"/>
    </justification>
  </clause>

  <clause id="23547">
    <literal><![CDATA[
      (x * K(y,z)) * u = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1838,a,23523,a),flip(a)].">
      <j1 rule="hyper" parents="1838 23523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23548">
    <literal><![CDATA[
      K(x,y) * ((z * K(x,y)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(1411,a,23523,a)].">
      <j1 rule="hyper" parents="1411 23523"/>
    </justification>
  </clause>

  <clause id="23559">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7539,a(flip),b,23523,a)].">
      <j1 rule="hyper" parents="60 7539 23523"/>
    </justification>
  </clause>

  <clause id="23562">
    <literal><![CDATA[
      (x * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(23523(a,1),336(a,1,2))].">
      <j1 rule="para" parents="23523 336"/>
    </justification>
  </clause>

  <clause id="23572">
    <literal><![CDATA[
      x / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(21557,a,23532,a)].">
      <j1 rule="hyper" parents="21557 23532"/>
    </justification>
  </clause>

  <clause id="23573">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10278,a,23532,a),flip(a)].">
      <j1 rule="hyper" parents="10278 23532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23574">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10153,a,23532,a)].">
      <j1 rule="hyper" parents="10153 23532"/>
    </justification>
  </clause>

  <clause id="23591">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,21540,a,b,23532,a)].">
      <j1 rule="hyper" parents="60 21540 23532"/>
    </justification>
  </clause>

  <clause id="23593">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,20207,a,b,23532,a)].">
      <j1 rule="hyper" parents="60 20207 23532"/>
    </justification>
  </clause>

  <clause id="23594">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,22816,a(flip),b,23532,a)].">
      <j1 rule="hyper" parents="60 22816 23532"/>
    </justification>
  </clause>

  <clause id="23596">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7522,a(flip),b,23532,a)].">
      <j1 rule="hyper" parents="60 7522 23532"/>
    </justification>
  </clause>

  <clause id="23599">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(129,a,23532,a(flip),b,94,a(flip))].">
      <j1 rule="hyper" parents="129 23532 94"/>
    </justification>
  </clause>

  <clause id="23600">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(23532(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="23532 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23601">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23532(a,1),47(a,2))].">
      <j1 rule="para" parents="23532 47"/>
    </justification>
  </clause>

  <clause id="23602">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / u = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(23532(a,1),213(a,1,2))].">
      <j1 rule="para" parents="23532 213"/>
    </justification>
  </clause>

  <clause id="23604">
    <literal><![CDATA[
      (K(x,y) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[para(23532(a,1),727(a,1,2))].">
      <j1 rule="para" parents="23532 727"/>
    </justification>
  </clause>

  <clause id="23605">
    <literal><![CDATA[
      (K(x,y) * z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(23532(a,1),336(a,1,2))].">
      <j1 rule="para" parents="23532 336"/>
    </justification>
  </clause>

  <clause id="23612">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23532(a,1),10278(a,1))].">
      <j1 rule="para" parents="23532 10278"/>
    </justification>
  </clause>

  <clause id="23614">
    <literal><![CDATA[
      x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(23532(a,1),15635(a,1,1))].">
      <j1 rule="para" parents="23532 15635"/>
    </justification>
  </clause>

  <clause id="23615">
    <literal><![CDATA[
      T(x \ (y * z),K(z,y)) * u = K(y,z) * ((x \ (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(23532(a,1),16149(a,1,2))].">
      <j1 rule="para" parents="23532 16149"/>
    </justification>
  </clause>

  <clause id="23619">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5894,a,23540,a)].">
      <j1 rule="hyper" parents="5894 23540"/>
    </justification>
  </clause>

  <clause id="23620">
    <literal><![CDATA[
      a(x,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3284,a,23540,a),flip(a)].">
      <j1 rule="hyper" parents="3284 23540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23621">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(3282,a,23540,a)].">
      <j1 rule="hyper" parents="3282 23540"/>
    </justification>
  </clause>

  <clause id="23622">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(504,a,23540,a)].">
      <j1 rule="hyper" parents="504 23540"/>
    </justification>
  </clause>

  <clause id="23624">
    <literal><![CDATA[
      T(x,a(y,z,u)) = w \ (w * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a,b,23540,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 23540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23628">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(162,a,23540,a),flip(a)].">
      <j1 rule="hyper" parents="162 23540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23629">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,14961,a,b,23540,a)].">
      <j1 rule="hyper" parents="60 14961 23540"/>
    </justification>
  </clause>

  <clause id="23630">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) \ u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,13581,a(flip),b,23540,a)].">
      <j1 rule="hyper" parents="60 13581 23540"/>
    </justification>
  </clause>

  <clause id="23631">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,23540,a(flip),b,15635,a)].">
      <j1 rule="hyper" parents="129 23540 15635"/>
    </justification>
  </clause>

  <clause id="23634">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23540(a,1),264(a,1,2,2))].">
      <j1 rule="para" parents="23540 264"/>
    </justification>
  </clause>

  <clause id="23635">
    <literal><![CDATA[
      a(x,y,z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(23540(a,1),158(a,1)),flip(a)].">
      <j1 rule="para" parents="23540 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23636">
    <literal><![CDATA[
      a(x,y,z) * u != w * a(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(23540(a,1),277(a,1,2))].">
      <j1 rule="para" parents="23540 277"/>
    </justification>
  </clause>

  <clause id="23637">
    <literal><![CDATA[
      a(x,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23540(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23540 328"/>
    </justification>
  </clause>

  <clause id="23638">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(23540(a,1),399(a,1,2,2))].">
      <j1 rule="para" parents="23540 399"/>
    </justification>
  </clause>

  <clause id="23639">
    <literal><![CDATA[
      x / a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(23540(a,1),494(a,1))].">
      <j1 rule="para" parents="23540 494"/>
    </justification>
  </clause>

  <clause id="23640">
    <literal><![CDATA[
      x \ (a(y,z,u) * w) = x \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23540(a,1),258(a,1,2,2))].">
      <j1 rule="para" parents="23540 258"/>
    </justification>
  </clause>

  <clause id="23641">
    <literal><![CDATA[
      x * (a(y,z,u) * w) = x * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23540(a,1),259(a,1,2,2))].">
      <j1 rule="para" parents="23540 259"/>
    </justification>
  </clause>

  <clause id="23642">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(23540(a,1),260(a,1,1,2))].">
      <j1 rule="para" parents="23540 260"/>
    </justification>
  </clause>

  <clause id="23643">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,v5) = a(u,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23540(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23540 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23644">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(23540(a,1),162(a,1)),flip(a)].">
      <j1 rule="para" parents="23540 162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23645">
    <literal><![CDATA[
      (a(x,y,z) * u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) * w = v5
    ]]></literal>
    <justification jstring="[para(23540(a,1),756(a,1,1,2))].">
      <j1 rule="para" parents="23540 756"/>
    </justification>
  </clause>

  <clause id="23648">
    <literal><![CDATA[
      x * (a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(23540(a,1),787(a,1,2,2))].">
      <j1 rule="para" parents="23540 787"/>
    </justification>
  </clause>

  <clause id="23651">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(w,x,a(y,z,u)) = a(y,z,u) * (x * w)
    ]]></literal>
    <justification jstring="[para(23540(a,1),12481(a,2,2,1))].">
      <j1 rule="para" parents="23540 12481"/>
    </justification>
  </clause>

  <clause id="23652">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(23540(a,1),12489(a,1,1,1))].">
      <j1 rule="para" parents="23540 12489"/>
    </justification>
  </clause>

  <clause id="23653">
    <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(23540(a,1),22433(a,1,2,2,1))].">
      <j1 rule="para" parents="23540 22433"/>
    </justification>
  </clause>

  <clause id="23654">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7150,a,23593,a)].">
      <j1 rule="hyper" parents="7150 23593"/>
    </justification>
  </clause>

  <clause id="23673">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      R(x,z,K(u,w)) = y
    ]]></literal>
    <justification jstring="[para(23593(a,1),2774(a,1))].">
      <j1 rule="para" parents="23593 2774"/>
    </justification>
  </clause>

  <clause id="23699">
    <literal><![CDATA[
      x * K(L(x,y,z),u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,23390,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 23390 5230"/>
    </justification>
  </clause>

  <clause id="23701">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,16414,a,b,23390,a)].">
      <j1 rule="hyper" parents="60 16414 23390"/>
    </justification>
  </clause>

  <clause id="23710">
    <literal><![CDATA[
      K(x,y) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(23390(a,1),5302(a,1,1))].">
      <j1 rule="para" parents="23390 5302"/>
    </justification>
  </clause>

  <clause id="23712">
    <literal><![CDATA[
      K(x,y * z) * (y * (z * x)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(23390(a,1),7477(a,1,1))].">
      <j1 rule="para" parents="23390 7477"/>
    </justification>
  </clause>

  <clause id="23713">
    <literal><![CDATA[
      L(x,y,z) * T(u,L(T(x,w),y,z)) = T(u * L(x,y,z),K(x,w))
    ]]></literal>
    <justification jstring="[para(23390(a,1),8489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23390 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23719">
    <literal><![CDATA[
      K(x,y) * R(x,z,u) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(23390(a,1),16489(a,1,1))].">
      <j1 rule="para" parents="23390 16489"/>
    </justification>
  </clause>

  <clause id="23720">
    <literal><![CDATA[
      K(x,y) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(23390(a,1),16495(a,1,1))].">
      <j1 rule="para" parents="23390 16495"/>
    </justification>
  </clause>

  <clause id="23723">
    <literal><![CDATA[
      K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(21637,a,23391,a),flip(a)].">
      <j1 rule="hyper" parents="21637 23391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23724">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16415,a,23391,a)].">
      <j1 rule="hyper" parents="16415 23391"/>
    </justification>
  </clause>

  <clause id="23728">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,23391,a,b,23391,a)].">
      <j1 rule="hyper" parents="370 23391 23391"/>
    </justification>
  </clause>

  <clause id="23746">
    <literal><![CDATA[
      K(x,(y / z) / u) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16481,a(flip),b,23391,a),flip(a)].">
      <j1 rule="hyper" parents="60 16481 23391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23767">
    <literal><![CDATA[
      K(x,(y * z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(23391(a,1),21637(a,1))].">
      <j1 rule="para" parents="23391 21637"/>
    </justification>
  </clause>

  <clause id="23785">
    <literal><![CDATA[
      x * K(y \ L(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(12999(a,2),23492(a,1,2))].">
      <j1 rule="para" parents="12999 23492"/>
    </justification>
  </clause>

  <clause id="23790">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,23496,a)].">
      <j1 rule="hyper" parents="53 23496"/>
    </justification>
  </clause>

  <clause id="23794">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(23515(a,1),335(a,1))].">
      <j1 rule="para" parents="23515 335"/>
    </justification>
  </clause>

  <clause id="23796">
    <literal><![CDATA[
      x * (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(23515(a,1),6778(a,1))].">
      <j1 rule="para" parents="23515 6778"/>
    </justification>
  </clause>

  <clause id="23798">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(53,a,23516,a)].">
      <j1 rule="hyper" parents="53 23516"/>
    </justification>
  </clause>

  <clause id="23804">
    <literal><![CDATA[
      (x * a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) * w = v5
    ]]></literal>
    <justification jstring="[para(23519(a,1),12086(a,1,2))].">
      <j1 rule="para" parents="23519 12086"/>
    </justification>
  </clause>

  <clause id="23805">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(23519(a,1),12091(a,1))].">
      <j1 rule="para" parents="23519 12091"/>
    </justification>
  </clause>

  <clause id="23810">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,23525,a)].">
      <j1 rule="hyper" parents="53 23525"/>
    </justification>
  </clause>

  <clause id="23816">
    <literal><![CDATA[
      (x * a(y,z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) \ w = v5
    ]]></literal>
    <justification jstring="[para(23541(a,1),12091(a,1))].">
      <j1 rule="para" parents="23541 12091"/>
    </justification>
  </clause>

  <clause id="23817">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(14973,a,23591,a)].">
      <j1 rule="hyper" parents="14973 23591"/>
    </justification>
  </clause>

  <clause id="23818">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),u) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6489,a,23591,a)].">
      <j1 rule="hyper" parents="6489 23591"/>
    </justification>
  </clause>

  <clause id="23819">
    <literal><![CDATA[
      ((x * a(y,z,u)) \ x) \ x = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(6455,a,23591,a)].">
      <j1 rule="hyper" parents="6455 23591"/>
    </justification>
  </clause>

  <clause id="23820">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2131,a,23591,a)].">
      <j1 rule="hyper" parents="2131 23591"/>
    </justification>
  </clause>

  <clause id="23821">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (a(x,y,z) \ 1)) = u
    ]]></literal>
    <justification jstring="[hyper(504,a,23591,a)].">
      <j1 rule="hyper" parents="504 23591"/>
    </justification>
  </clause>

  <clause id="23823">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,23591,a)].">
      <j1 rule="hyper" parents="52 23591"/>
    </justification>
  </clause>

  <clause id="23824">
    <literal><![CDATA[
      T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(51,a,23591,a)].">
      <j1 rule="hyper" parents="51 23591"/>
    </justification>
  </clause>

  <clause id="23825">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ 1) \ x = w
    ]]></literal>
    <justification jstring="[para(23591(a,1),494(a,1))].">
      <j1 rule="para" parents="23591 494"/>
    </justification>
  </clause>

  <clause id="23828">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(16594,a,23594,a)].">
      <j1 rule="hyper" parents="16594 23594"/>
    </justification>
  </clause>

  <clause id="23829">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,23594,a),flip(a)].">
      <j1 rule="hyper" parents="494 23594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23838">
    <literal><![CDATA[
      T(x / y,L(y,z,u)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,109,a(flip),b,23594,a),flip(a)].">
      <j1 rule="hyper" parents="370 109 23594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23839">
    <literal><![CDATA[
      x * T(y,L(x,z,u)) = y * x
    ]]></literal>
    <justification jstring="[hyper(129,a,23594,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 23594 17"/>
    </justification>
  </clause>

  <clause id="23840">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,16399,a,b,23594,a)].">
      <j1 rule="hyper" parents="60 16399 23594"/>
    </justification>
  </clause>

  <clause id="23841">
    <literal><![CDATA[
      T(L(1 / x,x,y) * y,1 / x) = y / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14845,a(flip),b,23594,a),flip(a)].">
      <j1 rule="hyper" parents="60 14845 23594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23842">
    <literal><![CDATA[
      T(x,L(y,z,u) \ 1) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,13055,a(flip),b,23594,a)].">
      <j1 rule="hyper" parents="60 13055 23594"/>
    </justification>
  </clause>

  <clause id="23843">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,23594,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 23594 17"/>
    </justification>
  </clause>

  <clause id="23845">
    <literal><![CDATA[
      T(x / L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(23594(a,1),494(a,1))].">
      <j1 rule="para" parents="23594 494"/>
    </justification>
  </clause>

  <clause id="23847">
    <literal><![CDATA[
      T(x,(y * z) \ u) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),23594(a,1,2))].">
      <j1 rule="para" parents="344 23594"/>
    </justification>
  </clause>

  <clause id="23848">
    <literal><![CDATA[
      T(x,y \ ((y / z) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(658(a,1),23594(a,1,2))].">
      <j1 rule="para" parents="658 23594"/>
    </justification>
  </clause>

  <clause id="23852">
    <literal><![CDATA[
      T(x,(y * z) \ (z * u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(663(a,1),23594(a,1,2))].">
      <j1 rule="para" parents="663 23594"/>
    </justification>
  </clause>

  <clause id="23855">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ ((y * z) * w)) = T(x,L(u,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(669(a,1),23594(a,1,2))].">
      <j1 rule="para" parents="669 23594"/>
    </justification>
  </clause>

  <clause id="23856">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) / T(x * y,L(z,y,x)) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(23594(a,1),1597(a,1,2))].">
      <j1 rule="para" parents="23594 1597"/>
    </justification>
  </clause>

  <clause id="23860">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(23594(a,1),16401(a,1,2))].">
      <j1 rule="para" parents="23594 16401"/>
    </justification>
  </clause>

  <clause id="23872">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,23629,a),flip(a)].">
      <j1 rule="hyper" parents="4977 23629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23873">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(3284,a,23629,a),flip(a)].">
      <j1 rule="hyper" parents="3284 23629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23874">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * (L(x,y,z) \ x))) = L(u,L(x,y,z) \ x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1151,a,23629,a)].">
      <j1 rule="hyper" parents="1151 23629"/>
    </justification>
  </clause>

  <clause id="23876">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23629(a,1),46(a,2))].">
      <j1 rule="para" parents="23629 46"/>
    </justification>
  </clause>

  <clause id="23878">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) * w) = x \ (w * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(23629(a,1),258(a,1,2,2))].">
      <j1 rule="para" parents="23629 258"/>
    </justification>
  </clause>

  <clause id="23880">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) / u = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(23629(a,1),6453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23629 6453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23881">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * (L(x,y,z) \ x)) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(23629(a,1),14734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23629 14734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23883">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(8462,a,23701,a)].">
      <j1 rule="hyper" parents="8462 23701"/>
    </justification>
  </clause>

  <clause id="23924">
    <literal><![CDATA[
      T(x,R(y,z,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,23724,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 23724 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23929">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(23724(a,1),7481(a,1,1))].">
      <j1 rule="para" parents="23724 7481"/>
    </justification>
  </clause>

  <clause id="23942">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (y \ R(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,23810,a),flip(a)].">
      <j1 rule="hyper" parents="4977 23810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23943">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3284,a,23810,a),flip(a)].">
      <j1 rule="hyper" parents="3284 23810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23944">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,23810,a)].">
      <j1 rule="hyper" parents="51 23810"/>
    </justification>
  </clause>

  <clause id="23947">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      u / (x \ R(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(23810(a,1),287(a,1)),flip(a)].">
      <j1 rule="para" parents="23810 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23953">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) \ u = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5894,a,23817,a)].">
      <j1 rule="hyper" parents="5894 23817"/>
    </justification>
  </clause>

  <clause id="23954">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = (y \ L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,23817,a),flip(a)].">
      <j1 rule="hyper" parents="4977 23817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23955">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3284,a,23817,a),flip(a)].">
      <j1 rule="hyper" parents="3284 23817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23959">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (x \ L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(23817(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23817 328"/>
    </justification>
  </clause>

  <clause id="23963">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(23817(a,1),4304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23817 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23967">
    <literal><![CDATA[
      T(x / R(y,z,u),y) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(494,a,23840,a),flip(a)].">
      <j1 rule="hyper" parents="494 23840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23978">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) != w
    ]]></literal>
    <literal><![CDATA[
      u * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23840(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23840 328"/>
    </justification>
  </clause>

  <clause id="23979">
    <literal><![CDATA[
      T(x / R(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(23840(a,1),494(a,1))].">
      <j1 rule="para" parents="23840 494"/>
    </justification>
  </clause>

  <clause id="23985">
    <literal><![CDATA[
      K(T(x,y) * R(y,z,u),w) = K(R(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[para(23840(a,1),12598(a,1,1,1))].">
      <j1 rule="para" parents="23840 12598"/>
    </justification>
  </clause>

  <clause id="23995">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(23518(a,1),158(a,1))].">
      <j1 rule="para" parents="23518 158"/>
    </justification>
  </clause>

  <clause id="23996">
    <literal><![CDATA[
      x * a(y,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(23518(a,1),277(a,1,2))].">
      <j1 rule="para" parents="23518 277"/>
    </justification>
  </clause>

  <clause id="23997">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(23518(a,1),399(a,1,2,2))].">
      <j1 rule="para" parents="23518 399"/>
    </justification>
  </clause>

  <clause id="23998">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ w = u
    ]]></literal>
    <justification jstring="[para(23518(a,1),366(a,1))].">
      <j1 rule="para" parents="23518 366"/>
    </justification>
  </clause>

  <clause id="23999">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(23518(a,1),368(a,1,2))].">
      <j1 rule="para" parents="23518 368"/>
    </justification>
  </clause>

  <clause id="24000">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23518(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23518 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24003">
    <literal><![CDATA[
      x * (a(y,z,u) * (x \ 1)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(23518(a,1),2081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23518 2081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24012">
    <literal><![CDATA[
      L(x,y,z / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(14469,a,23573,a),flip(a)].">
      <j1 rule="hyper" parents="14469 23573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24013">
    <literal><![CDATA[
      L(x,y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(14466,a,23573,a)].">
      <j1 rule="hyper" parents="14466 23573"/>
    </justification>
  </clause>

  <clause id="24015">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3173,a,23573,a)].">
      <j1 rule="hyper" parents="3173 23573"/>
    </justification>
  </clause>

  <clause id="24027">
    <literal><![CDATA[
      L(T(x,y),z,T(u,w)) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a(flip),b,23573,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 23573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24028">
    <literal><![CDATA[
      L(x,y,z * (u / z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14019,a,b,23573,a)].">
      <j1 rule="hyper" parents="60 14019 23573"/>
    </justification>
  </clause>

  <clause id="24029">
    <literal><![CDATA[
      L(x,y,z * (u * z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,16037,a(flip),b,23573,a),flip(a)].">
      <j1 rule="hyper" parents="60 16037 23573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24030">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(17(a,1),23573(a,1,3))].">
      <j1 rule="para" parents="17 23573"/>
    </justification>
  </clause>

  <clause id="24037">
    <literal><![CDATA[
      L(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(23573(a,1),14466(a,1))].">
      <j1 rule="para" parents="23573 14466"/>
    </justification>
  </clause>

  <clause id="24038">
    <literal><![CDATA[
      L(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(23573(a,1),14469(a,1))].">
      <j1 rule="para" parents="23573 14469"/>
    </justification>
  </clause>

  <clause id="24042">
    <literal><![CDATA[
      (K(x,y) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      z \ (K(y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(7522(a,1),23600(a,1)),flip(b)].">
      <j1 rule="para" parents="7522 23600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24043">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(21548(a,1),23600(a,1)),flip(b)].">
      <j1 rule="para" parents="21548 23600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24046">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,v5)) = R(x,y,T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,23593,a,b,23654,a)].">
      <j1 rule="hyper" parents="370 23593 23654"/>
    </justification>
  </clause>

  <clause id="24054">
    <literal><![CDATA[
      T(x,y) \ ((y \ ((y \ 1) \ x)) * y) = R(T(T(y,x),y \ 1),y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,6185,a(flip),b,23654,a)].">
      <j1 rule="hyper" parents="60 6185 23654"/>
    </justification>
  </clause>

  <clause id="24056">
    <literal><![CDATA[
      R(x,y,z / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(109(a,1),23654(a,1,3)),flip(a)].">
      <j1 rule="para" parents="109 23654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24065">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(23499(a,2),5870(a,1))].">
      <j1 rule="para" parents="23499 5870"/>
    </justification>
  </clause>

  <clause id="24067">
    <literal><![CDATA[
      x * T(y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * y = v5
    ]]></literal>
    <justification jstring="[para(23624(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="23624 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24068">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,23699,a(flip),b,7139,a)].">
      <j1 rule="hyper" parents="125 23699 7139"/>
    </justification>
  </clause>

  <clause id="24069">
    <literal><![CDATA[
      T(x * K(y \ L(y,z,u),w),a(v5,v6,v7) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,23591,a,b,23785,a)].">
      <j1 rule="hyper" parents="60 23591 23785"/>
    </justification>
  </clause>

  <clause id="24070">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (y \ L(y,z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(23785(a,1),335(a,1))].">
      <j1 rule="para" parents="23785 335"/>
    </justification>
  </clause>

  <clause id="24072">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / L(x,y,z) = u / x
    ]]></literal>
    <justification jstring="[hyper(316,a,23838,a)].">
      <j1 rule="hyper" parents="316 23838"/>
    </justification>
  </clause>

  <clause id="24073">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,23838,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 23838 17"/>
    </justification>
  </clause>

  <clause id="24074">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (u / x) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23838(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23838 328"/>
    </justification>
  </clause>

  <clause id="24076">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(23838(a,1),16401(a,1,2))].">
      <j1 rule="para" parents="23838 16401"/>
    </justification>
  </clause>

  <clause id="24078">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),23839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 23839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24083">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(23924(a,2),5265(a,1))].">
      <j1 rule="para" parents="23924 5265"/>
    </justification>
  </clause>

  <clause id="24094">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(5300(a,2),23520(a,1))].">
      <j1 rule="para" parents="5300 23520"/>
    </justification>
  </clause>

  <clause id="24096">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(7479(a,1),23542(a,1))].">
      <j1 rule="para" parents="7479 23542"/>
    </justification>
  </clause>

  <clause id="24100">
    <literal><![CDATA[
      x \ (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(15583(a,1),23543(a,1)),flip(b)].">
      <j1 rule="para" parents="15583 23543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24102">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14791,a(flip),b,23572,a),flip(a)].">
      <j1 rule="hyper" parents="60 14791 23572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24103">
    <literal><![CDATA[
      R((a(x,y,z) \ u) / w,w,a(x,y,z)) = u / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23572(a,1),349(a,1,1,1))].">
      <j1 rule="para" parents="23572 349"/>
    </justification>
  </clause>

  <clause id="24105">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z),u) * u = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(23572(a,1),1961(a,2,1))].">
      <j1 rule="para" parents="23572 1961"/>
    </justification>
  </clause>

  <clause id="24106">
    <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(23572(a,1),3864(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23572 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24107">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z) \ w) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),12500(a,2,2,1))].">
      <j1 rule="para" parents="23572 12500"/>
    </justification>
  </clause>

  <clause id="24108">
    <literal><![CDATA[
      R(a(x,y,y) \ z,a(x,y,y),x) = (z * x) / R(x,y,y)
    ]]></literal>
    <justification jstring="[para(23572(a,1),16519(a,1,1))].">
      <j1 rule="para" parents="23572 16519"/>
    </justification>
  </clause>

  <clause id="24112">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ v5 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23619(a,1),12742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23619 12742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24114">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,19684,a(flip),b,23620,a),flip(a)].">
      <j1 rule="hyper" parents="370 19684 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24115">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,16503,a(flip),b,23620,a),flip(a)].">
      <j1 rule="hyper" parents="370 16503 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24116">
    <literal><![CDATA[
      a(x,y,z) * (z \ 1) = z \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,14787,a(flip),b,23620,a),flip(a)].">
      <j1 rule="hyper" parents="370 14787 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24117">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14786,a(flip),b,23620,a),flip(a)].">
      <j1 rule="hyper" parents="370 14786 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24118">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) * (1 / a(z,u,w)) = a(z,u,w) * (x * (y * (a(z,u,w) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(370,a,1768,a(flip),b,23620,a)].">
      <j1 rule="hyper" parents="370 1768 23620"/>
    </justification>
  </clause>

  <clause id="24120">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,15090,a,b,23620,a)].">
      <j1 rule="hyper" parents="60 15090 23620"/>
    </justification>
  </clause>

  <clause id="24121">
    <literal><![CDATA[
      x * (T(y,x * a(z,u,w)) * a(z,u,w)) = L(y,a(z,u,w),x) * (x * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,23620,a(flip),b,870,a)].">
      <j1 rule="hyper" parents="129 23620 870"/>
    </justification>
  </clause>

  <clause id="24122">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,23620,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="125 23620 92"/>
    </justification>
  </clause>

  <clause id="24123">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ ((u * a(x,y,z)) * w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23620(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23620 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24125">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (a(y,z,u) * (w * x)) = L(T(w,x),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23620(a,1),270(a,1,1))].">
      <j1 rule="para" parents="23620 270"/>
    </justification>
  </clause>

  <clause id="24126">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(T(w,a(x,y,z)),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(23620(a,2),270(a,1,1))].">
      <j1 rule="para" parents="23620 270"/>
    </justification>
  </clause>

  <clause id="24127">
    <literal><![CDATA[
      (x * a(y,z,u)) \ L(x,a(y,z,u),a(y,z,u)) = T(1 / a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(23620(a,1),583(a,1,1))].">
      <j1 rule="para" parents="23620 583"/>
    </justification>
  </clause>

  <clause id="24128">
    <literal><![CDATA[
      (a(x,y,z) * u) / (a(x,y,z) * a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23620(a,2),1101(a,1,1))].">
      <j1 rule="para" parents="23620 1101"/>
    </justification>
  </clause>

  <clause id="24129">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(23620(a,1),629(a,1,2))].">
      <j1 rule="para" parents="23620 629"/>
    </justification>
  </clause>

  <clause id="24130">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,w)) * y) = R(T(a(z,u,w),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(23620(a,1),880(a,1,2,1))].">
      <j1 rule="para" parents="23620 880"/>
    </justification>
  </clause>

  <clause id="24131">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(23620(a,1),1029(a,1,1,2))].">
      <j1 rule="para" parents="23620 1029"/>
    </justification>
  </clause>

  <clause id="24133">
    <literal><![CDATA[
      L(L((a(x,y,z) \ 1) \ u,w,v5),a(x,y,z),a(x,y,z)) = L(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(23620(a,1),2084(a,2,1))].">
      <j1 rule="para" parents="23620 2084"/>
    </justification>
  </clause>

  <clause id="24134">
    <literal><![CDATA[
      R(x * K(a(y,z,u),x),a(y,z,u),w) = ((a(y,z,u) * x) * w) / (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23620(a,1),5349(a,2,2))].">
      <j1 rule="para" parents="23620 5349"/>
    </justification>
  </clause>

  <clause id="24136">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = (x \ u) * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(23620(a,2),14790(a,1,2))].">
      <j1 rule="para" parents="23620 14790"/>
    </justification>
  </clause>

  <clause id="24140">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(u * a(x,y,z),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(23621(a,1),3966(a,1))].">
      <j1 rule="para" parents="23621 3966"/>
    </justification>
  </clause>

  <clause id="24141">
    <literal><![CDATA[
      (x \ (a(y,z,x) \ u)) * a(y,z,x) = x \ u
    ]]></literal>
    <justification jstring="[para(23621(a,1),14790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23621 14790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24142">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * v6) = (v6 * a(u,w,v5)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,23620,a,b,23622,a)].">
      <j1 rule="hyper" parents="129 23620 23622"/>
    </justification>
  </clause>

  <clause id="24162">
    <literal><![CDATA[
      K(x,L(y \ z,u,w)) = K(x,(v5 * y) \ (v5 * z))
    ]]></literal>
    <justification jstring="[hyper(11545,a,23728,a),flip(a)].">
      <j1 rule="hyper" parents="11545 23728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24619">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(23728(a,1),11061(a,1))].">
      <j1 rule="para" parents="23728 11061"/>
    </justification>
  </clause>

  <clause id="24911">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,659,a(flip),b,24012,a),flip(a)].">
      <j1 rule="hyper" parents="60 659 24012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24912">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,97,a(flip),b,24012,a),flip(a)].">
      <j1 rule="hyper" parents="60 97 24012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24915">
    <literal><![CDATA[
      L(x,y,(((z \ u) \ 1) \ 1) \ z) = L(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[para(3492(a,1),24012(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3492 24012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24916">
    <literal><![CDATA[
      L(x,y,z / (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(24012(a,2),3363(a,1))].">
      <j1 rule="para" parents="24012 3363"/>
    </justification>
  </clause>

  <clause id="24917">
    <literal><![CDATA[
      L(x,y,(y * z) \ z) * ((z / (y * z)) * y) = (z / (y * z)) * (y * x)
    ]]></literal>
    <justification jstring="[para(24012(a,1),22306(a,1,1))].">
      <j1 rule="para" parents="24012 22306"/>
    </justification>
  </clause>

  <clause id="24918">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(16539,a,24013,a),flip(a)].">
      <j1 rule="hyper" parents="16539 24013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24919">
    <literal><![CDATA[
      L(x \ y,x,y * x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(13893,a,24013,a),flip(a)].">
      <j1 rule="hyper" parents="13893 24013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24922">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,z * y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,16537,a(flip),b,24013,a),flip(a)].">
      <j1 rule="hyper" parents="370 16537 24013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24923">
    <literal><![CDATA[
      L(1 / x,x,y * x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5656,a(flip),b,24013,a),flip(a)].">
      <j1 rule="hyper" parents="370 5656 24013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24924">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (w * u)) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(92(a,1),24013(a,1,3)),flip(a)].">
      <j1 rule="para" parents="92 24013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24925">
    <literal><![CDATA[
      L(x,y,(z * u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(24013(a,1),3574(a,1))].">
      <j1 rule="para" parents="24013 3574"/>
    </justification>
  </clause>

  <clause id="24927">
    <literal><![CDATA[
      L(x,x,y * z) \ (z * y) = T((z * y) * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(24013(a,1),6537(a,2,1)),flip(a)].">
      <j1 rule="para" parents="24013 6537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24929">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,z * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(24013(a,1),16535(a,1))].">
      <j1 rule="para" parents="24013 16535"/>
    </justification>
  </clause>

  <clause id="24930">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,u,z)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,u,z) = x
    ]]></literal>
    <justification jstring="[para(24013(a,1),16538(a,1))].">
      <j1 rule="para" parents="24013 16538"/>
    </justification>
  </clause>

  <clause id="24933">
    <literal><![CDATA[
      L(((x \ y) \ y) \ L((x \ y) \ y,z,u),x,x \ y) = L(y \ (L(x,z,u) * (x \ y)),w,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14879,a,b,24015,a)].">
      <j1 rule="hyper" parents="60 14879 24015"/>
    </justification>
  </clause>

  <clause id="24934">
    <literal><![CDATA[
      L(x,y,(z * T(u,w * z)) \ (u * (w * z))) = L(x,y,R(w,z,T(u,w * z)))
    ]]></literal>
    <justification jstring="[para(677(a,1),24015(a,1,3,1))].">
      <j1 rule="para" parents="677 24015"/>
    </justification>
  </clause>

  <clause id="24935">
    <literal><![CDATA[
      a(L((x \ y) * y,z,x),u,w) = a((x \ y) * y,u,w)
    ]]></literal>
    <justification jstring="[para(24015(a,1),14092(a,1,1))].">
      <j1 rule="para" parents="24015 14092"/>
    </justification>
  </clause>

  <clause id="24938">
    <literal><![CDATA[
      L(x \ 1,x,y * x) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(12528,a,24030,a)].">
      <j1 rule="hyper" parents="12528 24030"/>
    </justification>
  </clause>

  <clause id="24939">
    <literal><![CDATA[
      T(x,(y * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(344(a,1),24043(a,1,2))].">
      <j1 rule="para" parents="344 24043"/>
    </justification>
  </clause>

  <clause id="24941">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ ((y * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(669(a,1),24043(a,1,2))].">
      <j1 rule="para" parents="669 24043"/>
    </justification>
  </clause>

  <clause id="24943">
    <literal><![CDATA[
      R(1 / x,x,y \ z) \ (z / y) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(24056(a,1),467(a,1,1))].">
      <j1 rule="para" parents="24056 467"/>
    </justification>
  </clause>

  <clause id="24945">
    <literal><![CDATA[
      K((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),u) = w
    ]]></literal>
    <justification jstring="[para(344(a,1),24065(a,1,1))].">
      <j1 rule="para" parents="344 24065"/>
    </justification>
  </clause>

  <clause id="24970">
    <literal><![CDATA[
      K((x \ y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(16570(a,1),24619(a,1))].">
      <j1 rule="para" parents="16570 24619"/>
    </justification>
  </clause>

  <clause id="24975">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(17(a,1),23612(a,1,3))].">
      <j1 rule="para" parents="17 23612"/>
    </justification>
  </clause>

  <clause id="24979">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(14013(a,2),23612(a,1))].">
      <j1 rule="para" parents="14013 23612"/>
    </justification>
  </clause>

  <clause id="24985">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(398,a,23842,a),flip(a)].">
      <j1 rule="hyper" parents="398 23842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24988">
    <literal><![CDATA[
      T(x * L(x \ L(x,y,z),u,w),(x \ L(x,y,z)) \ 1) = (L(x \ L(x,y,z),u,w) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,14718,a(flip),b,23842,a),flip(a)].">
      <j1 rule="hyper" parents="60 14718 23842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24990">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(23842(a,2),7331(a,1))].">
      <j1 rule="para" parents="23842 7331"/>
    </justification>
  </clause>

  <clause id="25021">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,u) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(15182(a,1),23453(a,1,1,2))].">
      <j1 rule="para" parents="15182 23453"/>
    </justification>
  </clause>

  <clause id="25034">
    <literal><![CDATA[
      x \ (y * T(y \ z,u)) = (x \ z) * K(y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,6322,a,b,23455,a)].">
      <j1 rule="hyper" parents="125 6322 23455"/>
    </justification>
  </clause>

  <clause id="25035">
    <literal><![CDATA[
      x \ (y * (z * K(u,w))) = (x \ (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(125,a,23454,a(flip),b,23455,a)].">
      <j1 rule="hyper" parents="125 23454 23455"/>
    </justification>
  </clause>

  <clause id="25036">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,u) = x \ (y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,15179,a(flip),b,23455,a),flip(a)].">
      <j1 rule="hyper" parents="125 15179 23455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25037">
    <literal><![CDATA[
      (x \ (y \ 1)) * K(z,u) = x \ (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,15133,a(flip),b,23455,a),flip(a)].">
      <j1 rule="hyper" parents="125 15133 23455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25038">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,u) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,6270,a(flip),b,23455,a),flip(a)].">
      <j1 rule="hyper" parents="125 6270 23455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25041">
    <literal><![CDATA[
      x * K(y * (z \ x),u) = z * (y \ T(y * (z \ x),u))
    ]]></literal>
    <justification jstring="[para(15215(a,2),23455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15215 23455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25050">
    <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(23481(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23481 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25051">
    <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(23481(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23481 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25052">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(23481(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23481 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25058">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) * w) / (K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(23481(a,1),693(a,1,2))].">
      <j1 rule="para" parents="23481 693"/>
    </justification>
  </clause>

  <clause id="25060">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u
    ]]></literal>
    <justification jstring="[para(7858(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25061">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * u) = (T(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(7873(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7873 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25064">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) * z) * u) = ((y / x) * z) * u
    ]]></literal>
    <justification jstring="[para(8364(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8364 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25068">
    <literal><![CDATA[
      K(x,x \ y) * ((y \ z) * u) = (((x \ y) * x) \ z) * u
    ]]></literal>
    <justification jstring="[para(12088(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12088 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25070">
    <literal><![CDATA[
      K(x,y) * (((y * x) * z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[para(12466(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12466 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25073">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ u) * w) = (z \ (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[para(22739(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22739 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25078">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * w = K(x,y) * ((z * u) * w)
    ]]></literal>
    <justification jstring="[para(23481(a,2),23481(a,1,1))].">
      <j1 rule="para" parents="23481 23481"/>
    </justification>
  </clause>

  <clause id="25084">
    <literal><![CDATA[
      x / (y * K(z,z \ 1)) = (x / y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4354(a,1),23546(a,1,2))].">
      <j1 rule="para" parents="4354 23546"/>
    </justification>
  </clause>

  <clause id="25089">
    <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(23547(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23547 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25090">
    <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(23547(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23547 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25091">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(23547(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23547 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25092">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) * w) / (u * w) = R(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23547(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="23547 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25093">
    <literal><![CDATA[
      ((x * (y * K(z,u))) * w) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(23547(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="23547 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25100">
    <literal><![CDATA[
      (x * T(y,z)) * (K(z,y) * u) = (x * y) * u
    ]]></literal>
    <justification jstring="[para(5860(a,1),23547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5860 23547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25101">
    <literal><![CDATA[
      (x * y) * (K(y,z) * u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6270(a,1),23547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 23547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25107">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * u) = (x \ K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(15133(a,1),23547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15133 23547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25109">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(23454(a,1),23547(a,1,1))].">
      <j1 rule="para" parents="23454 23547"/>
    </justification>
  </clause>

  <clause id="25110">
    <literal><![CDATA[
      K(x,y) * ((z * y) \ u) = (z * T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5860(a,1),23548(a,1,2,1))].">
      <j1 rule="para" parents="5860 23548"/>
    </justification>
  </clause>

  <clause id="25112">
    <literal><![CDATA[
      K(x,y) * ((z * T(x,y)) \ u) = (z * x) \ u
    ]]></literal>
    <justification jstring="[para(6270(a,1),23548(a,1,2,1))].">
      <j1 rule="para" parents="6270 23548"/>
    </justification>
  </clause>

  <clause id="25116">
    <literal><![CDATA[
      K(x,y) * ((z \ K(x,y)) \ u) = (z \ 1) \ u
    ]]></literal>
    <justification jstring="[para(15133(a,1),23548(a,1,2,1))].">
      <j1 rule="para" parents="15133 23548"/>
    </justification>
  </clause>

  <clause id="25119">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ u) = (z \ T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(15203(a,1),23548(a,1,2,1))].">
      <j1 rule="para" parents="15203 23548"/>
    </justification>
  </clause>

  <clause id="25121">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ w = K(u,z) * ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(23453(a,1),23548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23453 23548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25122">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,T(x \ y,z),x) = K(z,x \ y) * (y \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(6415,a,23559,a)].">
      <j1 rule="hyper" parents="6415 23559"/>
    </justification>
  </clause>

  <clause id="25124">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * u) = K(z,y) * u
    ]]></literal>
    <justification jstring="[hyper(370,a,173,a(flip),b,23559,a),flip(a)].">
      <j1 rule="hyper" parents="370 173 23559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25129">
    <literal><![CDATA[
      (x * y) \ (K(z,x) * u) = (T(x,z) * y) \ u
    ]]></literal>
    <justification jstring="[para(7864(a,1),23596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 23596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25131">
    <literal><![CDATA[
      ((x \ y) * z) \ (K(x \ y,x) * u) = ((y / x) * z) \ u
    ]]></literal>
    <justification jstring="[para(8364(a,1),23596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8364 23596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25133">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) \ u = (x * (z * y)) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(12392(a,2),23596(a,1,1))].">
      <j1 rule="para" parents="12392 23596"/>
    </justification>
  </clause>

  <clause id="25134">
    <literal><![CDATA[
      (1 / x) \ (K(y,z) * u) = (K(z,y) / x) \ u
    ]]></literal>
    <justification jstring="[para(15121(a,1),23596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15121 23596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25136">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * w) = (T(x,K(y,z)) * u) \ w
    ]]></literal>
    <justification jstring="[para(22775(a,1),23596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22775 23596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25137">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,7481,a(flip),b,23599,a)].">
      <j1 rule="hyper" parents="128 7481 23599"/>
    </justification>
  </clause>

  <clause id="25138">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(103(a,1),23602(a,1,1,2))].">
      <j1 rule="para" parents="103 23602"/>
    </justification>
  </clause>

  <clause id="25141">
    <literal><![CDATA[
      K(x,y) * ((x * z) / u) = (T(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(7864(a,1),23604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7864 23604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25142">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) / u) = (y * z) / u
    ]]></literal>
    <justification jstring="[para(7908(a,1),23604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7908 23604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25143">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,7893,a,b,23710,a)].">
      <j1 rule="hyper" parents="60 7893 23710"/>
    </justification>
  </clause>

  <clause id="25145">
    <literal><![CDATA[
      L(x,y,z) * (K(x,u) * w) = L(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(23710(a,1),9583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23710 9583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25146">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(23710(a,1),15371(a,1,1))].">
      <j1 rule="para" parents="23710 15371"/>
    </justification>
  </clause>

  <clause id="25148">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) * w) = L(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(23710(a,1),23481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23710 23481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25149">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ w) = K(x,y) * w
    ]]></literal>
    <justification jstring="[para(23710(a,1),23599(a,1,1))].">
      <j1 rule="para" parents="23710 23599"/>
    </justification>
  </clause>

  <clause id="25150">
    <literal><![CDATA[
      (x \ y) \ R(T(y / x,x),z,u) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,23719,a(flip),b,7897,a)].">
      <j1 rule="hyper" parents="125 23719 7897"/>
    </justification>
  </clause>

  <clause id="25151">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,23719,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="125 23719 7860"/>
    </justification>
  </clause>

  <clause id="25154">
    <literal><![CDATA[
      K(x,R(y,z,T(u,z)) / (w / (u * z))) = K(x,((y * z) * T(u,z)) / w)
    ]]></literal>
    <justification jstring="[para(679(a,1),23723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="679 23723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25155">
    <literal><![CDATA[
      K(x,((y * z) / u) / w) = K(x,y / ((w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,23723,a(flip),b,23746,a),flip(a)].">
      <j1 rule="hyper" parents="370 23723 23746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25161">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(y \ L(y,z,u),w,v5) * x = v6
    ]]></literal>
    <justification jstring="[para(23790(a,1),489(a,1,2,1))].">
      <j1 rule="para" parents="23790 489"/>
    </justification>
  </clause>

  <clause id="25162">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) = L(y \ L(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(23790(a,1),425(a,1,2,1))].">
      <j1 rule="para" parents="23790 425"/>
    </justification>
  </clause>

  <clause id="25167">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * u) = x * (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(23798(a,1),14760(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23798 14760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25168">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = v5 * L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(23824(a,1),273(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23824 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25170">
    <literal><![CDATA[
      T(x,y \ (z * u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(22309,a,23828,a),flip(a)].">
      <j1 rule="hyper" parents="22309 23828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25176">
    <literal><![CDATA[
      T(((L(x,y,z) \ 1) \ u) / L(x,y,z),x) * L(x,y,z) = (L(x,y,z) \ 1) \ T(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(23829(a,2),2874(a,1,1))].">
      <j1 rule="para" parents="23829 2874"/>
    </justification>
  </clause>

  <clause id="25177">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(12452(a,1),23829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12452 23829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25178">
    <literal><![CDATA[
      (x / L(L(y,z,u),w,v5)) * y = y * (L(L(y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(23829(a,1),23839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23829 23839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25179">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,13070,a,b,23843,a)].">
      <j1 rule="hyper" parents="60 13070 23843"/>
    </justification>
  </clause>

  <clause id="25181">
    <literal><![CDATA[
      L(x,y,z) * (u * x) = x * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,23843,a(flip),b,2154,a),flip(a)].">
      <j1 rule="hyper" parents="129 23843 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25182">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,23843,a(flip),b,13070,a)].">
      <j1 rule="hyper" parents="128 23843 13070"/>
    </justification>
  </clause>

  <clause id="25185">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,u) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(262(a,1),23843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 23843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25193">
    <literal><![CDATA[
      T(x,a(y,z,u) \ ((y * (z * u)) \ w)) = T(x,((y * z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(82(a,1),23847(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 23847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25195">
    <literal><![CDATA[
      R(x,y,z) * (u * x) = x * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(23860(a,1),1949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23860 1949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25206">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(24027(a,1),12498(a,1))].">
      <j1 rule="para" parents="24027 12498"/>
    </justification>
  </clause>

  <clause id="25209">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (y \ 1)) / (y \ a(y,z,u)) = R(x,a(y,z,u),y \ 1)
    ]]></literal>
    <justification jstring="[para(24114(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="24114 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25210">
    <literal><![CDATA[
      (x \ a(y,z,x)) * (u * u) = a(y,z,x) * (x \ (u * u))
    ]]></literal>
    <justification jstring="[para(24116(a,1),574(a,1,1))].">
      <j1 rule="para" parents="24116 574"/>
    </justification>
  </clause>

  <clause id="25211">
    <literal><![CDATA[
      (a(x,y,z) * (z \ (u * u))) * w = (z \ a(x,y,z)) * ((u * u) * w)
    ]]></literal>
    <justification jstring="[para(24116(a,1),1192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24116 1192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25212">
    <literal><![CDATA[
      (x \ a(y,z,x)) \ (a(y,z,x) * u) = L((x \ 1) \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(24116(a,1),3410(a,2,1)),flip(a)].">
      <j1 rule="para" parents="24116 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25213">
    <literal><![CDATA[
      a(L(x \ 1,x,y),z,u) = a(L(x,x,y * x),z,u)
    ]]></literal>
    <justification jstring="[para(24923(a,1),3803(a,1,1))].">
      <j1 rule="para" parents="24923 3803"/>
    </justification>
  </clause>

  <clause id="25214">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u * x) = L(L(1 / x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(24938(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24938 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25215">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(x \ 1,x,y * x),(y * x) * x) = ((y * x) * (x * (x \ 1))) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[para(24938(a,1),669(a,1,1,1))].">
      <j1 rule="para" parents="24938 669"/>
    </justification>
  </clause>

  <clause id="25216">
    <literal><![CDATA[
      K(x,y * z) * (y * (z * x)) = (x * (y * z)) / a(y,z,x)
    ]]></literal>
    <justification jstring="[para(9(a,2),25137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 25137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25217">
    <literal><![CDATA[
      (x * y) / L(y * x,z,z) = K(x,y) * a(z,z,y * x)
    ]]></literal>
    <justification jstring="[para(3943(a,1),25137(a,1,2))].">
      <j1 rule="para" parents="3943 25137"/>
    </justification>
  </clause>

  <clause id="25218">
    <literal><![CDATA[
      K(x * y,z) * (z * ((x * y) / x)) = ((x * y) * z) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12455(a,2),25137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12455 25137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25221">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),25170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 25170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25227">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(77(a,1),25221(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 25221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25235">
    <literal><![CDATA[
      a(x,y,z) * u != z * (w * a(x,y,z))
    ]]></literal>
    <literal><![CDATA[
      z * w = u
    ]]></literal>
    <justification jstring="[para(14786(a,1),23636(a,2)),flip(b)].">
      <j1 rule="para" parents="14786 23636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25238">
    <literal><![CDATA[
      T(x * a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(24120(a,2),23794(a,1))].">
      <j1 rule="para" parents="24120 23794"/>
    </justification>
  </clause>

  <clause id="25240">
    <literal><![CDATA[
      L(x,y,(z * u) * (u \ R(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * (z * (u \ R(u,w,v5)))) = v6
    ]]></literal>
    <justification jstring="[para(2924(a,1),24037(a,1,3))].">
      <j1 rule="para" parents="2924 24037"/>
    </justification>
  </clause>

  <clause id="25241">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(3426(a,2),24037(a,1))].">
      <j1 rule="para" parents="3426 24037"/>
    </justification>
  </clause>

  <clause id="25242">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(3438(a,2),24037(a,1))].">
      <j1 rule="para" parents="3438 24037"/>
    </justification>
  </clause>

  <clause id="25243">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ R(x,y,z),x,z * y) = u
    ]]></literal>
    <justification jstring="[para(16534(a,2),24037(a,1))].">
      <j1 rule="para" parents="16534 24037"/>
    </justification>
  </clause>

  <clause id="25250">
    <literal><![CDATA[
      R(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(24046(a,1),702(a,1)),flip(b)].">
      <j1 rule="para" parents="24046 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25255">
    <literal><![CDATA[
      L(x * a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u) * x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(3931(a,1),24096(a,1))].">
      <j1 rule="para" parents="3931 24096"/>
    </justification>
  </clause>

  <clause id="25261">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,24911,a)].">
      <j1 rule="hyper" parents="60 94 24911"/>
    </justification>
  </clause>

  <clause id="25263">
    <literal><![CDATA[
      L(x,y,z * (u / (w * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(1098(a,1),24916(a,1,3))].">
      <j1 rule="para" parents="1098 24916"/>
    </justification>
  </clause>

  <clause id="25264">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(1101(a,1),24916(a,1,3))].">
      <j1 rule="para" parents="1101 24916"/>
    </justification>
  </clause>

  <clause id="25265">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2698(a,2),24916(a,1))].">
      <j1 rule="para" parents="2698 24916"/>
    </justification>
  </clause>

  <clause id="25266">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3906(a,1),24916(a,1,3))].">
      <j1 rule="para" parents="3906 24916"/>
    </justification>
  </clause>

  <clause id="25268">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * R(L(z,y,x),y,x)) = a(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,669,a(flip),b,24918,a)].">
      <j1 rule="hyper" parents="370 669 24918"/>
    </justification>
  </clause>

  <clause id="25269">
    <literal><![CDATA[
      a(x,y,z) = ((z * y) * x) \ ((z * y) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,94,a(flip),b,24918,a),flip(a)].">
      <j1 rule="hyper" parents="370 94 24918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25270">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,24918,a,b,94,a(flip))].">
      <j1 rule="hyper" parents="129 24918 94"/>
    </justification>
  </clause>

  <clause id="25271">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),v5,v6),x,z * y) = L(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(24918(a,2),112(a,2,1,1))].">
      <j1 rule="para" parents="24918 112"/>
    </justification>
  </clause>

  <clause id="25272">
    <literal><![CDATA[
      L(x,y,L(z * R(z,u,w),z,w * u)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(24918(a,2),4054(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24918 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25273">
    <literal><![CDATA[
      (a(x,y,z) \ (x \ R(x,y,z))) * ((x \ R(x,y,z)) \ 1) = L(x \ R(x,y,z),x,z * y) \ 1
    ]]></literal>
    <justification jstring="[para(24918(a,2),7784(a,1,1,1))].">
      <j1 rule="para" parents="24918 7784"/>
    </justification>
  </clause>

  <clause id="25274">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(13(a,2),24979(a,1,3,1))].">
      <j1 rule="para" parents="13 24979"/>
    </justification>
  </clause>

  <clause id="25275">
    <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(3931(a,1),24979(a,1,3))].">
      <j1 rule="para" parents="3931 24979"/>
    </justification>
  </clause>

  <clause id="25283">
    <literal><![CDATA[
      L(x,L(1 / y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(3790(a,1),25265(a,1,2))].">
      <j1 rule="para" parents="3790 25265"/>
    </justification>
  </clause>

  <clause id="25284">
    <literal><![CDATA[
      L(x,L(((y * y) \ z) * u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z * u,w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(3781(a,2),25265(a,1,2))].">
      <j1 rule="para" parents="3781 25265"/>
    </justification>
  </clause>

  <clause id="25292">
    <literal><![CDATA[
      T(K(x,x \ y) * z,y) = ((x \ y) * x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(12535,a,23614,a),flip(a)].">
      <j1 rule="hyper" parents="12535 23614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25293">
    <literal><![CDATA[
      L(x,(a(y,z,u) * w) * ((w * a(y,z,u)) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(v5,a(y,z,u) * w,a(y,z,u) * w),v6) = v7
    ]]></literal>
    <justification jstring="[para(23642(a,1),3544(a,1,2,2))].">
      <j1 rule="para" parents="23642 3544"/>
    </justification>
  </clause>

  <clause id="25294">
    <literal><![CDATA[
      T(1 / (x * a(y,z,u)),(a(y,z,u) * x) * w) = T((x * a(y,z,u)) \ 1,(x * a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(23642(a,2),7721(a,1,2))].">
      <j1 rule="para" parents="23642 7721"/>
    </justification>
  </clause>

  <clause id="25296">
    <literal><![CDATA[
      (x * y) \ ((T(x,y) * z) * u) = (y * x) \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(125,a,23720,a(flip),b,12472,a)].">
      <j1 rule="hyper" parents="125 23720 12472"/>
    </justification>
  </clause>

  <clause id="25300">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14796(a,1),23819(a,1,1))].">
      <j1 rule="para" parents="14796 23819"/>
    </justification>
  </clause>

  <clause id="25302">
    <literal><![CDATA[
      T(x * y,(x * y) \ (y * z)) = T(x * y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,11791,a(flip),b,23852,a),flip(a)].">
      <j1 rule="hyper" parents="370 11791 23852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25303">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) = x * (u / (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,14758,a(flip),b,23872,a),flip(a)].">
      <j1 rule="hyper" parents="60 14758 23872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25304">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (L(x,v5,v6) \ x) = x * (L(x,v5,v6) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14880,a(flip),b,23873,a),flip(a)].">
      <j1 rule="hyper" parents="60 14880 23873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25305">
    <literal><![CDATA[
      (x * x) * (y * (L(x,z,u) \ x)) = (L(x \ 1,z,u) \ x) * y
    ]]></literal>
    <justification jstring="[para(23873(a,1),4018(a,1,2))].">
      <j1 rule="para" parents="23873 4018"/>
    </justification>
  </clause>

  <clause id="25306">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ (R(y,z,u) * x) = w
    ]]></literal>
    <justification jstring="[para(23929(a,1),12509(a,1,2))].">
      <j1 rule="para" parents="23929 12509"/>
    </justification>
  </clause>

  <clause id="25307">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = y * (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(3016,a,23943,a)].">
      <j1 rule="hyper" parents="3016 23943"/>
    </justification>
  </clause>

  <clause id="25308">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = y * (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,2569,a,b,23943,a)].">
      <j1 rule="hyper" parents="60 2569 23943"/>
    </justification>
  </clause>

  <clause id="25309">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ R(z,u,w))) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      R(T(z \ R(z,u,w),x * y),x,y) = v5
    ]]></literal>
    <justification jstring="[para(23943(a,1),1393(a,1,2,1))].">
      <j1 rule="para" parents="23943 1393"/>
    </justification>
  </clause>

  <clause id="25310">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3583,a,23953,a)].">
      <j1 rule="hyper" parents="3583 23953"/>
    </justification>
  </clause>

  <clause id="25311">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * v5) = L(x,u,w) * (v5 / (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14700,a(flip),b,23954,a),flip(a)].">
      <j1 rule="hyper" parents="60 14700 23954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25312">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * (L(x,y,z) \ x)) = u * ((L(x,y,z) \ x) / (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,14230,a(flip),b,23954,a),flip(a)].">
      <j1 rule="hyper" parents="60 14230 23954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25314">
    <literal><![CDATA[
      (x \ y) \ (y * L(y \ (x \ y),z,u)) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(4049,a,23955,a)].">
      <j1 rule="hyper" parents="4049 23955"/>
    </justification>
  </clause>

  <clause id="25315">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,14688,a(flip),b,23955,a),flip(a)].">
      <j1 rule="hyper" parents="370 14688 23955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25316">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * u) = (x \ u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,23955,a,b,14687,a)].">
      <j1 rule="hyper" parents="125 23955 14687"/>
    </justification>
  </clause>

  <clause id="25318">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ ((z \ L(z,u,w)) * (x * y)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(125,a,23955,a,b,82,a)].">
      <j1 rule="hyper" parents="125 23955 82"/>
    </justification>
  </clause>

  <clause id="25319">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = y * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3834,a,b,23955,a)].">
      <j1 rule="hyper" parents="60 3834 23955"/>
    </justification>
  </clause>

  <clause id="25320">
    <literal><![CDATA[
      (x \ y) * (x \ L(x,z,u)) = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3831,a(flip),b,23955,a),flip(a)].">
      <j1 rule="hyper" parents="60 3831 23955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25321">
    <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(23955(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="23955 84"/>
    </justification>
  </clause>

  <clause id="25322">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ L(z,u,w))) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      R(T(z \ L(z,u,w),x * y),x,y) = v5
    ]]></literal>
    <justification jstring="[para(23955(a,1),1393(a,1,2,1))].">
      <j1 rule="para" parents="23955 1393"/>
    </justification>
  </clause>

  <clause id="25323">
    <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(23955(a,1),4174(a,1,2,2))].">
      <j1 rule="para" parents="23955 4174"/>
    </justification>
  </clause>

  <clause id="25324">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,x,x * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(23955(a,1),4175(a,1,2,2))].">
      <j1 rule="para" parents="23955 4175"/>
    </justification>
  </clause>

  <clause id="25325">
    <literal><![CDATA[
      L(T(x * y,y \ 1),z,u) \ ((y \ 1) \ R(x,y,y)) = L(x * (y \ 1),z,u) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,13794,a,b,24068,a)].">
      <j1 rule="hyper" parents="60 13794 24068"/>
    </justification>
  </clause>

  <clause id="25326">
    <literal><![CDATA[
      L(x \ y,z,u) \ T(y / x,x) = L(y / x,z,u) \ (y / x)
    ]]></literal>
    <justification jstring="[para(109(a,1),24068(a,1,1,1))].">
      <j1 rule="para" parents="109 24068"/>
    </justification>
  </clause>

  <clause id="25327">
    <literal><![CDATA[
      (x / y) * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * (y \ x) = w
    ]]></literal>
    <justification jstring="[para(24072(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="24072 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25328">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / L(x,y,z))) = u / x
    ]]></literal>
    <justification jstring="[hyper(370,a,2475,a(flip),b,24073,a),flip(a)].">
      <j1 rule="hyper" parents="370 2475 24073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25330">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) / x) * L(x,u,w) = x \ L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,10442,a(flip),b,24073,a),flip(a)].">
      <j1 rule="hyper" parents="60 10442 24073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25331">
    <literal><![CDATA[
      x * ((y / x) * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,24073,a(flip),b,2156,a)].">
      <j1 rule="hyper" parents="129 24073 2156"/>
    </justification>
  </clause>

  <clause id="25332">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(24073(a,2),10557(a,2,2))].">
      <j1 rule="para" parents="24073 10557"/>
    </justification>
  </clause>

  <clause id="25334">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2467,a,b,24078,a)].">
      <j1 rule="hyper" parents="60 2467 24078"/>
    </justification>
  </clause>

  <clause id="25335">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[para(24078(a,1),2470(a,1,1))].">
      <j1 rule="para" parents="24078 2470"/>
    </justification>
  </clause>

  <clause id="25337">
    <literal><![CDATA[
      T(x,y \ (z * (L(z,u,w) \ y))) = T(x,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(24078(a,1),23848(a,1,2,2))].">
      <j1 rule="para" parents="24078 23848"/>
    </justification>
  </clause>

  <clause id="25338">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),24102(a,2,2))].">
      <j1 rule="para" parents="23572 24102"/>
    </justification>
  </clause>

  <clause id="25339">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ (u * a(w,v5,R(x,y,z))))) = a(w,v5,R(x,y,z)) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1954,a,b,24117,a)].">
      <j1 rule="hyper" parents="370 1954 24117"/>
    </justification>
  </clause>

  <clause id="25340">
    <literal><![CDATA[
      a(x,y,z) * (z * u) != z * w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(24117(a,2),40(a,1))].">
      <j1 rule="para" parents="24117 40"/>
    </justification>
  </clause>

  <clause id="25342">
    <literal><![CDATA[
      a(x,y,z) \ (z \ u) = z \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(23999,a,24141,a)].">
      <j1 rule="hyper" parents="23999 24141"/>
    </justification>
  </clause>

  <clause id="25346">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (1 / x) = x \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(24985(a,1),5170(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24985 5170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25347">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(24990,a,5085,a),flip(a)].">
      <j1 rule="hyper" parents="24990 5085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25348">
    <literal><![CDATA[
      (x * (y \ 1)) * (K(z,u) * w) = (x * (y \ K(z,u))) * w
    ]]></literal>
    <justification jstring="[para(25021(a,1),23547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25021 23547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25349">
    <literal><![CDATA[
      K(x,y) * ((z * (u \ 1)) \ w) = (z * (u \ K(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(25021(a,1),23559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25021 23559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25351">
    <literal><![CDATA[
      (x \ (y * z)) * (K(z,u) * w) = (x \ (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[para(25038(a,1),23547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25038 23547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25352">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ z) * u) = x * ((x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,25060,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 25060 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25355">
    <literal><![CDATA[
      (T(x,y) \ z) * T(u,x \ z) = K(y,x) * (u * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(787,a,25061,a),flip(a)].">
      <j1 rule="hyper" parents="787 25061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25357">
    <literal><![CDATA[
      (x * T(y,y \ z)) * (((y \ z) \ z) \ u) = (x * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(7947(a,2),25100(a,1,2))].">
      <j1 rule="para" parents="7947 25100"/>
    </justification>
  </clause>

  <clause id="25358">
    <literal><![CDATA[
      (x * y) * (K(y,z) * R((x * T(y,z)) \ 1,u,w)) = (x * T(y,z)) \ R(x * T(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,1987,a(flip),b,25101,a),flip(a)].">
      <j1 rule="hyper" parents="370 1987 25101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25360">
    <literal><![CDATA[
      x * ((x \ K(y,z)) * u) = L(K(y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,25107,a(flip),b,2072,a)].">
      <j1 rule="hyper" parents="129 25107 2072"/>
    </justification>
  </clause>

  <clause id="25361">
    <literal><![CDATA[
      L(x,(y \ K(z,u)) * w,v5) = L(x,y * (K(z,u) * w),v5)
    ]]></literal>
    <justification jstring="[para(25107(a,1),3464(a,1,2))].">
      <j1 rule="para" parents="25107 3464"/>
    </justification>
  </clause>

  <clause id="25365">
    <literal><![CDATA[
      a(x,y,((K(z,u) \ 1) * ((T(u,z) * w) / v5)) * v6) = a(x,y,((u * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(25142(a,1),3138(a,2,3,1))].">
      <j1 rule="para" parents="25142 3138"/>
    </justification>
  </clause>

  <clause id="25367">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((x * (y \ L(y,u,w))) * T(y,z)) = a(x,y \ L(y,u,w),T(y,z))
    ]]></literal>
    <justification jstring="[para(25143(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="25143 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25368">
    <literal><![CDATA[
      L(x,T(y,z),y \ L(y,u,w)) * ((y \ L(y,u,w)) * T(y,z)) = (y \ L(y,u,w)) * (T(y,z) * T(x,L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(25143(a,1),869(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="25143 869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25369">
    <literal><![CDATA[
      T(R(R(x,y,z),u,w) / R(x,y,z),x) = T(R(x,y,z),v5) \ R(T(R(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,23967,a,b,25151,a)].">
      <j1 rule="hyper" parents="370 23967 25151"/>
    </justification>
  </clause>

  <clause id="25370">
    <literal><![CDATA[
      (x \ 1) \ ((y / (x * x)) * R((y / (x * x)) \ (x \ 1),z,u)) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13637,a,b,25151,a)].">
      <j1 rule="hyper" parents="60 13637 25151"/>
    </justification>
  </clause>

  <clause id="25371">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[para(2155(a,1),25179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2155 25179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25373">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) * (L(x,y,z) \ u) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(25182(a,1),4277(a,1,1))].">
      <j1 rule="para" parents="25182 4277"/>
    </justification>
  </clause>

  <clause id="25381">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ x = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,23953,a,b,25310,a)].">
      <j1 rule="hyper" parents="36 23953 25310"/>
    </justification>
  </clause>

  <clause id="25382">
    <literal><![CDATA[
      (x \ y) \ (y / L(x \ y,z,u)) = L(x \ y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,74,a(flip),b,25328,a),flip(a)].">
      <j1 rule="hyper" parents="125 74 25328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25384">
    <literal><![CDATA[
      T(x,(y \ L(z,u,w)) * (z \ (v5 / L(z,u,w)))) = T(x,y \ (v5 / z))
    ]]></literal>
    <justification jstring="[para(25328(a,1),25170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="25328 25170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25386">
    <literal><![CDATA[
      (1 / x) * ((y * (x * x)) * L(1 / x,z,u)) = L(1 / x,z,u) * (y * x)
    ]]></literal>
    <justification jstring="[para(855(a,1),25331(a,1,2,1))].">
      <j1 rule="para" parents="855 25331"/>
    </justification>
  </clause>

  <clause id="25387">
    <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(3845,a,25334,a),flip(a)].">
      <j1 rule="hyper" parents="3845 25334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25391">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[para(25334(a,1),23829(a,1,1))].">
      <j1 rule="para" parents="25334 23829"/>
    </justification>
  </clause>

  <clause id="25392">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(25335(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="25335 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25393">
    <literal><![CDATA[
      x * (a(y,z,x) \ 1) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(391,a,25338,a),flip(a)].">
      <j1 rule="hyper" parents="391 25338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25394">
    <literal><![CDATA[
      a(x,y,z) \ (z \ ((a(x,y,z) * a(x,y,z)) * u)) = z \ ((1 / a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(554(a,1),25342(a,2,2))].">
      <j1 rule="para" parents="554 25342"/>
    </justification>
  </clause>

  <clause id="25395">
    <literal><![CDATA[
      (L(x,y,z) \ L(x,u,w)) \ L(x,u,w) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,3838,a(flip),b,25371,a)].">
      <j1 rule="hyper" parents="125 3838 25371"/>
    </justification>
  </clause>

  <clause id="25396">
    <literal><![CDATA[
      R(x,y,y) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) * ((y \ 1) * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(1111(a,1),23461(a,1,1))].">
      <j1 rule="para" parents="1111 23461"/>
    </justification>
  </clause>

  <clause id="25401">
    <literal><![CDATA[
      (x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ K(u,w)) * (K(w,u) * y) = z
    ]]></literal>
    <justification jstring="[para(15182(a,1),23562(a,1,1))].">
      <j1 rule="para" parents="15182 23562"/>
    </justification>
  </clause>

  <clause id="25405">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(y \ L(y,z,u),w,v5) \ x = v6
    ]]></literal>
    <justification jstring="[para(23817(a,1),23845(a,1))].">
      <j1 rule="para" parents="23817 23845"/>
    </justification>
  </clause>

  <clause id="25410">
    <literal><![CDATA[
      K(x,L(y \ z,u,w)) = K(x,(v5 \ y) \ (v5 \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,18704,a,b,24162,a),flip(a)].">
      <j1 rule="hyper" parents="370 18704 24162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25413">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) != u \ z
    ]]></literal>
    <literal><![CDATA[
      (z / (y * x)) * y = u
    ]]></literal>
    <justification jstring="[para(24912(a,2),45(a,1))].">
      <j1 rule="para" parents="24912 45"/>
    </justification>
  </clause>

  <clause id="25415">
    <literal><![CDATA[
      T(x,T(L(y,z,u) * w,K(w,v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,L(T(y,T(w,v5)),z,u) \ (w \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(8490(a,2),24939(a,1,2,1))].">
      <j1 rule="para" parents="8490 24939"/>
    </justification>
  </clause>

  <clause id="25417">
    <literal><![CDATA[
      K((x \ y) \ (z \ y),y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[hyper(24945,a,23883,a)].">
      <j1 rule="hyper" parents="24945 23883"/>
    </justification>
  </clause>

  <clause id="25422">
    <literal><![CDATA[
      K(x \ (y * (z \ x)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,23451,a(flip),b,25417,a)].">
      <j1 rule="hyper" parents="60 23451 25417"/>
    </justification>
  </clause>

  <clause id="25437">
    <literal><![CDATA[
      ((x * x) \ L(y,y \ z,x * x)) \ z = T((x * x) * (z / y),y)
    ]]></literal>
    <justification jstring="[hyper(1080,a,25177,a)].">
      <j1 rule="hyper" parents="1080 25177"/>
    </justification>
  </clause>

  <clause id="25439">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(24013(a,1),25241(a,1))].">
      <j1 rule="para" parents="24013 25241"/>
    </justification>
  </clause>

  <clause id="25440">
    <literal><![CDATA[
      L(x,y,z \ a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(24114(a,1),25241(a,1,3))].">
      <j1 rule="para" parents="24114 25241"/>
    </justification>
  </clause>

  <clause id="25446">
    <literal><![CDATA[
      L(K(x,y) * z,u,u) \ (u * ((u \ K(x,y)) * (z * w))) = L(L(w,z,u \ K(x,y)),(u \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(25360(a,1),621(a,1,1))].">
      <j1 rule="para" parents="25360 621"/>
    </justification>
  </clause>

  <clause id="25449">
    <literal><![CDATA[
      K(x,(y \ z) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(25410(a,1),11061(a,1))].">
      <j1 rule="para" parents="25410 11061"/>
    </justification>
  </clause>

  <clause id="25452">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(25449,a,22285,a),flip(a)].">
      <j1 rule="hyper" parents="25449 22285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25457">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20890(a,1),25449(a,1))].">
      <j1 rule="para" parents="20890 25449"/>
    </justification>
  </clause>

  <clause id="25458">
    <literal><![CDATA[
      K(x,y \ (z * u)) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),25452(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 25452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25459">
    <literal><![CDATA[
      K(x,(y / z) \ u) = K(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(77(a,1),25452(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 25452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25465">
    <literal><![CDATA[
      T(L(1 / x,x,y) * y,x \ 1) = y / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6532,a,23841,a)].">
      <j1 rule="hyper" parents="6532 23841"/>
    </justification>
  </clause>

  <clause id="25467">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,12501,a(flip),b,24000,a),flip(a)].">
      <j1 rule="hyper" parents="370 12501 24000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25468">
    <literal><![CDATA[
      (1 / a(x,y,z)) * (u * L(a(x,y,z),w,v5)) = a(x,y,z) * (L(a(x,y,z) \ 1,w,v5) * u)
    ]]></literal>
    <justification jstring="[para(24000(a,1),4102(a,1,2))].">
      <j1 rule="para" parents="24000 4102"/>
    </justification>
  </clause>

  <clause id="25472">
    <literal><![CDATA[
      L(x \ R(x,y \ z,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),24929(a,1,3))].">
      <j1 rule="para" parents="5 24929"/>
    </justification>
  </clause>

  <clause id="25473">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),24929(a,1))].">
      <j1 rule="para" parents="94 24929"/>
    </justification>
  </clause>

  <clause id="25543">
    <literal><![CDATA[
      x \ (y * (z * (u * K(w,v5)))) = (x \ (y * (z * u))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(23454(a,1),25035(a,1,2,2))].">
      <j1 rule="para" parents="23454 25035"/>
    </justification>
  </clause>

  <clause id="25544">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,25078,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="128 25078 103"/>
    </justification>
  </clause>

  <clause id="25547">
    <literal><![CDATA[
      K(x,y) * (L(T(x,y),z,u) \ w) = L(x,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,25145,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 25145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25548">
    <literal><![CDATA[
      (L(T(x,y),z,u) * w) \ T(x,y) != v5
    ]]></literal>
    <literal><![CDATA[
      (L(x,z,u) * w) \ x = v5
    ]]></literal>
    <justification jstring="[para(25148(a,1),15371(a,1,1))].">
      <j1 rule="para" parents="25148 15371"/>
    </justification>
  </clause>

  <clause id="25549">
    <literal><![CDATA[
      L(x \ y,z,u) * (L(y / x,z,u) \ w) = K(y / x,x) * w
    ]]></literal>
    <justification jstring="[para(109(a,1),25149(a,1,1,1))].">
      <j1 rule="para" parents="109 25149"/>
    </justification>
  </clause>

  <clause id="25551">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (y * (z * w))) / w)) = K(x,a(y,z,w) / u)
    ]]></literal>
    <justification jstring="[para(19661(a,2),25155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19661 25155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25552">
    <literal><![CDATA[
      a(L(x,x,y * x),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3869,a(flip),b,25213,a),flip(a)].">
      <j1 rule="hyper" parents="60 3869 25213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25556">
    <literal><![CDATA[
      (((x * y) / x) * z) \ (x * y) = (y * z) \ ((x \ (x * y)) * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),25261(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 25261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25557">
    <literal><![CDATA[
      a(x,y,z) * ((z * y) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23995,a,25269,a)].">
      <j1 rule="hyper" parents="23995 25269"/>
    </justification>
  </clause>

  <clause id="25558">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * R(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(25269(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="25269 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25559">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ ((a(y,z,u) * x) * R(w,a(y,z,u),x)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(23620(a,2),25269(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23620 25269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25561">
    <literal><![CDATA[
      (x * y) / T(z * x,z \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(25302(a,1),308(a,1,2))].">
      <j1 rule="para" parents="25302 308"/>
    </justification>
  </clause>

  <clause id="25562">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5749(a,1),25352(a,1,2,1))].">
      <j1 rule="para" parents="5749 25352"/>
    </justification>
  </clause>

  <clause id="25563">
    <literal><![CDATA[
      T(L(x,y,z) * (L(L(x,y,z),u,w) \ L(x,u,w)),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,2198,a(flip),b,25391,a),flip(a)].">
      <j1 rule="hyper" parents="370 2198 25391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25564">
    <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(25391(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="25391 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25566">
    <literal><![CDATA[
      (x \ T(x / y,y \ 1)) * x = x / L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4854,a(flip),b,25465,a)].">
      <j1 rule="hyper" parents="60 4854 25465"/>
    </justification>
  </clause>

  <clause id="25567">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ w) = L(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(7518,a,25547,a)].">
      <j1 rule="hyper" parents="7518 25547"/>
    </justification>
  </clause>

  <clause id="25568">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,25547,a(flip),b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="129 25547 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25570">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) * (L(T(x,v5),y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(25547(a,1),7877(a,1,2))].">
      <j1 rule="para" parents="25547 7877"/>
    </justification>
  </clause>

  <clause id="25571">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (R(y,z,z) * x) = (a(y,z,z) * y) * R(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(16508(a,1),25557(a,1,2,1))].">
      <j1 rule="para" parents="16508 25557"/>
    </justification>
  </clause>

  <clause id="25572">
    <literal><![CDATA[
      (x * (x \ y)) \ ((x \ y) * z) = ((x \ y) * z) / T(y,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),25561(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 25561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25573">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ z) * u) = T(x,z) * ((x \ T(z,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,25352,a,b,25562,a)].">
      <j1 rule="hyper" parents="370 25352 25562"/>
    </justification>
  </clause>

  <clause id="25574">
    <literal><![CDATA[
      K(x,y) * (y * (L(y,z,u) \ w)) = L(T(y,x),z,u) \ (y * w)
    ]]></literal>
    <justification jstring="[para(2160(a,1),25567(a,1,2))].">
      <j1 rule="para" parents="2160 25567"/>
    </justification>
  </clause>

  <clause id="25579">
    <literal><![CDATA[
      R(a(x,y,z),u,u) != w
    ]]></literal>
    <literal><![CDATA[
      ((1 / u) * a(x,y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(2060(a,1),23645(a,1))].">
      <j1 rule="para" parents="2060 23645"/>
    </justification>
  </clause>

  <clause id="25581">
    <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(24117(a,1),23648(a,1))].">
      <j1 rule="para" parents="24117 23648"/>
    </justification>
  </clause>

  <clause id="25584">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ w),x,a(y,z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      (x * a(y,z,u)) \ w = v5
    ]]></literal>
    <justification jstring="[para(344(a,2),23805(a,1))].">
      <j1 rule="para" parents="344 23805"/>
    </justification>
  </clause>

  <clause id="25585">
    <literal><![CDATA[
      L(a(x,y,z) \ L(u,w,v5),a(x,y,z),v5 * w) != v6
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) * (v5 * w)) \ (v5 * (w * u)) = v6
    ]]></literal>
    <justification jstring="[para(670(a,2),23816(a,1))].">
      <j1 rule="para" parents="670 23816"/>
    </justification>
  </clause>

  <clause id="25588">
    <literal><![CDATA[
      L(x,y,((z * z) \ L(u,w,v5)) * (v5 * w)) = L(x,y,v5 * (w * u))
    ]]></literal>
    <justification jstring="[hyper(3575,a,24924,a)].">
      <j1 rule="hyper" parents="3575 24924"/>
    </justification>
  </clause>

  <clause id="25589">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z \ ((1 / z) \ u),w) * (w * (z \ ((1 / z) \ u)))) = L(x,y,w * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(2116(a,1),24924(a,2,3,2))].">
      <j1 rule="para" parents="2116 24924"/>
    </justification>
  </clause>

  <clause id="25593">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(1101(a,1),25263(a,1,3,2))].">
      <j1 rule="para" parents="1101 25263"/>
    </justification>
  </clause>

  <clause id="25594">
    <literal><![CDATA[
      L(x,y,z * L(u \ 1,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(3906(a,1),25263(a,1,3,2))].">
      <j1 rule="para" parents="3906 25263"/>
    </justification>
  </clause>

  <clause id="25598">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ (x * (y \ L(y,z,u)))) = w
    ]]></literal>
    <justification jstring="[para(3843(a,1),25392(a,1))].">
      <j1 rule="para" parents="3843 25392"/>
    </justification>
  </clause>

  <clause id="25600">
    <literal><![CDATA[
      K(x,y * (z \ (y \ u))) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(25457,a,25459,a),flip(a)].">
      <j1 rule="hyper" parents="25457 25459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25612">
    <literal><![CDATA[
      x * (y \ ((L(z,u,w) \ z) * v5)) = x * (y \ (v5 * (L(z,u,w) \ z)))
    ]]></literal>
    <justification jstring="[hyper(129,a,23878,a,b,4,a)].">
      <j1 rule="hyper" parents="129 23878 4"/>
    </justification>
  </clause>

  <clause id="25613">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ L(x,y,z),u) = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9925,a,b,23880,a)].">
      <j1 rule="hyper" parents="60 9925 23880"/>
    </justification>
  </clause>

  <clause id="25614">
    <literal><![CDATA[
      L(x,y,((z \ u) \ 1) \ z) = L(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(3576,a,24915,a)].">
      <j1 rule="hyper" parents="3576 24915"/>
    </justification>
  </clause>

  <clause id="25615">
    <literal><![CDATA[
      L(x,y,(z \ u) \ z) = L(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(3576,a,25614,a)].">
      <j1 rule="hyper" parents="3576 25614"/>
    </justification>
  </clause>

  <clause id="25624">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ x) * u) = (z \ T(x,y)) * u
    ]]></literal>
    <justification jstring="[para(5275(a,2),25073(a,2,1,2))].">
      <j1 rule="para" parents="5275 25073"/>
    </justification>
  </clause>

  <clause id="25625">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) \ (x * (u * (L(x,y,z) \ x))) = L(T(x,u),u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(25167(a,1),270(a,1,2))].">
      <j1 rule="para" parents="25167 270"/>
    </justification>
  </clause>

  <clause id="25626">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * (L(x,y,z) \ 1)) = x * (L(x,y,z) \ ((1 / L(x,y,z)) * x))
    ]]></literal>
    <justification jstring="[para(2073(a,2),25167(a,2,2))].">
      <j1 rule="para" parents="2073 25167"/>
    </justification>
  </clause>

  <clause id="25628">
    <literal><![CDATA[
      L(a(x,y,z) * (z \ (u * u)),w,v5) * v6 = L(z \ a(x,y,z),w,v5) * ((u * u) * v6)
    ]]></literal>
    <justification jstring="[para(25210(a,1),3900(a,1,1,1))].">
      <j1 rule="para" parents="25210 3900"/>
    </justification>
  </clause>

  <clause id="25629">
    <literal><![CDATA[
      L(x * y,z,z) \ (y * x) = K(y,x) * a(z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12770,a(flip),b,25217,a)].">
      <j1 rule="hyper" parents="60 12770 25217"/>
    </justification>
  </clause>

  <clause id="25630">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) = x * ((L(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(23872(a,1),25303(a,2,2))].">
      <j1 rule="para" parents="23872 25303"/>
    </justification>
  </clause>

  <clause id="25631">
    <literal><![CDATA[
      (x * R(x \ (a(y,z,u) \ x),w,v5)) * a(y,z,u) = x * (a(y,z,u) \ R(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(23637,a,25307,a)].">
      <j1 rule="hyper" parents="23637 25307"/>
    </justification>
  </clause>

  <clause id="25632">
    <literal><![CDATA[
      R(T(x,y * z),y,z) \ R(R(T(x,y * z),y,z),u,w) = (y * z) \ ((y * (x \ R(x,u,w))) * z)
    ]]></literal>
    <justification jstring="[para(25308(a,1),13791(a,2,2,1))].">
      <j1 rule="para" parents="25308 13791"/>
    </justification>
  </clause>

  <clause id="25634">
    <literal><![CDATA[
      ((x \ y) \ y) \ L((x \ y) \ y,z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3967,a,25314,a)].">
      <j1 rule="hyper" parents="3967 25314"/>
    </justification>
  </clause>

  <clause id="25636">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) \ (((x \ L(x,z,u)) * x) * y) = a(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(25315(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25315 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25637">
    <literal><![CDATA[
      (x \ (((x \ L(x,y,z)) \ x) * u)) * (x \ L(x,y,z)) = L(u,(x \ L(x,y,z)) \ x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1061,a,25316,a),flip(a)].">
      <j1 rule="hyper" parents="1061 25316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25638">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(2584,a,25319,a),flip(a)].">
      <j1 rule="hyper" parents="2584 25319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25639">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(845,a,25332,a)].">
      <j1 rule="hyper" parents="845 25332"/>
    </justification>
  </clause>

  <clause id="25640">
    <literal><![CDATA[
      T(x,y \ (z * (L(z,u,w) \ y))) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,23629,a(flip),b,25337,a),flip(a)].">
      <j1 rule="hyper" parents="370 23629 25337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25641">
    <literal><![CDATA[
      T(x,y \ (z * (L(z,u,w) \ y))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(25337(a,2),23876(a,1))].">
      <j1 rule="para" parents="25337 23876"/>
    </justification>
  </clause>

  <clause id="25643">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(25640(a,1),308(a,1,2))].">
      <j1 rule="para" parents="25640 308"/>
    </justification>
  </clause>

  <clause id="25644">
    <literal><![CDATA[
      (x \ y) \ (L(y / x,z,u) \ y) = L(x \ y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(12743(a,1),25382(a,1,2))].">
      <j1 rule="para" parents="12743 25382"/>
    </justification>
  </clause>

  <clause id="25654">
    <literal><![CDATA[
      T(x,y) \ (L(1 / x,z,u) \ L(w,x,x)) = L(T(x,y),z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(125,a,4100,a,b,25568,a)].">
      <j1 rule="hyper" parents="125 4100 25568"/>
    </justification>
  </clause>

  <clause id="25655">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) != x * w
    ]]></literal>
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = w
    ]]></literal>
    <justification jstring="[para(25630(a,2),40(a,1))].">
      <j1 rule="para" parents="25630 40"/>
    </justification>
  </clause>

  <clause id="25656">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * L(((z * x) * y) \ (x * y),u,w)) = R(z,x,y) \ L(((z * x) * y) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(15(a,2),25638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 25638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25657">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = L(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(156,a,25644,a)].">
      <j1 rule="hyper" parents="156 25644"/>
    </justification>
  </clause>

  <clause id="25661">
    <literal><![CDATA[
      L(R(x,y,z) / x,x,z * y) \ R(x,y,z) = (x \ R(x,y,z)) * (a(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(24918(a,2),25657(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24918 25657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25662">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * ((y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,23454,a(flip),b,23456,a),flip(a)].">
      <j1 rule="hyper" parents="370 23454 23456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25665">
    <literal><![CDATA[
      T(x,(y * z) \ (u \ ((u * y) * w))) = T(x,L(z,y,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(24939,a,23855,a)].">
      <j1 rule="hyper" parents="24939 23855"/>
    </justification>
  </clause>

  <clause id="25667">
    <literal><![CDATA[
      K(x,y * z) * (y * (z * x)) = a(y,z,x) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,23572,a(flip),b,25216,a),flip(a)].">
      <j1 rule="hyper" parents="370 23572 25216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25668">
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),z,w * u)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(4149,a,25272,a)].">
      <j1 rule="hyper" parents="4149 25272"/>
    </justification>
  </clause>

  <clause id="25672">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25138,a(flip),b,25544,a),flip(a)].">
      <j1 rule="hyper" parents="60 25138 25544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25674">
    <literal><![CDATA[
      R(K(x,y) * T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,8712,a(flip),b,25672,a),flip(a)].">
      <j1 rule="hyper" parents="370 8712 25672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25675">
    <literal><![CDATA[
      x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,25672,a,b,7857,a)].">
      <j1 rule="hyper" parents="129 25672 7857"/>
    </justification>
  </clause>

  <clause id="25677">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = K(y,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4746(a,1),25672(a,1,1))].">
      <j1 rule="para" parents="4746 25672"/>
    </justification>
  </clause>

  <clause id="25680">
    <literal><![CDATA[
      (x * R(K(y,z) * (K(z,y) * (x \ u)),w,v5)) * K(z,y) = x * R(x \ (u * K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(25672(a,2),7704(a,1,1,2))].">
      <j1 rule="para" parents="25672 7704"/>
    </justification>
  </clause>

  <clause id="25681">
    <literal><![CDATA[
      x * R(K(y \ x,y) * (((y \ x) * y) \ z),u,w) = (y \ x) * (y * R(y \ ((y \ x) \ z),u,w))
    ]]></literal>
    <justification jstring="[para(25672(a,2),12096(a,1,2))].">
      <j1 rule="para" parents="25672 12096"/>
    </justification>
  </clause>

  <clause id="25682">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) \ v5 = R(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(25672(a,2),23596(a,1,1))].">
      <j1 rule="para" parents="25672 23596"/>
    </justification>
  </clause>

  <clause id="25686">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(7858(a,1),25675(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7858 25675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25687">
    <literal><![CDATA[
      R(x * K(y,z),u,w) = R(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8711(a,1),25674(a,1,1))].">
      <j1 rule="para" parents="8711 25674"/>
    </justification>
  </clause>

  <clause id="25688">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,12260,a,b,25687,a)].">
      <j1 rule="hyper" parents="370 12260 25687"/>
    </justification>
  </clause>

  <clause id="25690">
    <literal><![CDATA[
      x \ R(y * K(z,u),w,v5) = (x \ R(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,25687,a,b,23455,a)].">
      <j1 rule="hyper" parents="125 25687 23455"/>
    </justification>
  </clause>

  <clause id="25695">
    <literal><![CDATA[
      R(x * K(y,z),u,w) * v5 = R(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(25687(a,2),23547(a,1,1))].">
      <j1 rule="para" parents="25687 23547"/>
    </justification>
  </clause>

  <clause id="25696">
    <literal><![CDATA[
      R(x * K(y,z),u,w) \ v5 = K(z,y) * (R(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(25687(a,2),23559(a,1,1))].">
      <j1 rule="para" parents="25687 23559"/>
    </justification>
  </clause>

  <clause id="25699">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(w * u) \ ((z * u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(25688(a,1),24038(a,1,3))].">
      <j1 rule="para" parents="25688 24038"/>
    </justification>
  </clause>

  <clause id="25700">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = R(z * K(y,x),y,x) \ L(((z * y) * x) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(25688(a,1),25638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25688 25638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25705">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2926,a(flip),b,25686,a)].">
      <j1 rule="hyper" parents="60 2926 25686"/>
    </justification>
  </clause>

  <clause id="25706">
    <literal><![CDATA[
      T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (T(x,z) * R(T(x,z) \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(25686(a,1),7762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25686 7762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25707">
    <literal><![CDATA[
      ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ (u * z)),w,v5)) = (x * R(x \ u,w,v5)) * z
    ]]></literal>
    <justification jstring="[para(25686(a,1),2646(a,2,1))].">
      <j1 rule="para" parents="25686 2646"/>
    </justification>
  </clause>

  <clause id="25710">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(u,w) = x * R(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,2144,a(flip),b,25690,a),flip(a)].">
      <j1 rule="hyper" parents="60 2144 25690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25713">
    <literal><![CDATA[
      x * R(x \ K(y,z),u,u) = a(x,u,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(16509(a,1),25710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16509 25710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25715">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ 1))) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(25593,a,xx),flip(a)].">
      <j1 rule="hyper" parents="25593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25718">
    <literal><![CDATA[
      L(x,y,z * (u * ((w * w) \ v5))) = L(x,y,z * (u * (v5 \ (w * w))))
    ]]></literal>
    <justification jstring="[para(578(a,1),25715(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="578 25715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25719">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,v5) \ u)) = L(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2162(a,1),25715(a,1,3,2))].">
      <j1 rule="para" parents="2162 25715"/>
    </justification>
  </clause>

  <clause id="25720">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * ((w \ 1) \ 1))) = L(x,y,z * L(u * (1 / w),w,w))
    ]]></literal>
    <justification jstring="[para(4641(a,2),25715(a,2,3,2))].">
      <j1 rule="para" parents="4641 25715"/>
    </justification>
  </clause>

  <clause id="25721">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(23454(a,1),25662(a,2,2))].">
      <j1 rule="para" parents="23454 25662"/>
    </justification>
  </clause>

  <clause id="25722">
    <literal><![CDATA[
      T(x,y \ (z \ (u \ ((u * z) * w)))) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(24939,a,25665,a)].">
      <j1 rule="hyper" parents="24939 25665"/>
    </justification>
  </clause>

  <clause id="25723">
    <literal><![CDATA[
      T(x,L(y \ z,y,u) \ w) = T(x,z \ (u \ ((u * y) * w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),25665(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 25665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25724">
    <literal><![CDATA[
      K(x,y * z) * (y * (z * x)) = x * (a(y,z,x) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,25338,a(flip),b,25667,a),flip(a)].">
      <j1 rule="hyper" parents="370 25338 25667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25725">
    <literal><![CDATA[
      L(x * K(y,z),u,w) = L(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(625,a,25721,a)].">
      <j1 rule="hyper" parents="625 25721"/>
    </justification>
  </clause>

  <clause id="25727">
    <literal><![CDATA[
      K(x,y) * L(K(x,y) \ z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3904,a,25725,a)].">
      <j1 rule="hyper" parents="3904 25725"/>
    </justification>
  </clause>

  <clause id="25728">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = K(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3879,a,25725,a),flip(a)].">
      <j1 rule="hyper" parents="3879 25725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25729">
    <literal><![CDATA[
      x \ L(y * K(z,u),w,v5) = (x \ L(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,25725,a,b,23455,a)].">
      <j1 rule="hyper" parents="125 25725 23455"/>
    </justification>
  </clause>

  <clause id="25731">
    <literal><![CDATA[
      L(x \ y,z,u) * K(x,x \ y) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(5279(a,1),25725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5279 25725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25738">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * L(y * K(w,v5),z,u)) = K(w,v5)
    ]]></literal>
    <justification jstring="[para(25725(a,2),23445(a,1,2,2))].">
      <j1 rule="para" parents="25725 23445"/>
    </justification>
  </clause>

  <clause id="25739">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(u,w) = x * L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[para(25727(a,1),3834(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25727 3834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25740">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(25727(a,1),7232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25727 7232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25741">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(7506(a,1),25727(a,1,2,1))].">
      <j1 rule="para" parents="7506 25727"/>
    </justification>
  </clause>

  <clause id="25742">
    <literal><![CDATA[
      K(x,y) * L(T(x,y) \ z,u,w) = L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(7853(a,1),25727(a,1,2,1))].">
      <j1 rule="para" parents="7853 25727"/>
    </justification>
  </clause>

  <clause id="25743">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,u,w)) = z * L(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(25727(a,1),25319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25727 25319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25744">
    <literal><![CDATA[
      (x \ y) * L(K(x,x \ y) * z,u,w) = (y / x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,25728,a,b,8382,a)].">
      <j1 rule="hyper" parents="129 25728 8382"/>
    </justification>
  </clause>

  <clause id="25748">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) * v5 = K(x,y) * (L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(25728(a,2),23481(a,1,1))].">
      <j1 rule="para" parents="25728 23481"/>
    </justification>
  </clause>

  <clause id="25749">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ v5 = L(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(25728(a,2),23596(a,1,1))].">
      <j1 rule="para" parents="25728 23596"/>
    </justification>
  </clause>

  <clause id="25750">
    <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(25728(a,2),24042(a,1,1))].">
      <j1 rule="para" parents="25728 24042"/>
    </justification>
  </clause>

  <clause id="25751">
    <literal><![CDATA[
      K(x,y) * L(z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(25741(a,1),7537(a,1,2)),flip(b)].">
      <j1 rule="para" parents="25741 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25753">
    <literal><![CDATA[
      L(x / y,z,u) \ (L(y \ x,z,u) * w) = K(y \ x,y) * w
    ]]></literal>
    <justification jstring="[para(25731(a,1),25124(a,1,1))].">
      <j1 rule="para" parents="25731 25124"/>
    </justification>
  </clause>

  <clause id="25755">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(y,w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(5256(a,2),25729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5256 25729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25756">
    <literal><![CDATA[
      x \ L(R(y * K(z,u),w,v5),v6,v7) = (x \ L(R(y,w,v5),v6,v7)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(25687(a,2),25729(a,1,2,1))].">
      <j1 rule="para" parents="25687 25729"/>
    </justification>
  </clause>

  <clause id="25758">
    <literal><![CDATA[
      (x * L(y \ T(z,u),w,v5)) \ (x * L(y \ z,w,v5)) = K(u,z)
    ]]></literal>
    <justification jstring="[para(15203(a,1),25738(a,1,2,2,1))].">
      <j1 rule="para" parents="15203 25738"/>
    </justification>
  </clause>

  <clause id="25759">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),w) = x * L(x \ T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3194,a(flip),b,25740,a)].">
      <j1 rule="hyper" parents="60 3194 25740"/>
    </justification>
  </clause>

  <clause id="25761">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(25740(a,1),2435(a,2,2))].">
      <j1 rule="para" parents="25740 2435"/>
    </justification>
  </clause>

  <clause id="25764">
    <literal><![CDATA[
      K(x,y) * (z * L(z \ K(y,x),u,w)) = z \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(7518,a,25743,a)].">
      <j1 rule="hyper" parents="7518 25743"/>
    </justification>
  </clause>

  <clause id="25766">
    <literal><![CDATA[
      (R(L(K(x,y) * z,u,w),v5,v6) \ L(K(x,y) * z,u,w)) \ 1 = L(z,u,w) \ (K(y,x) * R(L(K(x,y) * z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,13572,a,b,25749,a)].">
      <j1 rule="hyper" parents="60 13572 25749"/>
    </justification>
  </clause>

  <clause id="25767">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ (K(z * y,u) * w),v5) = L(x,((u * z) \ ((z * y) * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25749(a,1),16148(a,1,2))].">
      <j1 rule="para" parents="25749 16148"/>
    </justification>
  </clause>

  <clause id="25768">
    <literal><![CDATA[
      L(R(K(x,y) * z,u,w),v5,v6) \ v7 = L(R(z,u,w),v5,v6) \ (K(y,x) * v7)
    ]]></literal>
    <justification jstring="[para(25672(a,2),25749(a,1,1,1))].">
      <j1 rule="para" parents="25672 25749"/>
    </justification>
  </clause>

  <clause id="25771">
    <literal><![CDATA[
      T(x,L(y,z,u) \ L(w,z,u)) = T(x,y \ (z \ (z * w)))
    ]]></literal>
    <justification jstring="[para(341(a,1),25722(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="341 25722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25772">
    <literal><![CDATA[
      T(x,L(y,z,u) \ L(w,z,u)) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(4(a,1),25771(a,2,2,2))].">
      <j1 rule="para" parents="4 25771"/>
    </justification>
  </clause>

  <clause id="25773">
    <literal><![CDATA[
      x * (a(y,z,x) \ (y * z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,23712,a(flip),b,25724,a),flip(a)].">
      <j1 rule="hyper" parents="60 23712 25724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25774">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = a(x,y,z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(31,a,25331,a,b,25773,a)].">
      <j1 rule="hyper" parents="31 25331 25773"/>
    </justification>
  </clause>

  <clause id="25775">
    <literal><![CDATA[
      a(x,y,y) \ (x * y) = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(31,a,25181,a(flip),b,25773,a),flip(a)].">
      <j1 rule="hyper" parents="31 25181 25773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25776">
    <literal><![CDATA[
      a(x,y,y) \ (x * y) != x * z
    ]]></literal>
    <literal><![CDATA[
      L(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(25775(a,2),40(a,1))].">
      <j1 rule="para" parents="25775 40"/>
    </justification>
  </clause>

  <clause id="25777">
    <literal><![CDATA[
      a(x,y,z) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(2493,a,25774,a),flip(a)].">
      <j1 rule="hyper" parents="2493 25774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25778">
    <literal><![CDATA[
      a(x,T(y,x),z) \ (x * T(y,x)) = ((y * x) / z) * L(z,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),25774(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 25774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25779">
    <literal><![CDATA[
      a(x,y,z) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (y * z)) / z = u
    ]]></literal>
    <justification jstring="[para(25774(a,1),2493(a,1))].">
      <j1 rule="para" parents="25774 2493"/>
    </justification>
  </clause>

  <clause id="25780">
    <literal><![CDATA[
      (a(x,y,z) \ (x * y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(155,a,25777,a(flip))].">
      <j1 rule="hyper" parents="155 25777"/>
    </justification>
  </clause>

  <clause id="25781">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(25777(a,1),23619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25777 23619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25782">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(25777(a,1),24094(a,1,1))].">
      <j1 rule="para" parents="25777 24094"/>
    </justification>
  </clause>

  <clause id="25783">
    <literal><![CDATA[
      (a(x,x \ y,z) \ y) * z = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),25780(a,1,1,2))].">
      <j1 rule="para" parents="5 25780"/>
    </justification>
  </clause>

  <clause id="25784">
    <literal><![CDATA[
      (a(x,T(y,x),z) \ (y * x)) * z = x * ((x \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),25783(a,1,1,1,2))].">
      <j1 rule="para" parents="17 25783"/>
    </justification>
  </clause>

  <clause id="25786">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * w) * a(y,z,u)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,23620,a(flip),b,23651,a)].">
      <j1 rule="hyper" parents="125 23620 23651"/>
    </justification>
  </clause>

  <clause id="25787">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,23640,a(flip),b,23652,a),flip(a)].">
      <j1 rule="hyper" parents="370 23640 23652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25788">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ x) * (a(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(24103(a,1),1122(a,1))].">
      <j1 rule="para" parents="24103 1122"/>
    </justification>
  </clause>

  <clause id="25789">
    <literal><![CDATA[
      1 * ((a(x,y,z) * u) \ ((u * w) * a(x,y,z))) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,24122,a,b,62,a)].">
      <j1 rule="hyper" parents="129 24122 62"/>
    </justification>
  </clause>

  <clause id="25790">
    <literal><![CDATA[
      (x * a(y,z,u)) * T(a(w,v5,v6),v7) = a(w,v5,v6) * (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(23518(a,2),24142(a,2,2)),flip(a)].">
      <j1 rule="para" parents="23518 24142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25791">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = (y \ x) \ R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),25150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="109 25150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25792">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,2514,a(flip),b,25791,a),flip(a)].">
      <j1 rule="hyper" parents="370 2514 25791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25794">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) \ (x * R(x \ (((x \ y) \ 1) \ 1),z,u)) = (x * (y \ x)) \ R(x / (((x \ y) \ 1) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(3492(a,1),25792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3492 25792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25795">
    <literal><![CDATA[
      (x \ (y * R(y \ x,z,u))) \ 1 = R(y / x,z,u) \ (y / x)
    ]]></literal>
    <justification jstring="[para(25792(a,1),13549(a,1,1))].">
      <j1 rule="para" parents="25792 13549"/>
    </justification>
  </clause>

  <clause id="25796">
    <literal><![CDATA[
      (x \ 1) \ (y * (L(x,z,u) \ x)) = (L(x \ 1,z,u) \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(14773,a,25305,a)].">
      <j1 rule="hyper" parents="14773 25305"/>
    </justification>
  </clause>

  <clause id="25797">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),25326(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 25326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25798">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ ((x \ y) \ y) = L(x,z,u) \ (y / (x \ y))
    ]]></literal>
    <justification jstring="[para(74(a,1),25797(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 25797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25799">
    <literal><![CDATA[
      L(((x * x) * y) / x,z,u) \ (((x * x) * y) / x) = L((1 / x) \ y,z,u) \ (x \ ((x * x) * y))
    ]]></literal>
    <justification jstring="[para(554(a,1),25797(a,2,1,1))].">
      <j1 rule="para" parents="554 25797"/>
    </justification>
  </clause>

  <clause id="25800">
    <literal><![CDATA[
      x * ((y * y) \ (L((y * y) \ x,z,u) \ ((y * y) \ x))) = L(1 / (x / (y * y)),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(25797(a,1),3888(a,1,2,2))].">
      <j1 rule="para" parents="25797 3888"/>
    </justification>
  </clause>

  <clause id="25801">
    <literal><![CDATA[
      (x * y) * ((y \ 1) * K(z,u)) = R(x * K(z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(25396,a,25687,a(flip))].">
      <j1 rule="hyper" parents="25396 25687"/>
    </justification>
  </clause>

  <clause id="25802">
    <literal><![CDATA[
      (x * y) * (y \ K(z,u)) = R(x * K(z,u),y,y)
    ]]></literal>
    <justification jstring="[para(15133(a,1),25801(a,1,2))].">
      <j1 rule="para" parents="15133 25801"/>
    </justification>
  </clause>

  <clause id="25804">
    <literal><![CDATA[
      L(x \ y,z,u) * (L(y / x,z,u) \ w) = K(x \ y,x) * w
    ]]></literal>
    <justification jstring="[para(5674(a,1),25549(a,2,1))].">
      <j1 rule="para" parents="5674 25549"/>
    </justification>
  </clause>

  <clause id="25805">
    <literal><![CDATA[
      (((x * y) / x) * z) \ (x * y) = (y * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),25556(a,2,2,1))].">
      <j1 rule="para" parents="4 25556"/>
    </justification>
  </clause>

  <clause id="25806">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(25185(a,1),25805(a,1,1))].">
      <j1 rule="para" parents="25185 25805"/>
    </justification>
  </clause>

  <clause id="25807">
    <literal><![CDATA[
      L((x \ (L(x,y,z) * u)) \ u,x \ (L(x,y,z) * u),x) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(1207,a,25806,a)].">
      <j1 rule="hyper" parents="1207 25806"/>
    </justification>
  </clause>

  <clause id="25808">
    <literal><![CDATA[
      T((x * y) \ (x * L(y,z,u)),(L(y,z,u) * x) \ (y * x)) = (((x * y) \ (x * L(y,z,u))) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(25806(a,2),3511(a,1,2))].">
      <j1 rule="para" parents="25806 3511"/>
    </justification>
  </clause>

  <clause id="25809">
    <literal><![CDATA[
      ((x \ y) * z) / T(y,x \ z) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(404,a,25572,a),flip(a)].">
      <j1 rule="hyper" parents="404 25572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25812">
    <literal><![CDATA[
      x * (K(y,x) * (L(x,z,u) \ w)) = L(T(x,y),z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(8443,a,25574,a)].">
      <j1 rule="hyper" parents="8443 25574"/>
    </justification>
  </clause>

  <clause id="25814">
    <literal><![CDATA[
      (x / y) * L((x / y) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(8383(a,1),25744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8383 25744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25815">
    <literal><![CDATA[
      L(1 / x,y,z) \ (L(x \ 1,y,z) * u) = K(x,x \ 1) * u
    ]]></literal>
    <justification jstring="[para(1716(a,1),25753(a,2,1))].">
      <j1 rule="para" parents="1716 25753"/>
    </justification>
  </clause>

  <clause id="25816">
    <literal><![CDATA[
      (x * L(y \ T(y * z,u),w,v5)) \ (x * L(z,w,v5)) = K(u,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),25758(a,1,2,2,1))].">
      <j1 rule="para" parents="4 25758"/>
    </justification>
  </clause>

  <clause id="25817">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * ((y * v5) * a(z,u,w))) = L(L(v5,y,a(z,u,w)),y * a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(25786(a,1),94(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25786 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25818">
    <literal><![CDATA[
      R(x / y,z,u) \ (x / y) = R(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,13550,a(flip),b,25795,a),flip(a)].">
      <j1 rule="hyper" parents="60 13550 25795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25819">
    <literal><![CDATA[
      (x \ 1) \ ((x \ (R(x \ 1,y,z) \ (x \ 1))) * u) = x \ ((R(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(25818(a,1),2139(a,1,2,1,2))].">
      <j1 rule="para" parents="25818 2139"/>
    </justification>
  </clause>

  <clause id="25820">
    <literal><![CDATA[
      L(x \ y,z,u) \ K(x \ y,x) = L(y / x,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,3,a(flip),b,25804,a)].">
      <j1 rule="hyper" parents="125 3 25804"/>
    </justification>
  </clause>

  <clause id="25821">
    <literal><![CDATA[
      L(x \ y,z,u) \ K(x \ y,(x \ 1) \ 1) = L(y / x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5428(a,2),25820(a,1,2))].">
      <j1 rule="para" parents="5428 25820"/>
    </justification>
  </clause>

  <clause id="25822">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (x * w) = x * (L(T(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[para(25567(a,1),25812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25567 25812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25824">
    <literal><![CDATA[
      T(x * L(y,z,u),K(y,w)) = L(y,z,u) * T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23594(a,1),23713(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23594 23713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25826">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,w)) * y) = R(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(23518(a,1),24130(a,2,1))].">
      <j1 rule="para" parents="23518 24130"/>
    </justification>
  </clause>

  <clause id="25828">
    <literal><![CDATA[
      T(x,a(y,z,u) \ ((y * (z * u)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(25193(a,2),24939(a,1))].">
      <j1 rule="para" parents="25193 24939"/>
    </justification>
  </clause>

  <clause id="25829">
    <literal><![CDATA[
      x * (K(y * z,x) * ((y * z) / y)) = ((y * z) * x) / L(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(8443,a,25218,a)].">
      <j1 rule="hyper" parents="8443 25218"/>
    </justification>
  </clause>

  <clause id="25830">
    <literal><![CDATA[
      T((x * x) * (y / z),z) = ((x * x) \ z) \ y
    ]]></literal>
    <justification jstring="[para(615(a,1),25437(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="615 25437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25831">
    <literal><![CDATA[
      K(x,a(y,z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (((w * (y * (z * u))) / u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(25551(a,1),23767(a,1))].">
      <j1 rule="para" parents="25551 23767"/>
    </justification>
  </clause>

  <clause id="25832">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,v5) * (v5 * w)) = L(x,y,v5 * (w * u))
    ]]></literal>
    <justification jstring="[para(3789(a,2),25588(a,1,3,1))].">
      <j1 rule="para" parents="3789 25588"/>
    </justification>
  </clause>

  <clause id="25833">
    <literal><![CDATA[
      L(x,y,z * L(u \ 1,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(25594,a,xx),flip(a)].">
      <j1 rule="hyper" parents="25594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25834">
    <literal><![CDATA[
      ((x * y) * z) / L(x,y,z) = z * (T(x * y,z) / x)
    ]]></literal>
    <justification jstring="[para(15370(a,1),25829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15370 25829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25835">
    <literal><![CDATA[
      L(x,y,z * (u * ((w * w) \ v5))) = L(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[hyper(25274,a,25832,a)].">
      <j1 rule="hyper" parents="25274 25832"/>
    </justification>
  </clause>

  <clause id="25836">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) * w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(944(a,1),25835(a,1,3,2))].">
      <j1 rule="para" parents="944 25835"/>
    </justification>
  </clause>

  <clause id="25837">
    <literal><![CDATA[
      (x * (y * L(z,u,w))) / T(x * y,z) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(23594(a,1),23856(a,1,2))].">
      <j1 rule="para" parents="23594 23856"/>
    </justification>
  </clause>

  <clause id="25840">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ ((x * a(z,u,w)) * y) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(23805,a,24123,a)].">
      <j1 rule="hyper" parents="23805 24123"/>
    </justification>
  </clause>

  <clause id="25841">
    <literal><![CDATA[
      a(x,y,z) * (u / (a(x,y,z) * a(x,y,z))) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,1098,a(flip),b,24128,a)].">
      <j1 rule="hyper" parents="60 1098 24128"/>
    </justification>
  </clause>

  <clause id="25842">
    <literal><![CDATA[
      (x \ a(y,z,x)) \ (u * a(y,z,x)) = L((x \ 1) \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,23640,a(flip),b,25212,a)].">
      <j1 rule="hyper" parents="60 23640 25212"/>
    </justification>
  </clause>

  <clause id="25843">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,y,x))) = a(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[para(529(a,1),25268(a,1,2))].">
      <j1 rule="para" parents="529 25268"/>
    </justification>
  </clause>

  <clause id="25844">
    <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(370,a,9931,a(flip),b,25387,a),flip(a)].">
      <j1 rule="hyper" parents="370 9931 25387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25845">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x * L(x,y,z),u) = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9931,a(flip),b,25613,a)].">
      <j1 rule="hyper" parents="60 9931 25613"/>
    </justification>
  </clause>

  <clause id="25846">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ (v5 * v5)))) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25835,a(flip),b,25718,a),flip(a)].">
      <j1 rule="hyper" parents="60 25835 25718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25849">
    <literal><![CDATA[
      a(x,T(y,x),z) \ (x * T(y,x)) = ((y * x) / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(12477(a,1),25778(a,2,2))].">
      <j1 rule="para" parents="12477 25778"/>
    </justification>
  </clause>

  <clause id="25850">
    <literal><![CDATA[
      1 * ((a(x,y,z) * z) \ (z * (u * a(x,y,z)))) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14786(a,1),25789(a,1,2,2))].">
      <j1 rule="para" parents="14786 25789"/>
    </justification>
  </clause>

  <clause id="25851">
    <literal><![CDATA[
      1 * ((a(x,y,z) * L(z,u,w)) \ (L(z,u,w) * (v5 * a(x,y,z)))) = L(v5,L(z,u,w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14797(a,1),25789(a,1,2,2))].">
      <j1 rule="para" parents="14797 25789"/>
    </justification>
  </clause>

  <clause id="25852">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x)) = x * ((L(x \ 1,z,u) \ x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(25796(a,1),14867(a,2,2))].">
      <j1 rule="para" parents="25796 14867"/>
    </justification>
  </clause>

  <clause id="25853">
    <literal><![CDATA[
      x * ((y \ 1) \ ((L(y,z,u) \ y) * w)) = x * ((L(y \ 1,z,u) \ y) * (y \ w))
    ]]></literal>
    <justification jstring="[para(25796(a,1),25612(a,2,2))].">
      <j1 rule="para" parents="25796 25612"/>
    </justification>
  </clause>

  <clause id="25854">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ ((x \ y) \ y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(74(a,1),25798(a,2,2))].">
      <j1 rule="para" parents="74 25798"/>
    </justification>
  </clause>

  <clause id="25857">
    <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(25814(a,1),4038(a,1))].">
      <j1 rule="para" parents="25814 4038"/>
    </justification>
  </clause>

  <clause id="25858">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),w) \ (x * L(y,z,u)) = K(w,x * y)
    ]]></literal>
    <justification jstring="[para(25759(a,2),25816(a,1,1))].">
      <j1 rule="para" parents="25759 25816"/>
    </justification>
  </clause>

  <clause id="25859">
    <literal><![CDATA[
      x * (L(x,y,z) \ K(x \ 1,(x \ 1) \ 1)) = (x \ 1) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,25821,a(flip),b,4015,a),flip(a)].">
      <j1 rule="hyper" parents="129 25821 4015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25860">
    <literal><![CDATA[
      a(x,y,z) * (u \ (w / (a(x,y,z) * a(x,y,z)))) = (u \ w) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1100(a,1),25841(a,1,2))].">
      <j1 rule="para" parents="1100 25841"/>
    </justification>
  </clause>

  <clause id="25861">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ (w * (x \ L(x,z,u)))) = R(w,x * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(25570,a,25844,a)].">
      <j1 rule="hyper" parents="25570 25844"/>
    </justification>
  </clause>

  <clause id="25862">
    <literal><![CDATA[
      R(x,y * L(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25323,a(flip),b,25844,a),flip(a)].">
      <j1 rule="hyper" parents="60 25323 25844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25863">
    <literal><![CDATA[
      T(x * L(y,z,u),w) \ (x * L(y,z,u)) = K(w,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),25858(a,1,1,1,2,1))].">
      <j1 rule="para" parents="4 25858"/>
    </justification>
  </clause>

  <clause id="25864">
    <literal><![CDATA[
      K(x,y * L(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(5710,a,25863,a)].">
      <j1 rule="hyper" parents="5710 25863"/>
    </justification>
  </clause>

  <clause id="25871">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),25864(a,2,2))].">
      <j1 rule="para" parents="5 25864"/>
    </justification>
  </clause>

  <clause id="25875">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(871(a,1),25871(a,1,2))].">
      <j1 rule="para" parents="871 25871"/>
    </justification>
  </clause>

  <clause id="25881">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),25875(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 25875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25885">
    <literal><![CDATA[
      T(x,y) \ ((y \ ((y \ 1) \ x)) * y) = R(T(T(y,x),y \ 1),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2759,a(flip),b,24054,a),flip(a)].">
      <j1 rule="hyper" parents="370 2759 24054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25886">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(23481(a,1),25052(a,1,2))].">
      <j1 rule="para" parents="23481 25052"/>
    </justification>
  </clause>

  <clause id="25887">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(23547(a,1),25091(a,1,2))].">
      <j1 rule="para" parents="23547 25091"/>
    </justification>
  </clause>

  <clause id="25888">
    <literal><![CDATA[
      ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(25109(a,1),25093(a,1,1))].">
      <j1 rule="para" parents="25109 25093"/>
    </justification>
  </clause>

  <clause id="25889">
    <literal><![CDATA[
      K(x,R(y,z,T(u,z)) / (w / (u * z))) = K(x,(y * z) / (w / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,23723,a(flip),b,25154,a),flip(a)].">
      <j1 rule="hyper" parents="370 23723 25154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25890">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) * u = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(25161,a,25639,a)].">
      <j1 rule="hyper" parents="25161 25639"/>
    </justification>
  </clause>

  <clause id="25891">
    <literal><![CDATA[
      L(x,L((1 / y) * z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(313(a,1),25284(a,1,2,1,1))].">
      <j1 rule="para" parents="313 25284"/>
    </justification>
  </clause>

  <clause id="25893">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(3846(a,1),25891(a,1,2,1))].">
      <j1 rule="para" parents="3846 25891"/>
    </justification>
  </clause>

  <clause id="25894">
    <literal><![CDATA[
      (L(x \ (y * L(y \ x,z,u)),w,v5) / (x \ y)) * L(x \ y,w,v5) = (x \ y) \ L(L(x \ y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(3823(a,1),25330(a,1,1,1,1))].">
      <j1 rule="para" parents="3823 25330"/>
    </justification>
  </clause>

  <clause id="25895">
    <literal><![CDATA[
      T(x,y) \ (L(1 / x,z,u) \ L(w,x,x)) = x * (L(T(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,25822,a(flip),b,25654,a),flip(a)].">
      <j1 rule="hyper" parents="370 25822 25654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25896">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(1199,a,25886,a)].">
      <j1 rule="hyper" parents="1199 25886"/>
    </justification>
  </clause>

  <clause id="25898">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(23601,a,25896,a),flip(a)].">
      <j1 rule="hyper" parents="23601 25896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25901">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(25896(a,1),23600(a,1)),flip(b)].">
      <j1 rule="para" parents="25896 23600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25902">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24037,a,25898,a)].">
      <j1 rule="hyper" parents="24037 25898"/>
    </justification>
  </clause>

  <clause id="25908">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),25898(a,1,3))].">
      <j1 rule="para" parents="7864 25898"/>
    </justification>
  </clause>

  <clause id="25911">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(8364(a,1),25898(a,1,3))].">
      <j1 rule="para" parents="8364 25898"/>
    </justification>
  </clause>

  <clause id="25912">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),25898(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10354 25898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25913">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * v5)) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(22739(a,1),25898(a,1,3))].">
      <j1 rule="para" parents="22739 25898"/>
    </justification>
  </clause>

  <clause id="25920">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,25091,a,b,25902,a)].">
      <j1 rule="hyper" parents="60 25091 25902"/>
    </justification>
  </clause>

  <clause id="25921">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,15190,a,b,25902,a)].">
      <j1 rule="hyper" parents="60 15190 25902"/>
    </justification>
  </clause>

  <clause id="25922">
    <literal><![CDATA[
      L(x,y,z * (u / w)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(5631(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="5631 25902"/>
    </justification>
  </clause>

  <clause id="25923">
    <literal><![CDATA[
      L(x,y,z * (u * w)) = L(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(6770(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="6770 25902"/>
    </justification>
  </clause>

  <clause id="25924">
    <literal><![CDATA[
      L(x,y,z * (u * T(w,v5))) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(6930(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="6930 25902"/>
    </justification>
  </clause>

  <clause id="25925">
    <literal><![CDATA[
      L(x,y,z * (u * K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11016(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="11016 25902"/>
    </justification>
  </clause>

  <clause id="25927">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(20260(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="20260 25902"/>
    </justification>
  </clause>

  <clause id="25928">
    <literal><![CDATA[
      L(x,y,z \ (u \ T(w,v5))) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(25036(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="25036 25902"/>
    </justification>
  </clause>

  <clause id="25929">
    <literal><![CDATA[
      L(x,y,z \ (u \ K(w,v5))) = L(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(25037(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="25037 25902"/>
    </justification>
  </clause>

  <clause id="25930">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),v5,v6)) = L(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(25687(a,2),25902(a,1,3))].">
      <j1 rule="para" parents="25687 25902"/>
    </justification>
  </clause>

  <clause id="25931">
    <literal><![CDATA[
      L(x,y,z \ L(T(u,w),v5,v6)) = L(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25755(a,1),25902(a,1,3))].">
      <j1 rule="para" parents="25755 25902"/>
    </justification>
  </clause>

  <clause id="25941">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(6130(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="6130 25901"/>
    </justification>
  </clause>

  <clause id="25942">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(7864(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="7864 25901"/>
    </justification>
  </clause>

  <clause id="25943">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(7873(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="7873 25901"/>
    </justification>
  </clause>

  <clause id="25944">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(8016(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="8016 25901"/>
    </justification>
  </clause>

  <clause id="25945">
    <literal><![CDATA[
      L(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(8364(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="8364 25901"/>
    </justification>
  </clause>

  <clause id="25946">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * v5) = v6
    ]]></literal>
    <justification jstring="[para(12016(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="12016 25901"/>
    </justification>
  </clause>

  <clause id="25948">
    <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(25110(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="25110 25901"/>
    </justification>
  </clause>

  <clause id="25949">
    <literal><![CDATA[
      L(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(5631(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="5631 25944"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      L(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(6770(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="6770 25944"/>
    </justification>
  </clause>

  <clause id="25951">
    <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(6930(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="6930 25944"/>
    </justification>
  </clause>

  <clause id="25954">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(20260(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="20260 25944"/>
    </justification>
  </clause>

  <clause id="25956">
    <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(25036(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="25036 25944"/>
    </justification>
  </clause>

  <clause id="25957">
    <literal><![CDATA[
      L(x,y,z \ L(T(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ L(u,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(25755(a,1),25944(a,1,3))].">
      <j1 rule="para" parents="25755 25944"/>
    </justification>
  </clause>

  <clause id="25960">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * z)) * v5) = L(x,y,R(w * K(u,z),u,z) * v5)
    ]]></literal>
    <justification jstring="[para(25688(a,1),25911(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="25688 25911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25962">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),v5,v6) * v7) = L(x,y,R(z,v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(25695(a,2),25912(a,1,3))].">
      <j1 rule="para" parents="25695 25912"/>
    </justification>
  </clause>

  <clause id="25963">
    <literal><![CDATA[
      L(x,y,z \ (T(u,w) \ v5)) = L(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(7858(a,1),25913(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7858 25913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25964">
    <literal><![CDATA[
      L(x,y,z \ ((T(u,w) * v5) / v6)) = L(x,y,z \ ((u * v5) / v6))
    ]]></literal>
    <justification jstring="[para(25141(a,1),25913(a,1,3,2))].">
      <j1 rule="para" parents="25141 25913"/>
    </justification>
  </clause>

  <clause id="25965">
    <literal><![CDATA[
      L(x,y,z * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(25923(a,1),3574(a,1))].">
      <j1 rule="para" parents="25923 3574"/>
    </justification>
  </clause>

  <clause id="25970">
    <literal><![CDATA[
      L(x,y,z * (u * (w / v5))) = L(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5631(a,1),25925(a,1,3,2))].">
      <j1 rule="para" parents="5631 25925"/>
    </justification>
  </clause>

  <clause id="25972">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5 * K(w,u),w,u))
    ]]></literal>
    <justification jstring="[para(25688(a,1),25927(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="25688 25927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25973">
    <literal><![CDATA[
      L(T(x,y) \ 1,T(x,y),z * x) = L(1 / T(x,y),T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(25941,a,24938,a)].">
      <j1 rule="hyper" parents="25941 24938"/>
    </justification>
  </clause>

  <clause id="25974">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ T(w,v5))) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(25941,a,4109,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="25941 4109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25976">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w / v5))) = L(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(109(a,1),25928(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="109 25928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25977">
    <literal><![CDATA[
      L(x,y,z \ (u \ K(w,v5))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3460,a(flip),b,25929,a),flip(a)].">
      <j1 rule="hyper" parents="370 3460 25929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25980">
    <literal><![CDATA[
      L(x,y,(z * u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(24013(a,1),25965(a,1))].">
      <j1 rule="para" parents="24013 25965"/>
    </justification>
  </clause>

  <clause id="25981">
    <literal><![CDATA[
      L(x,y,z * ((u \ (w * w)) \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(1258(a,1),25974(a,1,3,2))].">
      <j1 rule="para" parents="1258 25974"/>
    </justification>
  </clause>

  <clause id="25982">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * w))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(25264,a,25981,a)].">
      <j1 rule="hyper" parents="25264 25981"/>
    </justification>
  </clause>

  <clause id="25983">
    <literal><![CDATA[
      L(x,y,z * (u * (L(u,w,v5) \ u))) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2160(a,1),25982(a,1,3,2))].">
      <j1 rule="para" parents="2160 25982"/>
    </justification>
  </clause>

  <clause id="25984">
    <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(6128(a,1),25946(a,1,3,2))].">
      <j1 rule="para" parents="6128 25946"/>
    </justification>
  </clause>

  <clause id="25985">
    <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(8364(a,1),25946(a,1,3,2))].">
      <j1 rule="para" parents="8364 25946"/>
    </justification>
  </clause>

  <clause id="25989">
    <literal><![CDATA[
      L(x,y,z * (u * (1 / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(25970(a,2),25593(a,1))].">
      <j1 rule="para" parents="25970 25593"/>
    </justification>
  </clause>

  <clause id="25991">
    <literal><![CDATA[
      L(x,y,z) = (z * (K(y * x,z) * y)) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(5278(a,1),25920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5278 25920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25992">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x * y,z))) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(12587(a,1),25991(a,2,1,2))].">
      <j1 rule="para" parents="12587 25991"/>
    </justification>
  </clause>

  <clause id="25993">
    <literal><![CDATA[
      L(x,y,z) = K(z,x * y) * ((z * y) \ ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,25121,a(flip),b,25992,a),flip(a)].">
      <j1 rule="hyper" parents="370 25121 25992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25994">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((w * v5) * u))) = L(x,y,z \ L(v5,w,u))
    ]]></literal>
    <justification jstring="[para(25993(a,2),25913(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="25993 25913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25995">
    <literal><![CDATA[
      L(x,y,z \ (u \ (T(w,v5) * v6))) = L(x,y,z \ ((w * v6) / u))
    ]]></literal>
    <justification jstring="[hyper(25954,a,25964,a)].">
      <j1 rule="hyper" parents="25954 25964"/>
    </justification>
  </clause>

  <clause id="25996">
    <literal><![CDATA[
      L(x,y,z * (u * (L(u,w,v5) \ u))) = L(x,y,z * L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,25833,a,b,25983,a),flip(a)].">
      <j1 rule="hyper" parents="370 25833 25983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25997">
    <literal><![CDATA[
      L(x,y,z \ (u \ (T(w,v5) * v6))) = L(x,y,z \ (u \ (w * v6)))
    ]]></literal>
    <justification jstring="[hyper(370,a,25927,a(flip),b,25995,a),flip(a)].">
      <j1 rule="hyper" parents="370 25927 25995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25998">
    <literal><![CDATA[
      L(x,y,z \ (R(1 / u,u,T(w,v5) * v6) \ (w * v6))) = L(x,y,z \ (u * (T(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(467(a,1),25997(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="467 25997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25999">
    <literal><![CDATA[
      L(x,y,z \ (u \ (T(w / v5,v6) * (v5 * v5)))) = L(x,y,z \ (u \ (w / (1 / v5))))
    ]]></literal>
    <justification jstring="[para(856(a,1),25997(a,2,3,2,2))].">
      <j1 rule="para" parents="856 25997"/>
    </justification>
  </clause>

  <clause id="26000">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(T(v5,w),w,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),25994(a,1,3,2,2,1))].">
      <j1 rule="para" parents="107 25994"/>
    </justification>
  </clause>

  <clause id="26001">
    <literal><![CDATA[
      L(x,y,z \ ((((u * u) * w) \ (w * v5)) * (u * u))) = L(x,y,z \ L(v5,w,u * u))
    ]]></literal>
    <justification jstring="[para(513(a,1),25994(a,1,3,2))].">
      <j1 rule="para" parents="513 25994"/>
    </justification>
  </clause>

  <clause id="26002">
    <literal><![CDATA[
      L(x,y,z * (u * (L(u,w,v5) \ u))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(25996(a,2),25594(a,1))].">
      <j1 rule="para" parents="25996 25594"/>
    </justification>
  </clause>

  <clause id="26003">
    <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(1199,a,25887,a)].">
      <j1 rule="hyper" parents="1199 25887"/>
    </justification>
  </clause>

  <clause id="26004">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w * K(y,z))
    ]]></literal>
    <justification jstring="[para(23532(a,1),26003(a,1,1))].">
      <j1 rule="para" parents="23532 26003"/>
    </justification>
  </clause>

  <clause id="26005">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,25902,a(flip),b,26004,a),flip(a)].">
      <j1 rule="hyper" parents="370 25902 26004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26006">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,w),v5) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,23523,a(flip),b,26004,a),flip(a)].">
      <j1 rule="hyper" parents="370 23523 26004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26008">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26004(a,2),25944(a,1))].">
      <j1 rule="para" parents="26004 25944"/>
    </justification>
  </clause>

  <clause id="26015">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1811(a,2),26005(a,1,2))].">
      <j1 rule="para" parents="1811 26005"/>
    </justification>
  </clause>

  <clause id="26017">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5228(a,2),26005(a,1,2))].">
      <j1 rule="para" parents="5228 26005"/>
    </justification>
  </clause>

  <clause id="26018">
    <literal><![CDATA[
      L(x,y / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="5232 26005"/>
    </justification>
  </clause>

  <clause id="26019">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(5300(a,2),26005(a,1,2))].">
      <j1 rule="para" parents="5300 26005"/>
    </justification>
  </clause>

  <clause id="26020">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5302(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="5302 26005"/>
    </justification>
  </clause>

  <clause id="26021">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(6130(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="6130 26005"/>
    </justification>
  </clause>

  <clause id="26023">
    <literal><![CDATA[
      L(x,y * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="7481 26005"/>
    </justification>
  </clause>

  <clause id="26024">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7479(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="7479 26005"/>
    </justification>
  </clause>

  <clause id="26026">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(7477(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="7477 26005"/>
    </justification>
  </clause>

  <clause id="26028">
    <literal><![CDATA[
      L(x,y * K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(8016(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="8016 26005"/>
    </justification>
  </clause>

  <clause id="26029">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(7881(a,1),26005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7881 26005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26030">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(8210(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="8210 26005"/>
    </justification>
  </clause>

  <clause id="26033">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) * w,v5) = L(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(25060(a,1),26005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25060 26005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26034">
    <literal><![CDATA[
      L(x,(y * T(z,u)) \ w,v5) = L(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25110(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="25110 26005"/>
    </justification>
  </clause>

  <clause id="26037">
    <literal><![CDATA[
      L(x,(y * z) \ ((z * u) * y),w) = L(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(25993(a,2),26005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25993 26005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26039">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,T(y,w),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26015,a,b,26015,a)].">
      <j1 rule="hyper" parents="370 26015 26015"/>
    </justification>
  </clause>

  <clause id="26052">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,z * x) = L(1 / T(x,y),T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25973,a(flip),b,26015,a),flip(a)].">
      <j1 rule="hyper" parents="60 25973 26015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26053">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,x \ y,x) = K(z,x \ y) * (y \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25122,a(flip),b,26015,a),flip(a)].">
      <j1 rule="hyper" parents="60 25122 26015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26055">
    <literal><![CDATA[
      x * L(T(y,z),y,x) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,26015,a(flip),b,2481,a(flip))].">
      <j1 rule="hyper" parents="129 26015 2481"/>
    </justification>
  </clause>

  <clause id="26056">
    <literal><![CDATA[
      (x * T(y,z)) * L(u,y,x) = x * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(129,a,26015,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 26015 13"/>
    </justification>
  </clause>

  <clause id="26067">
    <literal><![CDATA[
      L(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(26015(a,1),14836(a,1))].">
      <j1 rule="para" parents="26015 14836"/>
    </justification>
  </clause>

  <clause id="26075">
    <literal><![CDATA[
      L(T(x,y),x \ K(y,x),z) = (z * (K(y,x) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(5807,a,26018,a),flip(a)].">
      <j1 rule="hyper" parents="5807 26018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26083">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),w) = L(x,(z * u) \ ((z * y) * u),w)
    ]]></literal>
    <justification jstring="[para(5349(a,2),26018(a,1,2))].">
      <j1 rule="para" parents="5349 26018"/>
    </justification>
  </clause>

  <clause id="26084">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) * (z * ((z \ y) / y)) = z * (((z \ y) / y) * x)
    ]]></literal>
    <justification jstring="[para(26018(a,1),22307(a,1,1))].">
      <j1 rule="para" parents="26018 22307"/>
    </justification>
  </clause>

  <clause id="26086">
    <literal><![CDATA[
      L(x,y,L(z,u \ w,v5) * (v5 * (w / u))) = L(x,y,v5 * ((w / u) * z))
    ]]></literal>
    <justification jstring="[para(26018(a,1),24924(a,1,3,1))].">
      <j1 rule="para" parents="26018 24924"/>
    </justification>
  </clause>

  <clause id="26087">
    <literal><![CDATA[
      L(x,y \ (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(3593,a,26019,a)].">
      <j1 rule="hyper" parents="3593 26019"/>
    </justification>
  </clause>

  <clause id="26090">
    <literal><![CDATA[
      L(x,(y * T(z,u * y)) \ (z * (u * y)),w) = L(x,R(u,y,T(z,u * y)),w)
    ]]></literal>
    <justification jstring="[para(677(a,1),26019(a,1,2,1))].">
      <j1 rule="para" parents="677 26019"/>
    </justification>
  </clause>

  <clause id="26091">
    <literal><![CDATA[
      L(x,y * z,u * w) = L(x,z * y,w * u)
    ]]></literal>
    <justification jstring="[hyper(24037,a,26023,a)].">
      <j1 rule="hyper" parents="24037 26023"/>
    </justification>
  </clause>

  <clause id="26092">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(3546,a,26023,a),flip(a)].">
      <j1 rule="hyper" parents="3546 26023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26094">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3778,a,b,26023,a)].">
      <j1 rule="hyper" parents="370 3778 26023"/>
    </justification>
  </clause>

  <clause id="26095">
    <literal><![CDATA[
      L(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(26023(a,1),3540(a,1))].">
      <j1 rule="para" parents="26023 3540"/>
    </justification>
  </clause>

  <clause id="26096">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(26023(a,1),3546(a,1))].">
      <j1 rule="para" parents="26023 3546"/>
    </justification>
  </clause>

  <clause id="26097">
    <literal><![CDATA[
      L(x,y * z,u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,w * u) = v5
    ]]></literal>
    <justification jstring="[para(26023(a,1),24037(a,1))].">
      <j1 rule="para" parents="26023 24037"/>
    </justification>
  </clause>

  <clause id="26098">
    <literal><![CDATA[
      x * L((y \ z) * y,z,x) = x / (((y \ z) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,26024,a(flip),b,2481,a(flip))].">
      <j1 rule="hyper" parents="129 26024 2481"/>
    </justification>
  </clause>

  <clause id="26103">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15139,a,b,26028,a)].">
      <j1 rule="hyper" parents="60 15139 26028"/>
    </justification>
  </clause>

  <clause id="26105">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26028(a,1,2))].">
      <j1 rule="para" parents="5631 26028"/>
    </justification>
  </clause>

  <clause id="26107">
    <literal><![CDATA[
      L(x,y * (z * K(u,w)),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(11016(a,1),26028(a,1,2))].">
      <j1 rule="para" parents="11016 26028"/>
    </justification>
  </clause>

  <clause id="26111">
    <literal><![CDATA[
      L(x,y \ (z / u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(20260(a,1),26028(a,1,2))].">
      <j1 rule="para" parents="20260 26028"/>
    </justification>
  </clause>

  <clause id="26171">
    <literal><![CDATA[
      L(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(26039(a,1),12506(a,1))].">
      <j1 rule="para" parents="26039 12506"/>
    </justification>
  </clause>

  <clause id="26182">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(20(a,2),26171(a,1,2))].">
      <j1 rule="para" parents="20 26171"/>
    </justification>
  </clause>

  <clause id="26184">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(108(a,1),26171(a,1,2))].">
      <j1 rule="para" parents="108 26171"/>
    </justification>
  </clause>

  <clause id="26186">
    <literal><![CDATA[
      L(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(14815(a,1),26171(a,1))].">
      <j1 rule="para" parents="14815 26171"/>
    </justification>
  </clause>

  <clause id="26187">
    <literal><![CDATA[
      L(x,L(T(y,T(z,u)),z,z),w) = L(x,z * (y * z),w)
    ]]></literal>
    <justification jstring="[hyper(8491,a,26021,a)].">
      <j1 rule="hyper" parents="8491 26021"/>
    </justification>
  </clause>

  <clause id="26189">
    <literal><![CDATA[
      L(x,(y * (z / u)) * u,w) = L(x,(y * (u \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(6394(a,1),26021(a,1,2))].">
      <j1 rule="para" parents="6394 26021"/>
    </justification>
  </clause>

  <clause id="26191">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(7479(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="7479 26008"/>
    </justification>
  </clause>

  <clause id="26192">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(7477(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="7477 26008"/>
    </justification>
  </clause>

  <clause id="26193">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(7873(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="7873 26008"/>
    </justification>
  </clause>

  <clause id="26195">
    <literal><![CDATA[
      L(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(8364(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="8364 26008"/>
    </justification>
  </clause>

  <clause id="26197">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(12016(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="12016 26008"/>
    </justification>
  </clause>

  <clause id="26198">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(22739(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="22739 26008"/>
    </justification>
  </clause>

  <clause id="26200">
    <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(25110(a,1),26008(a,1,2))].">
      <j1 rule="para" parents="25110 26008"/>
    </justification>
  </clause>

  <clause id="26201">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,R(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(25677(a,2),26008(a,1,2))].">
      <j1 rule="para" parents="25677 26008"/>
    </justification>
  </clause>

  <clause id="26211">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = L(y,y,x) * x
    ]]></literal>
    <justification jstring="[hyper(489,a,26055,a),flip(a)].">
      <j1 rule="hyper" parents="489 26055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26212">
    <literal><![CDATA[
      x * T(L(y,y,x),z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(20(a,1),26055(a,1,2))].">
      <j1 rule="para" parents="20 26055"/>
    </justification>
  </clause>

  <clause id="26214">
    <literal><![CDATA[
      L(x,y * (z * (u * u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),26095(a,1,2))].">
      <j1 rule="para" parents="30 26095"/>
    </justification>
  </clause>

  <clause id="26215">
    <literal><![CDATA[
      L(x,y \ (1 / z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(865(a,1),26095(a,1,2))].">
      <j1 rule="para" parents="865 26095"/>
    </justification>
  </clause>

  <clause id="26216">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(26103(a,1),26184(a,1))].">
      <j1 rule="para" parents="26103 26184"/>
    </justification>
  </clause>

  <clause id="26217">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(3778(a,2),26186(a,1))].">
      <j1 rule="para" parents="3778 26186"/>
    </justification>
  </clause>

  <clause id="26220">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(26094(a,2),26186(a,1))].">
      <j1 rule="para" parents="26094 26186"/>
    </justification>
  </clause>

  <clause id="26221">
    <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(1286(a,1),26020(a,1,2,1))].">
      <j1 rule="para" parents="1286 26020"/>
    </justification>
  </clause>

  <clause id="26225">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u) \ w,v5) = L(x,((z * u) \ ((z * y) * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(5349(a,2),26030(a,1,2,1))].">
      <j1 rule="para" parents="5349 26030"/>
    </justification>
  </clause>

  <clause id="26228">
    <literal><![CDATA[
      L(x,y * (z / (1 / u)),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3773,a(flip),b,26105,a),flip(a)].">
      <j1 rule="hyper" parents="370 3773 26105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26230">
    <literal><![CDATA[
      L(x,y * (z * (u * (1 / w))),v5) = L(x,y * (z * (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,4238,a(flip),b,26107,a)].">
      <j1 rule="hyper" parents="60 4238 26107"/>
    </justification>
  </clause>

  <clause id="26231">
    <literal><![CDATA[
      L(x,y * (z * (u / w)),v5) = L(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26107(a,1,2,2))].">
      <j1 rule="para" parents="5631 26107"/>
    </justification>
  </clause>

  <clause id="26232">
    <literal><![CDATA[
      L(x,y * (z * (u \ K(w,v5))),v6) = L(x,y * (z * (u \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(25021(a,1),26107(a,1,2,2))].">
      <j1 rule="para" parents="25021 26107"/>
    </justification>
  </clause>

  <clause id="26233">
    <literal><![CDATA[
      L(x,y \ (z \ u),x) \ x = a(x,y \ (u / z),x)
    ]]></literal>
    <justification jstring="[para(26111(a,1),11510(a,1,1))].">
      <j1 rule="para" parents="26111 11510"/>
    </justification>
  </clause>

  <clause id="26234">
    <literal><![CDATA[
      (x * T(y,z)) * u != x * (T(y,z) * w)
    ]]></literal>
    <literal><![CDATA[
      L(w,y,x) = u
    ]]></literal>
    <justification jstring="[para(26056(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="26056 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26235">
    <literal><![CDATA[
      x * (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(26056(a,1),756(a,1))].">
      <j1 rule="para" parents="26056 756"/>
    </justification>
  </clause>

  <clause id="26236">
    <literal><![CDATA[
      (T(x,y) * T(z,x)) * L(u,T(x,z),T(z,x)) = T(z,x) * (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[para(5754(a,1),26056(a,1,1))].">
      <j1 rule="para" parents="5754 26056"/>
    </justification>
  </clause>

  <clause id="26242">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(26111(a,1),26215(a,1))].">
      <j1 rule="para" parents="26111 26215"/>
    </justification>
  </clause>

  <clause id="26243">
    <literal><![CDATA[
      L(x,y \ a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(24114(a,1),26217(a,1,2))].">
      <j1 rule="para" parents="24114 26217"/>
    </justification>
  </clause>

  <clause id="26244">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(26023(a,1),26217(a,1))].">
      <j1 rule="para" parents="26023 26217"/>
    </justification>
  </clause>

  <clause id="26246">
    <literal><![CDATA[
      L(x,R(y,z,u) \ y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * R(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(1957(a,1),26220(a,1,2))].">
      <j1 rule="para" parents="1957 26220"/>
    </justification>
  </clause>

  <clause id="26253">
    <literal><![CDATA[
      L(x,y \ L(z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(2072(a,2),26244(a,1,2))].">
      <j1 rule="para" parents="2072 26244"/>
    </justification>
  </clause>

  <clause id="26254">
    <literal><![CDATA[
      L(x,((y / z) \ u) * w,v5) = L(x,((z \ y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26033(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 26033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26255">
    <literal><![CDATA[
      L(x,(K(y \ z,y) * T(z \ u,w)) \ v5,v6) = L(x,((y * (z / y)) \ u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(12097(a,1),26034(a,2,2,1))].">
      <j1 rule="para" parents="12097 26034"/>
    </justification>
  </clause>

  <clause id="26256">
    <literal><![CDATA[
      L(x,(y / z) \ (y * z),u) = L(x,(y * z) * (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4250,a(flip),b,26228,a)].">
      <j1 rule="hyper" parents="60 4250 26228"/>
    </justification>
  </clause>

  <clause id="26257">
    <literal><![CDATA[
      L(x,y * (z \ u),x) \ x = a(x,y \ (u / z),x)
    ]]></literal>
    <justification jstring="[para(14596(a,1),26233(a,1,1))].">
      <j1 rule="para" parents="14596 26233"/>
    </justification>
  </clause>

  <clause id="26258">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) = L(x,u * (z * (y \ 1)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3787,a,b,26026,a),flip(a)].">
      <j1 rule="hyper" parents="370 3787 26026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26259">
    <literal><![CDATA[
      (x * (K(y,z) / z)) \ x = L(T(z,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(26216,a,26075,a),flip(a)].">
      <j1 rule="hyper" parents="26216 26075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26261">
    <literal><![CDATA[
      L(x,y / (z \ 1),u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,z,y) * y,w * u) = v5
    ]]></literal>
    <justification jstring="[para(2480(a,1),26097(a,1,2))].">
      <j1 rule="para" parents="2480 26097"/>
    </justification>
  </clause>

  <clause id="26262">
    <literal><![CDATA[
      L(x,y * (z * y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(26182,a,26187,a),flip(a)].">
      <j1 rule="hyper" parents="26182 26187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26263">
    <literal><![CDATA[
      L(x,y * (z * y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(26187(a,1),26182(a,1))].">
      <j1 rule="para" parents="26187 26182"/>
    </justification>
  </clause>

  <clause id="26264">
    <literal><![CDATA[
      L(x,(y * z) * z,u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(26186,a,26262,a)].">
      <j1 rule="hyper" parents="26186 26262"/>
    </justification>
  </clause>

  <clause id="26267">
    <literal><![CDATA[
      T(x * K((y / z) * u,x),((y / z) * u) * x) = L(x,(z \ y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(26195,a,5498,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26195 5498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26268">
    <literal><![CDATA[
      L(x,(1 / (y / z)) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(26195,a,3389,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26195 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26269">
    <literal><![CDATA[
      L(x,(1 / (y / z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(3389(a,2),26195(a,1))].">
      <j1 rule="para" parents="3389 26195"/>
    </justification>
  </clause>

  <clause id="26270">
    <literal><![CDATA[
      L(x,y * (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(5232(a,1),26197(a,1,2,2))].">
      <j1 rule="para" parents="5232 26197"/>
    </justification>
  </clause>

  <clause id="26271">
    <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(6130(a,1),26197(a,1,2,2))].">
      <j1 rule="para" parents="6130 26197"/>
    </justification>
  </clause>

  <clause id="26272">
    <literal><![CDATA[
      L(x,(y \ K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(25361(a,2),26197(a,1))].">
      <j1 rule="para" parents="25361 26197"/>
    </justification>
  </clause>

  <clause id="26273">
    <literal><![CDATA[
      L(x,y \ (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(5232(a,1),26198(a,1,2,2))].">
      <j1 rule="para" parents="5232 26198"/>
    </justification>
  </clause>

  <clause id="26274">
    <literal><![CDATA[
      L(x,y \ (z \ K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,v5) = v6
    ]]></literal>
    <justification jstring="[para(15264(a,2),26198(a,1))].">
      <j1 rule="para" parents="15264 26198"/>
    </justification>
  </clause>

  <clause id="26275">
    <literal><![CDATA[
      L(x,(T(y,z) * u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(y * u) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(25129(a,1),26198(a,1,2))].">
      <j1 rule="para" parents="25129 26198"/>
    </justification>
  </clause>

  <clause id="26277">
    <literal><![CDATA[
      L(x,y * ((z * u) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * R(z,u,u),w) = v5
    ]]></literal>
    <justification jstring="[para(103(a,1),26214(a,1,2,2))].">
      <j1 rule="para" parents="103 26214"/>
    </justification>
  </clause>

  <clause id="26278">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,L(z,x,x)) = L(1 / T(x,y),T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(24925,a,26052,a)].">
      <j1 rule="hyper" parents="24925 26052"/>
    </justification>
  </clause>

  <clause id="26280">
    <literal><![CDATA[
      L(x,(y / z) \ (y * z),u) = L(x,a(y,z,z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3396,a(flip),b,26256,a),flip(a)].">
      <j1 rule="hyper" parents="370 3396 26256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26281">
    <literal><![CDATA[
      L(x,(y / z) \ (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * (y * z),u) = w
    ]]></literal>
    <justification jstring="[para(26256(a,2),26186(a,1))].">
      <j1 rule="para" parents="26256 26186"/>
    </justification>
  </clause>

  <clause id="26282">
    <literal><![CDATA[
      L(x,y * ((1 / z) * u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(26271,a,4041,a)].">
      <j1 rule="hyper" parents="26271 4041"/>
    </justification>
  </clause>

  <clause id="26283">
    <literal><![CDATA[
      L(x,a(y,y,y \ z),u) = L(x,(y \ z) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3969,a,b,26282,a)].">
      <j1 rule="hyper" parents="60 3969 26282"/>
    </justification>
  </clause>

  <clause id="26284">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),1 / z,1 / z),u) = L(x,(z \ 1) * ((y * (1 / z)) * z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,5152,a(flip),b,26282,a)].">
      <j1 rule="hyper" parents="60 5152 26282"/>
    </justification>
  </clause>

  <clause id="26285">
    <literal><![CDATA[
      L(x,y * ((z * u) * z),w) = L(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(579(a,1),26282(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="579 26282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26286">
    <literal><![CDATA[
      L(x,y * L(T(z,u \ 1),u,u),w) = L(x,y * R(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,4235,a(flip),b,26285,a),flip(a)].">
      <j1 rule="hyper" parents="60 4235 26285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26287">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(26258(a,1),26192(a,1))].">
      <j1 rule="para" parents="26258 26192"/>
    </justification>
  </clause>

  <clause id="26288">
    <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(2162(a,1),26287(a,1,2,2))].">
      <j1 rule="para" parents="2162 26287"/>
    </justification>
  </clause>

  <clause id="26290">
    <literal><![CDATA[
      L(x,y * (z * (u * (w \ 1))),v5) = L(x,y * (z * (u * w)),v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),26230(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="74 26230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26291">
    <literal><![CDATA[
      L(x,y * (z * (u \ K(w,v5))),v6) = L(x,y * (z * u),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,3787,a(flip),b,26232,a),flip(a)].">
      <j1 rule="hyper" parents="370 3787 26232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26292">
    <literal><![CDATA[
      L(x,y * (z * ((u * (w * w)) \ K(v5,v6))),v7) = L(x,y * ((z * u) * (w * w)),v7)
    ]]></literal>
    <justification jstring="[para(30(a,2),26291(a,2,2,2))].">
      <j1 rule="para" parents="30 26291"/>
    </justification>
  </clause>

  <clause id="26293">
    <literal><![CDATA[
      L(x,y * (z * ((u * u) \ (w \ K(v5,v6)))),v7) = L(x,y * ((z / (u * u)) * w),v7)
    ]]></literal>
    <justification jstring="[para(935(a,1),26291(a,1,2,2))].">
      <j1 rule="para" parents="935 26291"/>
    </justification>
  </clause>

  <clause id="26294">
    <literal><![CDATA[
      L(x,y * ((((1 / z) * u) * z) * (z \ K(w,v5))),v6) = L(x,y * ((z \ 1) * ((u * z) * z)),v6)
    ]]></literal>
    <justification jstring="[para(13650(a,1),26291(a,2,2,2))].">
      <j1 rule="para" parents="13650 26291"/>
    </justification>
  </clause>

  <clause id="26295">
    <literal><![CDATA[
      L(x,y * ((z \ K(u,w)) / (T(v5,z \ K(u,w)) \ 1)),v6) = L(x,y * (L(v5,v5,z \ K(u,w)) * z),v6)
    ]]></literal>
    <justification jstring="[para(26211(a,2),26291(a,1,2,2))].">
      <j1 rule="para" parents="26211 26291"/>
    </justification>
  </clause>

  <clause id="26296">
    <literal><![CDATA[
      L(x,y * (z * (u * (z \ 1))),w) = L(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(2081(a,1),26286(a,1,2,2))].">
      <j1 rule="para" parents="2081 26286"/>
    </justification>
  </clause>

  <clause id="26297">
    <literal><![CDATA[
      L(x,y * (z * (u * z)),w) = L(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26296,a(flip),b,26290,a),flip(a)].">
      <j1 rule="hyper" parents="60 26296 26290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26298">
    <literal><![CDATA[
      T(x \ y,z) * (K(z,x \ y) * (y \ (x * T(u,z)))) = T((x \ y) * (y \ (x * u)),z)
    ]]></literal>
    <justification jstring="[para(26053(a,1),3196(a,1,2))].">
      <j1 rule="para" parents="26053 3196"/>
    </justification>
  </clause>

  <clause id="26299">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),w) = L(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(26201,a,26083,a),flip(a)].">
      <j1 rule="hyper" parents="26201 26083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26300">
    <literal><![CDATA[
      L(x,(y * z) \ ((T(y,u) * w) * z),v5) = L(x,R(w,T(y,u),z),v5)
    ]]></literal>
    <justification jstring="[hyper(26275,a,26299,a)].">
      <j1 rule="hyper" parents="26275 26299"/>
    </justification>
  </clause>

  <clause id="26302">
    <literal><![CDATA[
      L(x,(y * z) \ ((z * u) * y),w) = L(x,R(u,T(z,y),y),w)
    ]]></literal>
    <justification jstring="[para(25296(a,1),26300(a,1,2))].">
      <j1 rule="para" parents="25296 26300"/>
    </justification>
  </clause>

  <clause id="26303">
    <literal><![CDATA[
      L(x,R(y,T(z,u),u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26037,a(flip),b,26302,a),flip(a)].">
      <j1 rule="hyper" parents="60 26037 26302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26304">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(25284,a,26221,a),flip(a)].">
      <j1 rule="hyper" parents="25284 26221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26305">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(26221(a,1),25284(a,1))].">
      <j1 rule="para" parents="26221 25284"/>
    </justification>
  </clause>

  <clause id="26307">
    <literal><![CDATA[
      L(x,L(L(y,z,u) \ y,w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(2162(a,1),26304(a,1,2,1))].">
      <j1 rule="para" parents="2162 26304"/>
    </justification>
  </clause>

  <clause id="26308">
    <literal><![CDATA[
      L(x,L(R(y,z,u) \ y,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * R(y,z,u),w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(1957(a,1),26305(a,1,2,1))].">
      <j1 rule="para" parents="1957 26305"/>
    </justification>
  </clause>

  <clause id="26309">
    <literal><![CDATA[
      R(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(25888(a,1),693(a,1))].">
      <j1 rule="para" parents="25888 693"/>
    </justification>
  </clause>

  <clause id="26310">
    <literal><![CDATA[
      K(x,R(y,z,T(u,z)) / (w / (u * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((w / T(u,z)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(25889(a,2),23767(a,1))].">
      <j1 rule="para" parents="25889 23767"/>
    </justification>
  </clause>

  <clause id="26311">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,25931,a(flip),b,26000,a),flip(a)].">
      <j1 rule="hyper" parents="370 25931 26000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26312">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ L(v5,w,u)) = v6
    ]]></literal>
    <justification jstring="[para(26000(a,2),25957(a,1))].">
      <j1 rule="para" parents="26000 25957"/>
    </justification>
  </clause>

  <clause id="26314">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,(u * w) \ ((v5 * w) * u)) \ L(v5,w,u)) = L(x,y,T(((u * w) \ ((v5 * w) * u)) * z,z \ 1))
    ]]></literal>
    <justification jstring="[para(6487(a,1),26311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6487 26311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26315">
    <literal><![CDATA[
      L(x,y,L(z * u,((z * u) / z) \ 1,w) * (w * (1 / ((z * u) / z)))) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(12651(a,1),26086(a,2,3,2))].">
      <j1 rule="para" parents="12651 26086"/>
    </justification>
  </clause>

  <clause id="26316">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,L((1 / y) \ 1,z,u)) = ((1 / y) \ L(1 / y,z,u)) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),23963(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 23963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26318">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (y \ 1)) / (y \ a(y,z,u)) = R(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a(flip),b,25209,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 25209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26319">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * v5) = L(x,u,w) * ((x \ L(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(23954(a,1),25311(a,2,2))].">
      <j1 rule="para" parents="23954 25311"/>
    </justification>
  </clause>

  <clause id="26320">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) \ (L(x,z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x * L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(25321(a,2),14779(a,1))].">
      <j1 rule="para" parents="25321 14779"/>
    </justification>
  </clause>

  <clause id="26323">
    <literal><![CDATA[
      (1 / x) * (y * ((x * x) * L(1 / x,z,u))) = L(1 / x,z,u) * (y * x)
    ]]></literal>
    <justification jstring="[para(29(a,1),25386(a,1,2))].">
      <j1 rule="para" parents="29 25386"/>
    </justification>
  </clause>

  <clause id="26324">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(w * u) \ ((z * u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(25930(a,1),25699(a,1))].">
      <j1 rule="para" parents="25930 25699"/>
    </justification>
  </clause>

  <clause id="26327">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * w))) / w) / u)) = K(x,z \ a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(25831,a,19349,a)].">
      <j1 rule="hyper" parents="25831 19349"/>
    </justification>
  </clause>

  <clause id="26328">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / (u * w)) / K(w \ 1,w))) = K(x,z \ a(y,K(w \ 1,w),u * w))
    ]]></literal>
    <justification jstring="[para(4401(a,1),26327(a,1,2,2,1,1,2,2))].">
      <j1 rule="para" parents="4401 26327"/>
    </justification>
  </clause>

  <clause id="26329">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / T(u,w)) / (1 / (1 / w)))) = K(x,z \ a(y,1 / (1 / w),T(u,w)))
    ]]></literal>
    <justification jstring="[para(4445(a,1),26327(a,1,2,2,1,1,2,2))].">
      <j1 rule="para" parents="4445 26327"/>
    </justification>
  </clause>

  <clause id="26330">
    <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(3733,a,26319,a),flip(a)].">
      <j1 rule="hyper" parents="3733 26319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26331">
    <literal><![CDATA[
      (1 / x) * (y * L((x * x) * (1 / x),z,u)) = L(1 / x,z,u) * (y * x)
    ]]></literal>
    <justification jstring="[para(3782(a,2),26323(a,1,2,2))].">
      <j1 rule="para" parents="3782 26323"/>
    </justification>
  </clause>

  <clause id="26332">
    <literal><![CDATA[
      L(1 / x,y,z) * (u * x) = (1 / x) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(254(a,1),26331(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="254 26331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26333">
    <literal><![CDATA[
      L(1 / x,x,x) * (y * x) = (1 / x) * (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1317(a,1),26332(a,2,2,2))].">
      <j1 rule="para" parents="1317 26332"/>
    </justification>
  </clause>

  <clause id="26334">
    <literal><![CDATA[
      (1 / x) * (y * ((x \ 1) \ 1)) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(1229(a,1),26333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1229 26333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26335">
    <literal><![CDATA[
      L(x,y,y) * ((y \ 1) \ 1) = y * ((y \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[para(26334(a,1),4148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26334 4148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26336">
    <literal><![CDATA[
      L(x,y,y) * ((y \ 1) \ 1) = L(x * y,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2074,a(flip),b,26335,a),flip(a)].">
      <j1 rule="hyper" parents="370 2074 26335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26337">
    <literal><![CDATA[
      L(x,y,y) * L(y,y,y) = L(x * y,y,y)
    ]]></literal>
    <justification jstring="[para(1317(a,2),26336(a,1,2))].">
      <j1 rule="para" parents="1317 26336"/>
    </justification>
  </clause>

  <clause id="26338">
    <literal><![CDATA[
      L(x * y,y,y) \ L(x,y,y) = L(1 / y,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(26336(a,1),3543(a,2,1)),flip(a)].">
      <j1 rule="para" parents="26336 3543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26339">
    <literal><![CDATA[
      L(x,L(y * z,z,z),u) = L(x,L(y,z,z) * z,u)
    ]]></literal>
    <justification jstring="[para(26337(a,1),14825(a,1,2))].">
      <j1 rule="para" parents="26337 14825"/>
    </justification>
  </clause>

  <clause id="26340">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * (L(x,y,z) \ x))) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3785,a(flip),b,23874,a),flip(a)].">
      <j1 rule="hyper" parents="370 3785 23874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26341">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,23628,a(flip),b,24126,a),flip(a)].">
      <j1 rule="hyper" parents="370 23628 24126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26342">
    <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(24126(a,2),23644(a,1))].">
      <j1 rule="para" parents="24126 23644"/>
    </justification>
  </clause>

  <clause id="26344">
    <literal><![CDATA[
      (a(x,y,z) * L(u,w,a(x,y,z))) \ (a(x,y,z) * (T(w,a(x,y,z)) * T(u,w * a(x,y,z)))) = L(w,a(x,y,z),L(u,w,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12491(a,2),26341(a,1,2))].">
      <j1 rule="para" parents="12491 26341"/>
    </justification>
  </clause>

  <clause id="26345">
    <literal><![CDATA[
      1 * L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(26341(a,1),25850(a,1,2))].">
      <j1 rule="para" parents="26341 25850"/>
    </justification>
  </clause>

  <clause id="26346">
    <literal><![CDATA[
      L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,26345,a)].">
      <j1 rule="hyper" parents="131 26345"/>
    </justification>
  </clause>

  <clause id="26347">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,u,y),y) = w
    ]]></literal>
    <justification jstring="[para(26345(a,1),130(a,1)),flip(b)].">
      <j1 rule="para" parents="26345 130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26348">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,a(x,y,z)) = (z \ a(x,y,z)) \ ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,14800,a(flip),b,26346,a),flip(a)].">
      <j1 rule="hyper" parents="60 14800 26346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26349">
    <literal><![CDATA[
      L(T(a(x,y,z),z) \ u,z,a(x,y,z)) = (a(x,y,z) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12489,a(flip),b,26346,a),flip(a)].">
      <j1 rule="hyper" parents="60 12489 26346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26350">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,a(x,y,z)) = (a(x,y,z) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[para(23518(a,1),26349(a,1,1,1))].">
      <j1 rule="para" parents="23518 26349"/>
    </justification>
  </clause>

  <clause id="26351">
    <literal><![CDATA[
      (x \ a(y,z,x)) \ ((x \ 1) * u) = (a(y,z,x) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26348,a(flip),b,26350,a)].">
      <j1 rule="hyper" parents="60 26348 26350"/>
    </justification>
  </clause>

  <clause id="26353">
    <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(23620(a,2),24131(a,1,2,1))].">
      <j1 rule="para" parents="23620 24131"/>
    </justification>
  </clause>

  <clause id="26354">
    <literal><![CDATA[
      L(x,y,R(z,u,T(w,z * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * w) \ (w * (z * u))) = v5
    ]]></literal>
    <justification jstring="[para(24934(a,1),25948(a,1))].">
      <j1 rule="para" parents="24934 25948"/>
    </justification>
  </clause>

  <clause id="26355">
    <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(23547(a,2),25050(a,1,2,1))].">
      <j1 rule="para" parents="23547 25050"/>
    </justification>
  </clause>

  <clause id="26356">
    <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(25078(a,1),25051(a,1,2))].">
      <j1 rule="para" parents="25078 25051"/>
    </justification>
  </clause>

  <clause id="26357">
    <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(25109(a,1),25089(a,1,2))].">
      <j1 rule="para" parents="25109 25089"/>
    </justification>
  </clause>

  <clause id="26358">
    <literal><![CDATA[
      L(x,L(y,z,u) * L(L(y,z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * L(y,w,v5),z,u),v6) = v7
    ]]></literal>
    <justification jstring="[para(10446(a,2),25893(a,1))].">
      <j1 rule="para" parents="10446 25893"/>
    </justification>
  </clause>

  <clause id="26359">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * z)) * v5) = L(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,25962,a(flip),b,25960,a),flip(a)].">
      <j1 rule="hyper" parents="370 25962 25960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26361">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,(z \ R(v5,w,u)) * K(w,u))
    ]]></literal>
    <justification jstring="[para(25690(a,1),25972(a,2,3))].">
      <j1 rule="para" parents="25690 25972"/>
    </justification>
  </clause>

  <clause id="26362">
    <literal><![CDATA[
      L(x,R(y,z,T(u,y * z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z * u) \ (u * (y * z)),w) = v5
    ]]></literal>
    <justification jstring="[para(26090(a,1),26200(a,1))].">
      <j1 rule="para" parents="26090 26200"/>
    </justification>
  </clause>

  <clause id="26363">
    <literal><![CDATA[
      L(x,((y * z) \ ((y * u) * z)) \ w,v5) = L(x,K(u,y) * (R(u,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(25696(a,1),26225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25696 26225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26364">
    <literal><![CDATA[
      (T(x,y) * T(z,x)) * L(u,x,z) = T(z,x) * (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[para(9146(a,1),26236(a,1,2))].">
      <j1 rule="para" parents="9146 26236"/>
    </justification>
  </clause>

  <clause id="26366">
    <literal><![CDATA[
      (K(x,y) * (z * x)) * L(u,x,z) = T(z,x) * (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[para(7861(a,2),26364(a,1,1))].">
      <j1 rule="para" parents="7861 26364"/>
    </justification>
  </clause>

  <clause id="26367">
    <literal><![CDATA[
      K(x,y) * ((z * x) * L(u,x,z)) = T(z,x) * (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[hyper(23605,a,26366,a)].">
      <j1 rule="hyper" parents="23605 26366"/>
    </justification>
  </clause>

  <clause id="26368">
    <literal><![CDATA[
      T(x,y) * (T(T(y,x),z) * u) = K(y,z) * (x * (y * u))
    ]]></literal>
    <justification jstring="[para(92(a,1),26367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="92 26367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26369">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25090,a(flip),b,26355,a)].">
      <j1 rule="hyper" parents="60 25090 26355"/>
    </justification>
  </clause>

  <clause id="26371">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u,w)) = a(K(u,w) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1201,a,26356,a)].">
      <j1 rule="hyper" parents="1201 26356"/>
    </justification>
  </clause>

  <clause id="26372">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23601,a,26371,a),flip(a)].">
      <j1 rule="hyper" parents="23601 26371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26373">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26371(a,1),23600(a,1)),flip(b)].">
      <j1 rule="para" parents="26371 23600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26375">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1811(a,2),26372(a,1,1))].">
      <j1 rule="para" parents="1811 26372"/>
    </justification>
  </clause>

  <clause id="26376">
    <literal><![CDATA[
      a(x / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="5232 26372"/>
    </justification>
  </clause>

  <clause id="26377">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5300(a,2),26372(a,1,1))].">
      <j1 rule="para" parents="5300 26372"/>
    </justification>
  </clause>

  <clause id="26379">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(6130(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="6130 26372"/>
    </justification>
  </clause>

  <clause id="26380">
    <literal><![CDATA[
      a(x \ T(y,z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="6128 26372"/>
    </justification>
  </clause>

  <clause id="26381">
    <literal><![CDATA[
      a(x * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="7481 26372"/>
    </justification>
  </clause>

  <clause id="26383">
    <literal><![CDATA[
      a(L(x,y,z) * (z * y),u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[para(7477(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="7477 26372"/>
    </justification>
  </clause>

  <clause id="26384">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(7858(a,1),26372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 26372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26385">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="7864 26372"/>
    </justification>
  </clause>

  <clause id="26386">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(8016(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="8016 26372"/>
    </justification>
  </clause>

  <clause id="26387">
    <literal><![CDATA[
      a((x / y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(8210(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="8210 26372"/>
    </justification>
  </clause>

  <clause id="26388">
    <literal><![CDATA[
      a((x / y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(8364(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="8364 26372"/>
    </justification>
  </clause>

  <clause id="26389">
    <literal><![CDATA[
      a(R(T(x,y),z,u) * w,v5,v6) = a(R(x,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(7913(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="7913 26372"/>
    </justification>
  </clause>

  <clause id="26390">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),26372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10354 26372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26393">
    <literal><![CDATA[
      a((T(x,y) * z) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(16495(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="16495 26372"/>
    </justification>
  </clause>

  <clause id="26394">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="22739 26372"/>
    </justification>
  </clause>

  <clause id="26395">
    <literal><![CDATA[
      a((T(x,y) \ z) * u,w,v5) = a((x \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25060(a,1),26372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25060 26372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26396">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(((y * x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25070(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="25070 26372"/>
    </justification>
  </clause>

  <clause id="26397">
    <literal><![CDATA[
      a(L(T(x,y),z,u) * w,v5,v6) = a(L(x,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25148(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="25148 26372"/>
    </justification>
  </clause>

  <clause id="26398">
    <literal><![CDATA[
      a((((x \ y) * x) \ z) * u,w,v5) = a((y \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25068(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="25068 26372"/>
    </justification>
  </clause>

  <clause id="26399">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) * w,v5,v6) = a((x \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25073(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="25073 26372"/>
    </justification>
  </clause>

  <clause id="26400">
    <literal><![CDATA[
      a((x \ T(y,z)) * u,w,v5) = a((x \ y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25624(a,1),26372(a,1,1))].">
      <j1 rule="para" parents="25624 26372"/>
    </justification>
  </clause>

  <clause id="26401">
    <literal><![CDATA[
      a(L(K(x,y) * z,u,w),v5,v6) = a(L(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(25728(a,2),26372(a,1,1))].">
      <j1 rule="para" parents="25728 26372"/>
    </justification>
  </clause>

  <clause id="26402">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(9539,a,26375,a),flip(a)].">
      <j1 rule="hyper" parents="9539 26375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26403">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,(w * w) * z,u)
    ]]></literal>
    <justification jstring="[hyper(3038,a,26375,a)].">
      <j1 rule="hyper" parents="3038 26375"/>
    </justification>
  </clause>

  <clause id="26411">
    <literal><![CDATA[
      a(x * K(y,x),z,u) = a(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5353(a,1),26375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5353 26375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26412">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(26375(a,1),9539(a,1))].">
      <j1 rule="para" parents="26375 9539"/>
    </justification>
  </clause>

  <clause id="26416">
    <literal><![CDATA[
      a(((x * x) \ y) \ z,u,w) = a((x * x) * (z / y),u,w)
    ]]></literal>
    <justification jstring="[para(25830(a,1),26375(a,1,1))].">
      <j1 rule="para" parents="25830 26375"/>
    </justification>
  </clause>

  <clause id="26420">
    <literal><![CDATA[
      (a(x,y,z) \ (y * x)) * z = x * ((x \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[para(26402(a,1),25784(a,1,1,1))].">
      <j1 rule="para" parents="26402 25784"/>
    </justification>
  </clause>

  <clause id="26421">
    <literal><![CDATA[
      a(x,y,z) \ (x * T(y,x)) = ((y * x) / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(26402(a,1),25849(a,1,1))].">
      <j1 rule="para" parents="26402 25849"/>
    </justification>
  </clause>

  <clause id="26423">
    <literal><![CDATA[
      a((((x \ y) \ 1) \ 1) \ x,z,u) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(3492(a,1),26376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3492 26376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26424">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(2978,a,26381,a),flip(a)].">
      <j1 rule="hyper" parents="2978 26381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26427">
    <literal><![CDATA[
      a((L(x,y,x) \ z) * u,w,v5) = a(u * (x \ z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,14463,a(flip),b,26381,a),flip(a)].">
      <j1 rule="hyper" parents="370 14463 26381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26428">
    <literal><![CDATA[
      a((x * y) * L(x,z,u),w,v5) = a(x * (L(x,z,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(2153(a,1),26381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2153 26381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26429">
    <literal><![CDATA[
      a((x * y) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(y,x,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(26381(a,1),2976(a,1))].">
      <j1 rule="para" parents="26381 2976"/>
    </justification>
  </clause>

  <clause id="26430">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26381(a,1),2978(a,1))].">
      <j1 rule="para" parents="26381 2978"/>
    </justification>
  </clause>

  <clause id="26431">
    <literal><![CDATA[
      a((x * x) * (L(y,z,u) * w),v5,v6) = a(w * L((x * x) * y,z,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(3791(a,1),26381(a,1,1))].">
      <j1 rule="para" parents="3791 26381"/>
    </justification>
  </clause>

  <clause id="26432">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w * v5),L(z,u,w * v5),(w * v5) * u)) = a(x,y,a(v5 * w,u,z))
    ]]></literal>
    <justification jstring="[para(26381(a,1),16008(a,2,3))].">
      <j1 rule="para" parents="26381 16008"/>
    </justification>
  </clause>

  <clause id="26437">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26369,a(flip),b,26386,a)].">
      <j1 rule="hyper" parents="60 26369 26386"/>
    </justification>
  </clause>

  <clause id="26438">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="5631 26386"/>
    </justification>
  </clause>

  <clause id="26439">
    <literal><![CDATA[
      a(x * ((y \ z) \ z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(5944(a,1),26386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5944 26386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26440">
    <literal><![CDATA[
      a(x * (y * z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(6770(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="6770 26386"/>
    </justification>
  </clause>

  <clause id="26441">
    <literal><![CDATA[
      a(x * (y * T(z,u)),w,v5) = a(x * (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(6930(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="6930 26386"/>
    </justification>
  </clause>

  <clause id="26442">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(11016(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="11016 26386"/>
    </justification>
  </clause>

  <clause id="26445">
    <literal><![CDATA[
      a(x \ (y \ T(z,u)),w,v5) = a(x \ (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(25036(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="25036 26386"/>
    </justification>
  </clause>

  <clause id="26446">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(25038(a,1),26386(a,1,1))].">
      <j1 rule="para" parents="25038 26386"/>
    </justification>
  </clause>

  <clause id="26447">
    <literal><![CDATA[
      a(R(x * K(y,z),u,w),v5,v6) = a(R(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(25687(a,2),26386(a,1,1))].">
      <j1 rule="para" parents="25687 26386"/>
    </justification>
  </clause>

  <clause id="26451">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(1811(a,2),26437(a,1,2))].">
      <j1 rule="para" parents="1811 26437"/>
    </justification>
  </clause>

  <clause id="26453">
    <literal><![CDATA[
      a(x,(y * z) / y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5228(a,2),26437(a,1,2))].">
      <j1 rule="para" parents="5228 26437"/>
    </justification>
  </clause>

  <clause id="26454">
    <literal><![CDATA[
      a(x,y / z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="5232 26437"/>
    </justification>
  </clause>

  <clause id="26456">
    <literal><![CDATA[
      a(x,y / (y / z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5837(a,2),26437(a,1,2))].">
      <j1 rule="para" parents="5837 26437"/>
    </justification>
  </clause>

  <clause id="26457">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="6128 26437"/>
    </justification>
  </clause>

  <clause id="26459">
    <literal><![CDATA[
      a(x,y * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="7481 26437"/>
    </justification>
  </clause>

  <clause id="26461">
    <literal><![CDATA[
      a(x,L(y,z,u) * (u * z),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(7477(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="7477 26437"/>
    </justification>
  </clause>

  <clause id="26462">
    <literal><![CDATA[
      a(x,T(y,z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(7858(a,1),26437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 26437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26463">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="7864 26437"/>
    </justification>
  </clause>

  <clause id="26464">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(8016(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="8016 26437"/>
    </justification>
  </clause>

  <clause id="26465">
    <literal><![CDATA[
      a(x,(y / z) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(8364(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="8364 26437"/>
    </justification>
  </clause>

  <clause id="26466">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),26437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10354 26437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26467">
    <literal><![CDATA[
      a(x,(T(y,z) * u) * w,v5) = a(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(16495(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="16495 26437"/>
    </justification>
  </clause>

  <clause id="26468">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="22739 26437"/>
    </justification>
  </clause>

  <clause id="26469">
    <literal><![CDATA[
      a(x,(y * T(z,u)) \ w,v5) = a(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25110(a,1),26437(a,1,2))].">
      <j1 rule="para" parents="25110 26437"/>
    </justification>
  </clause>

  <clause id="26470">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,w,v5),v6) = a(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(25728(a,2),26437(a,1,2))].">
      <j1 rule="para" parents="25728 26437"/>
    </justification>
  </clause>

  <clause id="26476">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) = a(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(285(a,1),26451(a,1,2)),flip(a)].">
      <j1 rule="para" parents="285 26451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26481">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ ((y * (z / (x \ 1))) * x)) = a(y,(x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(2665,a,26454,a)].">
      <j1 rule="hyper" parents="2665 26454"/>
    </justification>
  </clause>

  <clause id="26482">
    <literal><![CDATA[
      a(x,y \ z,y) * (x * z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(26454(a,1),19673(a,1,1))].">
      <j1 rule="para" parents="26454 19673"/>
    </justification>
  </clause>

  <clause id="26483">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(3140,a,26459,a)].">
      <j1 rule="hyper" parents="3140 26459"/>
    </justification>
  </clause>

  <clause id="26484">
    <literal><![CDATA[
      a(x,(y * z) * y,u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(3062,a,26459,a),flip(a)].">
      <j1 rule="hyper" parents="3062 26459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26485">
    <literal><![CDATA[
      a(x,y * (z \ a(u,w,u)),v5) = a(x,z * y,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,15017,a(flip),b,26459,a),flip(a)].">
      <j1 rule="hyper" parents="370 15017 26459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26486">
    <literal><![CDATA[
      a(x,y * ((1 / z) \ u),w) = a(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3069,a(flip),b,26459,a),flip(a)].">
      <j1 rule="hyper" parents="370 3069 26459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26493">
    <literal><![CDATA[
      a(x,y * (z / u),w) = a(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26464(a,1,2))].">
      <j1 rule="para" parents="5631 26464"/>
    </justification>
  </clause>

  <clause id="26494">
    <literal><![CDATA[
      a(x,y * ((z \ u) \ u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(5944(a,1),26464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5944 26464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26495">
    <literal><![CDATA[
      a(x,y * (z * u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(6770(a,1),26464(a,1,2))].">
      <j1 rule="para" parents="6770 26464"/>
    </justification>
  </clause>

  <clause id="26496">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(11016(a,1),26464(a,1,2))].">
      <j1 rule="para" parents="11016 26464"/>
    </justification>
  </clause>

  <clause id="26498">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,26379,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 26379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26500">
    <literal><![CDATA[
      a(x * (L(y,y,z) \ z),u,w) = a(x * (z * (1 / y)),u,w)
    ]]></literal>
    <justification jstring="[para(6537(a,1),26379(a,1,1,2))].">
      <j1 rule="para" parents="6537 26379"/>
    </justification>
  </clause>

  <clause id="26501">
    <literal><![CDATA[
      a(x * (((y * y) \ z) \ u),w,v5) = a(x * ((y * y) * (u / z)),w,v5)
    ]]></literal>
    <justification jstring="[para(25830(a,1),26379(a,1,1,2))].">
      <j1 rule="para" parents="25830 26379"/>
    </justification>
  </clause>

  <clause id="26504">
    <literal><![CDATA[
      a((x * (y * z)) \ (K(y,z) * u),w,v5) = a((x * (z * y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(25133(a,1),26384(a,1,1))].">
      <j1 rule="para" parents="25133 26384"/>
    </justification>
  </clause>

  <clause id="26505">
    <literal><![CDATA[
      a(K(x,y) * ((z \ (y * x)) * u),w,v5) = a((z \ (x * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(23615(a,1),26385(a,1,1))].">
      <j1 rule="para" parents="23615 26385"/>
    </justification>
  </clause>

  <clause id="26506">
    <literal><![CDATA[
      a(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(26403(a,2),3038(a,1))].">
      <j1 rule="para" parents="26403 3038"/>
    </justification>
  </clause>

  <clause id="26512">
    <literal><![CDATA[
      a(x,(y * y) * ((((y \ 1) \ z) * u) \ w),v5) = a(x,((y \ z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2241(a,1),26462(a,1,2))].">
      <j1 rule="para" parents="2241 26462"/>
    </justification>
  </clause>

  <clause id="26514">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26459,a,b,26463,a),flip(a)].">
      <j1 rule="hyper" parents="370 26459 26463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26515">
    <literal><![CDATA[
      a(x,K(y,z) * ((u \ (z * y)) * w),v5) = a(x,w * (u \ (y * z)),v5)
    ]]></literal>
    <justification jstring="[para(23615(a,1),26514(a,1,2))].">
      <j1 rule="para" parents="23615 26514"/>
    </justification>
  </clause>

  <clause id="26516">
    <literal><![CDATA[
      a(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(5232(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="5232 26373"/>
    </justification>
  </clause>

  <clause id="26517">
    <literal><![CDATA[
      a(x * T(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(6130(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="6130 26373"/>
    </justification>
  </clause>

  <clause id="26519">
    <literal><![CDATA[
      a(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(7481(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="7481 26373"/>
    </justification>
  </clause>

  <clause id="26520">
    <literal><![CDATA[
      a((x \ y) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(7479(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="7479 26373"/>
    </justification>
  </clause>

  <clause id="26521">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(K(w,v5) * x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7500(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="7500 26373"/>
    </justification>
  </clause>

  <clause id="26522">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(7864(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="7864 26373"/>
    </justification>
  </clause>

  <clause id="26523">
    <literal><![CDATA[
      a(x * K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(8016(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="8016 26373"/>
    </justification>
  </clause>

  <clause id="26524">
    <literal><![CDATA[
      a((x / y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(8364(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="8364 26373"/>
    </justification>
  </clause>

  <clause id="26526">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(12016(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="12016 26373"/>
    </justification>
  </clause>

  <clause id="26527">
    <literal><![CDATA[
      a((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * x) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(12083(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="12083 26373"/>
    </justification>
  </clause>

  <clause id="26528">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(22739(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="22739 26373"/>
    </justification>
  </clause>

  <clause id="26530">
    <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(25061(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="25061 26373"/>
    </justification>
  </clause>

  <clause id="26531">
    <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(25148(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="25148 26373"/>
    </justification>
  </clause>

  <clause id="26532">
    <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(25567(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="25567 26373"/>
    </justification>
  </clause>

  <clause id="26534">
    <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(25624(a,1),26373(a,1,1))].">
      <j1 rule="para" parents="25624 26373"/>
    </justification>
  </clause>

  <clause id="26536">
    <literal><![CDATA[
      a(R(x * K(y,x),y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ ((y * x) * z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(5349(a,2),26516(a,1,1))].">
      <j1 rule="para" parents="5349 26516"/>
    </justification>
  </clause>

  <clause id="26538">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((y * x) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2956(a,1),26519(a,1))].">
      <j1 rule="para" parents="2956 26519"/>
    </justification>
  </clause>

  <clause id="26539">
    <literal><![CDATA[
      a(x * (a(y,z,y) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(14307(a,2),26519(a,1))].">
      <j1 rule="para" parents="14307 26519"/>
    </justification>
  </clause>

  <clause id="26540">
    <literal><![CDATA[
      a(x * T(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26379(a,2),26519(a,1))].">
      <j1 rule="para" parents="26379 26519"/>
    </justification>
  </clause>

  <clause id="26542">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(14070(a,1),26520(a,1))].">
      <j1 rule="para" parents="14070 26520"/>
    </justification>
  </clause>

  <clause id="26546">
    <literal><![CDATA[
      a(x * (y \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z / y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6282(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="6282 26523"/>
    </justification>
  </clause>

  <clause id="26548">
    <literal><![CDATA[
      a(x * (y * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6770(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="6770 26523"/>
    </justification>
  </clause>

  <clause id="26549">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * y,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(11016(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="11016 26523"/>
    </justification>
  </clause>

  <clause id="26550">
    <literal><![CDATA[
      a(x \ (y / z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (z \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(20260(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="20260 26523"/>
    </justification>
  </clause>

  <clause id="26552">
    <literal><![CDATA[
      a(L(x / y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(L(y \ x,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(25731(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="25731 26523"/>
    </justification>
  </clause>

  <clause id="26553">
    <literal><![CDATA[
      a(x \ L(T(y,z),u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ L(y,u,w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(25755(a,1),26523(a,1,1))].">
      <j1 rule="para" parents="25755 26523"/>
    </justification>
  </clause>

  <clause id="26554">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26369(a,1),26523(a,1))].">
      <j1 rule="para" parents="26369 26523"/>
    </justification>
  </clause>

  <clause id="26556">
    <literal><![CDATA[
      a(L(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(26411(a,1),26523(a,1))].">
      <j1 rule="para" parents="26411 26523"/>
    </justification>
  </clause>

  <clause id="26557">
    <literal><![CDATA[
      a(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1811(a,2),26554(a,1,2))].">
      <j1 rule="para" parents="1811 26554"/>
    </justification>
  </clause>

  <clause id="26558">
    <literal><![CDATA[
      a(x,(y * z) / y,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(5228(a,2),26554(a,1,2))].">
      <j1 rule="para" parents="5228 26554"/>
    </justification>
  </clause>

  <clause id="26559">
    <literal><![CDATA[
      a(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5232(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="5232 26554"/>
    </justification>
  </clause>

  <clause id="26560">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5300(a,2),26554(a,1,2))].">
      <j1 rule="para" parents="5300 26554"/>
    </justification>
  </clause>

  <clause id="26562">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(6128(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="6128 26554"/>
    </justification>
  </clause>

  <clause id="26564">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(7481(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="7481 26554"/>
    </justification>
  </clause>

  <clause id="26566">
    <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(7477(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="7477 26554"/>
    </justification>
  </clause>

  <clause id="26567">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,w) = v5
    ]]></literal>
    <justification jstring="[para(7864(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="7864 26554"/>
    </justification>
  </clause>

  <clause id="26569">
    <literal><![CDATA[
      a(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(8016(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="8016 26554"/>
    </justification>
  </clause>

  <clause id="26570">
    <literal><![CDATA[
      a(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(8364(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="8364 26554"/>
    </justification>
  </clause>

  <clause id="26572">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(12016(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="12016 26554"/>
    </justification>
  </clause>

  <clause id="26574">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(22739(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="22739 26554"/>
    </justification>
  </clause>

  <clause id="26576">
    <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(365(a,1),26557(a,1,2))].">
      <j1 rule="para" parents="365 26557"/>
    </justification>
  </clause>

  <clause id="26577">
    <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(902(a,1),26558(a,1,2))].">
      <j1 rule="para" parents="902 26558"/>
    </justification>
  </clause>

  <clause id="26579">
    <literal><![CDATA[
      a(x,R(y \ 1,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(2786(a,2),26559(a,1,2))].">
      <j1 rule="para" parents="2786 26559"/>
    </justification>
  </clause>

  <clause id="26580">
    <literal><![CDATA[
      a(x,y \ (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3066(a,1),26560(a,1))].">
      <j1 rule="para" parents="3066 26560"/>
    </justification>
  </clause>

  <clause id="26582">
    <literal><![CDATA[
      a(x,a(y,z,y) * (u * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w * (a(y,z,y) * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(13913(a,1),26564(a,1,2))].">
      <j1 rule="para" parents="13913 26564"/>
    </justification>
  </clause>

  <clause id="26584">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(26483(a,2),26564(a,1))].">
      <j1 rule="para" parents="26483 26564"/>
    </justification>
  </clause>

  <clause id="26585">
    <literal><![CDATA[
      a(x,y * (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(5631(a,1),26569(a,1,2))].">
      <j1 rule="para" parents="5631 26569"/>
    </justification>
  </clause>

  <clause id="26586">
    <literal><![CDATA[
      a(x,y * (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(6770(a,1),26569(a,1,2))].">
      <j1 rule="para" parents="6770 26569"/>
    </justification>
  </clause>

  <clause id="26587">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,v5) = v6
    ]]></literal>
    <justification jstring="[para(11016(a,1),26569(a,1,2))].">
      <j1 rule="para" parents="11016 26569"/>
    </justification>
  </clause>

  <clause id="26589">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3051(a,2),26580(a,1))].">
      <j1 rule="para" parents="3051 26580"/>
    </justification>
  </clause>

  <clause id="26590">
    <literal><![CDATA[
      a(x,L((1 / y) * z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y * z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(4208(a,1),26580(a,1))].">
      <j1 rule="para" parents="4208 26580"/>
    </justification>
  </clause>

  <clause id="26593">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(94(a,2),26589(a,1,2))].">
      <j1 rule="para" parents="94 26589"/>
    </justification>
  </clause>

  <clause id="26594">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z * u,w) = v5
    ]]></literal>
    <justification jstring="[para(514(a,1),26589(a,1,2))].">
      <j1 rule="para" parents="514 26589"/>
    </justification>
  </clause>

  <clause id="26595">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(26387(a,2),2977(a,1))].">
      <j1 rule="para" parents="26387 2977"/>
    </justification>
  </clause>

  <clause id="26596">
    <literal><![CDATA[
      a((((x * x) * y) / L(x,z,u)) * w,v5,v6) = a((L(1 / x,z,u) \ y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3800(a,1),26388(a,2,1,1))].">
      <j1 rule="para" parents="3800 26388"/>
    </justification>
  </clause>

  <clause id="26597">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) * u,w,v5) = a(R(z * K(y,x),y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25688(a,1),26388(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="25688 26388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26598">
    <literal><![CDATA[
      a(x * (y \ T(z,u)),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26390(a,1,1,2))].">
      <j1 rule="para" parents="6128 26390"/>
    </justification>
  </clause>

  <clause id="26599">
    <literal><![CDATA[
      a(x * (T(y,z) \ u),w,v5) = a(x * (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(7858(a,1),26390(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7858 26390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26600">
    <literal><![CDATA[
      a(x * ((y / z) \ u),w,v5) = a(x * ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(8210(a,1),26390(a,1,1,2))].">
      <j1 rule="para" parents="8210 26390"/>
    </justification>
  </clause>

  <clause id="26601">
    <literal><![CDATA[
      a((x * T(y,z)) * u,w,v5) = a((x * y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25100(a,1),26390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25100 26390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26602">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) * w,v5,v6) = a((x * (y \ 1)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25348(a,1),26390(a,1,1))].">
      <j1 rule="para" parents="25348 26390"/>
    </justification>
  </clause>

  <clause id="26603">
    <literal><![CDATA[
      a(x * L(T(y,z) \ u,w,v5),v6,v7) = a(x * L(y \ u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(25742(a,1),26390(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25742 26390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26605">
    <literal><![CDATA[
      a(x \ (((y \ z) \ z) * u),w,v5) = a(x \ (y * u),w,v5)
    ]]></literal>
    <justification jstring="[para(7966(a,1),26394(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7966 26394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26606">
    <literal><![CDATA[
      a(x \ (y \ (K(z,u) * w)),v5,v6) = a(x \ (y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26394(a,1,1,2))].">
      <j1 rule="para" parents="22739 26394"/>
    </justification>
  </clause>

  <clause id="26607">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(26438(a,1),3006(a,1))].">
      <j1 rule="para" parents="26438 3006"/>
    </justification>
  </clause>

  <clause id="26608">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(2991,a,26440,a),flip(a)].">
      <j1 rule="hyper" parents="2991 26440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26609">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2976,a,26440,a),flip(a)].">
      <j1 rule="hyper" parents="2976 26440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26610">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26440(a,1),2991(a,1))].">
      <j1 rule="para" parents="26440 2991"/>
    </justification>
  </clause>

  <clause id="26611">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26609,a)].">
      <j1 rule="hyper" parents="26519 26609"/>
    </justification>
  </clause>

  <clause id="26612">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((x * y) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(26609(a,1),26519(a,1))].">
      <j1 rule="para" parents="26609 26519"/>
    </justification>
  </clause>

  <clause id="26613">
    <literal><![CDATA[
      a(R(x,y,y),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2992,a,26611,a)].">
      <j1 rule="hyper" parents="2992 26611"/>
    </justification>
  </clause>

  <clause id="26614">
    <literal><![CDATA[
      a(L(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * (x * y),z,u) = w
    ]]></literal>
    <justification jstring="[para(26611(a,1),26519(a,1))].">
      <j1 rule="para" parents="26611 26519"/>
    </justification>
  </clause>

  <clause id="26615">
    <literal><![CDATA[
      a(x * (y * (z / u)),w,v5) = a(x * (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26442(a,1,1,2))].">
      <j1 rule="para" parents="5631 26442"/>
    </justification>
  </clause>

  <clause id="26616">
    <literal><![CDATA[
      a(x,y * (z \ T(u,w)),v5) = a(x,y * (z \ u),v5)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26466(a,1,2,2))].">
      <j1 rule="para" parents="6128 26466"/>
    </justification>
  </clause>

  <clause id="26617">
    <literal><![CDATA[
      a(x,y * (T(z,u) * w),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26466(a,1,2,2))].">
      <j1 rule="para" parents="7864 26466"/>
    </justification>
  </clause>

  <clause id="26618">
    <literal><![CDATA[
      a(x,(y * T(z,u)) * w,v5) = a(x,(y * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(25100(a,1),26466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25100 26466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26619">
    <literal><![CDATA[
      a(x,y \ ((z / u) * w),v5) = a(x,y \ ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(8364(a,1),26468(a,1,2,2))].">
      <j1 rule="para" parents="8364 26468"/>
    </justification>
  </clause>

  <clause id="26620">
    <literal><![CDATA[
      a(x,((y / z) * u) \ w,v5) = a(x,((z \ y) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25131(a,1),26468(a,1,2))].">
      <j1 rule="para" parents="25131 26468"/>
    </justification>
  </clause>

  <clause id="26621">
    <literal><![CDATA[
      a(x,(T(y,K(z,u)) * w) \ v5,v6) = a(x,(y * (K(z,u) * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25136(a,1),26468(a,1,2))].">
      <j1 rule="para" parents="25136 26468"/>
    </justification>
  </clause>

  <clause id="26622">
    <literal><![CDATA[
      a(x,y * ((z * u) \ z),w) = a(x,y * (z \ (z / u)),w)
    ]]></literal>
    <justification jstring="[para(3501(a,1),26494(a,1,2,2))].">
      <j1 rule="para" parents="3501 26494"/>
    </justification>
  </clause>

  <clause id="26623">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(3125,a,26495,a),flip(a)].">
      <j1 rule="hyper" parents="3125 26495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26624">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,w) = v5
    ]]></literal>
    <justification jstring="[para(26495(a,1),3125(a,1))].">
      <j1 rule="para" parents="26495 3125"/>
    </justification>
  </clause>

  <clause id="26625">
    <literal><![CDATA[
      a(x,y * (z * (u / w)),v5) = a(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5631(a,1),26496(a,1,2,2))].">
      <j1 rule="para" parents="5631 26496"/>
    </justification>
  </clause>

  <clause id="26626">
    <literal><![CDATA[
      a(x,y * (z \ (u / w)),v5) = a(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(20260(a,1),26496(a,1,2,2))].">
      <j1 rule="para" parents="20260 26496"/>
    </justification>
  </clause>

  <clause id="26627">
    <literal><![CDATA[
      a(x * (a(y,z,y) \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(14300(a,1),26542(a,1,1))].">
      <j1 rule="para" parents="14300 26542"/>
    </justification>
  </clause>

  <clause id="26628">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),26608(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 26608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26629">
    <literal><![CDATA[
      a(x,y * (z * (z * u)),w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(92(a,1),26623(a,1,2,2))].">
      <j1 rule="para" parents="92 26623"/>
    </justification>
  </clause>

  <clause id="26630">
    <literal><![CDATA[
      a((x * (y \ 1)) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(1117(a,1),26628(a,1,1))].">
      <j1 rule="para" parents="1117 26628"/>
    </justification>
  </clause>

  <clause id="26631">
    <literal><![CDATA[
      a((x \ (y \ 1)) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(1470(a,1),26628(a,1,1))].">
      <j1 rule="para" parents="1470 26628"/>
    </justification>
  </clause>

  <clause id="26632">
    <literal><![CDATA[
      a((x * (y * (z \ 1))) * u,w,v5) = a((x * (y * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1468(a,1),26628(a,1,1))].">
      <j1 rule="para" parents="1468 26628"/>
    </justification>
  </clause>

  <clause id="26633">
    <literal><![CDATA[
      L(x,(y * (y / z)) * z,u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(26482(a,1),3776(a,1,2))].">
      <j1 rule="para" parents="26482 3776"/>
    </justification>
  </clause>

  <clause id="26638">
    <literal><![CDATA[
      a(x * (T(y,z) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26393,a)].">
      <j1 rule="hyper" parents="26519 26393"/>
    </justification>
  </clause>

  <clause id="26639">
    <literal><![CDATA[
      a((x \ (y / z)) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26400(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 26400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26640">
    <literal><![CDATA[
      a((x \ ((y \ z) * (y * y))) * u,w,v5) = a((x \ ((y \ 1) \ z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(950(a,1),26400(a,1,1,1,2))].">
      <j1 rule="para" parents="950 26400"/>
    </justification>
  </clause>

  <clause id="26641">
    <literal><![CDATA[
      a(x * (((1 / y) \ 1) \ L(z,y,y)),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(581(a,1),26424(a,2,1,1))].">
      <j1 rule="para" parents="581 26424"/>
    </justification>
  </clause>

  <clause id="26642">
    <literal><![CDATA[
      a(x * (y \ (((1 / y) \ z) / (u \ 1))),w,v5) = a((y \ ((y \ z) / (u \ 1))) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(4178(a,1),26424(a,1,1,2))].">
      <j1 rule="para" parents="4178 26424"/>
    </justification>
  </clause>

  <clause id="26643">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (y \ z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(26424(a,2),26519(a,1))].">
      <j1 rule="para" parents="26424 26519"/>
    </justification>
  </clause>

  <clause id="26645">
    <literal><![CDATA[
      a(x * (T(y,z) * u),w,v5) = a(x * (u * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26440,a,b,26441,a)].">
      <j1 rule="hyper" parents="60 26440 26441"/>
    </justification>
  </clause>

  <clause id="26646">
    <literal><![CDATA[
      a(x \ (y \ (z / u)),w,v5) = a(x \ (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26445(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 26445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26647">
    <literal><![CDATA[
      a(x \ (y \ (z * (u * (z \ (1 / z))))),w,v5) = a(x \ (y \ ((z \ 1) * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(7124(a,1),26445(a,1,1,2,2))].">
      <j1 rule="para" parents="7124 26445"/>
    </justification>
  </clause>

  <clause id="26648">
    <literal><![CDATA[
      a(x \ (y * (z / u)),w,v5) = a(x \ (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26446(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 26446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26649">
    <literal><![CDATA[
      a(x,(y * (z / u)) \ w,v5) = a(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26469(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 26469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26650">
    <literal><![CDATA[
      a(x,(K(y,z) * (u * (z \ w))) \ v5,v6) = a(x,((T(z,y) \ w) * u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25355(a,1),26469(a,1,2,1))].">
      <j1 rule="para" parents="25355 26469"/>
    </justification>
  </clause>

  <clause id="26651">
    <literal><![CDATA[
      a(x,L(y * z,u,w),v5) = a(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26470(a,1,2,1))].">
      <j1 rule="para" parents="7481 26470"/>
    </justification>
  </clause>

  <clause id="26652">
    <literal><![CDATA[
      a(x,((y \ z) * y) \ (y \ z),u) = a(x,L(y \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(12525(a,2),26476(a,1,2))].">
      <j1 rule="para" parents="12525 26476"/>
    </justification>
  </clause>

  <clause id="26653">
    <literal><![CDATA[
      a((x * (y / z)) * u,w,v5) = a((x * (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26601(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 26601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26654">
    <literal><![CDATA[
      a((x * ((y * z) * (y \ 1))) * u,w,v5) = a((x * R(z,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1131(a,1),26601(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1131 26601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26655">
    <literal><![CDATA[
      a(x,y * (z \ (u * (w * (u \ (1 / u))))),v5) = a(x,y * (z \ ((u \ 1) * w)),v5)
    ]]></literal>
    <justification jstring="[para(7124(a,1),26616(a,1,2,2,2))].">
      <j1 rule="para" parents="7124 26616"/>
    </justification>
  </clause>

  <clause id="26656">
    <literal><![CDATA[
      a(x,y * ((z * z) * ((u * (z \ 1)) * w)),v5) = a(x,y * ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(1563(a,1),26617(a,1,2,2))].">
      <j1 rule="para" parents="1563 26617"/>
    </justification>
  </clause>

  <clause id="26657">
    <literal><![CDATA[
      a(x,(y * (z / u)) * w,v5) = a(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26618(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 26618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26658">
    <literal><![CDATA[
      a(x * (y * (z \ 1)),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26630,a)].">
      <j1 rule="hyper" parents="26519 26630"/>
    </justification>
  </clause>

  <clause id="26659">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * u,w,v5) = a((x * (z \ (y * y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(578(a,1),26630(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="578 26630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26660">
    <literal><![CDATA[
      a((x * (y \ (z * z))) * u,w,v5) = a((x * y) * ((z * z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(1192(a,1),26630(a,1,1))].">
      <j1 rule="para" parents="1192 26630"/>
    </justification>
  </clause>

  <clause id="26661">
    <literal><![CDATA[
      a((L(x,y,y) * ((y \ 1) \ 1)) * z,u,w) = a(L(x * (1 / y),y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4641(a,2),26630(a,2,1,1))].">
      <j1 rule="para" parents="4641 26630"/>
    </justification>
  </clause>

  <clause id="26662">
    <literal><![CDATA[
      a((x * (a(y,z,y) \ u)) * w,v5,v6) = a((x * (u \ a(y,z,y))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(13912(a,1),26630(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13912 26630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26663">
    <literal><![CDATA[
      a((x * ((y * z) \ (K(u,y) * 1))) * w,v5,v6) = a((x * (T(y,u) * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25129(a,2),26630(a,1,1,1,2))].">
      <j1 rule="para" parents="25129 26630"/>
    </justification>
  </clause>

  <clause id="26664">
    <literal><![CDATA[
      a(((x \ 1) / (T(y,x \ 1) \ 1)) * z,u,w) = a((L(y,y,x \ 1) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(26211(a,2),26630(a,1,1,1))].">
      <j1 rule="para" parents="26211 26630"/>
    </justification>
  </clause>

  <clause id="26665">
    <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(26638(a,2),26519(a,1))].">
      <j1 rule="para" parents="26638 26519"/>
    </justification>
  </clause>

  <clause id="26666">
    <literal><![CDATA[
      a(x * (((y * z) * K(y,u)) * w),v5,v6) = a(x * (w * (T(y,u) * z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(8937(a,1),26645(a,1,1,2,1))].">
      <j1 rule="para" parents="8937 26645"/>
    </justification>
  </clause>

  <clause id="26667">
    <literal><![CDATA[
      a(x * (y * (z \ 1)),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,26658,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 26658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26668">
    <literal><![CDATA[
      a(x * ((y \ 1) * z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26440,a,b,26667,a)].">
      <j1 rule="hyper" parents="60 26440 26667"/>
    </justification>
  </clause>

  <clause id="26669">
    <literal><![CDATA[
      a(x * (y * (z \ 1)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26667(a,2),26519(a,1))].">
      <j1 rule="para" parents="26667 26519"/>
    </justification>
  </clause>

  <clause id="26670">
    <literal><![CDATA[
      a(L(x * y,1 / ((x * y) / x),z) * (z * (1 / ((x * y) / x))),u,w) = a(z * L(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(12651(a,1),26383(a,2,1,2))].">
      <j1 rule="para" parents="12651 26383"/>
    </justification>
  </clause>

  <clause id="26671">
    <literal><![CDATA[
      a(T(x / y,x) * ((x * y) * y),z,u) = a((x * y) * (y * (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[para(24919(a,1),26383(a,1,1,1))].">
      <j1 rule="para" parents="24919 26383"/>
    </justification>
  </clause>

  <clause id="26673">
    <literal><![CDATA[
      a(x,L((y * y) * z,u,w) * (w * u),v5) = a(x,w * ((u * (y * y)) * z),v5)
    ]]></literal>
    <justification jstring="[para(29(a,2),26461(a,2,2,2))].">
      <j1 rule="para" parents="29 26461"/>
    </justification>
  </clause>

  <clause id="26674">
    <literal><![CDATA[
      a(x,L((T(y,z) * u) / w,K(z,y),v5) * (v5 * K(z,y)),v6) = a(x,v5 * ((y * u) / w),v6)
    ]]></literal>
    <justification jstring="[para(25142(a,1),26461(a,2,2,2))].">
      <j1 rule="para" parents="25142 26461"/>
    </justification>
  </clause>

  <clause id="26675">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,w * (v5 \ 1),v6) * (v6 * (w * (v5 \ 1))),v7) = a(x,v6 * ((w * (v5 \ K(y,z))) * u),v7)
    ]]></literal>
    <justification jstring="[para(25348(a,1),26461(a,2,2,2))].">
      <j1 rule="para" parents="25348 26461"/>
    </justification>
  </clause>

  <clause id="26679">
    <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(6128(a,1),26526(a,1,1,2))].">
      <j1 rule="para" parents="6128 26526"/>
    </justification>
  </clause>

  <clause id="26681">
    <literal><![CDATA[
      a(x * (y * (K(z,u) * w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * (y * w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(12016(a,1),26526(a,1,1,2))].">
      <j1 rule="para" parents="12016 26526"/>
    </justification>
  </clause>

  <clause id="26682">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x * z) \ (z * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(94(a,2),26527(a,1,1))].">
      <j1 rule="para" parents="94 26527"/>
    </justification>
  </clause>

  <clause id="26683">
    <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(7873(a,1),26528(a,1,1,2))].">
      <j1 rule="para" parents="7873 26528"/>
    </justification>
  </clause>

  <clause id="26684">
    <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(8364(a,1),26528(a,1,1,2))].">
      <j1 rule="para" parents="8364 26528"/>
    </justification>
  </clause>

  <clause id="26685">
    <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(25129(a,1),26528(a,1,1))].">
      <j1 rule="para" parents="25129 26528"/>
    </justification>
  </clause>

  <clause id="26686">
    <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(5631(a,1),26549(a,1,1,2))].">
      <j1 rule="para" parents="5631 26549"/>
    </justification>
  </clause>

  <clause id="26687">
    <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(15583(a,1),26549(a,1,1,2))].">
      <j1 rule="para" parents="15583 26549"/>
    </justification>
  </clause>

  <clause id="26688">
    <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(25731(a,1),26549(a,1,1,2))].">
      <j1 rule="para" parents="25731 26549"/>
    </justification>
  </clause>

  <clause id="26690">
    <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(8401(a,1),26572(a,1,2,2))].">
      <j1 rule="para" parents="8401 26572"/>
    </justification>
  </clause>

  <clause id="26692">
    <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(25129(a,1),26574(a,1,2))].">
      <j1 rule="para" parents="25129 26574"/>
    </justification>
  </clause>

  <clause id="26693">
    <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(20260(a,1),26587(a,1,2,2))].">
      <j1 rule="para" parents="20260 26587"/>
    </justification>
  </clause>

  <clause id="26694">
    <literal><![CDATA[
      a(x,y * L(z,R(u,u,z),R(u,u,z)),w) = a(x,y * (R(u,u,z) * ((1 / u) \ z)),w)
    ]]></literal>
    <justification jstring="[para(1961(a,1),26629(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1961 26629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26695">
    <literal><![CDATA[
      L(x,(y * (z \ y)) * z,u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26189,a(flip),b,26633,a)].">
      <j1 rule="hyper" parents="60 26189 26633"/>
    </justification>
  </clause>

  <clause id="26696">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(u * ((y * x) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26396,a),flip(a)].">
      <j1 rule="hyper" parents="26519 26396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26697">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a((y \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26399,a)].">
      <j1 rule="hyper" parents="26519 26399"/>
    </justification>
  </clause>

  <clause id="26698">
    <literal><![CDATA[
      a((x \ (y \ T(z,u))) * w,v5,v6) = a((x \ (y \ z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26399(a,1,1,1,2))].">
      <j1 rule="para" parents="6128 26399"/>
    </justification>
  </clause>

  <clause id="26699">
    <literal><![CDATA[
      a((x \ (y * z)) * u,w,v5) = a((x \ (z * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26399(a,1,1,1,2))].">
      <j1 rule="para" parents="7481 26399"/>
    </justification>
  </clause>

  <clause id="26700">
    <literal><![CDATA[
      a((x \ ((y / z) * u)) * w,v5,v6) = a((x \ ((z \ y) * u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(8364(a,1),26399(a,1,1,1,2))].">
      <j1 rule="para" parents="8364 26399"/>
    </justification>
  </clause>

  <clause id="26701">
    <literal><![CDATA[
      a((x \ (y \ (K(z,u) * w))) * v5,v6,v7) = a((x \ (y \ w)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26399(a,1,1,1,2))].">
      <j1 rule="para" parents="22739 26399"/>
    </justification>
  </clause>

  <clause id="26702">
    <literal><![CDATA[
      a(((x * x) \ y) \ z,u,w) = a(z / y,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2955,a(flip),b,26416,a),flip(a)].">
      <j1 rule="hyper" parents="370 2955 26416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26704">
    <literal><![CDATA[
      a(((x * x) \ y) \ z,u,w) = a(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26376,a(flip),b,26702,a),flip(a)].">
      <j1 rule="hyper" parents="370 26376 26702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26705">
    <literal><![CDATA[
      a(((1 / x) * y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(551(a,1),26704(a,1,1,1))].">
      <j1 rule="para" parents="551 26704"/>
    </justification>
  </clause>

  <clause id="26706">
    <literal><![CDATA[
      a(((x \ 1) \ y) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(940(a,1),26704(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="940 26704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26707">
    <literal><![CDATA[
      a(x \ ((y * y) * z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(849(a,1),26704(a,1,1))].">
      <j1 rule="para" parents="849 26704"/>
    </justification>
  </clause>

  <clause id="26708">
    <literal><![CDATA[
      a(R(T(x,y * y),y,y) \ z,u,w) = a(((x * y) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(880(a,1),26704(a,1,1,1))].">
      <j1 rule="para" parents="880 26704"/>
    </justification>
  </clause>

  <clause id="26709">
    <literal><![CDATA[
      a(x \ ((1 / y) * z),u,w) = a(x \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(314(a,1),26707(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="314 26707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26710">
    <literal><![CDATA[
      a(x \ (y * (y * z)),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(92(a,1),26707(a,1,1,2))].">
      <j1 rule="para" parents="92 26707"/>
    </justification>
  </clause>

  <clause id="26711">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ z),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(936(a,1),26707(a,1,1,2))].">
      <j1 rule="para" parents="936 26707"/>
    </justification>
  </clause>

  <clause id="26712">
    <literal><![CDATA[
      a(x \ ((y * y) * (x \ L(x,z,u))),w,v5) = a(L(x \ 1,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3817(a,1),26707(a,2,1))].">
      <j1 rule="para" parents="3817 26707"/>
    </justification>
  </clause>

  <clause id="26713">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),w,v5) = a(x \ (y * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(3855(a,1),26707(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3855 26707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26714">
    <literal><![CDATA[
      a(x \ L((y \ (y \ 1)) * y,y,y),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3937(a,2),26707(a,1,1,2))].">
      <j1 rule="para" parents="3937 26707"/>
    </justification>
  </clause>

  <clause id="26715">
    <literal><![CDATA[
      a(((x \ 1) * y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),26705(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 26705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26716">
    <literal><![CDATA[
      a(x \ ((y \ 1) * z),u,w) = a(x \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(74(a,1),26709(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="74 26709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26717">
    <literal><![CDATA[
      a(x \ (y * R(y,z,z)),u,w) = a(x \ a(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[para(16517(a,1),26709(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16517 26709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26718">
    <literal><![CDATA[
      a(((x \ 1) * (1 / y)) \ x,z,u) = a(x \ (x / (y \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(3413(a,1),26715(a,2,1))].">
      <j1 rule="para" parents="3413 26715"/>
    </justification>
  </clause>

  <clause id="26719">
    <literal><![CDATA[
      ((x * y) / z) * L(z,x,y) = a(y,x,z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,258,a(flip),b,26421,a),flip(a)].">
      <j1 rule="hyper" parents="60 258 26421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26721">
    <literal><![CDATA[
      a(x,y,z) \ (y * x) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) * (z \ (y * x)) = u
    ]]></literal>
    <justification jstring="[para(26719(a,1),25327(a,1))].">
      <j1 rule="para" parents="26719 25327"/>
    </justification>
  </clause>

  <clause id="26722">
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,u) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2977,a,26423,a)].">
      <j1 rule="hyper" parents="2977 26423"/>
    </justification>
  </clause>

  <clause id="26723">
    <literal><![CDATA[
      a((x \ y) \ x,z,u) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2977,a,26722,a)].">
      <j1 rule="hyper" parents="2977 26722"/>
    </justification>
  </clause>

  <clause id="26725">
    <literal><![CDATA[
      a(x * ((1 / y) \ z),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26424,a(flip),b,26600,a),flip(a)].">
      <j1 rule="hyper" parents="370 26424 26600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26726">
    <literal><![CDATA[
      a(x \ L(y * z,y,y),u,w) = a(x \ (y * L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[para(1326(a,1),26605(a,1,1,2))].">
      <j1 rule="para" parents="1326 26605"/>
    </justification>
  </clause>

  <clause id="26727">
    <literal><![CDATA[
      a(x \ (y \ (z \ (K(u,w) * v5))),v6,v7) = a(x \ (y \ (z \ v5)),v6,v7)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26606(a,1,1,2,2))].">
      <j1 rule="para" parents="22739 26606"/>
    </justification>
  </clause>

  <clause id="26728">
    <literal><![CDATA[
      a(x,((T(y \ 1,y * z) \ z) * u) \ w,v5) = a(x,(((y \ 1) \ z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(7583(a,1),26620(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7583 26620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26729">
    <literal><![CDATA[
      a(x,y * (z \ ((1 / u) \ w)),v5) = a(x,y * (z \ (w / u)),v5)
    ]]></literal>
    <justification jstring="[hyper(3141,a,26626,a),flip(a)].">
      <j1 rule="hyper" parents="3141 26626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26730">
    <literal><![CDATA[
      a(x,y * ((1 / z) \ (u \ w)),v5) = a(x,(z \ (w / u)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26486,a(flip),b,26626,a),flip(a)].">
      <j1 rule="hyper" parents="60 26486 26626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26731">
    <literal><![CDATA[
      a(x,y * (R(z / u,u,z \ (w / v5)) \ (v5 \ w)),v6) = a(x,y * (u * (z \ (w / v5))),v6)
    ]]></literal>
    <justification jstring="[para(673(a,1),26626(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="673 26626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26732">
    <literal><![CDATA[
      a(x * (y * L(z,u,z)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (y * z),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(11704(a,1),26627(a,1,1,2))].">
      <j1 rule="para" parents="11704 26627"/>
    </justification>
  </clause>

  <clause id="26734">
    <literal><![CDATA[
      a((x \ ((((y \ z) \ 1) \ 1) \ y)) * u,w,v5) = a((x \ (y * (z \ y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3492(a,1),26639(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3492 26639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26735">
    <literal><![CDATA[
      a((x \ (1 / ((y \ (y / z)) \ 1))) * u,w,v5) = a((x \ ((y * z) \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3501(a,1),26639(a,2,1,1,2))].">
      <j1 rule="para" parents="3501 26639"/>
    </justification>
  </clause>

  <clause id="26736">
    <literal><![CDATA[
      a(x \ (y * (z / (1 / u))),w,v5) = a(x \ (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,2987,a,b,26648,a)].">
      <j1 rule="hyper" parents="60 2987 26648"/>
    </justification>
  </clause>

  <clause id="26737">
    <literal><![CDATA[
      a(x,(y * ((K(z,u) * w) / (1 / v5))) \ v6,v7) = a(x,(y * ((K(u,z) / v5) \ w)) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(25134(a,1),26649(a,2,2,1,2))].">
      <j1 rule="para" parents="25134 26649"/>
    </justification>
  </clause>

  <clause id="26738">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(u * (z * (y * x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26440,a,b,26696,a),flip(a)].">
      <j1 rule="hyper" parents="370 26440 26696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26739">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) = a(((y * u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(25129(a,1),26697(a,1,1,2))].">
      <j1 rule="para" parents="25129 26697"/>
    </justification>
  </clause>

  <clause id="26741">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) * u,w,v5) = a(L(T(z,y),y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(270(a,1),26699(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="270 26699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26742">
    <literal><![CDATA[
      a(((x * y) \ (y * (z * x))) * u,w,v5) = a(R(T(z,x * y),x,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(880(a,1),26699(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="880 26699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26743">
    <literal><![CDATA[
      a(x * ((y * z) * u),w,v5) = a(x * (u * (z * y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26738,a)].">
      <j1 rule="hyper" parents="26519 26738"/>
    </justification>
  </clause>

  <clause id="26744">
    <literal><![CDATA[
      a(x * (y * (z * u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * ((u * z) * y),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(26738(a,1),26519(a,1))].">
      <j1 rule="para" parents="26738 26519"/>
    </justification>
  </clause>

  <clause id="26745">
    <literal><![CDATA[
      a(x * ((1 / y) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26600(a,2),26430(a,1))].">
      <j1 rule="para" parents="26600 26430"/>
    </justification>
  </clause>

  <clause id="26746">
    <literal><![CDATA[
      a(x * (L(y,y,z) \ z),u,w) = a(x * (z * (y \ 1)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26615,a(flip),b,26500,a),flip(a)].">
      <j1 rule="hyper" parents="370 26615 26500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26747">
    <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(3911(a,1),26576(a,1))].">
      <j1 rule="para" parents="3911 26576"/>
    </justification>
  </clause>

  <clause id="26748">
    <literal><![CDATA[
      a(x,L(y \ (y / z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(((y * z) \ y) \ 1,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(3503(a,1),26747(a,1,2,1))].">
      <j1 rule="para" parents="3503 26747"/>
    </justification>
  </clause>

  <clause id="26749">
    <literal><![CDATA[
      a(x,((y \ z) * y) \ (y \ z),u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3911,a(flip),b,26652,a),flip(a)].">
      <j1 rule="hyper" parents="370 3911 26652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26750">
    <literal><![CDATA[
      a(x,L(y \ 1,y,y \ z),u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(251(a,2),26749(a,1,2))].">
      <j1 rule="para" parents="251 26749"/>
    </justification>
  </clause>

  <clause id="26751">
    <literal><![CDATA[
      a(x,L(y,y,y \ z),u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(26747,a,26750,a)].">
      <j1 rule="hyper" parents="26747 26750"/>
    </justification>
  </clause>

  <clause id="26752">
    <literal><![CDATA[
      a(x,L(y,y,z * y),u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(24030(a,1),26751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24030 26751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26753">
    <literal><![CDATA[
      a(x * (L(y \ z,u,w) * v5),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x * (L(z / y,u,w) * v5),v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(285(a,1),26665(a,1,1,2,1))].">
      <j1 rule="para" parents="285 26665"/>
    </justification>
  </clause>

  <clause id="26754">
    <literal><![CDATA[
      a((x * (y \ 1)) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x * y) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26381(a,1),26669(a,1))].">
      <j1 rule="para" parents="26381 26669"/>
    </justification>
  </clause>

  <clause id="26755">
    <literal><![CDATA[
      a(x \ L((y * y) \ y,y,y),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(601(a,1),26714(a,1,1,2,1))].">
      <j1 rule="para" parents="601 26714"/>
    </justification>
  </clause>

  <clause id="26756">
    <literal><![CDATA[
      a(x \ L(1 / y,y,y),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(313(a,1),26755(a,1,1,2,1))].">
      <j1 rule="para" parents="313 26755"/>
    </justification>
  </clause>

  <clause id="26757">
    <literal><![CDATA[
      a(x \ (y \ 1),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1229(a,1),26756(a,1,1,2))].">
      <j1 rule="para" parents="1229 26756"/>
    </justification>
  </clause>

  <clause id="26758">
    <literal><![CDATA[
      a((x \ y) \ (x \ 1),z,u) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26723,a(flip),b,26757,a),flip(a)].">
      <j1 rule="hyper" parents="370 26723 26757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26759">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,z)),u,w) = a(x \ a(z,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(14176(a,1),26757(a,1,1,2))].">
      <j1 rule="para" parents="14176 26757"/>
    </justification>
  </clause>

  <clause id="26760">
    <literal><![CDATA[
      a(x * (L(y,y,z) \ z),u,w) = a((z * y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26658,a(flip),b,26746,a),flip(a)].">
      <j1 rule="hyper" parents="370 26658 26746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26761">
    <literal><![CDATA[
      a((L(x,x,y) \ y) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26760,a)].">
      <j1 rule="hyper" parents="26519 26760"/>
    </justification>
  </clause>

  <clause id="26762">
    <literal><![CDATA[
      a((L(x \ 1,x \ 1,L(y,x,x)) \ L(y,x,x)) * z,u,w) = a(L(y * (1 / x),x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4641(a,2),26761(a,2,1,1))].">
      <j1 rule="para" parents="4641 26761"/>
    </justification>
  </clause>

  <clause id="26763">
    <literal><![CDATA[
      a((L(a(x,y,z),a(x,y,z),(z * y) * x) \ ((z * y) * x)) * u,w,v5) = a(((z * y) * R(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25270(a,1),26761(a,2,1,1))].">
      <j1 rule="para" parents="25270 26761"/>
    </justification>
  </clause>

  <clause id="26764">
    <literal><![CDATA[
      a((L(x,x,y * z) \ (y * (z \ (u * u)))) * w,v5,v6) = a(((y * (z \ (u * u))) * x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25982(a,1),26761(a,1,1,1,1))].">
      <j1 rule="para" parents="25982 26761"/>
    </justification>
  </clause>

  <clause id="26766">
    <literal><![CDATA[
      a(x,L(y,z,u) * (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(26495(a,1),26566(a,1))].">
      <j1 rule="para" parents="26495 26566"/>
    </justification>
  </clause>

  <clause id="26767">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) * w,v5,v6) = a((x * y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26630,a(flip),b,26602,a),flip(a)].">
      <j1 rule="hyper" parents="370 26630 26602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26768">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) * w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x * y) * w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26602(a,2),26754(a,1))].">
      <j1 rule="para" parents="26602 26754"/>
    </justification>
  </clause>

  <clause id="26769">
    <literal><![CDATA[
      a((((x * y) * z) * (a(z,x,y) \ K(u,w))) * v5,v6,v7) = a(((x * y) * R(z,x,y)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(16503(a,1),26767(a,2,1,1))].">
      <j1 rule="para" parents="16503 26767"/>
    </justification>
  </clause>

  <clause id="26770">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((x * z) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26682,a,xx),flip(a)].">
      <j1 rule="hyper" parents="26682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26772">
    <literal><![CDATA[
      a((x \ (y \ (z / u))) * w,v5,v6) = a((x \ (y \ (u \ z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(109(a,1),26698(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 26698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26773">
    <literal><![CDATA[
      a(x \ (y * L(y,z,z)),u,w) = a(x \ a(z,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26759,a(flip),b,26713,a),flip(a)].">
      <j1 rule="hyper" parents="60 26759 26713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26774">
    <literal><![CDATA[
      a(((x \ 1) * (1 / y)) \ x,z,u) = a(x \ ((y \ 1) \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(26550,a,26718,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26550 26718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26775">
    <literal><![CDATA[
      a(x,y * (z \ ((1 / u) \ w)),v5) = a(x,y * (z \ (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26626,a(flip),b,26729,a),flip(a)].">
      <j1 rule="hyper" parents="370 26626 26729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26776">
    <literal><![CDATA[
      a(x,(y \ (z / u)) * w,v5) = a(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26486,a(flip),b,26730,a),flip(a)].">
      <j1 rule="hyper" parents="60 26486 26730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26777">
    <literal><![CDATA[
      a(x \ (y * ((1 / z) \ u)),w,v5) = a(x \ (y * (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26648,a(flip),b,26736,a)].">
      <j1 rule="hyper" parents="60 26648 26736"/>
    </justification>
  </clause>

  <clause id="26778">
    <literal><![CDATA[
      a(x \ (y * (z \ (1 / z))),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(197(a,1),26736(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="197 26736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26779">
    <literal><![CDATA[
      a(x \ (y \ (z * (u * (w \ (1 / w))))),v5,v6) = a(x \ (y \ (z * u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(1463(a,2),26778(a,1,1,2))].">
      <j1 rule="para" parents="1463 26778"/>
    </justification>
  </clause>

  <clause id="26780">
    <literal><![CDATA[
      a((T(x * y,z) \ u) * w,v5,v6) = a(w * ((T(x,v7) * y) \ u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26395,a,b,26739,a)].">
      <j1 rule="hyper" parents="370 26395 26739"/>
    </justification>
  </clause>

  <clause id="26781">
    <literal><![CDATA[
      a(((x \ 1) * (1 / y)) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26711,a(flip),b,26774,a),flip(a)].">
      <j1 rule="hyper" parents="370 26711 26774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26782">
    <literal><![CDATA[
      a(((x \ 1) * y) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2999,a(flip),b,26781,a)].">
      <j1 rule="hyper" parents="60 2999 26781"/>
    </justification>
  </clause>

  <clause id="26783">
    <literal><![CDATA[
      a((x * y) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26715,a(flip),b,26782,a)].">
      <j1 rule="hyper" parents="60 26715 26782"/>
    </justification>
  </clause>

  <clause id="26784">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(26527,a,26783,a)].">
      <j1 rule="hyper" parents="26527 26783"/>
    </justification>
  </clause>

  <clause id="26785">
    <literal><![CDATA[
      a(x * (y \ L(z,y,y)),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),26641(a,1,1,2,1))].">
      <j1 rule="para" parents="77 26641"/>
    </justification>
  </clause>

  <clause id="26786">
    <literal><![CDATA[
      a(x * ((y \ 1) * z),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(2072(a,1),26785(a,1,1,2))].">
      <j1 rule="para" parents="2072 26785"/>
    </justification>
  </clause>

  <clause id="26787">
    <literal><![CDATA[
      a(((x \ 1) * y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26786,a)].">
      <j1 rule="hyper" parents="26519 26786"/>
    </justification>
  </clause>

  <clause id="26788">
    <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(8210(a,1),26681(a,1,1,2,2))].">
      <j1 rule="para" parents="8210 26681"/>
    </justification>
  </clause>

  <clause id="26789">
    <literal><![CDATA[
      a(x * (y * ((z * z) \ (u / w))),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * (y * (w \ ((z * z) \ u))),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(998(a,1),26686(a,1,1,2,2))].">
      <j1 rule="para" parents="998 26686"/>
    </justification>
  </clause>

  <clause id="26790">
    <literal><![CDATA[
      a(x,y * ((z * u) \ z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z \ (u \ z)),w) = v5
    ]]></literal>
    <justification jstring="[para(26622(a,2),26693(a,1))].">
      <j1 rule="para" parents="26622 26693"/>
    </justification>
  </clause>

  <clause id="26792">
    <literal><![CDATA[
      a(x * (((y * y) \ z) \ u),w,v5) = a(x * (u / z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26608,a(flip),b,26501,a),flip(a)].">
      <j1 rule="hyper" parents="370 26608 26501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26794">
    <literal><![CDATA[
      a(x * (((y * y) \ z) \ u),w,v5) = a(x * (z \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26438,a(flip),b,26792,a),flip(a)].">
      <j1 rule="hyper" parents="370 26438 26792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26795">
    <literal><![CDATA[
      a(x * (y \ ((z * z) * u)),w,v5) = a(x * (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(849(a,1),26794(a,1,1,2))].">
      <j1 rule="para" parents="849 26794"/>
    </justification>
  </clause>

  <clause id="26797">
    <literal><![CDATA[
      a(x * (y \ ((1 / z) * u)),w,v5) = a(x * (y \ (z * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(314(a,1),26795(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="314 26795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26798">
    <literal><![CDATA[
      a((x \ ((1 / y) * z)) * u,w,v5) = a(u * (x \ (y * z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26797,a)].">
      <j1 rule="hyper" parents="26519 26797"/>
    </justification>
  </clause>

  <clause id="26799">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,v5) = a((x * (z * y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26528,a,26504,a)].">
      <j1 rule="hyper" parents="26528 26504"/>
    </justification>
  </clause>

  <clause id="26801">
    <literal><![CDATA[
      a((x * (y * ((z * z) \ u))) \ w,v5,v6) = a((x * (u * y)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(3291,a,26799,a),flip(a)].">
      <j1 rule="hyper" parents="3291 26799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26802">
    <literal><![CDATA[
      a((x * (y * ((y * y) \ z))) \ u,w,v5) = a((x * (z * (y \ 1))) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(944(a,2),26799(a,1,1,1,2))].">
      <j1 rule="para" parents="944 26799"/>
    </justification>
  </clause>

  <clause id="26804">
    <literal><![CDATA[
      a((x * ((y * z) * K(y,u))) \ w,v5,v6) = a((x * (T(y,u) * z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26799(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7864 26799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26805">
    <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(26505(a,1),26373(a,1))].">
      <j1 rule="para" parents="26505 26373"/>
    </justification>
  </clause>

  <clause id="26806">
    <literal><![CDATA[
      a((x \ (((y * y) / z) * u)) * w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x \ (((1 / z) * u) * (y * y))) * w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(576(a,1),26805(a,1,1,1,2))].">
      <j1 rule="para" parents="576 26805"/>
    </justification>
  </clause>

  <clause id="26807">
    <literal><![CDATA[
      a(x,(y \ (z * u)) * w,v5) = a(x,w * (y \ (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(26554,a,26515,a)].">
      <j1 rule="hyper" parents="26554 26515"/>
    </justification>
  </clause>

  <clause id="26809">
    <literal><![CDATA[
      a(x,(y \ (R(z,u,u) * ((u \ 1) \ 1))) * w,v5) = a(x,w * (y \ R(u * z,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(4484(a,1),26807(a,2,2,2,2))].">
      <j1 rule="para" parents="4484 26807"/>
    </justification>
  </clause>

  <clause id="26810">
    <literal><![CDATA[
      a(x * L((y / z) \ u,w,v5),v6,v7) = a(x * L((z \ y) \ u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(109(a,1),26603(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 26603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26811">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) \ v5,v6) = a(x,(y * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26692,a,26621,a),flip(a)].">
      <j1 rule="hyper" parents="26692 26621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26812">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26621(a,1),26692(a,1))].">
      <j1 rule="para" parents="26621 26692"/>
    </justification>
  </clause>

  <clause id="26814">
    <literal><![CDATA[
      a(x,(y * ((z / u) \ w)) \ v5,v6) = a(x,(y * ((u \ z) \ w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(8210(a,1),26811(a,1,2,1,2))].">
      <j1 rule="para" parents="8210 26811"/>
    </justification>
  </clause>

  <clause id="26815">
    <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(8210(a,1),26812(a,1,2,1,2))].">
      <j1 rule="para" parents="8210 26812"/>
    </justification>
  </clause>

  <clause id="26816">
    <literal><![CDATA[
      a((x * (y \ (z * z))) * u,w,v5) = a((x * y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26608,a(flip),b,26660,a),flip(a)].">
      <j1 rule="hyper" parents="370 26608 26660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26818">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26659,a,b,26816,a)].">
      <j1 rule="hyper" parents="60 26659 26816"/>
    </justification>
  </clause>

  <clause id="26819">
    <literal><![CDATA[
      a(x * (y * ((z * z) \ u)),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,26818,a)].">
      <j1 rule="hyper" parents="26519 26818"/>
    </justification>
  </clause>

  <clause id="26821">
    <literal><![CDATA[
      a((L(x \ 1,y,z) * u) * w,v5,v6) = a((L(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3910(a,1),26818(a,1,1,1))].">
      <j1 rule="para" parents="3910 26818"/>
    </justification>
  </clause>

  <clause id="26822">
    <literal><![CDATA[
      a(x * (L(y \ 1,z,u) * w),v5,v6) = a((L(y,z,u) * w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(3910(a,1),26819(a,1,1,2))].">
      <j1 rule="para" parents="3910 26819"/>
    </justification>
  </clause>

  <clause id="26823">
    <literal><![CDATA[
      a(L(x \ (y * y),z,u),w,v5) = a(L(x \ 1,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4266(a,1),26712(a,1,1))].">
      <j1 rule="para" parents="4266 26712"/>
    </justification>
  </clause>

  <clause id="26824">
    <literal><![CDATA[
      a(L(x \ (y * y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,3869,a(flip),b,26823,a),flip(a)].">
      <j1 rule="hyper" parents="370 3869 26823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26825">
    <literal><![CDATA[
      a(x \ (y \ (z \ (T(u,w) * v5))),v6,v7) = a(x \ (y \ (z \ (u * v5))),v6,v7)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26727(a,1,1,2,2,2))].">
      <j1 rule="para" parents="7864 26727"/>
    </justification>
  </clause>

  <clause id="26826">
    <literal><![CDATA[
      a((x \ (R(1 / y,y,z \ u) \ (z \ u))) * w,v5,v6) = a((x \ (y * (u / z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24943(a,1),26772(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24943 26772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26827">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(((y * u) \ w) * x,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26780(a,1),26530(a,1))].">
      <j1 rule="para" parents="26780 26530"/>
    </justification>
  </clause>

  <clause id="26828">
    <literal><![CDATA[
      a(x * (L(y \ 1,z,u) * w),v5,v6) = a(x * (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,26822,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 26822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26829">
    <literal><![CDATA[
      a(x * (y * L(z \ 1,u,w)),v5,v6) = a(x * (L(z,u,w) * y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26548,a,26828,a)].">
      <j1 rule="hyper" parents="26548 26828"/>
    </justification>
  </clause>

  <clause id="26830">
    <literal><![CDATA[
      a(x * (L(1 / y,z,u) * w),v5,v6) = a(x * (w * L(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(77(a,1),26829(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 26829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26831">
    <literal><![CDATA[
      a(x * (y * (z * (z * (L(z,u,w) \ 1)))),v5,v6) = a(x * (L(L(z \ 1,u,w),z,z) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(4020(a,1),26829(a,1,1,2,2))].">
      <j1 rule="para" parents="4020 26829"/>
    </justification>
  </clause>

  <clause id="26832">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ ((y * (z / (x \ 1))) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x \ z,x) = u
    ]]></literal>
    <justification jstring="[para(26481(a,2),3063(a,1))].">
      <j1 rule="para" parents="26481 3063"/>
    </justification>
  </clause>

  <clause id="26833">
    <literal><![CDATA[
      a(x,y * (a(z,u,z) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(26582,a,15010,a)].">
      <j1 rule="hyper" parents="26582 15010"/>
    </justification>
  </clause>

  <clause id="26834">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) * u,w,v5) = a(L(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26397,a(flip),b,26741,a),flip(a)].">
      <j1 rule="hyper" parents="370 26397 26741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26836">
    <literal><![CDATA[
      a(x * L((y * y) * z,u,w),v5,v6) = a(L(z,u,w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(2975,a,26431,a),flip(a)].">
      <j1 rule="hyper" parents="2975 26431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26838">
    <literal><![CDATA[
      a(x * L((y \ 1) \ z,u,w),v5,v6) = a(L(y \ z,u,w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(936(a,1),26836(a,1,1,2,1))].">
      <j1 rule="para" parents="936 26836"/>
    </justification>
  </clause>

  <clause id="26839">
    <literal><![CDATA[
      a(x,(((y \ 1) \ z) * u) \ w,v5) = a(x,((y \ z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(3038,a,26512,a)].">
      <j1 rule="hyper" parents="3038 26512"/>
    </justification>
  </clause>

  <clause id="26841">
    <literal><![CDATA[
      a(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ ((y * x) * z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(26447(a,1),26536(a,1))].">
      <j1 rule="para" parents="26447 26536"/>
    </justification>
  </clause>

  <clause id="26843">
    <literal><![CDATA[
      a(((x \ (y \ z)) * (y * y)) * u,w,v5) = a((x \ ((y \ 1) \ z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(513(a,1),26640(a,1,1,1))].">
      <j1 rule="para" parents="513 26640"/>
    </justification>
  </clause>

  <clause id="26844">
    <literal><![CDATA[
      a(x,(y * (z \ u)) \ (K(z,w) * v5),v6) = a(x,((T(z,w) \ u) * y) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(23596(a,1),26650(a,1,2))].">
      <j1 rule="para" parents="23596 26650"/>
    </justification>
  </clause>

  <clause id="26845">
    <literal><![CDATA[
      a(x,y * ((z * (u \ 1)) * w),v5) = a(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(26624,a,26656,a)].">
      <j1 rule="hyper" parents="26624 26656"/>
    </justification>
  </clause>

  <clause id="26846">
    <literal><![CDATA[
      a(x,y * (z * (u * (w \ 1))),v5) = a(x,y * ((u * w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(26586,a,26845,a)].">
      <j1 rule="hyper" parents="26586 26845"/>
    </justification>
  </clause>

  <clause id="26848">
    <literal><![CDATA[
      a((x * (y \ a(x,z,x))) * u,w,v5) = a((L(x,z,x) * y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(11712(a,1),26662(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11712 26662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26849">
    <literal><![CDATA[
      a((x * (y \ a(z,u,z))) * w,v5,v6) = a((x * y) * (a(z,u,z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14323(a,1),26662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14323 26662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26850">
    <literal><![CDATA[
      a(x * ((y * z) * (K(y,u) * w)),v5,v6) = a(x * (w * (T(y,u) * z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(23547(a,1),26666(a,1,1,2))].">
      <j1 rule="para" parents="23547 26666"/>
    </justification>
  </clause>

  <clause id="26851">
    <literal><![CDATA[
      a((x / y) * ((x * y) * y),z,u) = a((x * y) * (y * (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(26522,a,26671,a)].">
      <j1 rule="hyper" parents="26522 26671"/>
    </justification>
  </clause>

  <clause id="26852">
    <literal><![CDATA[
      a((x \ y) * ((y * x) * x),z,u) = a((y * x) * (x * (x \ y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(26524,a,26851,a)].">
      <j1 rule="hyper" parents="26524 26851"/>
    </justification>
  </clause>

  <clause id="26854">
    <literal><![CDATA[
      a((x \ y) * ((y * x) * x),z,u) = a((y * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),26852(a,2,1,2))].">
      <j1 rule="para" parents="5 26852"/>
    </justification>
  </clause>

  <clause id="26856">
    <literal><![CDATA[
      a((x \ y) * ((y * x) * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(26854(a,2),26429(a,1))].">
      <j1 rule="para" parents="26854 26429"/>
    </justification>
  </clause>

  <clause id="26857">
    <literal><![CDATA[
      a((x * (y * (z \ 1))) \ u,w,v5) = a((x * (y * z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26801,a(flip),b,26802,a),flip(a)].">
      <j1 rule="hyper" parents="60 26801 26802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26859">
    <literal><![CDATA[
      a(K(x,y) * ((z * (y * u)) \ w),v5,v6) = a((z * (T(y,x) * u)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25121(a,1),26804(a,1,1))].">
      <j1 rule="para" parents="25121 26804"/>
    </justification>
  </clause>

  <clause id="26860">
    <literal><![CDATA[
      a(x * L((y \ 1) \ a(z,u,y),w,v5),v6,v7) = a(x * L(y * a(z,u,y),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(14788(a,1),26810(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14788 26810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26861">
    <literal><![CDATA[
      a(x \ (y \ (z \ (u * (T(w,u) * v5)))),v6,v7) = a(x \ (y \ (z \ (u * (w * v5)))),v6,v7)
    ]]></literal>
    <justification jstring="[para(7946(a,1),26825(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7946 26825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26862">
    <literal><![CDATA[
      a(x \ (y \ (z \ (K(u,w) * (v5 * (u * v6))))),v7,v8) = a(x \ (y \ (z \ (v5 * (T(T(u,v5),w) * v6)))),v7,v8)
    ]]></literal>
    <justification jstring="[para(26368(a,1),26825(a,1,1,2,2,2))].">
      <j1 rule="para" parents="26368 26825"/>
    </justification>
  </clause>

  <clause id="26863">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((y * y) * u),w,v5) = a((x \ ((y \ 1) \ z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),26843(a,1,1))].">
      <j1 rule="para" parents="29 26843"/>
    </justification>
  </clause>

  <clause id="26864">
    <literal><![CDATA[
      a(x,((T(y,z) \ u) * w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,(w * (y \ u)) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26844(a,1),26574(a,1))].">
      <j1 rule="para" parents="26844 26574"/>
    </justification>
  </clause>

  <clause id="26866">
    <literal><![CDATA[
      a((x * (y \ a(z,u,z))) * w,v5,v6) = a((x * y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,14312,a(flip),b,26849,a),flip(a)].">
      <j1 rule="hyper" parents="370 14312 26849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26868">
    <literal><![CDATA[
      a((L(x,y,x) * z) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26848,a(flip),b,26866,a)].">
      <j1 rule="hyper" parents="60 26848 26866"/>
    </justification>
  </clause>

  <clause id="26870">
    <literal><![CDATA[
      a(x * (y * (T(z,u) * w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * ((z * w) * y),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26850(a,1),26681(a,1))].">
      <j1 rule="para" parents="26850 26681"/>
    </justification>
  </clause>

  <clause id="26871">
    <literal><![CDATA[
      a((x * (T(y,z) * u)) \ w,v5,v6) = a((x * (y * u)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26373,a,26859,a),flip(a)].">
      <j1 rule="hyper" parents="26373 26859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26872">
    <literal><![CDATA[
      a((x * (T(y,z) * u)) \ w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x * (y * u)) \ w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26859(a,1),26373(a,1))].">
      <j1 rule="para" parents="26859 26373"/>
    </justification>
  </clause>

  <clause id="26874">
    <literal><![CDATA[
      a((x \ ((y \ 1) \ z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ (y \ z)) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(26863(a,1),26610(a,1))].">
      <j1 rule="para" parents="26863 26610"/>
    </justification>
  </clause>

  <clause id="26876">
    <literal><![CDATA[
      a(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(26357(a,1),1029(a,1))].">
      <j1 rule="para" parents="26357 1029"/>
    </justification>
  </clause>

  <clause id="26877">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(26876,a,26464,a)].">
      <j1 rule="hyper" parents="26876 26464"/>
    </justification>
  </clause>

  <clause id="26880">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1811(a,2),26877(a,1,3))].">
      <j1 rule="para" parents="1811 26877"/>
    </justification>
  </clause>

  <clause id="26881">
    <literal><![CDATA[
      a(x,y,(z * u) / z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(5228(a,2),26877(a,1,3))].">
      <j1 rule="para" parents="5228 26877"/>
    </justification>
  </clause>

  <clause id="26882">
    <literal><![CDATA[
      a(x,y,z / u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(5232(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="5232 26877"/>
    </justification>
  </clause>

  <clause id="26883">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5300(a,2),26877(a,1,3))].">
      <j1 rule="para" parents="5300 26877"/>
    </justification>
  </clause>

  <clause id="26884">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(5302(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="5302 26877"/>
    </justification>
  </clause>

  <clause id="26885">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6130(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="6130 26877"/>
    </justification>
  </clause>

  <clause id="26886">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="6128 26877"/>
    </justification>
  </clause>

  <clause id="26888">
    <literal><![CDATA[
      a(x,y,z * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(7481(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="7481 26877"/>
    </justification>
  </clause>

  <clause id="26889">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(7479(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="7479 26877"/>
    </justification>
  </clause>

  <clause id="26890">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(7477(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="7477 26877"/>
    </justification>
  </clause>

  <clause id="26891">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(7858(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7858 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26892">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="7864 26877"/>
    </justification>
  </clause>

  <clause id="26893">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8016(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="8016 26877"/>
    </justification>
  </clause>

  <clause id="26894">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(7966(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7966 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26895">
    <literal><![CDATA[
      a(x,y,(z / u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(8210(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="8210 26877"/>
    </justification>
  </clause>

  <clause id="26896">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(8364(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="8364 26877"/>
    </justification>
  </clause>

  <clause id="26897">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(9765(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="9765 26877"/>
    </justification>
  </clause>

  <clause id="26898">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(10354(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10354 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26899">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(12083(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="12083 26877"/>
    </justification>
  </clause>

  <clause id="26900">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(12088(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="12088 26877"/>
    </justification>
  </clause>

  <clause id="26901">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(12466(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="12466 26877"/>
    </justification>
  </clause>

  <clause id="26903">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(16495(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="16495 26877"/>
    </justification>
  </clause>

  <clause id="26904">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(22739(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="22739 26877"/>
    </justification>
  </clause>

  <clause id="26906">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(25060(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25060 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26907">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) \ v5) = a(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(25116(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25116 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26908">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5) * v6) = a(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(25148(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="25148 26877"/>
    </justification>
  </clause>

  <clause id="26909">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(25064(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="25064 26877"/>
    </justification>
  </clause>

  <clause id="26910">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(25624(a,1),26877(a,1,3))].">
      <j1 rule="para" parents="25624 26877"/>
    </justification>
  </clause>

  <clause id="26911">
    <literal><![CDATA[
      a(x,y,L(T(z,u) \ w,v5,v6)) = a(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(25742(a,1),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25742 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26912">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(25993(a,2),26877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25993 26877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26913">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(K(w,v5) * x,y,K(v6,v7) * z) = u
    ]]></literal>
    <justification jstring="[para(26877(a,1),26521(a,1))].">
      <j1 rule="para" parents="26877 26521"/>
    </justification>
  </clause>

  <clause id="26915">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(26557,a,26880,a),flip(a)].">
      <j1 rule="hyper" parents="26557 26880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26917">
    <literal><![CDATA[
      a(x,T(y,z),T(u,w)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26451,a(flip),b,26880,a),flip(a)].">
      <j1 rule="hyper" parents="370 26451 26880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26920">
    <literal><![CDATA[
      a(x,y,z) = R(R(x,y,T(z,y)) / x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,19670,a,b,26880,a),flip(a)].">
      <j1 rule="hyper" parents="60 19670 26880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26921">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(285(a,1),26880(a,1,3)),flip(a)].">
      <j1 rule="para" parents="285 26880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26922">
    <literal><![CDATA[
      R(x,y * z,a(x,z,y)) \ ((x * z) * T(y,z)) = (z * T(y,z)) * a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(26880(a,1),2430(a,1,1,3))].">
      <j1 rule="para" parents="26880 2430"/>
    </justification>
  </clause>

  <clause id="26923">
    <literal><![CDATA[
      a(x,y,z * K(u,z)) = a(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(5353(a,1),26880(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5353 26880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26927">
    <literal><![CDATA[
      a(x,y,T(z / u,w)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26880,a,b,26882,a)].">
      <j1 rule="hyper" parents="60 26880 26882"/>
    </justification>
  </clause>

  <clause id="26928">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(3117,a,26888,a),flip(a)].">
      <j1 rule="hyper" parents="3117 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26929">
    <literal><![CDATA[
      a(x,y,(z * u) * z) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(3115,a,26888,a),flip(a)].">
      <j1 rule="hyper" parents="3115 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26930">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,19763,a,b,26888,a)].">
      <j1 rule="hyper" parents="370 19763 26888"/>
    </justification>
  </clause>

  <clause id="26931">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,15770,a,b,26888,a)].">
      <j1 rule="hyper" parents="370 15770 26888"/>
    </justification>
  </clause>

  <clause id="26932">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ (v5 * v5))) \ v6)) = a(x,y,((u \ w) \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3166,a(flip),b,26888,a),flip(a)].">
      <j1 rule="hyper" parents="370 3166 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26933">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * w) * v5)) = a(x,y,((u * w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3161,a(flip),b,26888,a),flip(a)].">
      <j1 rule="hyper" parents="370 3161 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26934">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3138,a(flip),b,26888,a),flip(a)].">
      <j1 rule="hyper" parents="370 3138 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26936">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ w) * z) = v5
    ]]></literal>
    <justification jstring="[para(26888(a,1),3117(a,1))].">
      <j1 rule="para" parents="26888 3117"/>
    </justification>
  </clause>

  <clause id="26937">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,23518,a,b,26893,a)].">
      <j1 rule="hyper" parents="370 23518 26893"/>
    </justification>
  </clause>

  <clause id="26939">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(5631(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="5631 26893"/>
    </justification>
  </clause>

  <clause id="26940">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(5944(a,1),26893(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5944 26893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26941">
    <literal><![CDATA[
      a(x,y,z * (u * w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(6770(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="6770 26893"/>
    </justification>
  </clause>

  <clause id="26942">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(6930(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="6930 26893"/>
    </justification>
  </clause>

  <clause id="26943">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(15583(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="15583 26893"/>
    </justification>
  </clause>

  <clause id="26944">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(20260(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="20260 26893"/>
    </justification>
  </clause>

  <clause id="26945">
    <literal><![CDATA[
      a(x,y,z \ (u \ T(w,v5))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(25036(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="25036 26893"/>
    </justification>
  </clause>

  <clause id="26946">
    <literal><![CDATA[
      a(x,y,z \ L(T(u,w),v5,v6)) = a(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25755(a,1),26893(a,1,3))].">
      <j1 rule="para" parents="25755 26893"/>
    </justification>
  </clause>

  <clause id="26947">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(26915(a,1),26412(a,1))].">
      <j1 rule="para" parents="26915 26412"/>
    </justification>
  </clause>

  <clause id="26949">
    <literal><![CDATA[
      a(x,y,z \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(17(a,1),26947(a,1,3))].">
      <j1 rule="para" parents="17 26947"/>
    </justification>
  </clause>

  <clause id="26951">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(108(a,1),26947(a,1,3))].">
      <j1 rule="para" parents="108 26947"/>
    </justification>
  </clause>

  <clause id="26952">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) \ v5)) = a(x,y,z * ((u * u) * (v5 / w)))
    ]]></literal>
    <justification jstring="[para(25830(a,1),26885(a,1,3,2))].">
      <j1 rule="para" parents="25830 26885"/>
    </justification>
  </clause>

  <clause id="26953">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5) * v6) = a(x,y,L(u \ z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(285(a,1),26892(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="285 26892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26954">
    <literal><![CDATA[
      a(x,y,(z * K(u,z)) * w) = a(x,y,L(z,u,z) * w)
    ]]></literal>
    <justification jstring="[para(5353(a,1),26892(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5353 26892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26955">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,((z * z) * (w / u)) * v5)
    ]]></literal>
    <justification jstring="[para(25830(a,1),26892(a,1,3,1))].">
      <j1 rule="para" parents="25830 26892"/>
    </justification>
  </clause>

  <clause id="26956">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(1141(a,2),26927(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1141 26927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26957">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(3108,a,26931,a)].">
      <j1 rule="hyper" parents="3108 26931"/>
    </justification>
  </clause>

  <clause id="26959">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(26937(a,1),225(a,1)),flip(b)].">
      <j1 rule="para" parents="26937 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26960">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26893,a(flip),b,26923,a),flip(a)].">
      <j1 rule="hyper" parents="60 26893 26923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26962">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(3130(a,1),26951(a,1))].">
      <j1 rule="para" parents="3130 26951"/>
    </justification>
  </clause>

  <clause id="26965">
    <literal><![CDATA[
      a(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(87(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="87 26959"/>
    </justification>
  </clause>

  <clause id="26966">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(353(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="353 26959"/>
    </justification>
  </clause>

  <clause id="26967">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(628(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="628 26959"/>
    </justification>
  </clause>

  <clause id="26968">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(2219(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="2219 26959"/>
    </justification>
  </clause>

  <clause id="26969">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = v5
    ]]></literal>
    <justification jstring="[para(2218(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="2218 26959"/>
    </justification>
  </clause>

  <clause id="26970">
    <literal><![CDATA[
      a(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(5279(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="5279 26959"/>
    </justification>
  </clause>

  <clause id="26972">
    <literal><![CDATA[
      a(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(5631(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="5631 26959"/>
    </justification>
  </clause>

  <clause id="26973">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(6280(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="6280 26959"/>
    </justification>
  </clause>

  <clause id="26974">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(6282(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="6282 26959"/>
    </justification>
  </clause>

  <clause id="26975">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(6353(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="6353 26959"/>
    </justification>
  </clause>

  <clause id="26976">
    <literal><![CDATA[
      a(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(6770(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="6770 26959"/>
    </justification>
  </clause>

  <clause id="26977">
    <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(6930(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="6930 26959"/>
    </justification>
  </clause>

  <clause id="26978">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(7997(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="7997 26959"/>
    </justification>
  </clause>

  <clause id="26979">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(8104(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="8104 26959"/>
    </justification>
  </clause>

  <clause id="26980">
    <literal><![CDATA[
      a(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(8564(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="8564 26959"/>
    </justification>
  </clause>

  <clause id="26981">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(20260(a,1),26959(a,1,3))].">
      <j1 rule="para" parents="20260 26959"/>
    </justification>
  </clause>

  <clause id="26982">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(25725(a,2),26959(a,1,3))].">
      <j1 rule="para" parents="25725 26959"/>
    </justification>
  </clause>

  <clause id="26984">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(26923(a,1),26959(a,1))].">
      <j1 rule="para" parents="26923 26959"/>
    </justification>
  </clause>

  <clause id="26985">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(94(a,2),26962(a,1,3))].">
      <j1 rule="para" parents="94 26962"/>
    </justification>
  </clause>

  <clause id="26986">
    <literal><![CDATA[
      a(x,y,z * (L(z,u,w) \ z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2160(a,1),26962(a,1,3))].">
      <j1 rule="para" parents="2160 26962"/>
    </justification>
  </clause>

  <clause id="26987">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3092(a,2),26962(a,1))].">
      <j1 rule="para" parents="3092 26962"/>
    </justification>
  </clause>

  <clause id="26988">
    <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(14751(a,1),26962(a,1,3))].">
      <j1 rule="para" parents="14751 26962"/>
    </justification>
  </clause>

  <clause id="26989">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w * w)) = u
    ]]></literal>
    <justification jstring="[para(3074(a,1),26965(a,1))].">
      <j1 rule="para" parents="3074 26965"/>
    </justification>
  </clause>

  <clause id="26990">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * (w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v5 * (w * a(z,u,z))) = v6
    ]]></literal>
    <justification jstring="[para(13924(a,1),26965(a,1,3))].">
      <j1 rule="para" parents="13924 26965"/>
    </justification>
  </clause>

  <clause id="26991">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(15770(a,2),26965(a,1))].">
      <j1 rule="para" parents="15770 26965"/>
    </justification>
  </clause>

  <clause id="26992">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * w) * z) = v5
    ]]></literal>
    <justification jstring="[para(15784(a,2),26965(a,1))].">
      <j1 rule="para" parents="15784 26965"/>
    </justification>
  </clause>

  <clause id="26993">
    <literal><![CDATA[
      a(x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,x,x * y) = z
    ]]></literal>
    <justification jstring="[para(26930(a,2),26965(a,1))].">
      <j1 rule="para" parents="26930 26965"/>
    </justification>
  </clause>

  <clause id="26994">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(26931(a,2),26965(a,1))].">
      <j1 rule="para" parents="26931 26965"/>
    </justification>
  </clause>

  <clause id="26995">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ u),w,v5) * z) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(3914(a,2),26966(a,1,3,1))].">
      <j1 rule="para" parents="3914 26966"/>
    </justification>
  </clause>

  <clause id="26996">
    <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(3931(a,1),26966(a,1,3))].">
      <j1 rule="para" parents="3931 26966"/>
    </justification>
  </clause>

  <clause id="26997">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(7947(a,2),26978(a,1,3))].">
      <j1 rule="para" parents="7947 26978"/>
    </justification>
  </clause>

  <clause id="26998">
    <literal><![CDATA[
      a(x,y,(z / u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(8210(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="8210 26978"/>
    </justification>
  </clause>

  <clause id="26999">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * v5) = v6
    ]]></literal>
    <justification jstring="[para(12016(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="12016 26978"/>
    </justification>
  </clause>

  <clause id="27000">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12083(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="12083 26978"/>
    </justification>
  </clause>

  <clause id="27001">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ w) = v5
    ]]></literal>
    <justification jstring="[para(12088(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="12088 26978"/>
    </justification>
  </clause>

  <clause id="27002">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(12466(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="12466 26978"/>
    </justification>
  </clause>

  <clause id="27003">
    <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(16495(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="16495 26978"/>
    </justification>
  </clause>

  <clause id="27004">
    <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(25119(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="25119 26978"/>
    </justification>
  </clause>

  <clause id="27006">
    <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(25064(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="25064 26978"/>
    </justification>
  </clause>

  <clause id="27007">
    <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(25624(a,1),26978(a,1,3))].">
      <j1 rule="para" parents="25624 26978"/>
    </justification>
  </clause>

  <clause id="27008">
    <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(25728(a,2),26978(a,1,3))].">
      <j1 rule="para" parents="25728 26978"/>
    </justification>
  </clause>

  <clause id="27009">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(551(a,1),26987(a,1,3))].">
      <j1 rule="para" parents="551 26987"/>
    </justification>
  </clause>

  <clause id="27010">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(94(a,2),26987(a,1,3))].">
      <j1 rule="para" parents="94 26987"/>
    </justification>
  </clause>

  <clause id="27011">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * w) = v5
    ]]></literal>
    <justification jstring="[para(514(a,1),26987(a,1,3))].">
      <j1 rule="para" parents="514 26987"/>
    </justification>
  </clause>

  <clause id="27012">
    <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(3789(a,2),26987(a,1,3))].">
      <j1 rule="para" parents="3789 26987"/>
    </justification>
  </clause>

  <clause id="27013">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,(z \ (z / u)) * w)
    ]]></literal>
    <justification jstring="[para(3501(a,1),26894(a,1,3,1))].">
      <j1 rule="para" parents="3501 26894"/>
    </justification>
  </clause>

  <clause id="27014">
    <literal><![CDATA[
      a(x,y,(1 / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(26895(a,2),3116(a,1))].">
      <j1 rule="para" parents="26895 3116"/>
    </justification>
  </clause>

  <clause id="27015">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,26896,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 26896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27016">
    <literal><![CDATA[
      a(x,y,(z / ((u \ 1) * z)) * w) = a(x,y,(z \ ((1 / u) \ z)) * w)
    ]]></literal>
    <justification jstring="[para(2771(a,1),26896(a,1,3,1))].">
      <j1 rule="para" parents="2771 26896"/>
    </justification>
  </clause>

  <clause id="27017">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((w * u) * z)) * v5) = a(x,y,R(w * K(u,z),u,z) * v5)
    ]]></literal>
    <justification jstring="[para(25688(a,1),26896(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="25688 26896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27019">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) * v6) = a(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[para(10354(a,1),26897(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10354 26897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27020">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) * v6) = a(x,y,((z * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(16495(a,1),26897(a,1,3,1))].">
      <j1 rule="para" parents="16495 26897"/>
    </justification>
  </clause>

  <clause id="27021">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) * v5) * v6) = a(x,y,(((u \ z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(25064(a,1),26897(a,1,3,1))].">
      <j1 rule="para" parents="25064 26897"/>
    </justification>
  </clause>

  <clause id="27022">
    <literal><![CDATA[
      a(x,y,((z \ T(u,w)) * v5) * v6) = a(x,y,((z \ u) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(25624(a,1),26897(a,1,3,1))].">
      <j1 rule="para" parents="25624 26897"/>
    </justification>
  </clause>

  <clause id="27023">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ v5)) = a(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(8210(a,1),26898(a,1,3,2))].">
      <j1 rule="para" parents="8210 26898"/>
    </justification>
  </clause>

  <clause id="27024">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8364(a,1),26898(a,1,3,2))].">
      <j1 rule="para" parents="8364 26898"/>
    </justification>
  </clause>

  <clause id="27025">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) = a(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[para(10354(a,1),26898(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10354 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27026">
    <literal><![CDATA[
      a(x,y,z * ((T(u,w) * v5) * v6)) = a(x,y,z * ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[para(16495(a,1),26898(a,1,3,2))].">
      <j1 rule="para" parents="16495 26898"/>
    </justification>
  </clause>

  <clause id="27027">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * v6))) = a(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(22739(a,1),26898(a,1,3,2))].">
      <j1 rule="para" parents="22739 26898"/>
    </justification>
  </clause>

  <clause id="27028">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) * v6)) = a(x,y,z * (((w \ u) * v5) * v6))
    ]]></literal>
    <justification jstring="[para(25064(a,1),26898(a,1,3,2))].">
      <j1 rule="para" parents="25064 26898"/>
    </justification>
  </clause>

  <clause id="27029">
    <literal><![CDATA[
      a(x,y,(z \ (u * T(w,v5))) * v6) = a(x,y,(z \ (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(25351(a,1),26898(a,1,3))].">
      <j1 rule="para" parents="25351 26898"/>
    </justification>
  </clause>

  <clause id="27030">
    <literal><![CDATA[
      a(x,y,z * R(K(u,w) * v5,v6,v7)) = a(x,y,z * R(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(25672(a,2),26898(a,1,3,2))].">
      <j1 rule="para" parents="25672 26898"/>
    </justification>
  </clause>

  <clause id="27031">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(26965,a,26901,a),flip(a)].">
      <j1 rule="hyper" parents="26965 26901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27032">
    <literal><![CDATA[
      a(x,y,(z * u) * u) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,26929,a(flip),b,26901,a),flip(a)].">
      <j1 rule="hyper" parents="370 26929 26901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27033">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(26901(a,1),26965(a,1))].">
      <j1 rule="para" parents="26901 26965"/>
    </justification>
  </clause>

  <clause id="27034">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(27032(a,1),26965(a,1))].">
      <j1 rule="para" parents="27032 26965"/>
    </justification>
  </clause>

  <clause id="27035">
    <literal><![CDATA[
      a(x,y,z \ K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26962,a,26904,a),flip(a)].">
      <j1 rule="hyper" parents="26962 26904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27036">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8364(a,1),26904(a,1,3,2))].">
      <j1 rule="para" parents="8364 26904"/>
    </justification>
  </clause>

  <clause id="27037">
    <literal><![CDATA[
      a(x,y,z \ (L(T(u,w),v5,v6) \ v7)) = a(x,y,z \ (L(u,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(25547(a,1),26904(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="25547 26904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27038">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,15781,a(flip),b,26939,a),flip(a)].">
      <j1 rule="hyper" parents="60 15781 26939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27039">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,15778,a(flip),b,26941,a),flip(a)].">
      <j1 rule="hyper" parents="370 15778 26941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27040">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * v5) * T(w,u))) = a(x,y,z * (w * ((w * u) * v5)))
    ]]></literal>
    <justification jstring="[para(12474(a,1),26941(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12474 26941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27041">
    <literal><![CDATA[
      a(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * z) = v5
    ]]></literal>
    <justification jstring="[para(26941(a,1),26965(a,1))].">
      <j1 rule="para" parents="26941 26965"/>
    </justification>
  </clause>

  <clause id="27042">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ 1))) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3158,a(flip),b,26943,a),flip(a)].">
      <j1 rule="hyper" parents="370 3158 26943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27043">
    <literal><![CDATA[
      a(x,y,z \ (u / (1 / w))) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15779,a,b,26944,a)].">
      <j1 rule="hyper" parents="60 15779 26944"/>
    </justification>
  </clause>

  <clause id="27044">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,3505,a,b,26944,a)].">
      <j1 rule="hyper" parents="60 3505 26944"/>
    </justification>
  </clause>

  <clause id="27045">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ ((v5 * w) * u))) = a(x,y,z \ R(v5 * K(w,u),w,u))
    ]]></literal>
    <justification jstring="[para(25688(a,1),26944(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="25688 26944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27046">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,3127,a,b,27031,a)].">
      <j1 rule="hyper" parents="60 3127 27031"/>
    </justification>
  </clause>

  <clause id="27047">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * u)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),27031(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5 27031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27048">
    <literal><![CDATA[
      a(x,y,((z * z) * (u * w)) * v5) = a(x,y,v5 * (w * ((z * z) * u)))
    ]]></literal>
    <justification jstring="[para(28(a,1),27031(a,1,3,1))].">
      <j1 rule="para" parents="28 27031"/>
    </justification>
  </clause>

  <clause id="27049">
    <literal><![CDATA[
      a(x,y,R((z * u) \ ((z * u) \ w),v5,v6) * (u * z)) = a(x,y,(z * u) \ R(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(2147(a,1),27031(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2147 27031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27050">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,w * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[para(2480(a,1),27031(a,2,3,2))].">
      <j1 rule="para" parents="2480 27031"/>
    </justification>
  </clause>

  <clause id="27052">
    <literal><![CDATA[
      a(x,y,z * ((1 / u) * w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(551(a,1),27038(a,1,3,2))].">
      <j1 rule="para" parents="551 27038"/>
    </justification>
  </clause>

  <clause id="27053">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(1470(a,1),27038(a,1,3))].">
      <j1 rule="para" parents="1470 27038"/>
    </justification>
  </clause>

  <clause id="27054">
    <literal><![CDATA[
      a(x,y,(z * (u * (w \ 1))) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[para(1468(a,1),27038(a,1,3))].">
      <j1 rule="para" parents="1468 27038"/>
    </justification>
  </clause>

  <clause id="27055">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(3910(a,1),27038(a,1,3))].">
      <j1 rule="para" parents="3910 27038"/>
    </justification>
  </clause>

  <clause id="27056">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * ((v5 * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,26892,a,b,27039,a)].">
      <j1 rule="hyper" parents="370 26892 27039"/>
    </justification>
  </clause>

  <clause id="27057">
    <literal><![CDATA[
      a(x,y,(z \ (u / (1 / w))) * v5) = a(x,y,(z \ (u / w)) * v5)
    ]]></literal>
    <justification jstring="[para(1218(a,1),27039(a,1,3))].">
      <j1 rule="para" parents="1218 27039"/>
    </justification>
  </clause>

  <clause id="27058">
    <literal><![CDATA[
      a(x,y,(z * u) \ u) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,26899,a,b,27044,a)].">
      <j1 rule="hyper" parents="60 26899 27044"/>
    </justification>
  </clause>

  <clause id="27059">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * T(u,w)) * z))) = a(x,y,(z * (K(w,u) / u)) \ z)
    ]]></literal>
    <justification jstring="[para(16278(a,2),27044(a,2,3,2)),flip(a)].">
      <j1 rule="para" parents="16278 27044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27060">
    <literal><![CDATA[
      a(x,y,z * L((u \ w) * u,v5,v6)) = a(x,y,L(w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(3920(a,2),27047(a,1,3,2))].">
      <j1 rule="para" parents="3920 27047"/>
    </justification>
  </clause>

  <clause id="27061">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5) * v6) = a(x,y,v6 * L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(3931(a,1),27047(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3931 27047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27063">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,T(z,y)),x,z * y)
    ]]></literal>
    <justification jstring="[para(2014(a,1),26920(a,2,1))].">
      <j1 rule="para" parents="2014 26920"/>
    </justification>
  </clause>

  <clause id="27064">
    <literal><![CDATA[
      a(x,y,R(z,u,(z * u) \ 1)) = a(x,y,(z * u) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),26957(a,1,3,1))].">
      <j1 rule="para" parents="6 26957"/>
    </justification>
  </clause>

  <clause id="27066">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1953(a,1),26991(a,1,3))].">
      <j1 rule="para" parents="1953 26991"/>
    </justification>
  </clause>

  <clause id="27067">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w) * w) = v5
    ]]></literal>
    <justification jstring="[para(25393(a,1),26991(a,1,3))].">
      <j1 rule="para" parents="25393 26991"/>
    </justification>
  </clause>

  <clause id="27068">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(26888(a,1),26991(a,1))].">
      <j1 rule="para" parents="26888 26991"/>
    </justification>
  </clause>

  <clause id="27071">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[para(12395(a,1),27063(a,2,1,2))].">
      <j1 rule="para" parents="12395 27063"/>
    </justification>
  </clause>

  <clause id="27072">
    <literal><![CDATA[
      R(L(x,y,z) \ R(L(x,y,z),x,u),L(x,y,z),u * x) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(2549,a,27071,a),flip(a)].">
      <j1 rule="hyper" parents="2549 27071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27073">
    <literal><![CDATA[
      R(x,y,z * u) != a(y,u,z)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,u,z) = x
    ]]></literal>
    <justification jstring="[para(27071(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="27071 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27074">
    <literal><![CDATA[
      a(x,y,(((z * z) \ T(u,w)) * v5) * v6) = a(x,y,(u * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(3121,a,26903,a)].">
      <j1 rule="hyper" parents="3121 26903"/>
    </justification>
  </clause>

  <clause id="27075">
    <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(285(a,1),26903(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="285 26903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27076">
    <literal><![CDATA[
      a(x,y,(((1 / z) * u) \ w) * v5) = a(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,3129,a(flip),b,26906,a)].">
      <j1 rule="hyper" parents="60 3129 26906"/>
    </justification>
  </clause>

  <clause id="27077">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ v5) = v6
    ]]></literal>
    <justification jstring="[para(26907(a,2),3116(a,1))].">
      <j1 rule="para" parents="26907 3116"/>
    </justification>
  </clause>

  <clause id="27078">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) * v5) = a(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(109(a,1),26910(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="109 26910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27079">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,26934,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 26934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27080">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(26934(a,2),26965(a,1))].">
      <j1 rule="para" parents="26934 26965"/>
    </justification>
  </clause>

  <clause id="27081">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(109(a,1),26942(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="109 26942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27082">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * u)) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[para(579(a,1),27046(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="579 27046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27083">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,(z \ u) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,4180,a,b,27052,a)].">
      <j1 rule="hyper" parents="60 4180 27052"/>
    </justification>
  </clause>

  <clause id="27084">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,27053,a)].">
      <j1 rule="hyper" parents="26965 27053"/>
    </justification>
  </clause>

  <clause id="27085">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(27056(a,1),26973(a,1))].">
      <j1 rule="para" parents="27056 26973"/>
    </justification>
  </clause>

  <clause id="27086">
    <literal><![CDATA[
      a(x,y,L(z,(u \ w) \ v5,v6) * (v6 * ((w / u) \ v5))) = a(x,y,v6 * (((w / u) \ v5) * z))
    ]]></literal>
    <justification jstring="[para(26030(a,1),26890(a,1,3,1))].">
      <j1 rule="para" parents="26030 26890"/>
    </justification>
  </clause>

  <clause id="27087">
    <literal><![CDATA[
      a(x,y,z * (K(u,z) * w)) = a(x,y,L(z,u,z) * w)
    ]]></literal>
    <justification jstring="[para(7845(a,1),26954(a,1,3))].">
      <j1 rule="para" parents="7845 26954"/>
    </justification>
  </clause>

  <clause id="27088">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) = a(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,26899,a,b,26956,a)].">
      <j1 rule="hyper" parents="60 26899 26956"/>
    </justification>
  </clause>

  <clause id="27089">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) = w
    ]]></literal>
    <justification jstring="[para(26336(a,1),26975(a,1,3))].">
      <j1 rule="para" parents="26336 26975"/>
    </justification>
  </clause>

  <clause id="27090">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(3505(a,2),26981(a,1))].">
      <j1 rule="para" parents="3505 26981"/>
    </justification>
  </clause>

  <clause id="27091">
    <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(6128(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="6128 26999"/>
    </justification>
  </clause>

  <clause id="27092">
    <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(7864(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="7864 26999"/>
    </justification>
  </clause>

  <clause id="27093">
    <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(7873(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="7873 26999"/>
    </justification>
  </clause>

  <clause id="27094">
    <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(8210(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="8210 26999"/>
    </justification>
  </clause>

  <clause id="27095">
    <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(8364(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="8364 26999"/>
    </justification>
  </clause>

  <clause id="27096">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * v6)) = v7
    ]]></literal>
    <justification jstring="[para(12016(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="12016 26999"/>
    </justification>
  </clause>

  <clause id="27097">
    <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(12466(a,1),26999(a,1,3,2))].">
      <j1 rule="para" parents="12466 26999"/>
    </justification>
  </clause>

  <clause id="27098">
    <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(25101(a,1),26999(a,1,3))].">
      <j1 rule="para" parents="25101 26999"/>
    </justification>
  </clause>

  <clause id="27099">
    <literal><![CDATA[
      a(x,y,R(z * u,z,z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(R(u,z,z) * ((z \ 1) \ 1)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(4484(a,1),27000(a,1,3,1))].">
      <j1 rule="para" parents="4484 27000"/>
    </justification>
  </clause>

  <clause id="27100">
    <literal><![CDATA[
      a(x,y,z \ ((z \ u) \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(27058(a,1),27001(a,1))].">
      <j1 rule="para" parents="27058 27001"/>
    </justification>
  </clause>

  <clause id="27101">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(551(a,1),27011(a,1,3,1))].">
      <j1 rule="para" parents="551 27011"/>
    </justification>
  </clause>

  <clause id="27103">
    <literal><![CDATA[
      a(x,y,R(z,u,(z * u) \ 1)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,27032,a(flip),b,27064,a),flip(a)].">
      <j1 rule="hyper" parents="370 27032 27064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27104">
    <literal><![CDATA[
      a(x,y,R(z,u,z * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(2711(a,1),27103(a,1,3))].">
      <j1 rule="para" parents="2711 27103"/>
    </justification>
  </clause>

  <clause id="27105">
    <literal><![CDATA[
      a(x,y,z * ((u * (u * w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (L(w,u,u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(624(a,1),27085(a,1,3,2))].">
      <j1 rule="para" parents="624 27085"/>
    </justification>
  </clause>

  <clause id="27107">
    <literal><![CDATA[
      a(x,y,L(z,u,z) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(26999,a,27087,a),flip(a)].">
      <j1 rule="hyper" parents="26999 27087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27108">
    <literal><![CDATA[
      a(x,y,L(z,u,z) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(27087(a,1),26999(a,1))].">
      <j1 rule="para" parents="27087 26999"/>
    </justification>
  </clause>

  <clause id="27110">
    <literal><![CDATA[
      a(x,y,z * (L(z,u,z) \ w)) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),27107(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 27107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27111">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,L(z,v5,z)) \ (u * w))) = a(x,y,L(L(z,v5,z),w,u) * (u * w))
    ]]></literal>
    <justification jstring="[para(25773(a,1),27107(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25773 27107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27112">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(11702(a,1),27110(a,1,3))].">
      <j1 rule="para" parents="11702 27110"/>
    </justification>
  </clause>

  <clause id="27113">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(14295(a,1),27112(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14295 27112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27114">
    <literal><![CDATA[
      a(x,y,((z \ a(u,w,u)) * v5) * v6) = a(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,14722,a,b,27113,a)].">
      <j1 rule="hyper" parents="60 14722 27113"/>
    </justification>
  </clause>

  <clause id="27115">
    <literal><![CDATA[
      a(x,y,z * L(u,w,u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11507(a,1),27113(a,1,3,2))].">
      <j1 rule="para" parents="11507 27113"/>
    </justification>
  </clause>

  <clause id="27116">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,26912,a(flip),b,27088,a),flip(a)].">
      <j1 rule="hyper" parents="60 26912 27088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27117">
    <literal><![CDATA[
      a(x,y,L(z,u,z * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27104,a(flip),b,27116,a),flip(a)].">
      <j1 rule="hyper" parents="60 27104 27116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27118">
    <literal><![CDATA[
      a(x,y,L(z,u * z,L(u,z,z))) = a(x,y,L(z,u * z,u * z))
    ]]></literal>
    <justification jstring="[para(24029(a,1),27117(a,1,3))].">
      <j1 rule="para" parents="24029 27117"/>
    </justification>
  </clause>

  <clause id="27119">
    <literal><![CDATA[
      a(x,y,((z \ (z * u)) * (z * u)) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,12652,a(flip),b,26909,a),flip(a)].">
      <j1 rule="hyper" parents="60 12652 26909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27120">
    <literal><![CDATA[
      a(x,y,((T(z,z \ 1) / (u * u)) * w) * v5) = a(x,y,(((z \ (u * u)) \ 1) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1258(a,1),26909(a,2,3,1,1))].">
      <j1 rule="para" parents="1258 26909"/>
    </justification>
  </clause>

  <clause id="27121">
    <literal><![CDATA[
      a(x,y,((1 / ((z \ (z / u)) \ 1)) * w) * v5) = a(x,y,(((z * u) \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(3501(a,1),26909(a,2,3,1,1))].">
      <j1 rule="para" parents="3501 26909"/>
    </justification>
  </clause>

  <clause id="27122">
    <literal><![CDATA[
      a(x,y,(((z \ u) / w) * K(u,v5)) * v6) = a(x,y,(w \ (z \ T(u,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(25036(a,1),26909(a,2,3,1))].">
      <j1 rule="para" parents="25036 26909"/>
    </justification>
  </clause>

  <clause id="27123">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * u))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3157,a(flip),b,26946,a)].">
      <j1 rule="hyper" parents="60 3157 26946"/>
    </justification>
  </clause>

  <clause id="27125">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,(w * w) \ v5,(w * w) \ v5)) = a(x,y,z \ (((w * w) \ v5) * ((u * (w \ 1)) * v5)))
    ]]></literal>
    <justification jstring="[para(1117(a,1),27123(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="1117 27123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27126">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * u) * (1 / u)))) = a(x,y,z \ L(w * (u \ 1),u,u))
    ]]></literal>
    <justification jstring="[para(1288(a,1),27123(a,1,3,2,2))].">
      <j1 rule="para" parents="1288 27123"/>
    </justification>
  </clause>

  <clause id="27127">
    <literal><![CDATA[
      a(x,y,(z * (u * T(w,v5))) * v6) = a(x,y,(z * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(6130(a,1),27019(a,1,3,1,2))].">
      <j1 rule="para" parents="6130 27019"/>
    </justification>
  </clause>

  <clause id="27128">
    <literal><![CDATA[
      a(x,y,(z * (u \ T(w,v5))) * v6) = a(x,y,(z * (u \ w)) * v6)
    ]]></literal>
    <justification jstring="[para(6128(a,1),27019(a,1,3,1,2))].">
      <j1 rule="para" parents="6128 27019"/>
    </justification>
  </clause>

  <clause id="27129">
    <literal><![CDATA[
      a(x,y,(z * ((u \ w) * u)) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(7479(a,1),27019(a,1,3,1,2))].">
      <j1 rule="para" parents="7479 27019"/>
    </justification>
  </clause>

  <clause id="27130">
    <literal><![CDATA[
      a(x,y,z * ((1 / ((u / (w * u)) \ 1)) * v5)) = a(x,y,z * (((w \ u) / u) * v5))
    ]]></literal>
    <justification jstring="[para(2806(a,1),27024(a,2,3,2,1))].">
      <j1 rule="para" parents="2806 27024"/>
    </justification>
  </clause>

  <clause id="27131">
    <literal><![CDATA[
      a(x,y,z * (u * (w * K(v5,v6)))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(8016(a,1),27025(a,1,3,2,2))].">
      <j1 rule="para" parents="8016 27025"/>
    </justification>
  </clause>

  <clause id="27132">
    <literal><![CDATA[
      a(x,y,z * (u \ (w / v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5232(a,1),27027(a,1,3,2,2))].">
      <j1 rule="para" parents="5232 27027"/>
    </justification>
  </clause>

  <clause id="27133">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * v5))) = a(x,y,z * (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(7481(a,1),27027(a,1,3,2,2))].">
      <j1 rule="para" parents="7481 27027"/>
    </justification>
  </clause>

  <clause id="27134">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ v5) * w))) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(7479(a,1),27027(a,1,3,2,2))].">
      <j1 rule="para" parents="7479 27027"/>
    </justification>
  </clause>

  <clause id="27135">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) * v6))) = a(x,y,z * (u \ (w * v6)))
    ]]></literal>
    <justification jstring="[para(7864(a,1),27027(a,1,3,2,2))].">
      <j1 rule="para" parents="7864 27027"/>
    </justification>
  </clause>

  <clause id="27136">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) \ v6)) = a(x,y,z * (((w \ u) * v5) \ v6))
    ]]></literal>
    <justification jstring="[para(25131(a,1),27027(a,1,3,2))].">
      <j1 rule="para" parents="25131 27027"/>
    </justification>
  </clause>

  <clause id="27137">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ w) * v5)) = a(x,y,z \ (w * ((u * u) \ v5)))
    ]]></literal>
    <justification jstring="[para(935(a,1),27036(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="935 27036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27138">
    <literal><![CDATA[
      a(x,y,L((1 / (z \ u)) \ 1,z \ u,u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(3418(a,1),27055(a,2,3,1))].">
      <j1 rule="para" parents="3418 27055"/>
    </justification>
  </clause>

  <clause id="27139">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27013,a,b,27078,a)].">
      <j1 rule="hyper" parents="60 27013 27078"/>
    </justification>
  </clause>

  <clause id="27140">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) \ v5))) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,15783,a(flip),b,27081,a),flip(a)].">
      <j1 rule="hyper" parents="60 15783 27081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27141">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * u) * v5)) = a(x,y,(v5 * w) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27129,a)].">
      <j1 rule="hyper" parents="27033 27129"/>
    </justification>
  </clause>

  <clause id="27142">
    <literal><![CDATA[
      a(x,y,(z * ((u \ w) * u)) * v5) = a(x,y,(w * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26901,a,b,27129,a),flip(a)].">
      <j1 rule="hyper" parents="370 26901 27129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27143">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 / v6)))) = a(x,y,z * (u * (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(5631(a,1),27131(a,1,3,2,2))].">
      <j1 rule="para" parents="5631 27131"/>
    </justification>
  </clause>

  <clause id="27144">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ ((v5 \ v6) * v5)))) = a(x,y,z * (u * (w \ v6)))
    ]]></literal>
    <justification jstring="[para(15746(a,1),27131(a,1,3,2,2))].">
      <j1 rule="para" parents="15746 27131"/>
    </justification>
  </clause>

  <clause id="27145">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(26965,a,27133,a)].">
      <j1 rule="hyper" parents="26965 27133"/>
    </justification>
  </clause>

  <clause id="27146">
    <literal><![CDATA[
      a(x,y,z * (u \ (((1 / w) \ v5) * w))) = a(x,y,z * (u \ ((w * w) * v5)))
    ]]></literal>
    <justification jstring="[para(553(a,1),27133(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="553 27133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27147">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (((1 / u) \ v5) * u))) = a(x,y,z * (((u \ 1) * w) \ v5))
    ]]></literal>
    <justification jstring="[para(2676(a,1),27134(a,1,3,2))].">
      <j1 rule="para" parents="2676 27134"/>
    </justification>
  </clause>

  <clause id="27148">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (w * v5)))) = a(x,y,z * (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(13(a,2),27140(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="13 27140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27149">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * ((v6 \ u) * v6)) * w) = v5
    ]]></literal>
    <justification jstring="[para(27141(a,1),27041(a,1))].">
      <j1 rule="para" parents="27141 27041"/>
    </justification>
  </clause>

  <clause id="27150">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * v5) = a(x,y,(w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),27142(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 27142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27151">
    <literal><![CDATA[
      a(x,y,(z * ((u \ w) * u)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(27142(a,2),27002(a,1))].">
      <j1 rule="para" parents="27142 27002"/>
    </justification>
  </clause>

  <clause id="27152">
    <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(27145(a,1),26965(a,1))].">
      <j1 rule="para" parents="27145 26965"/>
    </justification>
  </clause>

  <clause id="27153">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) = a(x,y,v5 * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(27033,a,27150,a),flip(a)].">
      <j1 rule="hyper" parents="27033 27150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27154">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v5 * (z * (w * u))) = v6
    ]]></literal>
    <justification jstring="[para(27150(a,1),27033(a,1))].">
      <j1 rule="para" parents="27150 27033"/>
    </justification>
  </clause>

  <clause id="27155">
    <literal><![CDATA[
      a(x,y,(z * (u * ((w * w) * v5))) * v6) = a(x,y,v6 * (z * ((w * w) * (v5 * u))))
    ]]></literal>
    <justification jstring="[para(28(a,1),27153(a,2,3,2,2))].">
      <j1 rule="para" parents="28 27153"/>
    </justification>
  </clause>

  <clause id="27156">
    <literal><![CDATA[
      a(x,y,(z * (((u * u) * w) * (v5 \ 1))) * v6) = a(x,y,v6 * (z * ((v5 \ (u * u)) * w)))
    ]]></literal>
    <justification jstring="[para(573(a,1),27153(a,2,3,2,2))].">
      <j1 rule="para" parents="573 27153"/>
    </justification>
  </clause>

  <clause id="27157">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * (w * ((u \ v5) * v6)))) = a(x,y,((((u \ 1) \ v5) * v6) * w) * z)
    ]]></literal>
    <justification jstring="[para(1252(a,1),27153(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1252 27153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27158">
    <literal><![CDATA[
      a(x,y,z * (u * (R(w \ (w \ v5),v6,v7) * w))) = a(x,y,(u * (w \ R(v5,v6,v7))) * z)
    ]]></literal>
    <justification jstring="[para(2147(a,1),27153(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="2147 27153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27159">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w \ (w \ v5),v6,v7) * w))) = a(x,y,(u * (w \ L(v5,v6,v7))) * z)
    ]]></literal>
    <justification jstring="[para(3877(a,1),27153(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="3877 27153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27160">
    <literal><![CDATA[
      a(x,y,z * (u * ((K(w \ v5,w) * v6) * v5))) = a(x,y,(u * (((w \ v5) * w) * v6)) * z)
    ]]></literal>
    <justification jstring="[para(12081(a,1),27153(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="12081 27153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27161">
    <literal><![CDATA[
      a(x,y,(z * ((K(u \ w,u) * v5) * w)) * v6) = a(x,y,v6 * (z * (((u \ w) * u) * v5)))
    ]]></literal>
    <justification jstring="[para(12081(a,1),27153(a,2,3,2,2))].">
      <j1 rule="para" parents="12081 27153"/>
    </justification>
  </clause>

  <clause id="27162">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((w * u) * z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(27153(a,2),27041(a,1))].">
      <j1 rule="para" parents="27153 27041"/>
    </justification>
  </clause>

  <clause id="27163">
    <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(109(a,1),26977(a,1,3,2,2))].">
      <j1 rule="para" parents="109 26977"/>
    </justification>
  </clause>

  <clause id="27164">
    <literal><![CDATA[
      a(x,y,L(z * T(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(2219(a,1),26982(a,1,3,1))].">
      <j1 rule="para" parents="2219 26982"/>
    </justification>
  </clause>

  <clause id="27165">
    <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(8104(a,1),26982(a,1,3,1))].">
      <j1 rule="para" parents="8104 26982"/>
    </justification>
  </clause>

  <clause id="27166">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(15393(a,1),26982(a,1,3))].">
      <j1 rule="para" parents="15393 26982"/>
    </justification>
  </clause>

  <clause id="27167">
    <literal><![CDATA[
      a(x,y,(z / u) \ (z * (u \ 1))) = a(x,y,(z * u) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(26992,a,3164,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26992 3164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27168">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * ((z \ 1) * u))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * (z * u)) * z) = w
    ]]></literal>
    <justification jstring="[para(13604(a,2),26992(a,1))].">
      <j1 rule="para" parents="13604 26992"/>
    </justification>
  </clause>

  <clause id="27169">
    <literal><![CDATA[
      a(x,y,L((z * u) * z,w,v5)) = a(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(26996,a,3977,a)].">
      <j1 rule="hyper" parents="26996 3977"/>
    </justification>
  </clause>

  <clause id="27170">
    <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(12466(a,1),27008(a,1,3,1))].">
      <j1 rule="para" parents="12466 27008"/>
    </justification>
  </clause>

  <clause id="27171">
    <literal><![CDATA[
      a(x,y,L((1 / z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(551(a,1),27012(a,1,3,1))].">
      <j1 rule="para" parents="551 27012"/>
    </justification>
  </clause>

  <clause id="27172">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,w * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,26939,a(flip),b,27050,a),flip(a)].">
      <j1 rule="hyper" parents="370 26939 27050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27173">
    <literal><![CDATA[
      a(x,y,z * ((1 / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(27024(a,2),27080(a,1))].">
      <j1 rule="para" parents="27024 27080"/>
    </justification>
  </clause>

  <clause id="27174">
    <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(109(a,1),27098(a,1,3,1,2))].">
      <j1 rule="para" parents="109 27098"/>
    </justification>
  </clause>

  <clause id="27175">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(3114(a,2),27101(a,1))].">
      <j1 rule="para" parents="3114 27101"/>
    </justification>
  </clause>

  <clause id="27176">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(26909(a,1),27101(a,1))].">
      <j1 rule="para" parents="26909 27101"/>
    </justification>
  </clause>

  <clause id="27177">
    <literal><![CDATA[
      a(x,y,(z * (u \ a(w,v5,w))) * v6) = a(x,y,(u * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(27002,a,27114,a)].">
      <j1 rule="hyper" parents="27002 27114"/>
    </justification>
  </clause>

  <clause id="27179">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26928,a(flip),b,27172,a),flip(a)].">
      <j1 rule="hyper" parents="370 26928 27172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27181">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,u) * (v5 \ 1))) * v6) = a(x,y,(v5 * z) * v6)
    ]]></literal>
    <justification jstring="[para(14299(a,2),27177(a,1,3,1,2))].">
      <j1 rule="para" parents="14299 27177"/>
    </justification>
  </clause>

  <clause id="27182">
    <literal><![CDATA[
      a(x,y,z * (u * (T(w,v5) * v6))) = a(x,y,((w * v6) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27020,a)].">
      <j1 rule="hyper" parents="27033 27020"/>
    </justification>
  </clause>

  <clause id="27183">
    <literal><![CDATA[
      a(x,y,((z \ (u / w)) * v5) * v6) = a(x,y,((z \ (w \ u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(109(a,1),27022(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="109 27022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27184">
    <literal><![CDATA[
      a(x,y,(z * (T(u,w) * v5)) * v6) = a(x,y,v6 * ((u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(27041,a,27026,a)].">
      <j1 rule="hyper" parents="27041 27026"/>
    </justification>
  </clause>

  <clause id="27185">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w / v5))) * v6) = a(x,y,(z \ (u * (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(109(a,1),27029(a,1,3,1,2,2)),flip(a)].">
      <j1 rule="para" parents="109 27029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27186">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) * v5))) = a(x,y,(u * (v5 * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27153,a(flip),b,27054,a)].">
      <j1 rule="hyper" parents="60 27153 27054"/>
    </justification>
  </clause>

  <clause id="27187">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,u) * ((v5 \ u) \ 1))) * v6) = a(x,y,(z * (v5 \ R(u,w,u))) * v6)
    ]]></literal>
    <justification jstring="[para(14313(a,1),27054(a,2,3,1,2))].">
      <j1 rule="para" parents="14313 27054"/>
    </justification>
  </clause>

  <clause id="27188">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / u) \ w)) * v5) = a(x,y,(z \ (w / u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27078,a(flip),b,27057,a)].">
      <j1 rule="hyper" parents="60 27078 27057"/>
    </justification>
  </clause>

  <clause id="27189">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) \ 1) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(1258(a,1),27074(a,1,3,1,1))].">
      <j1 rule="para" parents="1258 27074"/>
    </justification>
  </clause>

  <clause id="27191">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) \ w) * v5) = a(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),27076(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 27076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27192">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,(z \ u) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3148,a(flip),b,27083,a)].">
      <j1 rule="hyper" parents="60 3148 27083"/>
    </justification>
  </clause>

  <clause id="27193">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) * v6)) = a(x,y,(v6 * (u * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27127,a)].">
      <j1 rule="hyper" parents="27033 27127"/>
    </justification>
  </clause>

  <clause id="27194">
    <literal><![CDATA[
      a(x,y,z * ((u \ T(w,v5)) * v6)) = a(x,y,(v6 * (u \ w)) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27128,a)].">
      <j1 rule="hyper" parents="27033 27128"/>
    </justification>
  </clause>

  <clause id="27195">
    <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(27088(a,1),27166(a,1))].">
      <j1 rule="para" parents="27088 27166"/>
    </justification>
  </clause>

  <clause id="27196">
    <literal><![CDATA[
      a(x,y,(z / u) \ (z * (u \ 1))) = a(x,y,(z * u) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26939,a(flip),b,27167,a),flip(a)].">
      <j1 rule="hyper" parents="370 26939 27167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27197">
    <literal><![CDATA[
      a(x,y,(z * (T(K(u,u \ w),v5) * (w \ v6))) * v7) = a(x,y,v7 * ((((u \ w) * u) \ v6) * z))
    ]]></literal>
    <justification jstring="[para(12088(a,1),27184(a,2,3,2,1))].">
      <j1 rule="para" parents="12088 27184"/>
    </justification>
  </clause>

  <clause id="27198">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / u) \ w)) * v5) = a(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27078,a(flip),b,27188,a),flip(a)].">
      <j1 rule="hyper" parents="370 27078 27188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27199">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(27176,a,27189,a)].">
      <j1 rule="hyper" parents="27176 27189"/>
    </justification>
  </clause>

  <clause id="27200">
    <literal><![CDATA[
      a(x,y,(z / u) \ (z * (u \ 1))) = a(x,y,a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3087,a(flip),b,27196,a),flip(a)].">
      <j1 rule="hyper" parents="370 3087 27196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27201">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * (z \ 1))) = a(x,y,a(u,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(26998,a,27200,a)].">
      <j1 rule="hyper" parents="26998 27200"/>
    </justification>
  </clause>

  <clause id="27202">
    <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(5232(a,1),27096(a,1,3,2,2))].">
      <j1 rule="para" parents="5232 27096"/>
    </justification>
  </clause>

  <clause id="27203">
    <literal><![CDATA[
      a(x,y,z * (u * ((w / v5) \ v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * ((v5 \ w) \ v6))) = v7
    ]]></literal>
    <justification jstring="[para(8210(a,1),27096(a,1,3,2,2))].">
      <j1 rule="para" parents="8210 27096"/>
    </justification>
  </clause>

  <clause id="27204">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(4(a,1),27119(a,1,3,1,1))].">
      <j1 rule="para" parents="4 27119"/>
    </justification>
  </clause>

  <clause id="27205">
    <literal><![CDATA[
      a(x,y,(z * ((u * w) * u)) * v5) = a(x,y,v5 * (z * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27153,a,b,27148,a)].">
      <j1 rule="hyper" parents="60 27153 27148"/>
    </justification>
  </clause>

  <clause id="27206">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * ((v6 \ z) * v6)) * w) = v5
    ]]></literal>
    <justification jstring="[para(26901(a,1),27149(a,1))].">
      <j1 rule="para" parents="26901 27149"/>
    </justification>
  </clause>

  <clause id="27207">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * u) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(v5 * w) * z) = v6
    ]]></literal>
    <justification jstring="[para(27031(a,1),27151(a,1))].">
      <j1 rule="para" parents="27031 27151"/>
    </justification>
  </clause>

  <clause id="27210">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * u) * v5)) = a(x,y,z * (v5 * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(27033,a,27205,a)].">
      <j1 rule="hyper" parents="27033 27205"/>
    </justification>
  </clause>

  <clause id="27211">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((v5 * w) * v5) * u)) = v6
    ]]></literal>
    <justification jstring="[para(27205(a,1),27033(a,1))].">
      <j1 rule="para" parents="27205 27033"/>
    </justification>
  </clause>

  <clause id="27212">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * (v5 * (v5 * w)))) = v6
    ]]></literal>
    <justification jstring="[para(27205(a,1),27154(a,1))].">
      <j1 rule="para" parents="27205 27154"/>
    </justification>
  </clause>

  <clause id="27213">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) \ v5)) = a(x,y,z * (v5 / w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27039,a(flip),b,26952,a),flip(a)].">
      <j1 rule="hyper" parents="370 27039 26952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27215">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) \ v5)) = a(x,y,z * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,26939,a(flip),b,27213,a),flip(a)].">
      <j1 rule="hyper" parents="370 26939 27213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27216">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * v5))) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(849(a,1),27215(a,1,3,2))].">
      <j1 rule="para" parents="849 27215"/>
    </justification>
  </clause>

  <clause id="27217">
    <literal><![CDATA[
      a(x,y,z * (u \ ((1 / w) * v5))) = a(x,y,z * (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[para(314(a,1),27216(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="314 27216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27218">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ L(w,v5,v6)))) = a(x,y,z * (u \ (w * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(3855(a,1),27216(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3855 27216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27219">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,(z * z) * ((w / u) * v5))
    ]]></literal>
    <justification jstring="[para(28(a,1),26955(a,2,3))].">
      <j1 rule="para" parents="28 26955"/>
    </justification>
  </clause>

  <clause id="27220">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) \ u) * w) = a(x,y,(u \ ((1 / z) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(26980,a,27016,a)].">
      <j1 rule="hyper" parents="26980 27016"/>
    </justification>
  </clause>

  <clause id="27221">
    <literal><![CDATA[
      a(x,y,z \ (L(u / w,v5,v6) \ v7)) = a(x,y,z \ (L(w \ u,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(109(a,1),27037(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 27037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27222">
    <literal><![CDATA[
      a(x,y,(z * z) * ((u * w) * v5)) = a(x,y,v5 * (w * ((z * z) * u)))
    ]]></literal>
    <justification jstring="[para(28(a,1),27048(a,1,3))].">
      <j1 rule="para" parents="28 27048"/>
    </justification>
  </clause>

  <clause id="27223">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) \ v5))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,3150,a(flip),b,27137,a),flip(a)].">
      <j1 rule="hyper" parents="60 3150 27137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27225">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (w * v5)))) = a(x,y,z \ (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(13(a,2),27223(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="13 27223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27226">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ 1)) * v5)) = a(x,y,z \ ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(1117(a,1),27223(a,1,3,2))].">
      <j1 rule="para" parents="1117 27223"/>
    </justification>
  </clause>

  <clause id="27227">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) * w) * v5)) = a(x,y,z \ (R(u,w,w) * v5))
    ]]></literal>
    <justification jstring="[para(1111(a,1),27226(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="1111 27226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27228">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,u,u)) = a(x,y,z \ (u * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,3149,a(flip),b,27225,a)].">
      <j1 rule="hyper" parents="60 3149 27225"/>
    </justification>
  </clause>

  <clause id="27229">
    <literal><![CDATA[
      a(x,y,z * (R(u \ 1,u,w * (v5 / v6)) * (w * (v6 \ v5)))) = a(x,y,z * (u \ (w * (v5 / v6))))
    ]]></literal>
    <justification jstring="[para(2784(a,1),27143(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2784 27143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27230">
    <literal><![CDATA[
      a(x,y,z * (R(u,w / v5,v6) * (v6 * (v5 \ w)))) = a(x,y,z * ((u * (w / v5)) * T(v6,w / v5)))
    ]]></literal>
    <justification jstring="[para(12402(a,1),27143(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12402 27143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27231">
    <literal><![CDATA[
      a(x,y,((z \ ((u \ w) * u)) * v5) * v6) = a(x,y,v6 * (v5 * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(27041,a,27144,a)].">
      <j1 rule="hyper" parents="27041 27144"/>
    </justification>
  </clause>

  <clause id="27232">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,(w / u) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,3074,a(flip),b,27219,a),flip(a)].">
      <j1 rule="hyper" parents="370 3074 27219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27234">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26896,a(flip),b,27232,a),flip(a)].">
      <j1 rule="hyper" parents="370 26896 27232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27235">
    <literal><![CDATA[
      a(x,y,(((z \ 1) \ u) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(940(a,1),27234(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="940 27234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27236">
    <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(3790(a,1),27234(a,1,3,1,1))].">
      <j1 rule="para" parents="3790 27234"/>
    </justification>
  </clause>

  <clause id="27237">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) \ u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27198,a(flip),b,27220,a),flip(a)].">
      <j1 rule="hyper" parents="370 27198 27220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27238">
    <literal><![CDATA[
      a(x,y,((z * u) \ u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27191,a(flip),b,27237,a)].">
      <j1 rule="hyper" parents="60 27191 27237"/>
    </justification>
  </clause>

  <clause id="27239">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) * v5))) = a(x,y,(v5 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(3075,a,27222,a),flip(a)].">
      <j1 rule="hyper" parents="3075 27222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27240">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(v5 * u) * z) = v6
    ]]></literal>
    <justification jstring="[para(27222(a,1),3075(a,1))].">
      <j1 rule="para" parents="27222 3075"/>
    </justification>
  </clause>

  <clause id="27242">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) \ v5))) = a(x,y,((w \ v5) * u) * z)
    ]]></literal>
    <justification jstring="[para(936(a,1),27239(a,1,3,2,2))].">
      <j1 rule="para" parents="936 27239"/>
    </justification>
  </clause>

  <clause id="27243">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((w \ v5) * u) * z) = v6
    ]]></literal>
    <justification jstring="[para(936(a,1),27240(a,1,3,2,2))].">
      <j1 rule="para" parents="936 27240"/>
    </justification>
  </clause>

  <clause id="27244">
    <literal><![CDATA[
      a(x,y,((L(z,z,z) * L(u,z,z)) \ w) * v5) = a(x,y,(L(1 / (z * u),z,z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(1280(a,2),27236(a,2,3,1,1)),flip(a)].">
      <j1 rule="para" parents="1280 27236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27245">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,v5,w))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(26990,a,27112,a)].">
      <j1 rule="hyper" parents="26990 27112"/>
    </justification>
  </clause>

  <clause id="27246">
    <literal><![CDATA[
      a(x,y,z * (u * (w * a(v5,v6,v5)))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(14262(a,1),27245(a,1,3,2))].">
      <j1 rule="para" parents="14262 27245"/>
    </justification>
  </clause>

  <clause id="27247">
    <literal><![CDATA[
      a(x,y,z * (u * (R(w,v5,w) * v6))) = a(x,y,(u * (w * v6)) * z)
    ]]></literal>
    <justification jstring="[para(12048(a,1),27246(a,1,3,2,2))].">
      <j1 rule="para" parents="12048 27246"/>
    </justification>
  </clause>

  <clause id="27248">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(77(a,1),27138(a,1,3,1,1))].">
      <j1 rule="para" parents="77 27138"/>
    </justification>
  </clause>

  <clause id="27250">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * v5) * w)) = a(x,y,z * (w * ((w * u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(26977,a,27040,a)].">
      <j1 rule="hyper" parents="26977 27040"/>
    </justification>
  </clause>

  <clause id="27252">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * T(u,w)) * z))) = a(x,y,L(T(u,w),u,z))
    ]]></literal>
    <justification jstring="[para(26259(a,1),27059(a,2,3))].">
      <j1 rule="para" parents="26259 27059"/>
    </justification>
  </clause>

  <clause id="27253">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * T(u,w)) * z))) = a(x,y,L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26884,a(flip),b,27252,a),flip(a)].">
      <j1 rule="hyper" parents="370 26884 27252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27255">
    <literal><![CDATA[
      a(x,y,z \ ((K(u,w) / w) \ z)) = a(x,y,L(w,w,z))
    ]]></literal>
    <justification jstring="[para(16278(a,1),27253(a,1,3,2))].">
      <j1 rule="para" parents="16278 27253"/>
    </justification>
  </clause>

  <clause id="27256">
    <literal><![CDATA[
      a(x,y,((z \ u) / w) * (K(u,v5) * v6)) = a(x,y,(w \ (z \ T(u,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(23547(a,1),27122(a,1,3))].">
      <j1 rule="para" parents="23547 27122"/>
    </justification>
  </clause>

  <clause id="27257">
    <literal><![CDATA[
      a(x,y,z * (u \ (((1 / w) \ v5) * w))) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,27216,a(flip),b,27146,a),flip(a)].">
      <j1 rule="hyper" parents="370 27216 27146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27259">
    <literal><![CDATA[
      a(x,y,(z \ (u \ T(w,v5))) * v6) = a(x,y,((u \ w) / z) * v6)
    ]]></literal>
    <justification jstring="[hyper(26999,a,27256,a),flip(a)].">
      <j1 rule="hyper" parents="26999 27256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27261">
    <literal><![CDATA[
      a(x,y,(z \ (u \ T(w,v5))) * v6) = a(x,y,(z \ (u \ w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26896,a(flip),b,27259,a),flip(a)].">
      <j1 rule="hyper" parents="370 26896 27259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27262">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ T(v5,v6)))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,27261,a)].">
      <j1 rule="hyper" parents="26965 27261"/>
    </justification>
  </clause>

  <clause id="27263">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,25902,a(flip),b,26361,a),flip(a)].">
      <j1 rule="hyper" parents="370 25902 26361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27264">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,v5)) = L(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26312,a,27263,a),flip(a)].">
      <j1 rule="hyper" parents="26312 27263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27266">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(27263(a,1),26312(a,1))].">
      <j1 rule="para" parents="27263 26312"/>
    </justification>
  </clause>

  <clause id="27267">
    <literal><![CDATA[
      L(x,y,z \ R(L(u,z,z),w,v5)) = L(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2085(a,1),27264(a,2,3))].">
      <j1 rule="para" parents="2085 27264"/>
    </justification>
  </clause>

  <clause id="27268">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ R(L(z,u,w),v5,v6)) = L(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(10440(a,1),27264(a,2,3))].">
      <j1 rule="para" parents="10440 27264"/>
    </justification>
  </clause>

  <clause id="27269">
    <literal><![CDATA[
      L(x,y,z \ L(R(u,w,v5),z,z)) = L(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(24(a,1),27267(a,1,3,2))].">
      <j1 rule="para" parents="24 27267"/>
    </justification>
  </clause>

  <clause id="27270">
    <literal><![CDATA[
      L(x,y,(z \ 1) * R(u,w,v5)) = L(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2072(a,1),27269(a,1,3))].">
      <j1 rule="para" parents="2072 27269"/>
    </justification>
  </clause>

  <clause id="27271">
    <literal><![CDATA[
      L(x,y,(z \ 1) * L(u,w,v5)) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(25439,a,27270,a),flip(a)].">
      <j1 rule="hyper" parents="25439 27270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27272">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(25439,a,27271,a),flip(a)].">
      <j1 rule="hyper" parents="25439 27271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27273">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * v5) = L(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(25242,a,27271,a)].">
      <j1 rule="hyper" parents="25242 27271"/>
    </justification>
  </clause>

  <clause id="27274">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(27271(a,1),25439(a,1))].">
      <j1 rule="para" parents="27271 25439"/>
    </justification>
  </clause>

  <clause id="27275">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(7588,a,27272,a)].">
      <j1 rule="hyper" parents="7588 27272"/>
    </justification>
  </clause>

  <clause id="27276">
    <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(25(a,1),27272(a,2,3,2))].">
      <j1 rule="para" parents="25 27272"/>
    </justification>
  </clause>

  <clause id="27277">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (v5 * v5)) = L(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3366,a(flip),b,27273,a),flip(a)].">
      <j1 rule="hyper" parents="370 3366 27273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27278">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x * L(x,y,z)) = 1 \ ((R(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,13574,a(flip),b,27275,a),flip(a)].">
      <j1 rule="hyper" parents="60 13574 27275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27279">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(3528,a,27277,a),flip(a)].">
      <j1 rule="hyper" parents="3528 27277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27280">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27277(a,1),3528(a,1))].">
      <j1 rule="para" parents="27277 3528"/>
    </justification>
  </clause>

  <clause id="27281">
    <literal><![CDATA[
      L(x,y,L(z,u,T(w,z * u))) = L(x,y,(u * w) \ (w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(26354,a,27279,a),flip(a)].">
      <j1 rule="hyper" parents="26354 27279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27282">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((w * u) * z)) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(26324,a,27279,a)].">
      <j1 rule="hyper" parents="26324 27279"/>
    </justification>
  </clause>

  <clause id="27283">
    <literal><![CDATA[
      L(R((x \ 1) \ 1,y,z) \ u,R(x,y,z),L(x,y,z)) = 1 \ ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,7109,a(flip),b,27279,a),flip(a)].">
      <j1 rule="hyper" parents="60 7109 27279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27284">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,L(x,y,z)) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(27279(a,1),2604(a,1,2))].">
      <j1 rule="para" parents="27279 2604"/>
    </justification>
  </clause>

  <clause id="27285">
    <literal><![CDATA[
      L(x,y,R(T(z \ 1,z * u),z,u)) = L(x,y,T(u * z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(12766(a,1),27279(a,2,3))].">
      <j1 rule="para" parents="12766 27279"/>
    </justification>
  </clause>

  <clause id="27286">
    <literal><![CDATA[
      R(x,y,z) * T(L(u,u,L(x,y,z)),w) = R(x,y,z) / (T(u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(27279(a,1),26212(a,1,2,1))].">
      <j1 rule="para" parents="27279 26212"/>
    </justification>
  </clause>

  <clause id="27287">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[para(23573(a,1),27281(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23573 27281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27289">
    <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(24(a,1),27276(a,1,3,2))].">
      <j1 rule="para" parents="24 27276"/>
    </justification>
  </clause>

  <clause id="27290">
    <literal><![CDATA[
      R(x,y,z) * L(L(u,x,L(x,y,z)),x \ R(x,y,z),x) = x * (x * (R(x \ 1,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(129,a,27284,a(flip),b,617,a),flip(a)].">
      <j1 rule="hyper" parents="129 27284 617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27291">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) * R(y,z,u) = R(y,z,u) / (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(23978,a,27286,a)].">
      <j1 rule="hyper" parents="23978 27286"/>
    </justification>
  </clause>

  <clause id="27292">
    <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(92(a,1),27289(a,2,3))].">
      <j1 rule="para" parents="92 27289"/>
    </justification>
  </clause>

  <clause id="27293">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1) \ z) = L(x,y,(((u \ 1) \ 1) * z) \ z)
    ]]></literal>
    <justification jstring="[para(3741(a,1),27285(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3741 27285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27294">
    <literal><![CDATA[
      L(x,y,(((z \ 1) \ 1) * u) \ u) = L(x,y,(u * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(25943,a,27293,a),flip(a)].">
      <j1 rule="hyper" parents="25943 27293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27295">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,v5,v6))) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(92(a,1),27292(a,1,3))].">
      <j1 rule="para" parents="92 27292"/>
    </justification>
  </clause>

  <clause id="27296">
    <literal><![CDATA[
      L(x,y,z * (u \ R(u,w,v5))) = L(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,4113,a,b,27295,a)].">
      <j1 rule="hyper" parents="60 4113 27295"/>
    </justification>
  </clause>

  <clause id="27297">
    <literal><![CDATA[
      L(x,y,z * (u * L(u \ (u \ w),v5,v6))) = L(x,y,z * (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(2147(a,1),27295(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2147 27295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27298">
    <literal><![CDATA[
      L(x,y,z * (u \ R(w,v5,v6))) = L(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(3877(a,1),27297(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3877 27297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27299">
    <literal><![CDATA[
      L(x,((y * z) \ ((y * u) * z)) \ w,v5) = L(x,R(u,y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26005,a(flip),b,26363,a),flip(a)].">
      <j1 rule="hyper" parents="370 26005 26363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27301">
    <literal><![CDATA[
      L(x,((y * ((y * z) / y)) \ ((T(y,z) * u) * z)) \ w,v5) = L(x,R(u,T(y,z),z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(5448(a,1),27299(a,1,2,1,1))].">
      <j1 rule="para" parents="5448 27299"/>
    </justification>
  </clause>

  <clause id="27302">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) * u,w,v5) = a(R(z,y,x) * (K(y,x) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(25695(a,1),26597(a,2,1))].">
      <j1 rule="para" parents="25695 26597"/>
    </justification>
  </clause>

  <clause id="27303">
    <literal><![CDATA[
      a(x,(y * y) * (L(z,u,w) * (w * u)),v5) = a(x,w * ((u * (y * y)) * z),v5)
    ]]></literal>
    <justification jstring="[para(3791(a,1),26673(a,1,2))].">
      <j1 rule="para" parents="3791 26673"/>
    </justification>
  </clause>

  <clause id="27304">
    <literal><![CDATA[
      a(((x * y) \ (y * (z * x))) * u,w,v5) = a(R(z,x,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26389,a(flip),b,26742,a),flip(a)].">
      <j1 rule="hyper" parents="370 26389 26742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27306">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((w * u) * z)) * v5) = a(x,y,R(w,u,z) * (K(u,z) * v5))
    ]]></literal>
    <justification jstring="[para(25695(a,1),27017(a,2,3))].">
      <j1 rule="para" parents="25695 27017"/>
    </justification>
  </clause>

  <clause id="27307">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ ((v5 * w) * u))) = a(x,y,(z \ R(v5,w,u)) * K(w,u))
    ]]></literal>
    <justification jstring="[para(25690(a,1),27045(a,2,3))].">
      <j1 rule="para" parents="25690 27045"/>
    </justification>
  </clause>

  <clause id="27308">
    <literal><![CDATA[
      R(L(x,y,z) \ L(R(x,x,u),y,z),L(x,y,z),u * x) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(24(a,1),27072(a,1,1,2))].">
      <j1 rule="para" parents="24 27072"/>
    </justification>
  </clause>

  <clause id="27309">
    <literal><![CDATA[
      a(x,y,z \ L(u * (w \ 1),w,w)) = a(x,y,z \ R(w * u,w,w))
    ]]></literal>
    <justification jstring="[para(3283(a,1),27126(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3283 27126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27310">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ L(R(z,v5,v6),u,w)) = L(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(24(a,1),27268(a,1,3,2))].">
      <j1 rule="para" parents="24 27268"/>
    </justification>
  </clause>

  <clause id="27311">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(R(z,y,x) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27302(a,2),26526(a,1))].">
      <j1 rule="para" parents="27302 26526"/>
    </justification>
  </clause>

  <clause id="27312">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(27311,a,26834,a)].">
      <j1 rule="hyper" parents="27311 26834"/>
    </justification>
  </clause>

  <clause id="27314">
    <literal><![CDATA[
      a(L(x,y,z) * T(u,w),v5,v6) = a(u * R(x,y,z),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26540,a,27312,a),flip(a)].">
      <j1 rule="hyper" parents="26540 27312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27315">
    <literal><![CDATA[
      a(((x * y) \ (y * (z * x))) * u,w,v5) = a(L(z,x,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27304,a,b,27312,a)].">
      <j1 rule="hyper" parents="60 27304 27312"/>
    </justification>
  </clause>

  <clause id="27316">
    <literal><![CDATA[
      a(L(x,y,z) * 1,u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3(a,1),27312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 27312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27317">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) = a((1 / x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1961 27312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27318">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3(a,1),27316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 27316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27319">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26841,a,27318,a)].">
      <j1 rule="hyper" parents="26841 27318"/>
    </justification>
  </clause>

  <clause id="27320">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ (((1 / x) \ y) * z) = a(L(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1963,a,b,27318,a)].">
      <j1 rule="hyper" parents="60 1963 27318"/>
    </justification>
  </clause>

  <clause id="27321">
    <literal><![CDATA[
      a(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ ((y * x) * z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27318(a,1),26841(a,1))].">
      <j1 rule="para" parents="27318 26841"/>
    </justification>
  </clause>

  <clause id="27322">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2966,a(flip),b,27317,a),flip(a)].">
      <j1 rule="hyper" parents="370 2966 27317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27323">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(27317(a,2),26595(a,1))].">
      <j1 rule="para" parents="27317 26595"/>
    </justification>
  </clause>

  <clause id="27324">
    <literal><![CDATA[
      a(x * L(y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(26519,a,27322,a)].">
      <j1 rule="hyper" parents="26519 27322"/>
    </justification>
  </clause>

  <clause id="27325">
    <literal><![CDATA[
      a(x \ a(y,z,y),u,w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(13917(a,1),27322(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13917 27322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27326">
    <literal><![CDATA[
      a(x \ a(y,z,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(27325(a,2),14080(a,1))].">
      <j1 rule="para" parents="27325 14080"/>
    </justification>
  </clause>

  <clause id="27327">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((x * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),27319(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 27319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27328">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26540,a,27314,a),flip(a)].">
      <j1 rule="hyper" parents="26540 27314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27329">
    <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(27314(a,1),26540(a,1))].">
      <j1 rule="para" parents="27314 26540"/>
    </justification>
  </clause>

  <clause id="27330">
    <literal><![CDATA[
      a(L(x \ 1,y * x,y * x),z,u) = a((y * x) * L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(3001,a,27328,a)].">
      <j1 rule="hyper" parents="3001 27328"/>
    </justification>
  </clause>

  <clause id="27331">
    <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(25(a,1),27328(a,2,1,2))].">
      <j1 rule="para" parents="25 27328"/>
    </justification>
  </clause>

  <clause id="27332">
    <literal><![CDATA[
      a((x * y) * R(L(z,y,x),u,w),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(528(a,1),27328(a,2,1))].">
      <j1 rule="para" parents="528 27328"/>
    </justification>
  </clause>

  <clause id="27333">
    <literal><![CDATA[
      a(x * ((y * z) \ (z * (u * y))),w,v5) = a(L(u,y,z) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,27315,a)].">
      <j1 rule="hyper" parents="26519 27315"/>
    </justification>
  </clause>

  <clause id="27334">
    <literal><![CDATA[
      a(K(x,y) * ((z * u) \ (u * (w * z))),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(L(w,z,u),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(27333(a,2),26523(a,1))].">
      <j1 rule="para" parents="27333 26523"/>
    </justification>
  </clause>

  <clause id="27335">
    <literal><![CDATA[
      a(L(x \ 1,y * x,y * x),z,u) = a(y * (L(y,x,x) * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26428,a(flip),b,27330,a),flip(a)].">
      <j1 rule="hyper" parents="370 26428 27330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27336">
    <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(24(a,1),27331(a,1,1,2))].">
      <j1 rule="para" parents="24 27331"/>
    </justification>
  </clause>

  <clause id="27337">
    <literal><![CDATA[
      a(L(x,y * x,y * x),z,u) = a(y * (L(y,x,x) * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3869,a(flip),b,27335,a)].">
      <j1 rule="hyper" parents="60 3869 27335"/>
    </justification>
  </clause>

  <clause id="27338">
    <literal><![CDATA[
      a(x * (y * R(z,u,w)),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(529(a,1),27332(a,1,1))].">
      <j1 rule="para" parents="529 27332"/>
    </justification>
  </clause>

  <clause id="27339">
    <literal><![CDATA[
      a(L(x,x,y * R(z,u,w)) * (y * L(z,u,w)),v5,v6) = a(x \ (y * R(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(27323,a,27338,a),flip(a)].">
      <j1 rule="hyper" parents="27323 27338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27340">
    <literal><![CDATA[
      a((x * R(y,z,u)) * w,v5,v6) = a(w * (x * L(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26519,a,27338,a)].">
      <j1 rule="hyper" parents="26519 27338"/>
    </justification>
  </clause>

  <clause id="27341">
    <literal><![CDATA[
      a(x * (y * R(T(z,y),u,w)),v5,v6) = a(x * (L(z,u,w) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(273(a,1),27338(a,2,1,2))].">
      <j1 rule="para" parents="273 27338"/>
    </justification>
  </clause>

  <clause id="27342">
    <literal><![CDATA[
      a(x * (y * L(y \ (y \ z),u,w)),v5,v6) = a(x * (y \ R(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2147(a,1),27338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2147 27338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27343">
    <literal><![CDATA[
      a(x * ((R(y,z,u) \ ((R(y,z,u) \ 1) \ w)) * L(y,z,u)),v5,v6) = a(x * ((R(y,z,u) \ 1) \ T(w,R(y,z,u))),v5,v6)
    ]]></literal>
    <justification jstring="[para(2874(a,1),27338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2874 27338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27344">
    <literal><![CDATA[
      a((x * R(y,z,u)) * w,v5,v6) = a((x * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,27340,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 27340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27345">
    <literal><![CDATA[
      a(((x * y) * R(z,y,x)) * u,w,v5) = a(u * (x * (y * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(92(a,1),27340(a,2,1,2))].">
      <j1 rule="para" parents="92 27340"/>
    </justification>
  </clause>

  <clause id="27347">
    <literal><![CDATA[
      a((x * ((y * z) * (y \ 1))) * u,w,v5) = a((x * L(z,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26654,a,b,27344,a)].">
      <j1 rule="hyper" parents="60 26654 27344"/>
    </justification>
  </clause>

  <clause id="27348">
    <literal><![CDATA[
      a(x * (R(y,z,u) * w),v5,v6) = a(x * (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(274(a,1),27341(a,1,1,2))].">
      <j1 rule="para" parents="274 27341"/>
    </justification>
  </clause>

  <clause id="27349">
    <literal><![CDATA[
      a((x * ((y * z) * y)) * u,w,v5) = a((x * L(z,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26632,a(flip),b,27347,a)].">
      <j1 rule="hyper" parents="60 26632 27347"/>
    </justification>
  </clause>

  <clause id="27352">
    <literal><![CDATA[
      a(x * (y \ R(z,u,w)),v5,v6) = a(x * (y \ L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(3877(a,1),27342(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3877 27342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27353">
    <literal><![CDATA[
      a(x * ((y \ 1) \ L(z,u,w)),v5,v6) = a((y \ R(z,u,w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26430,a,27352,a),flip(a)].">
      <j1 rule="hyper" parents="26430 27352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27354">
    <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(27353(a,1),26430(a,1))].">
      <j1 rule="para" parents="27353 26430"/>
    </justification>
  </clause>

  <clause id="27355">
    <literal><![CDATA[
      a(x,L(y,z,u) * (u * z),w) = a(x,u * ((z * (v5 * v5)) * y),w)
    ]]></literal>
    <justification jstring="[hyper(3038,a,27303,a)].">
      <j1 rule="hyper" parents="3038 27303"/>
    </justification>
  </clause>

  <clause id="27356">
    <literal><![CDATA[
      a(x,y * ((z * (u * u)) * w),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(26566,a,27355,a),flip(a)].">
      <j1 rule="hyper" parents="26566 27355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27358">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) * w)),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),27356(a,1,2,2))].">
      <j1 rule="para" parents="29 27356"/>
    </justification>
  </clause>

  <clause id="27359">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * u),w) = a(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(248(a,1),27356(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="248 27356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27361">
    <literal><![CDATA[
      a(x,y * (z * ((1 / u) \ w)),v5) = a(x,y * (z * (u \ w)),v5)
    ]]></literal>
    <justification jstring="[para(943(a,1),27358(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="943 27358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27362">
    <literal><![CDATA[
      a(x,y * (z * (u \ 1)),w) = a(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(77(a,1),27361(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="77 27361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27363">
    <literal><![CDATA[
      a(x,y * (L(z,u,w) \ z),v5) = a(x,y * (z * L(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(2162(a,1),27362(a,1,2,2))].">
      <j1 rule="para" parents="2162 27362"/>
    </justification>
  </clause>

  <clause id="27364">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((w * u) * z)) * v5) = a(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26898,a(flip),b,27306,a),flip(a)].">
      <j1 rule="hyper" parents="370 26898 27306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27366">
    <literal><![CDATA[
      a(x,y,(((((z * u) * w) / (z * u)) * u) \ (T(z * u,w) * w)) * v5) = a(x,y,R(z,u,((z * u) * w) / (z * u)) * v5)
    ]]></literal>
    <justification jstring="[para(5448(a,2),27364(a,1,3,1,2))].">
      <j1 rule="para" parents="5448 27364"/>
    </justification>
  </clause>

  <clause id="27367">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,((w * u) \ ((z * u) * w)) / (((v5 \ v6) * v5) \ 1))
    ]]></literal>
    <justification jstring="[para(26098(a,1),27364(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26098 27364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27368">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ ((v5 * w) * u))) = a(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,26893,a(flip),b,27307,a),flip(a)].">
      <j1 rule="hyper" parents="370 26893 27307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27371">
    <literal><![CDATA[
      R(L(x \ R(x,x,y),z,u),L(x,z,u),y * x) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(7812(a,1),27308(a,1,1))].">
      <j1 rule="para" parents="7812 27308"/>
    </justification>
  </clause>

  <clause id="27372">
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),v5,v6)) = L(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(7812(a,1),27310(a,1,3))].">
      <j1 rule="para" parents="7812 27310"/>
    </justification>
  </clause>

  <clause id="27373">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6)) = L(x,y,L(z * R(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,4054,a(flip),b,27372,a),flip(a)].">
      <j1 rule="hyper" parents="60 4054 27372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27374">
    <literal><![CDATA[
      L(x,y,L(z * R(z,u,w),v5,v6)) = L(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,3981,a(flip),b,27373,a),flip(a)].">
      <j1 rule="hyper" parents="60 3981 27373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27375">
    <literal><![CDATA[
      L(x,y,L(z * L(z,u,w),z,w * u)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25272,a(flip),b,27374,a),flip(a)].">
      <j1 rule="hyper" parents="60 25272 27374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27376">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (z * (u * w))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,4155,a(flip),b,27375,a)].">
      <j1 rule="hyper" parents="60 4155 27375"/>
    </justification>
  </clause>

  <clause id="27377">
    <literal><![CDATA[
      (((x * (K(y,z) * u)) * w) / (u * w)) * K(z,y) = R(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(25058,a,23546,a),flip(a)].">
      <j1 rule="hyper" parents="25058 23546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27378">
    <literal><![CDATA[
      R(x * K(y,z),u,w) * K(z,y) = R(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(25092(a,1),27377(a,1,1))].">
      <j1 rule="para" parents="25092 27377"/>
    </justification>
  </clause>

  <clause id="27379">
    <literal><![CDATA[
      R((x * K(y,z)) * K(z,y),u,w) = R(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25687,a,b,27378,a)].">
      <j1 rule="hyper" parents="60 25687 27378"/>
    </justification>
  </clause>

  <clause id="27380">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(6281(a,1),27379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6281 27379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27384">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(1811(a,2),27380(a,1,2))].">
      <j1 rule="para" parents="1811 27380"/>
    </justification>
  </clause>

  <clause id="27386">
    <literal><![CDATA[
      R(x,y / z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="5232 27380"/>
    </justification>
  </clause>

  <clause id="27387">
    <literal><![CDATA[
      R(x,(y \ z) \ z,u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(5300(a,2),27380(a,1,2))].">
      <j1 rule="para" parents="5300 27380"/>
    </justification>
  </clause>

  <clause id="27388">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),v5) = R(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5302(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="5302 27380"/>
    </justification>
  </clause>

  <clause id="27389">
    <literal><![CDATA[
      R(x,y * T(z,u),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(6130(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="6130 27380"/>
    </justification>
  </clause>

  <clause id="27390">
    <literal><![CDATA[
      R(x,y * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(7481(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="7481 27380"/>
    </justification>
  </clause>

  <clause id="27391">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(8016(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="8016 27380"/>
    </justification>
  </clause>

  <clause id="27400">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(15644(a,1),27380(a,1,2))].">
      <j1 rule="para" parents="15644 27380"/>
    </justification>
  </clause>

  <clause id="27401">
    <literal><![CDATA[
      R(x,L(K(y,z) * u,w,v5),v6) = R(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(25728(a,2),27380(a,1,2))].">
      <j1 rule="para" parents="25728 27380"/>
    </justification>
  </clause>

  <clause id="27407">
    <literal><![CDATA[
      R(x,L(y / z,u,w),v5) = R(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(285(a,1),27384(a,1,2)),flip(a)].">
      <j1 rule="para" parents="285 27384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27410">
    <literal><![CDATA[
      L(x,R(y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(27384(a,1),26303(a,1,2))].">
      <j1 rule="para" parents="27384 26303"/>
    </justification>
  </clause>

  <clause id="27411">
    <literal><![CDATA[
      R(x,y \ z,T(u,w)) = R(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(25250,a,27386,a),flip(a)].">
      <j1 rule="hyper" parents="25250 27386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27412">
    <literal><![CDATA[
      R(R(x,y / z,u),w,K(v5,v6)) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(23673,a,27386,a)].">
      <j1 rule="hyper" parents="23673 27386"/>
    </justification>
  </clause>

  <clause id="27415">
    <literal><![CDATA[
      R(T(T(x,y),x \ 1),x \ K(y,x),y) = y / (((x * x) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,15804,a(flip),b,27386,a),flip(a)].">
      <j1 rule="hyper" parents="60 15804 27386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27416">
    <literal><![CDATA[
      R(x,y,z) * (((y \ u) \ u) * z) = (x * ((y \ u) \ u)) * z
    ]]></literal>
    <justification jstring="[para(27387(a,1),103(a,1,1))].">
      <j1 rule="para" parents="27387 103"/>
    </justification>
  </clause>

  <clause id="27418">
    <literal><![CDATA[
      R(x,(y * y) * z,u) = R(x,z,(y * y) * u)
    ]]></literal>
    <justification jstring="[hyper(2697,a,27390,a),flip(a)].">
      <j1 rule="hyper" parents="2697 27390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27419">
    <literal><![CDATA[
      (x * y) * R(z,y * x,z) = T(z * (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(129,a,27390,a,b,5536,a)].">
      <j1 rule="hyper" parents="129 27390 5536"/>
    </justification>
  </clause>

  <clause id="27422">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(26309,a,27391,a)].">
      <j1 rule="hyper" parents="26309 27391"/>
    </justification>
  </clause>

  <clause id="27426">
    <literal><![CDATA[
      R(x,y * (z / u),w) = R(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(5631(a,1),27391(a,1,2))].">
      <j1 rule="para" parents="5631 27391"/>
    </justification>
  </clause>

  <clause id="27427">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ u),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(5944(a,1),27391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5944 27391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27428">
    <literal><![CDATA[
      R(x,y * (z * T(u,w)),v5) = R(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(6930(a,1),27391(a,1,2))].">
      <j1 rule="para" parents="6930 27391"/>
    </justification>
  </clause>

  <clause id="27432">
    <literal><![CDATA[
      R(x,y,z \ T(u,w)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="6128 27422"/>
    </justification>
  </clause>

  <clause id="27433">
    <literal><![CDATA[
      R(x,y,z * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(7481(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="7481 27422"/>
    </justification>
  </clause>

  <clause id="27434">
    <literal><![CDATA[
      R(x,y,T(z,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(7864(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="7864 27422"/>
    </justification>
  </clause>

  <clause id="27435">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8016(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="8016 27422"/>
    </justification>
  </clause>

  <clause id="27436">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(8364(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="8364 27422"/>
    </justification>
  </clause>

  <clause id="27437">
    <literal><![CDATA[
      R(x,y,(T(z,u) * w) * v5) = R(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(16495(a,1),27422(a,1,3))].">
      <j1 rule="para" parents="16495 27422"/>
    </justification>
  </clause>

  <clause id="27438">
    <literal><![CDATA[
      R(x,y,z * ((u * u) \ w)) = R(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(2750,a,27433,a),flip(a)].">
      <j1 rule="hyper" parents="2750 27433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27439">
    <literal><![CDATA[
      R(1 / x,x,y * z) \ (z * y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(27433(a,1),467(a,1,1))].">
      <j1 rule="para" parents="27433 467"/>
    </justification>
  </clause>

  <clause id="27440">
    <literal><![CDATA[
      R(x,y,R(z \ (z \ u),w,v5) * z) = R(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2147(a,1),27433(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2147 27433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27441">
    <literal><![CDATA[
      R(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(27433(a,1),2709(a,1))].">
      <j1 rule="para" parents="27433 2709"/>
    </justification>
  </clause>

  <clause id="27442">
    <literal><![CDATA[
      R(x,y,L(z \ (z \ u),w,v5) * z) = R(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3877(a,1),27433(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3877 27433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27444">
    <literal><![CDATA[
      R(x,y,z * (u / w)) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(5631(a,1),27435(a,1,3))].">
      <j1 rule="para" parents="5631 27435"/>
    </justification>
  </clause>

  <clause id="27445">
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(20260(a,1),27435(a,1,3))].">
      <j1 rule="para" parents="20260 27435"/>
    </justification>
  </clause>

  <clause id="27446">
    <literal><![CDATA[
      R(x,y,(z \ u) * K(w,u)) = R(x,y,z \ L(u,w,u))
    ]]></literal>
    <justification jstring="[para(20263(a,1),27435(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20263 27435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27447">
    <literal><![CDATA[
      R(x,(y * z) * y,u) = R(x,R(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,9731,a(flip),b,27389,a),flip(a)].">
      <j1 rule="hyper" parents="60 9731 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27450">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(27400(a,2),2778(a,1))].">
      <j1 rule="para" parents="27400 2778"/>
    </justification>
  </clause>

  <clause id="27452">
    <literal><![CDATA[
      L(x,L(y,z,T(u,y * z)),w) = L(x,(z * u) \ (u * (y * z)),w)
    ]]></literal>
    <justification jstring="[hyper(26362,a,27410,a),flip(a)].">
      <j1 rule="hyper" parents="26362 27410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27453">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,u,w),v5) = L(x,R(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,4056,a,b,27410,a)].">
      <j1 rule="hyper" parents="370 4056 27410"/>
    </justification>
  </clause>

  <clause id="27454">
    <literal><![CDATA[
      L(x,L(L(y,z,u),y,y),w) = L(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,4037,a,b,27410,a)].">
      <j1 rule="hyper" parents="370 4037 27410"/>
    </justification>
  </clause>

  <clause id="27455">
    <literal><![CDATA[
      L(x,L(y,z,u),R(y,z,u)) \ x = a(R(y,z,u),R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(27410(a,1),1362(a,1,1))].">
      <j1 rule="para" parents="27410 1362"/>
    </justification>
  </clause>

  <clause id="27459">
    <literal><![CDATA[
      R(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(27411(a,1),25250(a,1))].">
      <j1 rule="para" parents="27411 25250"/>
    </justification>
  </clause>

  <clause id="27461">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(946(a,1),27441(a,1,3))].">
      <j1 rule="para" parents="946 27441"/>
    </justification>
  </clause>

  <clause id="27462">
    <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(3855(a,1),27441(a,1,3))].">
      <j1 rule="para" parents="3855 27441"/>
    </justification>
  </clause>

  <clause id="27466">
    <literal><![CDATA[
      R(x,(y * y) * z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2752,a(flip),b,27418,a),flip(a)].">
      <j1 rule="hyper" parents="370 2752 27418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27468">
    <literal><![CDATA[
      R(x,(1 / y) * z,u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(314(a,1),27466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 27466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27469">
    <literal><![CDATA[
      R(x,(y \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(936(a,1),27466(a,1,2))].">
      <j1 rule="para" parents="936 27466"/>
    </justification>
  </clause>

  <clause id="27470">
    <literal><![CDATA[
      R(x,(1 / y) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(943(a,1),27466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="943 27466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27471">
    <literal><![CDATA[
      R(x,L(T(y,z),z,z),u) = R(x,z * (y * z),u)
    ]]></literal>
    <justification jstring="[para(585(a,2),27468(a,1,2))].">
      <j1 rule="para" parents="585 27468"/>
    </justification>
  </clause>

  <clause id="27472">
    <literal><![CDATA[
      R(x,R(y,y,z \ 1) * z,u) = R(x,y \ (z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2782,a,b,27470,a)].">
      <j1 rule="hyper" parents="60 2782 27470"/>
    </justification>
  </clause>

  <clause id="27473">
    <literal><![CDATA[
      R(x,y \ a(y,z,u),w) = R(x,y * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(19685(a,1),27470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19685 27470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27474">
    <literal><![CDATA[
      (x / y) / R(x,x * (y \ T(x,y \ x)),x) = x \ (T(x,y \ x) / y)
    ]]></literal>
    <justification jstring="[para(27426(a,1),14549(a,1,2))].">
      <j1 rule="para" parents="27426 14549"/>
    </justification>
  </clause>

  <clause id="27475">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) / (1 / z)) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(19685(a,1),27436(a,2,3,1))].">
      <j1 rule="para" parents="19685 27436"/>
    </justification>
  </clause>

  <clause id="27476">
    <literal><![CDATA[
      R(x,y,(z \ (u \ 1)) * w) = R(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[para(1470(a,1),27438(a,1,3))].">
      <j1 rule="para" parents="1470 27438"/>
    </justification>
  </clause>

  <clause id="27477">
    <literal><![CDATA[
      R(x,y,z \ ((1 / u) \ w)) = R(x,y,z \ (w / u))
    ]]></literal>
    <justification jstring="[hyper(2738,a,27445,a),flip(a)].">
      <j1 rule="hyper" parents="2738 27445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27478">
    <literal><![CDATA[
      R(x,y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,z / y,u) = w
    ]]></literal>
    <justification jstring="[para(27412(a,1),702(a,1)),flip(b)].">
      <j1 rule="para" parents="27412 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27479">
    <literal><![CDATA[
      L(x,R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(27454(a,1),14842(a,1))].">
      <j1 rule="para" parents="27454 14842"/>
    </justification>
  </clause>

  <clause id="27480">
    <literal><![CDATA[
      R(x,y * (z * y),u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27388,a(flip),b,27471,a),flip(a)].">
      <j1 rule="hyper" parents="60 27388 27471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27482">
    <literal><![CDATA[
      R(x,L((y / z) / u,w,v5),v6) = R(x,L((z \ y) / u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(15605(a,1),27401(a,1,2,1))].">
      <j1 rule="para" parents="15605 27401"/>
    </justification>
  </clause>

  <clause id="27483">
    <literal><![CDATA[
      R(x,y,z * (T(u,w) * v5)) = R(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27433,a,b,27437,a)].">
      <j1 rule="hyper" parents="60 27433 27437"/>
    </justification>
  </clause>

  <clause id="27484">
    <literal><![CDATA[
      R(x,y,z * (u \ (w \ 1))) = R(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27433,a,b,27476,a)].">
      <j1 rule="hyper" parents="60 27433 27476"/>
    </justification>
  </clause>

  <clause id="27485">
    <literal><![CDATA[
      R(x,y,z \ ((1 / u) \ w)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27445,a(flip),b,27477,a),flip(a)].">
      <j1 rule="hyper" parents="370 27445 27477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27486">
    <literal><![CDATA[
      R(x,y,z \ (u / (w \ 1))) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(74(a,1),27477(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="74 27477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27487">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ w)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(74(a,1),27485(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="74 27485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27488">
    <literal><![CDATA[
      R(x,y,z \ (u \ 1)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(77(a,1),27485(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="77 27485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27489">
    <literal><![CDATA[
      a(R(x,x,y \ z) * (y \ z),u,w) = a(x \ (y \ (z \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(27488(a,1),3168(a,1,1,1))].">
      <j1 rule="para" parents="27488 3168"/>
    </justification>
  </clause>

  <clause id="27490">
    <literal><![CDATA[
      a(x * (R(y / z,z,y \ u) \ u),w,v5) = a(x * (z * (y \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(27488(a,1),3004(a,1,1,2,1))].">
      <j1 rule="para" parents="27488 3004"/>
    </justification>
  </clause>

  <clause id="27491">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ z)) = R(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(3479(a,1),27486(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3479 27486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27492">
    <literal><![CDATA[
      R(x,y,(z * u) \ z) = R(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,27487,a(flip),b,27491,a),flip(a)].">
      <j1 rule="hyper" parents="60 27487 27491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27493">
    <literal><![CDATA[
      R(x,y,z \ L(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27435,a(flip),b,27446,a),flip(a)].">
      <j1 rule="hyper" parents="60 27435 27446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27495">
    <literal><![CDATA[
      R(x,R(y,y,z) * z,u) = R(x,y \ (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2711(a,1),27472(a,1,2,1))].">
      <j1 rule="para" parents="2711 27472"/>
    </justification>
  </clause>

  <clause id="27496">
    <literal><![CDATA[
      R(x,(1 / y) \ z,u) = R(x,y \ (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27495(a,1,2))].">
      <j1 rule="para" parents="1961 27495"/>
    </justification>
  </clause>

  <clause id="27497">
    <literal><![CDATA[
      R(x,y \ (z \ 1),u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27470,a(flip),b,27496,a),flip(a)].">
      <j1 rule="hyper" parents="60 27470 27496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27498">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(27453(a,2),27479(a,1))].">
      <j1 rule="para" parents="27453 27479"/>
    </justification>
  </clause>

  <clause id="27499">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * u != w * (((y \ z) \ z) * u)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(27416(a,1),41(a,1))].">
      <j1 rule="para" parents="27416 41"/>
    </justification>
  </clause>

  <clause id="27500">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) \ x = a(R(y,z,u),R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(27279(a,1),27455(a,1,1))].">
      <j1 rule="para" parents="27279 27455"/>
    </justification>
  </clause>

  <clause id="27501">
    <literal><![CDATA[
      R(x,L((y \ z) / u,w,v5),v6) = R(x,L(u \ (z / y),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27407,a(flip),b,27482,a),flip(a)].">
      <j1 rule="hyper" parents="60 27407 27482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27502">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),u) = a(L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(1364,a,27500,a),flip(a)].">
      <j1 rule="hyper" parents="1364 27500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27503">
    <literal><![CDATA[
      R(x,L(y \ (z / u),w,v5),v6) = R(x,L(y \ (u \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27407,a(flip),b,27501,a),flip(a)].">
      <j1 rule="hyper" parents="60 27407 27501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27504">
    <literal><![CDATA[
      R(T(T(x,y),x \ 1),x,y) = y / (((x * x) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(27450,a,27415,a)].">
      <j1 rule="hyper" parents="27450 27415"/>
    </justification>
  </clause>

  <clause id="27505">
    <literal><![CDATA[
      R(T(T(x,y),x \ 1),x,y) = (y / (y * x)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,1084,a(flip),b,27504,a),flip(a)].">
      <j1 rule="hyper" parents="370 1084 27504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27507">
    <literal><![CDATA[
      T(x,y) \ ((y \ ((y \ 1) \ x)) * y) = (x / (x * y)) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,25885,a,b,27505,a)].">
      <j1 rule="hyper" parents="60 25885 27505"/>
    </justification>
  </clause>

  <clause id="27508">
    <literal><![CDATA[
      T(x,y) \ ((y \ 1) \ T(x,y)) = (x / (x * y)) * (y * y)
    ]]></literal>
    <justification jstring="[para(2874(a,1),27507(a,1,2))].">
      <j1 rule="para" parents="2874 27507"/>
    </justification>
  </clause>

  <clause id="27509">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(23573(a,1),27452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23573 27452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27511">
    <literal><![CDATA[
      a((1 / x) \ (y \ z),u,w) = a(x \ (y \ (z \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27489(a,1,1))].">
      <j1 rule="para" parents="1961 27489"/>
    </justification>
  </clause>

  <clause id="27512">
    <literal><![CDATA[
      a(x \ (y \ (z \ 1)),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26595,a,27511,a),flip(a)].">
      <j1 rule="hyper" parents="26595 27511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27514">
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L((1 / y) * z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(77(a,1),27498(a,1,2,1,1))].">
      <j1 rule="para" parents="77 27498"/>
    </justification>
  </clause>

  <clause id="27515">
    <literal><![CDATA[
      a(x * (y * (z \ (u \ 1))),w,v5) = a(x * (y * (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(673(a,1),27490(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="673 27490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27516">
    <literal><![CDATA[
      a(x * (y * (z \ ((u * u) \ w))),v5,v6) = a(x * (y * (z \ (w \ (u * u)))),v5,v6)
    ]]></literal>
    <justification jstring="[para(578(a,1),27515(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="578 27515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27517">
    <literal><![CDATA[
      a(x * (R(y,y,z \ (u \ 1)) * (z \ u)),w,v5) = a(x * ((1 / y) \ (z \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27515(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 27515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27518">
    <literal><![CDATA[
      a(R(x,x,y * (z \ (u \ 1))) * (y * (z \ u)),w,v5) = a((1 / x) \ (y * (z \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1961 27515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27519">
    <literal><![CDATA[
      a(x,y,(K(z,u) * ((T(z,u) * w) / v5)) * v6) = a(x,y,((z * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(5865(a,1),25365(a,1,3,1,1))].">
      <j1 rule="para" parents="5865 25365"/>
    </justification>
  </clause>

  <clause id="27520">
    <literal><![CDATA[
      a(x,y,K(z,u) * (((T(z,u) * w) / v5) * v6)) = a(x,y,((z * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(23481(a,1),27519(a,1,3))].">
      <j1 rule="para" parents="23481 27519"/>
    </justification>
  </clause>

  <clause id="27521">
    <literal><![CDATA[
      a(x,y,K(z,u) * ((w \ (T(z,u) * v5)) * v6)) = a(x,y,((z * v5) / w) * v6)
    ]]></literal>
    <justification jstring="[hyper(27095,a,27520,a)].">
      <j1 rule="hyper" parents="27095 27520"/>
    </justification>
  </clause>

  <clause id="27522">
    <literal><![CDATA[
      a(x,y,(z \ (T(u,w) * v5)) * v6) = a(x,y,((u * v5) / z) * v6)
    ]]></literal>
    <justification jstring="[hyper(26978,a,27521,a)].">
      <j1 rule="hyper" parents="26978 27521"/>
    </justification>
  </clause>

  <clause id="27524">
    <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(27522(a,2),26980(a,1))].">
      <j1 rule="para" parents="27522 26980"/>
    </justification>
  </clause>

  <clause id="27525">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * a(x,y,z)) * (z \ u)) = z \ ((1 / a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(21728(a,1),25394(a,1,2))].">
      <j1 rule="para" parents="21728 25394"/>
    </justification>
  </clause>

  <clause id="27526">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (R(y,z,z) * x) = R(y,z,z) * R(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(16508(a,1),25571(a,2,1))].">
      <j1 rule="para" parents="16508 25571"/>
    </justification>
  </clause>

  <clause id="27527">
    <literal><![CDATA[
      L(x,y,z * L(u * (1 / w),w,w)) = L(x,y,z * L(u * w,w,w))
    ]]></literal>
    <justification jstring="[para(26336(a,1),25720(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26336 25720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27528">
    <literal><![CDATA[
      x * (y \ ((L(1 / y,z,u) \ y) * w)) = x * ((L(y \ 1,z,u) \ y) * (y \ w))
    ]]></literal>
    <justification jstring="[para(4239(a,1),25853(a,1,2))].">
      <j1 rule="para" parents="4239 25853"/>
    </justification>
  </clause>

  <clause id="27529">
    <literal><![CDATA[
      x * (L(x,y,z) \ K(x \ 1,(x \ 1) \ 1)) = x \ (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,5202,a(flip),b,25859,a),flip(a)].">
      <j1 rule="hyper" parents="370 5202 25859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27530">
    <literal><![CDATA[
      x * (L(x,y,z) \ K(x \ 1,x)) = x \ (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1713(a,1),27529(a,1,2,2))].">
      <j1 rule="para" parents="1713 27529"/>
    </justification>
  </clause>

  <clause id="27531">
    <literal><![CDATA[
      x * (L(x,y,z) \ K(x,x \ 1)) = x \ (L(x \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1716(a,1),27530(a,1,2,2))].">
      <j1 rule="para" parents="1716 27530"/>
    </justification>
  </clause>

  <clause id="27532">
    <literal><![CDATA[
      x \ (L(x \ 1,y,z) \ 1) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6791(a,1),27531(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6791 27531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27533">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (1 / x) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,5051,a,b,27532,a)].">
      <j1 rule="hyper" parents="60 5051 27532"/>
    </justification>
  </clause>

  <clause id="27534">
    <literal><![CDATA[
      (1 / x) / L(x \ 1,y,z) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,12768,a,b,27533,a)].">
      <j1 rule="hyper" parents="60 12768 27533"/>
    </justification>
  </clause>

  <clause id="27535">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (a(y,z,u) \ 1) = a(y,z,u) * (x \ (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(310(a,1),25860(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="310 25860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27536">
    <literal><![CDATA[
      R(x,y * L(y,z,u),y) * L(T(y,w),z,u) = (x * (y \ L(y,z,u))) * T(y,w)
    ]]></literal>
    <justification jstring="[para(25861(a,1),25335(a,1,1))].">
      <j1 rule="para" parents="25861 25335"/>
    </justification>
  </clause>

  <clause id="27537">
    <literal><![CDATA[
      L(x,y,z \ ((u \ T(w / v5,v6)) * (v5 * v5))) = L(x,y,z \ (u \ (w / (1 / v5))))
    ]]></literal>
    <justification jstring="[para(513(a,1),25999(a,1,3,2))].">
      <j1 rule="para" parents="513 25999"/>
    </justification>
  </clause>

  <clause id="27538">
    <literal><![CDATA[
      L(x,T(y \ z,u) \ (K(w,w \ y) * v5),v6) = L(x,((w * (y / w)) \ z) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(23596(a,1),26255(a,1,2))].">
      <j1 rule="para" parents="23596 26255"/>
    </justification>
  </clause>

  <clause id="27539">
    <literal><![CDATA[
      L(x,y * (z * ((u * u) \ (w \ K(v5,v6)))),v7) = L(x,y * ((z * w) * (u * u)),v7)
    ]]></literal>
    <justification jstring="[para(517(a,1),26292(a,1,2,2,2))].">
      <j1 rule="para" parents="517 26292"/>
    </justification>
  </clause>

  <clause id="27540">
    <literal><![CDATA[
      K(x,R(y,z,T(u,z)) * ((u * z) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((w / T(u,z)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(22641(a,1),26310(a,1))].">
      <j1 rule="para" parents="22641 26310"/>
    </justification>
  </clause>

  <clause id="27541">
    <literal><![CDATA[
      a(((x * x) * (y / L(x,z,u))) * w,v5,v6) = a((L(1 / x,z,u) \ y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(853(a,1),26596(a,1,1,1))].">
      <j1 rule="para" parents="853 26596"/>
    </justification>
  </clause>

  <clause id="27542">
    <literal><![CDATA[
      a(x \ (y \ ((z \ 1) * u)),w,v5) = a(x \ (y \ (z * u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26779,a(flip),b,26647,a),flip(a)].">
      <j1 rule="hyper" parents="60 26779 26647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27544">
    <literal><![CDATA[
      a(x,y * (z \ ((u \ 1) * w)),v5) = a(x,y * (z \ (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,3139,a(flip),b,26655,a),flip(a)].">
      <j1 rule="hyper" parents="60 3139 26655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27546">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a(L(x * y,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(26336(a,1),26661(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26336 26661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27547">
    <literal><![CDATA[
      a((x * ((y * z) \ K(u,y))) * w,v5,v6) = a((x * (T(y,u) * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3(a,1),26663(a,1,1,1,2,2))].">
      <j1 rule="para" parents="3 26663"/>
    </justification>
  </clause>

  <clause id="27548">
    <literal><![CDATA[
      a((x * (T(y,z) * u)) * w,v5,v6) = a((x * (y * u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26768,a,27547,a),flip(a)].">
      <j1 rule="hyper" parents="26768 27547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27551">
    <literal><![CDATA[
      a(x,((T(y \ 1,y * z) \ z) * u) \ w,v5) = a(x,((y \ z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26839,a(flip),b,26728,a),flip(a)].">
      <j1 rule="hyper" parents="370 26839 26728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27552">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) \ u)) \ w,v5) = a(x,((z \ u) * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26864,a,27551,a)].">
      <j1 rule="hyper" parents="26864 27551"/>
    </justification>
  </clause>

  <clause id="27553">
    <literal><![CDATA[
      a((x \ (((y \ z) \ 1) \ y)) * u,w,v5) = a((x \ (y * (z \ y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26874,a,26734,a)].">
      <j1 rule="hyper" parents="26874 26734"/>
    </justification>
  </clause>

  <clause id="27554">
    <literal><![CDATA[
      a((x \ ((y \ z) \ y)) * u,w,v5) = a((x \ (y * (z \ y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26874,a,27553,a)].">
      <j1 rule="hyper" parents="26874 27553"/>
    </justification>
  </clause>

  <clause id="27555">
    <literal><![CDATA[
      a((x \ ((y * z) \ y)) * u,w,v5) = a((x \ (y \ (y / z))) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),26735(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 26735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27557">
    <literal><![CDATA[
      a((x \ ((y * z) \ y)) * u,w,v5) = a((x \ (y \ (z \ y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26772,a(flip),b,27555,a),flip(a)].">
      <j1 rule="hyper" parents="370 26772 27555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27558">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * w) * v5) = a(x,y,((z \ (z / u)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(74(a,1),27121(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="74 27121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27560">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * w) * v5) = a(x,y,((z \ (u \ z)) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27183,a(flip),b,27558,a),flip(a)].">
      <j1 rule="hyper" parents="370 27183 27558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27561">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) / w) * v5)) = a(x,y,z * ((w / (u * w)) * v5))
    ]]></literal>
    <justification jstring="[para(74(a,1),27130(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="74 27130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27563">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) / w) * v5)) = a(x,y,z * (((u * w) \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,27024,a(flip),b,27561,a),flip(a)].">
      <j1 rule="hyper" parents="370 27024 27561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27564">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ w) * v5)) = a(x,y,z * ((w \ (u \ w)) * v5))
    ]]></literal>
    <justification jstring="[hyper(27095,a,27563,a),flip(a)].">
      <j1 rule="hyper" parents="27095 27563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27566">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * w) \ v5)) = a(x,y,z * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,27257,a(flip),b,27147,a),flip(a)].">
      <j1 rule="hyper" parents="60 27257 27147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27568">
    <literal><![CDATA[
      a(x,y,(z * (u * ((w * w) * v5))) * v6) = a(x,y,((v5 * u) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,27239,a(flip),b,27155,a),flip(a)].">
      <j1 rule="hyper" parents="370 27239 27155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27569">
    <literal><![CDATA[
      a(x,y,(z * (u * ((w * w) * v5))) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((v5 * u) * z) * v6) = v7
    ]]></literal>
    <justification jstring="[para(27155(a,2),27240(a,1))].">
      <j1 rule="para" parents="27155 27240"/>
    </justification>
  </clause>

  <clause id="27571">
    <literal><![CDATA[
      a(x,y,(z * ((u \ (w * w)) * v5)) * v6) = a(x,y,((v5 * (u \ 1)) * z) * v6)
    ]]></literal>
    <justification jstring="[para(573(a,1),27568(a,1,3,1,2))].">
      <j1 rule="para" parents="573 27568"/>
    </justification>
  </clause>

  <clause id="27572">
    <literal><![CDATA[
      (1 / a(x,y,z)) \ (z \ u) = z \ ((1 / a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(597,a,27525,a)].">
      <j1 rule="hyper" parents="597 27525"/>
    </justification>
  </clause>

  <clause id="27573">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z \ u) = z \ ((1 / a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),27572(a,1,1))].">
      <j1 rule="para" parents="23572 27572"/>
    </justification>
  </clause>

  <clause id="27574">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z \ u) = z \ ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),27573(a,2,2,1))].">
      <j1 rule="para" parents="23572 27573"/>
    </justification>
  </clause>

  <clause id="27575">
    <literal><![CDATA[
      x * ((L(x \ 1,y,z) \ x) * (x \ u)) = (L(1 / x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(298,a,27528,a),flip(a)].">
      <j1 rule="hyper" parents="298 27528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27577">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * L(T(y,w),z,u) = (x * (y \ L(y,z,u))) * T(y,w)
    ]]></literal>
    <justification jstring="[para(25862(a,1),27536(a,1,1))].">
      <j1 rule="para" parents="25862 27536"/>
    </justification>
  </clause>

  <clause id="27578">
    <literal><![CDATA[
      L(x,y,(z \ (u \ T(w / v5,v6))) * (v5 * v5)) = L(x,y,z \ (u \ (w / (1 / v5))))
    ]]></literal>
    <justification jstring="[para(513(a,1),27537(a,1,3))].">
      <j1 rule="para" parents="513 27537"/>
    </justification>
  </clause>

  <clause id="27579">
    <literal><![CDATA[
      L(x,T(y \ z,u) \ w,v5) = L(x,((v6 * (y / v6)) \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26198,a,27538,a)].">
      <j1 rule="hyper" parents="26198 27538"/>
    </justification>
  </clause>

  <clause id="27581">
    <literal><![CDATA[
      L(x,((y * (z / y)) \ u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ u) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27579(a,1),26193(a,1))].">
      <j1 rule="para" parents="27579 26193"/>
    </justification>
  </clause>

  <clause id="27582">
    <literal><![CDATA[
      L(x,y * (z * ((u * u) \ (w \ K(v5,v6)))),v7) = L(x,y * (z * w),v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,3783,a(flip),b,27539,a),flip(a)].">
      <j1 rule="hyper" parents="370 3783 27539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27584">
    <literal><![CDATA[
      L(x,y * ((z / (u * u)) * w),v5) = L(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26293,a(flip),b,27582,a)].">
      <j1 rule="hyper" parents="60 26293 27582"/>
    </justification>
  </clause>

  <clause id="27586">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * u),w) = L(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(310(a,1),27584(a,1,2,2,1))].">
      <j1 rule="para" parents="310 27584"/>
    </justification>
  </clause>

  <clause id="27587">
    <literal><![CDATA[
      a((x * x) * ((y / L(x,z,u)) * w),v5,v6) = a((L(1 / x,z,u) \ y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(28(a,1),27541(a,1,1))].">
      <j1 rule="para" parents="28 27541"/>
    </justification>
  </clause>

  <clause id="27588">
    <literal><![CDATA[
      L(x,y,z \ (u \ T(w / v5,v6))) = L(x,y,z \ (u \ (w / (1 / v5))))
    ]]></literal>
    <justification jstring="[hyper(3528,a,27578,a)].">
      <j1 rule="hyper" parents="3528 27578"/>
    </justification>
  </clause>

  <clause id="27589">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w / (1 / v5)))) = L(x,y,z \ (u \ (w / v5)))
    ]]></literal>
    <justification jstring="[hyper(25956,a,27588,a),flip(a)].">
      <j1 rule="hyper" parents="25956 27588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27591">
    <literal><![CDATA[
      L(x,y,z \ (u \ ((1 / w) \ v5))) = L(x,y,z \ (u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,25976,a(flip),b,27589,a)].">
      <j1 rule="hyper" parents="60 25976 27589"/>
    </justification>
  </clause>

  <clause id="27592">
    <literal><![CDATA[
      L(x,y,z \ (u \ ((1 / w) \ v5))) = L(x,y,z \ (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(370,a,25976,a(flip),b,27591,a),flip(a)].">
      <j1 rule="hyper" parents="370 25976 27591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27593">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w \ 1))) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(77(a,1),27592(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="77 27592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27594">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25927,a,b,27593,a)].">
      <j1 rule="hyper" parents="60 25927 27593"/>
    </justification>
  </clause>

  <clause id="27595">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) / w)) = L(x,y,z \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(370,a,25927,a,b,27594,a),flip(a)].">
      <j1 rule="hyper" parents="370 25927 27594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27596">
    <literal><![CDATA[
      L(x,y,z \ ((z \ 1) / ((u \ 1) \ 1))) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(3479(a,1),27595(a,2,3))].">
      <j1 rule="para" parents="3479 27595"/>
    </justification>
  </clause>

  <clause id="27597">
    <literal><![CDATA[
      a((L(1 / x,y,z) \ u) * w,v5,v6) = a((u / L(x,y,z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(2975,a,27587,a),flip(a)].">
      <j1 rule="hyper" parents="2975 27587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27599">
    <literal><![CDATA[
      a((L(1 / x,y,z) \ u) * w,v5,v6) = a((L(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26388,a(flip),b,27597,a),flip(a)].">
      <j1 rule="hyper" parents="370 26388 27597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27601">
    <literal><![CDATA[
      L(L((a(x,y,z) \ 1) \ u,w,v5),a(x,y,z),a(x,y,z)) != L(v6,w,v5)
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(24133(a,2),47(a,1))].">
      <j1 rule="para" parents="24133 47"/>
    </justification>
  </clause>

  <clause id="27602">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (w * a(x,y,z)) = R(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(23515(a,1),24134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23515 24134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27603">
    <literal><![CDATA[
      L(x,y,(z * u) * (u * L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * (z * (u \ R(u,w,v5)))) = v6
    ]]></literal>
    <justification jstring="[para(27296(a,1),25240(a,1))].">
      <j1 rule="para" parents="27296 25240"/>
    </justification>
  </clause>

  <clause id="27604">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,z * y) \ R(x,y,z) = (x \ R(x,y,z)) * (a(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2014(a,1),25661(a,1,1,1))].">
      <j1 rule="para" parents="2014 25661"/>
    </justification>
  </clause>

  <clause id="27605">
    <literal><![CDATA[
      L(x,y,z \ ((u \ (((w * w) \ u) * v5)) * (w * w))) = L(x,y,z \ L(v5,u,w * w))
    ]]></literal>
    <justification jstring="[para(974(a,1),26001(a,1,3,2,1))].">
      <j1 rule="para" parents="974 26001"/>
    </justification>
  </clause>

  <clause id="27606">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),1 / z,1 / z),u) = L(x,(z \ 1) * R(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(2060(a,1),26284(a,2,2,2))].">
      <j1 rule="para" parents="2060 26284"/>
    </justification>
  </clause>

  <clause id="27607">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),1 / z,1 / z),u) = L(x,R((1 / z) * y,z,z),u)
    ]]></literal>
    <justification jstring="[para(4538(a,2),27606(a,2,2))].">
      <j1 rule="para" parents="4538 27606"/>
    </justification>
  </clause>

  <clause id="27608">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),1 / z,1 / z),u) = L(x,L((1 / z) * y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,27410,a(flip),b,27607,a),flip(a)].">
      <j1 rule="hyper" parents="370 27410 27607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27609">
    <literal><![CDATA[
      a(((T(x,y \ 1) \ 1) \ (y \ 1)) * z,u,w) = a((L(x,x,y \ 1) * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(26524,a,26664,a)].">
      <j1 rule="hyper" parents="26524 26664"/>
    </justification>
  </clause>

  <clause id="27610">
    <literal><![CDATA[
      a(x * (L(1 / y,z,u) * w),v5,v6) = a((L(y,z,u) * w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26753,a,26822,a)].">
      <j1 rule="hyper" parents="26753 26822"/>
    </justification>
  </clause>

  <clause id="27611">
    <literal><![CDATA[
      R(x,y * z,a(x,z,y)) \ ((x * z) * T(y,z)) = (y * z) * a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,260,a(flip),b,26922,a),flip(a)].">
      <j1 rule="hyper" parents="370 260 26922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27613">
    <literal><![CDATA[
      R(x,y * z,a(x,z,y)) \ ((x * z) * T(y,z)) = (y * z) * a(x,z,y)
    ]]></literal>
    <justification jstring="[para(26880(a,1),27611(a,2,2))].">
      <j1 rule="para" parents="26880 27611"/>
    </justification>
  </clause>

  <clause id="27614">
    <literal><![CDATA[
      R(x,y * z,a(x,z,y)) \ ((x * z) * T(y,z)) = y * (z * a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,14786,a(flip),b,27613,a),flip(a)].">
      <j1 rule="hyper" parents="370 14786 27613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27616">
    <literal><![CDATA[
      L(R((x \ 1) \ 1,y,z) \ u,L(x,y,z),L(x,y,z)) = 1 \ ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(27479,a,27283,a)].">
      <j1 rule="hyper" parents="27479 27283"/>
    </justification>
  </clause>

  <clause id="27617">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,y,z) \ x) = a(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(24918(a,2),27604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24918 27604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27618">
    <literal><![CDATA[
      L(x,y,z \ ((T(u * u,w) \ v5) * (u * u))) = L(x,y,z \ L(v5,w,u * u))
    ]]></literal>
    <justification jstring="[para(12676(a,1),27605(a,1,3,2,1))].">
      <j1 rule="para" parents="12676 27605"/>
    </justification>
  </clause>

  <clause id="27619">
    <literal><![CDATA[
      L(x,y,(z \ (T(u * u,w) \ v5)) * (u * u)) = L(x,y,z \ L(v5,w,u * u))
    ]]></literal>
    <justification jstring="[para(513(a,1),27618(a,1,3))].">
      <j1 rule="para" parents="513 27618"/>
    </justification>
  </clause>

  <clause id="27620">
    <literal><![CDATA[
      L(x,y,z \ (T(u * u,w) \ v5)) = L(x,y,z \ L(v5,w,u * u))
    ]]></literal>
    <justification jstring="[hyper(3528,a,27619,a)].">
      <j1 rule="hyper" parents="3528 27619"/>
    </justification>
  </clause>

  <clause id="27622">
    <literal><![CDATA[
      L(x,y,z \ L(u,w,v5 * v5)) = L(x,y,z \ ((v5 * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25963,a(flip),b,27620,a),flip(a)].">
      <j1 rule="hyper" parents="60 25963 27620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27624">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) \ w)) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(614(a,1),27622(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="614 27622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27625">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ w)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(940(a,1),27624(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="940 27624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27626">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) / (w \ 1))) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27594,a,b,27625,a)].">
      <j1 rule="hyper" parents="60 27594 27625"/>
    </justification>
  </clause>

  <clause id="27627">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27596,a(flip),b,27626,a),flip(a)].">
      <j1 rule="hyper" parents="60 27596 27626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27628">
    <literal><![CDATA[
      L(x,y,(z * u) \ z) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,27625,a(flip),b,27627,a),flip(a)].">
      <j1 rule="hyper" parents="60 27625 27627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27629">
    <literal><![CDATA[
      L(x,y,(((z \ 1) \ 1) * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27294,a,b,27628,a)].">
      <j1 rule="hyper" parents="60 27294 27628"/>
    </justification>
  </clause>

  <clause id="27630">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(4151,a,27629,a)].">
      <j1 rule="hyper" parents="4151 27629"/>
    </justification>
  </clause>

  <clause id="27631">
    <literal><![CDATA[
      L(x,y,(z * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(4151,a,27630,a)].">
      <j1 rule="hyper" parents="4151 27630"/>
    </justification>
  </clause>

  <clause id="27632">
    <literal><![CDATA[
      a(((T(x,y \ 1) \ 1) \ y) * z,u,w) = a((L(x,x,y \ 1) * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26631,a(flip),b,27609,a)].">
      <j1 rule="hyper" parents="60 26631 27609"/>
    </justification>
  </clause>

  <clause id="27633">
    <literal><![CDATA[
      a((L(x,x,y \ 1) * y) * z,u,w) = a((T(x,y \ 1) \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(2978,a,27632,a),flip(a)].">
      <j1 rule="hyper" parents="2978 27632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27634">
    <literal><![CDATA[
      a((L(x,x,y \ 1) * y) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26395,a(flip),b,27633,a),flip(a)].">
      <j1 rule="hyper" parents="370 26395 27633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27636">
    <literal><![CDATA[
      a((L(x,x,y) * y) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(1492(a,1),27634(a,1,1,1,1))].">
      <j1 rule="para" parents="1492 27634"/>
    </justification>
  </clause>

  <clause id="27637">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) * (a(z,u,w) \ 1) = a(z,u,w) * (x * (y * (a(z,u,w) \ 1)))
    ]]></literal>
    <justification jstring="[para(23572(a,1),24118(a,1,2))].">
      <j1 rule="para" parents="23572 24118"/>
    </justification>
  </clause>

  <clause id="27638">
    <literal><![CDATA[
      (x * a(y,z,u)) \ L(x,a(y,z,u),a(y,z,u)) = T(a(y,z,u) \ 1,a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(23572(a,1),24127(a,2,1))].">
      <j1 rule="para" parents="23572 24127"/>
    </justification>
  </clause>

  <clause id="27639">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) / (y \ L(y,z,u))) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,23881,a(flip),b,25312,a),flip(a)].">
      <j1 rule="hyper" parents="60 23881 25312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27640">
    <literal><![CDATA[
      x * ((y \ L(y,z,u)) \ (L(y,z,u) \ y)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(23954(a,1),27639(a,1,2))].">
      <j1 rule="para" parents="23954 27639"/>
    </justification>
  </clause>

  <clause id="27641">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) * (L(y,z,u) \ y)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(14172(a,1),27640(a,1,2))].">
      <j1 rule="para" parents="14172 27640"/>
    </justification>
  </clause>

  <clause id="27642">
    <literal><![CDATA[
      L(x * ((L(y,z,u) \ y) * (L(y,z,u) \ y)),w,v5) = (L(y,z,u) * L(y \ 1,z,u)) \ L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(4040,a,27641,a)].">
      <j1 rule="hyper" parents="4040 27641"/>
    </justification>
  </clause>

  <clause id="27643">
    <literal><![CDATA[
      x * (y * ((L(z,u,w) \ z) * (L(z,u,w) \ z))) = (L(z,u,w) * L(z \ 1,u,w)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(1188,a,27641,a)].">
      <j1 rule="hyper" parents="1188 27641"/>
    </justification>
  </clause>

  <clause id="27644">
    <literal><![CDATA[
      x \ (y * ((L(z,u,w) \ z) * (L(z,u,w) \ z))) = (L(z,u,w) * L(z \ 1,u,w)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,513,a,b,27641,a)].">
      <j1 rule="hyper" parents="60 513 27641"/>
    </justification>
  </clause>

  <clause id="27645">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ ((z \ L(z,u,w)) * (x * y)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3861,a(flip),b,25318,a),flip(a)].">
      <j1 rule="hyper" parents="370 3861 25318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27646">
    <literal><![CDATA[
      T(R(R(x,y,z),u,w) / R(x,y,z),x) = R(T(x,v5),y,z) \ R(T(R(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),25369(a,2,1))].">
      <j1 rule="para" parents="22 25369"/>
    </justification>
  </clause>

  <clause id="27647">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u) \ x),(L(x,z,u) \ x) * y) = L(T(x,y),y,L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(12257,a,25625,a)].">
      <j1 rule="hyper" parents="12257 25625"/>
    </justification>
  </clause>

  <clause id="27648">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((1 / L(x,y,z)) * x)) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2162(a,1),25626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2162 25626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27649">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = x * (L(x,y,z) \ (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(3954(a,1),27648(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3954 27648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27650">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ (L(y,z,u) \ y))) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(27649(a,1),27641(a,1,2))].">
      <j1 rule="para" parents="27649 27641"/>
    </justification>
  </clause>

  <clause id="27651">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ x = L(x,y,z) \ (L(x \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14780,a(flip),b,27650,a),flip(a)].">
      <j1 rule="hyper" parents="60 14780 27650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27652">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) \ (L(x,z,u) * y) = a(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(3838(a,1),25636(a,1,2,1))].">
      <j1 rule="para" parents="3838 25636"/>
    </justification>
  </clause>

  <clause id="27653">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(26320,a,27652,a),flip(a)].">
      <j1 rule="hyper" parents="26320 27652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27654">
    <literal><![CDATA[
      a(x * L(x,y,z),x,u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(3859,a,27653,a)].">
      <j1 rule="hyper" parents="3859 27653"/>
    </justification>
  </clause>

  <clause id="27655">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * L(x,y,z),x,u) = w
    ]]></literal>
    <justification jstring="[para(27653(a,1),3859(a,1))].">
      <j1 rule="para" parents="27653 3859"/>
    </justification>
  </clause>

  <clause id="27656">
    <literal><![CDATA[
      L((L(x,y,z) * (x \ u)) \ u,x \ (L(x,y,z) * u),x) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(2156(a,1),25807(a,1,1,1))].">
      <j1 rule="para" parents="2156 25807"/>
    </justification>
  </clause>

  <clause id="27657">
    <literal><![CDATA[
      T((x \ y) * (y \ (x * z)),u) = (x \ y) * (y \ (x * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(7982,a,26298,a),flip(a)].">
      <j1 rule="hyper" parents="7982 26298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27659">
    <literal><![CDATA[
      T((x \ y) * (y \ (x * (x \ (y * z)))),u) = (x \ y) * ((y \ x) * T((y \ x) \ z,u))
    ]]></literal>
    <justification jstring="[para(1624(a,1),27657(a,2,2))].">
      <j1 rule="para" parents="1624 27657"/>
    </justification>
  </clause>

  <clause id="27660">
    <literal><![CDATA[
      a((x \ ((x \ 1) / (y \ 1))) * z,u,w) = a(z * (x \ (x / (y \ 1))),u,w)
    ]]></literal>
    <justification jstring="[para(77(a,1),26642(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 26642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27661">
    <literal><![CDATA[
      a((x \ ((x \ 1) / ((y \ 1) \ 1))) * z,u,w) = a(z * ((x * y) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(3479(a,1),27660(a,2,1,2))].">
      <j1 rule="para" parents="3479 27660"/>
    </justification>
  </clause>

  <clause id="27662">
    <literal><![CDATA[
      a((x \ (((y \ 1) \ 1) \ (x \ 1))) * z,u,w) = a(z * ((x * y) \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26639,a(flip),b,27661,a)].">
      <j1 rule="hyper" parents="60 26639 27661"/>
    </justification>
  </clause>

  <clause id="27663">
    <literal><![CDATA[
      a((x \ ((y \ 1) \ (x \ 1))) * z,u,w) = a(z * ((x * y) \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26874,a,27662,a)].">
      <j1 rule="hyper" parents="26874 27662"/>
    </justification>
  </clause>

  <clause id="27664">
    <literal><![CDATA[
      a((x \ (y \ (x \ 1))) * z,u,w) = a(z * ((x * y) \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26874,a,27663,a)].">
      <j1 rule="hyper" parents="26874 27663"/>
    </justification>
  </clause>

  <clause id="27665">
    <literal><![CDATA[
      a(x,y * L(z,R(u,u,z),R(u,u,z)),w) = a(x,y * (R(u,u,z) * (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27361,a(flip),b,26694,a),flip(a)].">
      <j1 rule="hyper" parents="370 27361 26694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27666">
    <literal><![CDATA[
      a(x,y * L(z,R(u,u,z),R(u,u,z)),w) = a(x,y * (u \ ((1 / u) \ z)),w)
    ]]></literal>
    <justification jstring="[para(1980(a,1),27665(a,2,2,2))].">
      <j1 rule="para" parents="1980 27665"/>
    </justification>
  </clause>

  <clause id="27667">
    <literal><![CDATA[
      a(x,y * L(z,R(u,u,z),R(u,u,z)),w) = a(x,y * (u \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26775,a(flip),b,27666,a),flip(a)].">
      <j1 rule="hyper" parents="370 26775 27666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27668">
    <literal><![CDATA[
      a(x,y * L(z,R(u,u,z),L(u,u,z)),w) = a(x,y * (u \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[para(27279(a,1),27667(a,1,2,2))].">
      <j1 rule="para" parents="27279 27667"/>
    </justification>
  </clause>

  <clause id="27669">
    <literal><![CDATA[
      a(x,y * L(z,L(u,u,z),L(u,u,z)),w) = a(x,y * (u \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[para(27410(a,1),27668(a,1,2,2))].">
      <j1 rule="para" parents="27410 27668"/>
    </justification>
  </clause>

  <clause id="27670">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * (w / (1 / v5)))) \ v6,v7) = a(x,(y * ((K(u,z) / v5) \ w)) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(23604(a,1),26737(a,1,2,1,2))].">
      <j1 rule="para" parents="23604 26737"/>
    </justification>
  </clause>

  <clause id="27671">
    <literal><![CDATA[
      a(x,(y \ R(z * u,u,u)) * w,v5) = a(x,w * (y \ R(u * z,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(1517(a,1),26809(a,1,2,1,2))].">
      <j1 rule="para" parents="1517 26809"/>
    </justification>
  </clause>

  <clause id="27672">
    <literal><![CDATA[
      a(L(x \ a(y,z,x),u,w) * v5,v6,v7) = a(v5 * L(x * a(y,z,x),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,26838,a(flip),b,26860,a)].">
      <j1 rule="hyper" parents="60 26838 26860"/>
    </justification>
  </clause>

  <clause id="27673">
    <literal><![CDATA[
      a(x \ (y \ (z \ (u * (T(T(w,u),v5) * v6)))),v7,v8) = a(x \ (y \ (z \ (u * (T(w,v5) * v6)))),v7,v8)
    ]]></literal>
    <justification jstring="[para(18(a,1),26861(a,1,1,2,2,2,2,1))].">
      <j1 rule="para" parents="18 26861"/>
    </justification>
  </clause>

  <clause id="27674">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,L(z,v5,z)) \ (u * w))) = a(x,y,u * (w * L(z,v5,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26890,a(flip),b,27111,a),flip(a)].">
      <j1 rule="hyper" parents="370 26890 27111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27675">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,z) \ (u * w))) = a(x,y,u * (w * L(z,v5,z)))
    ]]></literal>
    <justification jstring="[para(26960(a,1),27674(a,1,3,2,1))].">
      <j1 rule="para" parents="26960 27674"/>
    </justification>
  </clause>

  <clause id="27676">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) = a(x,y,w * (u * L(z,v5,z)))
    ]]></literal>
    <justification jstring="[para(25773(a,1),27675(a,1,3))].">
      <j1 rule="para" parents="25773 27675"/>
    </justification>
  </clause>

  <clause id="27678">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u * w)) = v6
    ]]></literal>
    <justification jstring="[para(27676(a,1),26967(a,1))].">
      <j1 rule="para" parents="27676 26967"/>
    </justification>
  </clause>

  <clause id="27679">
    <literal><![CDATA[
      a(x,y,(T(z,z \ 1) * ((u * u) \ w)) * v5) = a(x,y,(((z \ (u * u)) \ 1) * w) * v5)
    ]]></literal>
    <justification jstring="[para(935(a,1),27120(a,1,3,1))].">
      <j1 rule="para" parents="935 27120"/>
    </justification>
  </clause>

  <clause id="27680">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * (w * (v5 \ 1)))) * v6) = a(x,y,v6 * (z * ((v5 \ (u * u)) * w)))
    ]]></literal>
    <justification jstring="[para(28(a,1),27156(a,1,3,1,2))].">
      <j1 rule="para" parents="28 27156"/>
    </justification>
  </clause>

  <clause id="27681">
    <literal><![CDATA[
      a(x,y,((((z \ 1) \ u) * w) * v5) * v6) = a(x,y,v6 * (v5 * ((z \ u) * w)))
    ]]></literal>
    <justification jstring="[hyper(27085,a,27157,a),flip(a)].">
      <j1 rule="hyper" parents="27085 27157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27683">
    <literal><![CDATA[
      a(x,y,(((((z * z) \ 1) \ T(u,u \ 1)) * w) * v5) * v6) = a(x,y,v6 * (v5 * (((u \ (z * z)) \ 1) * w)))
    ]]></literal>
    <justification jstring="[para(1258(a,1),27681(a,2,3,2,2,1))].">
      <j1 rule="para" parents="1258 27681"/>
    </justification>
  </clause>

  <clause id="27684">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w \ v5,w) * (v6 * v5)))) = a(x,y,(u * (((w \ v5) * w) * v6)) * z)
    ]]></literal>
    <justification jstring="[para(23481(a,1),27160(a,1,3,2,2))].">
      <j1 rule="para" parents="23481 27160"/>
    </justification>
  </clause>

  <clause id="27685">
    <literal><![CDATA[
      a(x,y,(z * (K(u \ w,u) * (v5 * w))) * v6) = a(x,y,v6 * (z * (((u \ w) * u) * v5)))
    ]]></literal>
    <justification jstring="[para(23481(a,1),27161(a,1,3,1,2))].">
      <j1 rule="para" parents="23481 27161"/>
    </justification>
  </clause>

  <clause id="27686">
    <literal><![CDATA[
      a(x,y,(z * (u \ R(w,v5,w))) * v6) = a(x,y,((u \ w) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27181,a(flip),b,27187,a),flip(a)].">
      <j1 rule="hyper" parents="60 27181 27187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27688">
    <literal><![CDATA[
      a(L(x,x,y * L(z,u,w)) * (y * L(z,u,w)),v5,v6) = a(x \ (y * R(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(27272(a,1),27339(a,1,1,1))].">
      <j1 rule="para" parents="27272 27339"/>
    </justification>
  </clause>

  <clause id="27689">
    <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(129,a,23824,a(flip),b,27638,a)].">
      <j1 rule="hyper" parents="129 23824 27638"/>
    </justification>
  </clause>

  <clause id="27690">
    <literal><![CDATA[
      (x * (K(y,z) * L(y,u,w))) \ ((y \ L(y,u,w)) * (x * T(y,z))) = a(x,T(y,z),y * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7860(a,1),27645(a,1,1,2))].">
      <j1 rule="para" parents="7860 27645"/>
    </justification>
  </clause>

  <clause id="27691">
    <literal><![CDATA[
      T(R(R(x,y,z),u,w) / R(x,y,z),x) = R(T(x,v5),y,z) \ R(R(T(x,v5),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),27646(a,2,2,1))].">
      <j1 rule="para" parents="22 27646"/>
    </justification>
  </clause>

  <clause id="27692">
    <literal><![CDATA[
      T(x * 1,(L(x,y,z) \ x) * u) = L(T(x,u),u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(23539(a,1),27647(a,1,1,2))].">
      <j1 rule="para" parents="23539 27647"/>
    </justification>
  </clause>

  <clause id="27693">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u) \ x) = T(x,(L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(3(a,1),27692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 27692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27695">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u) \ x) = T(x,x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,18840,a(flip),b,27693,a),flip(a)].">
      <j1 rule="hyper" parents="370 18840 27693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27696">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,12757,a(flip),b,27695,a),flip(a)].">
      <j1 rule="hyper" parents="370 12757 27695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27697">
    <literal><![CDATA[
      L(T(x,y),y,x * L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(14764,a,27696,a)].">
      <j1 rule="hyper" parents="14764 27696"/>
    </justification>
  </clause>

  <clause id="27699">
    <literal><![CDATA[
      L(x,y,x * L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(162,a,27697,a(flip))].">
      <j1 rule="hyper" parents="162 27697"/>
    </justification>
  </clause>

  <clause id="27701">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x * L(x,w,v5)) = x \ L(L(x,u,x * L(x,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(27699(a,1),10440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27699 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27702">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x * L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(27699(a,1),27701(a,2,2,1))].">
      <j1 rule="para" parents="27699 27701"/>
    </justification>
  </clause>

  <clause id="27703">
    <literal><![CDATA[
      L((L(x,y,z) * (x \ u)) \ u,L(x,y,z) * (x \ u),x) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(2156(a,1),27656(a,1,2))].">
      <j1 rule="para" parents="2156 27656"/>
    </justification>
  </clause>

  <clause id="27704">
    <literal><![CDATA[
      (x \ y) * ((y \ x) * T((y \ x) \ z,u)) = T((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(68(a,1),27659(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="68 27659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27705">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * z,u) = (y \ x) * T((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,27704,a)].">
      <j1 rule="hyper" parents="135 27704"/>
    </justification>
  </clause>

  <clause id="27707">
    <literal><![CDATA[
      x \ ((y \ z) * T((y \ z) \ x,u)) = K(((z \ y) \ 1) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,27705,a(flip),b,6321,a(flip))].">
      <j1 rule="hyper" parents="125 27705 6321"/>
    </justification>
  </clause>

  <clause id="27708">
    <literal><![CDATA[
      K(((x \ y) \ 1) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6412,a,27707,a),flip(a)].">
      <j1 rule="hyper" parents="6412 27707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27709">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15484,a,27708,a),flip(a)].">
      <j1 rule="hyper" parents="15484 27708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27711">
    <literal><![CDATA[
      K(x \ (y * z),u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(24970,a,27709,a)].">
      <j1 rule="hyper" parents="24970 27709"/>
    </justification>
  </clause>

  <clause id="27715">
    <literal><![CDATA[
      K((x \ y) * (y \ z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),27711(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 27711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27716">
    <literal><![CDATA[
      K((R(x,y,z) \ x) * u,w) = K(x * (R(x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(1956(a,1),27711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1956 27711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27720">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) \ 1) * w) * v5) = a(x,y,(z * ((u * u) \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(27003,a,27679,a),flip(a)].">
      <j1 rule="hyper" parents="27003 27679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27722">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) \ w)) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27189,a(flip),b,27720,a),flip(a)].">
      <j1 rule="hyper" parents="60 27189 27720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27724">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),27722(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="4 27722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27725">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) * w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1117(a,1),27722(a,1,3,1))].">
      <j1 rule="para" parents="1117 27722"/>
    </justification>
  </clause>

  <clause id="27726">
    <literal><![CDATA[
      a(x,y,(z * ((1 / u) \ w)) * v5) = a(x,y,(z * (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(943(a,1),27724(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="943 27724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27727">
    <literal><![CDATA[
      a(x,y,(z * ((u \ (w * w)) * v5)) * v6) = a(x,y,((v5 * u) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27571,a,b,27725,a)].">
      <j1 rule="hyper" parents="60 27571 27725"/>
    </justification>
  </clause>

  <clause id="27728">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * w)) * v5) = a(x,y,((w * u) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27150,a(flip),b,27725,a)].">
      <j1 rule="hyper" parents="60 27150 27725"/>
    </justification>
  </clause>

  <clause id="27729">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) * v5) * v6)) = a(x,y,((v5 * u) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27727,a)].">
      <j1 rule="hyper" parents="27033 27727"/>
    </justification>
  </clause>

  <clause id="27730">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ (v5 * v5)) * v6))) = a(x,y,(u * (v6 * (w \ 1))) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27724,a(flip),b,27680,a),flip(a)].">
      <j1 rule="hyper" parents="60 27724 27680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27732">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ (v5 * v5)) * v6))) = a(x,y,(u * (v6 * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,27054,a(flip),b,27730,a),flip(a)].">
      <j1 rule="hyper" parents="370 27054 27730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27733">
    <literal><![CDATA[
      a(x,y,(z * (u * (w \ (v5 * v5)))) * v6) = a(x,y,(z * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27153,a,b,27732,a)].">
      <j1 rule="hyper" parents="60 27153 27732"/>
    </justification>
  </clause>

  <clause id="27734">
    <literal><![CDATA[
      a(x,y,(z * (((u \ w) * u) * v5)) * v6) = a(x,y,v6 * (z * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(27096,a,27684,a),flip(a)].">
      <j1 rule="hyper" parents="27096 27684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27735">
    <literal><![CDATA[
      a(x,y,((z * ((u \ w) * u)) * v5) * v6) = a(x,y,v6 * (v5 * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(27162,a,27734,a)].">
      <j1 rule="hyper" parents="27162 27734"/>
    </justification>
  </clause>

  <clause id="27737">
    <literal><![CDATA[
      a(x,y,z * (u * (((w \ v5) * w) * v6))) = a(x,y,(u * (v6 * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27019,a(flip),b,27685,a),flip(a)].">
      <j1 rule="hyper" parents="60 27019 27685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27739">
    <literal><![CDATA[
      a(x,y,(z * (u * ((w \ v5) * w))) * v6) = a(x,y,(z * (u * v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27153,a,b,27737,a)].">
      <j1 rule="hyper" parents="60 27153 27737"/>
    </justification>
  </clause>

  <clause id="27740">
    <literal><![CDATA[
      a(x,y,z * ((u * ((w \ v5) * w)) * v6)) = a(x,y,(v6 * (u * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(27033,a,27739,a)].">
      <j1 rule="hyper" parents="27033 27739"/>
    </justification>
  </clause>

  <clause id="27741">
    <literal><![CDATA[
      a(x \ (y * R(z,u,w)),v5,v6) = a(x \ (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(27323,a,27688,a),flip(a)].">
      <j1 rule="hyper" parents="27323 27688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27742">
    <literal><![CDATA[
      a(x \ (y * L(y,z,z)),u,w) = a(x \ a(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26717,a(flip),b,27741,a),flip(a)].">
      <j1 rule="hyper" parents="60 26717 27741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27743">
    <literal><![CDATA[
      a(x \ a(y,z,z),u,w) = a(x \ a(z,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26773,a(flip),b,27742,a),flip(a)].">
      <j1 rule="hyper" parents="60 26773 27742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27745">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(R(T(x,y),z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,z,u) \ R(R(x,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27691(a,1),23979(a,1))].">
      <j1 rule="para" parents="27691 23979"/>
    </justification>
  </clause>

  <clause id="27746">
    <literal><![CDATA[
      T(x,L(T(y,T(z,u)),w,v5) \ (z \ v6)) = T(x,(L(y,w,v5) * z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(25415,a,17651,a)].">
      <j1 rule="hyper" parents="25415 17651"/>
    </justification>
  </clause>

  <clause id="27747">
    <literal><![CDATA[
      T(x,L(T(y,T(z,u)),w,v5) \ (z \ v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (L(y,w,v5) \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(27746(a,2),24939(a,1))].">
      <j1 rule="para" parents="27746 24939"/>
    </justification>
  </clause>

  <clause id="27748">
    <literal><![CDATA[
      L(x,((y * z) \ ((z * u) * y)) \ w,v5) = L(x,L(u \ 1,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26198,a,25767,a),flip(a)].">
      <j1 rule="hyper" parents="26198 25767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27750">
    <literal><![CDATA[
      L(x,((y * z) \ ((z * u) * y)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(u,z,y) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27748(a,2),4025(a,1))].">
      <j1 rule="para" parents="27748 4025"/>
    </justification>
  </clause>

  <clause id="27751">
    <literal><![CDATA[
      L(x,y,z \ (R(1 / u,u,w * v5) \ (w * v5))) = L(x,y,z \ (u * (T(w,v6) * v5)))
    ]]></literal>
    <justification jstring="[para(27434(a,1),25998(a,1,3,2,1))].">
      <j1 rule="para" parents="27434 25998"/>
    </justification>
  </clause>

  <clause id="27752">
    <literal><![CDATA[
      L(x,y,z \ (u * (T(w,v5) * v6))) = L(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(467(a,1),27751(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="467 27751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27754">
    <literal><![CDATA[
      L(x,y,R(1 / z,z,u * (T(w,v5) * v6)) \ (u * (w * v6))) = L(x,y,z * (u * (T(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(467(a,1),27752(a,1,3)),flip(a)].">
      <j1 rule="para" parents="467 27752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27755">
    <literal><![CDATA[
      a(x,((T(y,z) * u) / w) * (v5 * K(z,y)),v6) = a(x,v5 * ((y * u) / w),v6)
    ]]></literal>
    <justification jstring="[para(23523(a,1),26674(a,1,2,1))].">
      <j1 rule="para" parents="23523 26674"/>
    </justification>
  </clause>

  <clause id="27756">
    <literal><![CDATA[
      a(x,((T(y,z) * u) / w) * v5,v6) = a(x,v5 * ((y * u) / w),v6)
    ]]></literal>
    <justification jstring="[hyper(26587,a,27755,a)].">
      <j1 rule="hyper" parents="26587 27755"/>
    </justification>
  </clause>

  <clause id="27758">
    <literal><![CDATA[
      a(x,(y \ (T(z,u) * w)) * v5,v6) = a(x,v5 * ((z * w) / y),v6)
    ]]></literal>
    <justification jstring="[hyper(26570,a,27756,a)].">
      <j1 rule="hyper" parents="26570 27756"/>
    </justification>
  </clause>

  <clause id="27760">
    <literal><![CDATA[
      a(x,(y \ (T(z,u) * w)) * v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,v5 * (y \ (z * w)),v6) = v7
    ]]></literal>
    <justification jstring="[para(27758(a,2),26585(a,1))].">
      <j1 rule="para" parents="27758 26585"/>
    </justification>
  </clause>

  <clause id="27761">
    <literal><![CDATA[
      a(x,y * (R(z / u,u,z \ (w \ v5)) \ (w \ v5)),v6) = a(x,y * (u * (z \ (v5 / w))),v6)
    ]]></literal>
    <justification jstring="[para(27445(a,1),26731(a,1,2,2,1))].">
      <j1 rule="para" parents="27445 26731"/>
    </justification>
  </clause>

  <clause id="27762">
    <literal><![CDATA[
      a((x * (y / z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * (x * (z \ ((v7 * v7) \ y))),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(26819(a,1),26789(a,1))].">
      <j1 rule="para" parents="26819 26789"/>
    </justification>
  </clause>

  <clause id="27763">
    <literal><![CDATA[
      a(x * (y * (z \ ((u * u) \ w))),v5,v6) = a((y * (z \ w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(27762,a,26653,a)].">
      <j1 rule="hyper" parents="27762 26653"/>
    </justification>
  </clause>

  <clause id="27765">
    <literal><![CDATA[
      a(x * (y * (z \ (u \ (w * w)))),v5,v6) = a((y * (z \ u)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27516,a(flip),b,27763,a)].">
      <j1 rule="hyper" parents="60 27516 27763"/>
    </justification>
  </clause>

  <clause id="27767">
    <literal><![CDATA[
      a((x \ (y * (z / u))) * w,v5,v6) = a((x \ (y * (u \ z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(467(a,1),26826(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="467 26826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27768">
    <literal><![CDATA[
      L(x,((y * z) \ ((T(y,z) * u) * z)) \ w,v5) = L(x,R(u,T(y,z),z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(27581,a,27301,a)].">
      <j1 rule="hyper" parents="27581 27301"/>
    </justification>
  </clause>

  <clause id="27769">
    <literal><![CDATA[
      L(x,((y * z) \ ((z * u) * y)) \ w,v5) = L(x,R(u,T(z,y),y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25296(a,1),27768(a,1,2,1))].">
      <j1 rule="para" parents="25296 27768"/>
    </justification>
  </clause>

  <clause id="27770">
    <literal><![CDATA[
      L(x,R(y,T(z,u),u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(27750,a,27769,a),flip(a)].">
      <j1 rule="hyper" parents="27750 27769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27771">
    <literal><![CDATA[
      L(x,R(y,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(27384(a,1),27770(a,1,2,1))].">
      <j1 rule="para" parents="27384 27770"/>
    </justification>
  </clause>

  <clause id="27772">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(w,R(y,z,u),R(y,z,u)),v5) = L(x,R(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(26253,a,27771,a),flip(a)].">
      <j1 rule="hyper" parents="26253 27771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27773">
    <literal><![CDATA[
      L(x,R(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3785,a(flip),b,27771,a),flip(a)].">
      <j1 rule="hyper" parents="370 3785 27771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27775">
    <literal><![CDATA[
      L(x,y * R(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(26246,a,27773,a)].">
      <j1 rule="hyper" parents="26246 27773"/>
    </justification>
  </clause>

  <clause id="27776">
    <literal><![CDATA[
      L(x,R(L(y,z,u),w,v5) \ L(y,z,u),v6) = L(x,L(y * L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,10452,a(flip),b,27773,a),flip(a)].">
      <j1 rule="hyper" parents="370 10452 27773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27777">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(3586,a,27775,a)].">
      <j1 rule="hyper" parents="3586 27775"/>
    </justification>
  </clause>

  <clause id="27778">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(w,R(y,z,u),L(y,z,u)),v5) = L(x,R(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(27279(a,1),27772(a,1,2,2))].">
      <j1 rule="para" parents="27279 27772"/>
    </justification>
  </clause>

  <clause id="27779">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5) \ L(y,w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(24(a,1),27776(a,1,2,1))].">
      <j1 rule="para" parents="24 27776"/>
    </justification>
  </clause>

  <clause id="27780">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(w,L(y,z,u),L(y,z,u)),v5) = L(x,R(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(27410(a,1),27778(a,1,2,2))].">
      <j1 rule="para" parents="27410 27778"/>
    </justification>
  </clause>

  <clause id="27781">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(26253,a,27780,a),flip(a)].">
      <j1 rule="hyper" parents="26253 27780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27782">
    <literal><![CDATA[
      L(x,L(y,z,u) * (w \ 1),v5) = L(x,w * R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(26217,a,27781,a),flip(a)].">
      <j1 rule="hyper" parents="26217 27781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27783">
    <literal><![CDATA[
      L(x,y * R(z,u,w),v5) = L(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(26217,a,27782,a),flip(a)].">
      <j1 rule="hyper" parents="26217 27782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27784">
    <literal><![CDATA[
      L(x,y * (z * (u * z)),w) = L(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26297,a,b,27783,a)].">
      <j1 rule="hyper" parents="60 26297 27783"/>
    </justification>
  </clause>

  <clause id="27785">
    <literal><![CDATA[
      L(x,(y * z) * R(L(u,z,y),w,v5),v6) = L(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(528(a,1),27783(a,2,2))].">
      <j1 rule="para" parents="528 27783"/>
    </justification>
  </clause>

  <clause id="27786">
    <literal><![CDATA[
      L(x,y * (z * R(u,w,v5)),v6) = L(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(529(a,1),27785(a,1,2))].">
      <j1 rule="para" parents="529 27785"/>
    </justification>
  </clause>

  <clause id="27787">
    <literal><![CDATA[
      a(x * (R(y,y,z \ (u \ 1)) * (z \ u)),w,v5) = a((y \ (z \ (u \ 1))) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26725,a(flip),b,27517,a),flip(a)].">
      <j1 rule="hyper" parents="370 26725 27517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27788">
    <literal><![CDATA[
      a(x * (R(y,y,z \ u) * (z \ u)),w,v5) = a((y \ (z \ (u \ 1))) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(27488(a,1),27787(a,1,1,2,1))].">
      <j1 rule="para" parents="27488 27787"/>
    </justification>
  </clause>

  <clause id="27789">
    <literal><![CDATA[
      a((x \ (y \ (z \ 1))) * u,w,v5) = a(u * ((1 / x) \ (y \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27788(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 27788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27790">
    <literal><![CDATA[
      a((x \ (y \ (z \ 1))) * u,w,v5) = a((x \ (y \ z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26725,a(flip),b,27789,a),flip(a)].">
      <j1 rule="hyper" parents="370 26725 27789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27791">
    <literal><![CDATA[
      a((x \ (y \ (z \ 1))) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ (y \ z)) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27789(a,2),26745(a,1))].">
      <j1 rule="para" parents="27789 26745"/>
    </justification>
  </clause>

  <clause id="27792">
    <literal><![CDATA[
      a((x \ (y \ (z \ 1))) * u,w,v5) = a(u * (x \ (y \ z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,27790,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 27790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27793">
    <literal><![CDATA[
      a((x \ (y \ (z \ 1))) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * (x \ (y \ z)),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27790(a,2),26519(a,1))].">
      <j1 rule="para" parents="27790 26519"/>
    </justification>
  </clause>

  <clause id="27794">
    <literal><![CDATA[
      a(x * ((y * z) \ y),u,w) = a(x * (y \ (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27664,a(flip),b,27792,a)].">
      <j1 rule="hyper" parents="60 27664 27792"/>
    </justification>
  </clause>

  <clause id="27795">
    <literal><![CDATA[
      a(R(x,x,(y * z) \ y) * (y \ (z \ y)),u,w) = a((1 / x) \ ((y * z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1961 27794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27796">
    <literal><![CDATA[
      a(x * ((y * z) \ y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (y \ (z \ y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27664(a,1),27793(a,1))].">
      <j1 rule="para" parents="27664 27793"/>
    </justification>
  </clause>

  <clause id="27797">
    <literal><![CDATA[
      a(R(x,x,(y * z) \ y) * (y \ (z \ y)),u,w) = a(x \ ((y * z) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2966,a(flip),b,27795,a),flip(a)].">
      <j1 rule="hyper" parents="370 2966 27795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27798">
    <literal><![CDATA[
      a(R(x,x,y \ (z \ y)) * (y \ (z \ y)),u,w) = a(x \ ((y * z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(27492(a,1),27797(a,1,1,1))].">
      <j1 rule="para" parents="27492 27797"/>
    </justification>
  </clause>

  <clause id="27799">
    <literal><![CDATA[
      a((1 / x) \ (y \ (z \ y)),u,w) = a(x \ ((y * z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27798(a,1,1))].">
      <j1 rule="para" parents="1961 27798"/>
    </justification>
  </clause>

  <clause id="27800">
    <literal><![CDATA[
      a(x \ ((y * z) \ y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ (z \ y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27799(a,1),26595(a,1))].">
      <j1 rule="para" parents="27799 26595"/>
    </justification>
  </clause>

  <clause id="27801">
    <literal><![CDATA[
      a(x,y * (z * (u \ (w / v5))),v6) = a(x,y * (z * (u \ (v5 \ w))),v6)
    ]]></literal>
    <justification jstring="[para(673(a,1),27761(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="673 27761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27803">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x \ u) = L(u \ (L(x,y,z) * (x \ u)),w,x)
    ]]></literal>
    <justification jstring="[para(25634(a,1),24933(a,1,1))].">
      <j1 rule="para" parents="25634 24933"/>
    </justification>
  </clause>

  <clause id="27804">
    <literal><![CDATA[
      L((L(x,y,z) * (x \ u)) \ u,w,x) = ((L(x,y,z) * (x \ u)) \ (u * L(x \ L(x,y,z),x,x \ u))) * ((L(x,y,z) * (x \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(27803(a,2),4046(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="27803 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27806">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ (u * a(w,v5,R(x,y,z))))) = a(w,v5,L(x,y,z)) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(27116(a,1),25339(a,2,1))].">
      <j1 rule="para" parents="27116 25339"/>
    </justification>
  </clause>

  <clause id="27807">
    <literal><![CDATA[
      (x * y) * R(K(y,z) * ((x * T(y,z)) \ 1),u,w) = (x * T(y,z)) \ R(x * T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(25672(a,2),25358(a,1,2))].">
      <j1 rule="para" parents="25672 25358"/>
    </justification>
  </clause>

  <clause id="27808">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((x * (y \ L(y,u,w))) * T(y,z)) = a(x,y \ L(y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26880,a(flip),b,25367,a),flip(a)].">
      <j1 rule="hyper" parents="370 26880 25367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27810">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((x * (y \ L(y,u,w))) * T(y,z)) = a(x,y * L(y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3860,a(flip),b,27808,a),flip(a)].">
      <j1 rule="hyper" parents="370 3860 27808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27812">
    <literal><![CDATA[
      (x \ 1) \ ((y / (x * x)) * R((x * x) * (y \ (x \ 1)),z,u)) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(512(a,1),25370(a,1,2,2,1))].">
      <j1 rule="para" parents="512 25370"/>
    </justification>
  </clause>

  <clause id="27813">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * L(a(x,y,z),w,v5)) = a(x,y,z) * (L(a(x,y,z) \ 1,w,v5) * u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),25468(a,1,1))].">
      <j1 rule="para" parents="23572 25468"/>
    </justification>
  </clause>

  <clause id="27814">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * K(w,v5) = x * R(x \ (y * K(w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(7500(a,1),25680(a,1,1,2,1))].">
      <j1 rule="para" parents="7500 25680"/>
    </justification>
  </clause>

  <clause id="27816">
    <literal><![CDATA[
      T(x,y) * (z * R(z \ (T(x,y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(25686(a,1),25706(a,2,2))].">
      <j1 rule="para" parents="25686 25706"/>
    </justification>
  </clause>

  <clause id="27818">
    <literal><![CDATA[
      ((x \ y) \ y) * (z * R(z \ (T(x,x \ y) \ u),w,v5)) = z * (x * R(x \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(928,a,27816,a)].">
      <j1 rule="hyper" parents="928 27816"/>
    </justification>
  </clause>

  <clause id="27821">
    <literal><![CDATA[
      x * ((y * y) \ (L(x,z,u) \ ((y * y) * ((y * y) \ x)))) = L(1 / (x / (y * y)),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(3815(a,1),25800(a,1,2,2))].">
      <j1 rule="para" parents="3815 25800"/>
    </justification>
  </clause>

  <clause id="27822">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(1 / x,z,u) \ (1 / x)) = (L(1 / x,z,u) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,27575,a(flip),b,25852,a),flip(a)].">
      <j1 rule="hyper" parents="370 27575 25852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27823">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * (L(x,z,u) \ x) = (L(1 / x,z,u) \ x) * y
    ]]></literal>
    <justification jstring="[para(3985(a,1),27822(a,1,2))].">
      <j1 rule="para" parents="3985 27822"/>
    </justification>
  </clause>

  <clause id="27824">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (L(x,z,u) \ x)) = (L(1 / x,z,u) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(14759,a,27823,a)].">
      <j1 rule="hyper" parents="14759 27823"/>
    </justification>
  </clause>

  <clause id="27825">
    <literal><![CDATA[
      L(x,y * R(((1 / z) * u) * K(w,v5),z,z),v6) = L(x,y * ((z \ 1) * ((u * z) * z)),v6)
    ]]></literal>
    <justification jstring="[para(25802(a,1),26294(a,1,2,2))].">
      <j1 rule="para" parents="25802 26294"/>
    </justification>
  </clause>

  <clause id="27826">
    <literal><![CDATA[
      L(x,y * R((1 / z) * (u * K(w,v5)),z,z),v6) = L(x,y * ((z \ 1) * ((u * z) * z)),v6)
    ]]></literal>
    <justification jstring="[para(11016(a,1),27825(a,1,2,2,1))].">
      <j1 rule="para" parents="11016 27825"/>
    </justification>
  </clause>

  <clause id="27827">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,16008,a(flip),b,26432,a)].">
      <j1 rule="hyper" parents="60 16008 26432"/>
    </justification>
  </clause>

  <clause id="27828">
    <literal><![CDATA[
      a(x,y,(z * (K(u,T(u \ w,v5)) * (w \ v6))) * v7) = a(x,y,v7 * ((((u \ w) * u) \ v6) * z))
    ]]></literal>
    <justification jstring="[para(8019(a,2),27197(a,1,3,1,2,1))].">
      <j1 rule="para" parents="8019 27197"/>
    </justification>
  </clause>

  <clause id="27829">
    <literal><![CDATA[
      R(x,y,z) * L(L(u,x,L(x,y,z)),x * L(x,y,z),x) = x * (x * (R(x \ 1,y,z) * u))
    ]]></literal>
    <justification jstring="[para(27777(a,1),27290(a,1,2))].">
      <j1 rule="para" parents="27777 27290"/>
    </justification>
  </clause>

  <clause id="27830">
    <literal><![CDATA[
      x * (y * ((L(z,u,w) \ z) * (L(z,u,w) \ z))) = ((L(z,u,w) * L(z \ 1,u,w)) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,14856,a(flip),b,27643,a),flip(a)].">
      <j1 rule="hyper" parents="370 14856 27643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27831">
    <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(27641(a,1),27644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27641 27644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27832">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ (u * a(w,v5,L(x,y,z))))) = a(w,v5,L(x,y,z)) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(27116(a,1),27806(a,1,2,2,2,2))].">
      <j1 rule="para" parents="27116 27806"/>
    </justification>
  </clause>

  <clause id="27833">
    <literal><![CDATA[
      (x * T(y,z)) \ R(x * T(y,z),u,w) = (x * y) * R((x * y) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(25112(a,1),27807(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25112 27807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27834">
    <literal><![CDATA[
      (x * T(y,z)) \ R(x * T(y,z),u,w) = (x * y) \ R(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,1987,a(flip),b,27833,a),flip(a)].">
      <j1 rule="hyper" parents="370 1987 27833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27836">
    <literal><![CDATA[
      (x * (y \ z)) \ R(x * T(z / y,y),u,w) = (x * (z / y)) \ R(x * (z / y),u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),27834(a,1,1,2))].">
      <j1 rule="para" parents="109 27834"/>
    </justification>
  </clause>

  <clause id="27837">
    <literal><![CDATA[
      (x * (y / z)) \ R(x * (y / z),u,w) = (x * (z \ y)) \ R(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),27836(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="109 27836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27838">
    <literal><![CDATA[
      (x \ 1) \ (y * ((x * x) \ R((x * x) * (y \ (x \ 1)),z,u))) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(935(a,1),27812(a,1,2))].">
      <j1 rule="para" parents="935 27812"/>
    </justification>
  </clause>

  <clause id="27839">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * x)),u,w)) = (y * R(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,25707,a(flip),b,27818,a),flip(a)].">
      <j1 rule="hyper" parents="60 25707 27818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27841">
    <literal><![CDATA[
      x * (y * R(y \ T(z,x),u,w)) = (y * R(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(17(a,2),27839(a,1,2,2,1,2))].">
      <j1 rule="para" parents="17 27839"/>
    </justification>
  </clause>

  <clause id="27843">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = (z * R(z \ x,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4909(a,1),27841(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4909 27841"/>
    </justification>
  </clause>

  <clause id="27844">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ (x * K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27814,a(flip),b,27843,a),flip(a)].">
      <j1 rule="hyper" parents="370 27814 27843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27845">
    <literal><![CDATA[
      K(x,y) * (z * R(z \ x,u,w)) = z * R(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5256(a,2),27844(a,2,2,1,2))].">
      <j1 rule="para" parents="5256 27844"/>
    </justification>
  </clause>

  <clause id="27846">
    <literal><![CDATA[
      ((x * R(x \ y,z,u)) * ((y * w) / y)) \ (w * (x * R(x \ T(y,w),z,u))) = K(w,T(x * R(x \ y,z,u),y))
    ]]></literal>
    <justification jstring="[para(27845(a,1),9889(a,1,2,2))].">
      <j1 rule="para" parents="27845 9889"/>
    </justification>
  </clause>

  <clause id="27847">
    <literal><![CDATA[
      L(1 / (x / (y * y)),z,u) \ 1 = x * ((y * y) \ (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(5(a,1),27821(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 27821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27848">
    <literal><![CDATA[
      x * ((y * y) \ (L(x,z,u) \ x)) = L((y * y) / x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(806(a,1),27847(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="806 27847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27849">
    <literal><![CDATA[
      a(x,y,z * ((((u \ w) * u) \ v5) * v6)) = a(x,y,(v6 * (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27019,a(flip),b,27828,a),flip(a)].">
      <j1 rule="hyper" parents="60 27019 27828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27851">
    <literal><![CDATA[
      R(x,y,z) * L(L(u,x,L(x,y,z)),x,x * L(x,y,z)) = x * (x * (R(x \ 1,y,z) * u))
    ]]></literal>
    <justification jstring="[para(4170(a,1),27829(a,1,2))].">
      <j1 rule="para" parents="4170 27829"/>
    </justification>
  </clause>

  <clause id="27852">
    <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(27641(a,1),27830(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27641 27830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27853">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (R(z,u,w) * v5) = R(z,u,w) * (v5 * a(x,y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(1958,a,27832,a),flip(a)].">
      <j1 rule="hyper" parents="1958 27832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27854">
    <literal><![CDATA[
      (R(x,y,z) * u) * a(w,v5,L(x,y,z)) = R(x,y,z) * (u * a(w,v5,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(23637,a,27853,a)].">
      <j1 rule="hyper" parents="23637 27853"/>
    </justification>
  </clause>

  <clause id="27855">
    <literal><![CDATA[
      R(x,y,z) * (T(u,x) * a(w,v5,L(x,y,z))) = (u * R(x,y,z)) * a(w,v5,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(23860(a,1),27854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23860 27854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27856">
    <literal><![CDATA[
      R(x,y,z) * (T(u,x) * a(w,v5,R(x,y,z))) = (u * R(x,y,z)) * a(w,v5,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(27116(a,2),27855(a,1,2,2))].">
      <j1 rule="para" parents="27116 27855"/>
    </justification>
  </clause>

  <clause id="27857">
    <literal><![CDATA[
      (x \ 1) \ (y * ((x * x) * R((x * x) \ (y \ (x \ 1)),z,u))) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(2144(a,1),27838(a,1,2,2))].">
      <j1 rule="para" parents="2144 27838"/>
    </justification>
  </clause>

  <clause id="27858">
    <literal><![CDATA[
      x * (x * (R(x \ 1,y,z) * u)) = R(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(4303(a,1),27851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4303 27851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27859">
    <literal><![CDATA[
      a(x,y,L(R(z \ 1,u,w) * v5,z,z)) = a(x,y,R(z,u,w) * L(v5,z,z))
    ]]></literal>
    <justification jstring="[para(27858(a,1),3080(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27858 3080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27861">
    <literal><![CDATA[
      (x \ 1) \ (y * R((x * x) * ((x * x) \ (y \ (x \ 1))),z,u)) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(1853(a,2),27857(a,1,2,2))].">
      <j1 rule="para" parents="1853 27857"/>
    </justification>
  </clause>

  <clause id="27862">
    <literal><![CDATA[
      (x \ 1) \ (y * R(y \ (x \ 1),z,u)) = (y / x) \ R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),27861(a,1,2,2,1))].">
      <j1 rule="para" parents="5 27861"/>
    </justification>
  </clause>

  <clause id="27863">
    <literal><![CDATA[
      (x \ 1) \ (y * R(y \ (x \ 1),z,u)) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,25792,a(flip),b,27862,a),flip(a)].">
      <j1 rule="hyper" parents="370 25792 27862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27865">
    <literal><![CDATA[
      (x \ (x / y)) \ (1 * R(1 \ (x \ (x / y)),z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,10543,a(flip),b,27863,a),flip(a)].">
      <j1 rule="hyper" parents="60 10543 27863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27866">
    <literal><![CDATA[
      (x \ (x / y)) \ (1 * R(x \ (x / y),z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(62(a,1),27865(a,1,2,2,1))].">
      <j1 rule="para" parents="62 27865"/>
    </justification>
  </clause>

  <clause id="27867">
    <literal><![CDATA[
      (x \ (x / y)) \ R(x \ (x / y),z,u) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(392,a,27866,a)].">
      <j1 rule="hyper" parents="392 27866"/>
    </justification>
  </clause>

  <clause id="27868">
    <literal><![CDATA[
      x \ ((x / y) * R((x / y) \ x,z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,2514,a(flip),b,27867,a)].">
      <j1 rule="hyper" parents="60 2514 27867"/>
    </justification>
  </clause>

  <clause id="27869">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ ((x / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),27868(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="77 27868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27870">
    <literal><![CDATA[
      a(x,y,z) = (z * y) \ (((z * y) / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(25473,a,27869,a)].">
      <j1 rule="hyper" parents="25473 27869"/>
    </justification>
  </clause>

  <clause id="27871">
    <literal><![CDATA[
      x * ((y * z) \ (((y * z) / u) * R(u,z,y))) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,27870,a(flip),b,23634,a)].">
      <j1 rule="hyper" parents="129 27870 23634"/>
    </justification>
  </clause>

  <clause id="27872">
    <literal><![CDATA[
      T(x * L(x \ L(x,y,z),u,w),L(x,y,z) \ x) = (L(x \ L(x,y,z),u,w) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(6462,a,24988,a)].">
      <j1 rule="hyper" parents="6462 24988"/>
    </justification>
  </clause>

  <clause id="27874">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ 1) \ x = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23876,a,27872,a),flip(a)].">
      <j1 rule="hyper" parents="23876 27872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27876">
    <literal><![CDATA[
      (a(x,y,z) \ (x \ R(x,y,z))) * ((x \ R(x,y,z)) \ 1) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(24918(a,2),25273(a,2,1))].">
      <j1 rule="para" parents="24918 25273"/>
    </justification>
  </clause>

  <clause id="27878">
    <literal><![CDATA[
      L(T(x * y,y \ 1),z,u) \ T(x * y,y \ 1) = L(x * (y \ 1),z,u) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(1120(a,1),25325(a,1,2))].">
      <j1 rule="para" parents="1120 25325"/>
    </justification>
  </clause>

  <clause id="27879">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = L(x * y,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(25146,a,27878,a),flip(a)].">
      <j1 rule="hyper" parents="25146 27878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27880">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * y,z,u) \ (x * y) = w
    ]]></literal>
    <justification jstring="[para(27878(a,1),25146(a,1))].">
      <j1 rule="para" parents="27878 25146"/>
    </justification>
  </clause>

  <clause id="27882">
    <literal><![CDATA[
      a((x * y) * ((y * y) \ (L(x * y,z,u) \ (x * y))),w,v5) = a(L(x * (y \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(27879(a,1),3002(a,1,1,2,2))].">
      <j1 rule="para" parents="27879 3002"/>
    </justification>
  </clause>

  <clause id="27883">
    <literal><![CDATA[
      a(L((x * x) / (y * x),z,u) \ 1,w,v5) = a(L(y * (x \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(27848(a,1),27882(a,1,1))].">
      <j1 rule="para" parents="27848 27882"/>
    </justification>
  </clause>

  <clause id="27884">
    <literal><![CDATA[
      a(L((x * x) / (y * x),z,u),w,v5) = a(L(y * (x \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(2973,a,27883,a)].">
      <j1 rule="hyper" parents="2973 27883"/>
    </justification>
  </clause>

  <clause id="27885">
    <literal><![CDATA[
      a(L((x * y) \ (y * y),z,u),w,v5) = a(L(x * (y \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26552,a,27884,a)].">
      <j1 rule="hyper" parents="26552 27884"/>
    </justification>
  </clause>

  <clause id="27886">
    <literal><![CDATA[
      a(L(x * (y \ 1),z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26824,a(flip),b,27885,a),flip(a)].">
      <j1 rule="hyper" parents="60 26824 27885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27888">
    <literal><![CDATA[
      a(L(x * (1 / y),z,u),w,v5) = a(L(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(77(a,1),27886(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 27886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27889">
    <literal><![CDATA[
      1 * L(x,a(y,z,u),L(u,w,v5)) = L(x,L(u,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(26341(a,1),25851(a,1,2))].">
      <j1 rule="para" parents="26341 25851"/>
    </justification>
  </clause>

  <clause id="27890">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,27889,a),flip(a)].">
      <j1 rule="hyper" parents="131 27889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27892">
    <literal><![CDATA[
      a((x \ (((1 / y) * z) * (u * u))) * w,v5,v6) = a((x \ ((y \ (u * u)) * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26806,a,26700,a)].">
      <j1 rule="hyper" parents="26806 26700"/>
    </justification>
  </clause>

  <clause id="27893">
    <literal><![CDATA[
      a(((x \ ((1 / y) * z)) * (u * u)) * w,v5,v6) = a((x \ ((y \ (u * u)) * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(513(a,1),27892(a,1,1,1))].">
      <j1 rule="para" parents="513 27892"/>
    </justification>
  </clause>

  <clause id="27894">
    <literal><![CDATA[
      a((x \ ((1 / y) * z)) * ((u * u) * w),v5,v6) = a((x \ ((y \ (u * u)) * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),27893(a,1,1))].">
      <j1 rule="para" parents="29 27893"/>
    </justification>
  </clause>

  <clause id="27895">
    <literal><![CDATA[
      a((x \ ((y \ (z * z)) * u)) * w,v5,v6) = a((x \ ((1 / y) * u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26610,a,27894,a),flip(a)].">
      <j1 rule="hyper" parents="26610 27894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27897">
    <literal><![CDATA[
      a((x \ ((y \ (z * z)) * u)) * w,v5,v6) = a(w * (x \ (y * u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26798,a(flip),b,27895,a),flip(a)].">
      <j1 rule="hyper" parents="370 26798 27895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27898">
    <literal><![CDATA[
      a((x \ (y * (z \ (u * u)))) * w,v5,v6) = a(w * (x \ (z * y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26805,a,27897,a)].">
      <j1 rule="hyper" parents="26805 27897"/>
    </justification>
  </clause>

  <clause id="27899">
    <literal><![CDATA[
      a(((x * (y \ (z * z))) * u) * w,v5,v6) = a(w * (L(u,u,x * y) \ (y * x)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,26764,a(flip),b,27898,a)].">
      <j1 rule="hyper" parents="60 26764 27898"/>
    </justification>
  </clause>

  <clause id="27901">
    <literal><![CDATA[
      a(((x * (y \ (z * z))) * u) * w,v5,v6) = a(w * T((y * x) * (1 / u),u),v5,v6)
    ]]></literal>
    <justification jstring="[para(24927(a,1),27899(a,2,1,2))].">
      <j1 rule="para" parents="24927 27899"/>
    </justification>
  </clause>

  <clause id="27902">
    <literal><![CDATA[
      a(((x * (y \ (z * z))) * u) * w,v5,v6) = a(w * ((y * x) * (1 / u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26379,a(flip),b,27901,a),flip(a)].">
      <j1 rule="hyper" parents="370 26379 27901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27904">
    <literal><![CDATA[
      a(((x * (y \ (z * z))) * u) * w,v5,v6) = a(w * ((y * x) * (u \ 1)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26615,a(flip),b,27902,a),flip(a)].">
      <j1 rule="hyper" parents="370 26615 27902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27905">
    <literal><![CDATA[
      a(((x * (y \ (z * z))) * u) * w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(((y * x) * u) * w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(27904(a,2),26669(a,1))].">
      <j1 rule="para" parents="27904 26669"/>
    </justification>
  </clause>

  <clause id="27906">
    <literal><![CDATA[
      a(x * (L(L(y \ 1,z,u),y,y) * w),v5,v6) = a(x * (w * (y * (L(y,z,u) \ y))),v5,v6)
    ]]></literal>
    <justification jstring="[para(2162(a,1),26831(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2162 26831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27907">
    <literal><![CDATA[
      a(x * (L((1 / y) * 1,z,u) * w),v5,v6) = a(x * (w * (y * (L(y,z,u) \ y))),v5,v6)
    ]]></literal>
    <justification jstring="[para(593(a,1),27906(a,1,1,2,1))].">
      <j1 rule="para" parents="593 27906"/>
    </justification>
  </clause>

  <clause id="27908">
    <literal><![CDATA[
      a(x * (y * (z * (L(z,u,w) \ z))),v5,v6) = a(x * (L(1 / z,u,w) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(3(a,1),27907(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3 27907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27909">
    <literal><![CDATA[
      a(x * (y * (z * (L(z,u,w) \ z))),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26830,a(flip),b,27908,a),flip(a)].">
      <j1 rule="hyper" parents="370 26830 27908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27910">
    <literal><![CDATA[
      a(x,y,z * (R(u \ 1,u,w * (v5 \ v6)) * (w * (v5 \ v6)))) = a(x,y,z * (u \ (w * (v6 / v5))))
    ]]></literal>
    <justification jstring="[para(27444(a,1),27229(a,1,3,2,1))].">
      <j1 rule="para" parents="27444 27229"/>
    </justification>
  </clause>

  <clause id="27911">
    <literal><![CDATA[
      a(x,y,z * (R(u,w / v5,v6) * (v6 * (v5 \ w)))) = a(x,y,z * ((u * (w / v5)) * v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,26942,a(flip),b,27230,a),flip(a)].">
      <j1 rule="hyper" parents="370 26942 27230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27913">
    <literal><![CDATA[
      a(x,y,z * (R(u,w \ v5,v6) * (v6 * (w \ v5)))) = a(x,y,z * ((u * (v5 / w)) * v6))
    ]]></literal>
    <justification jstring="[para(27386(a,1),27911(a,1,3,2,1))].">
      <j1 rule="para" parents="27386 27911"/>
    </justification>
  </clause>

  <clause id="27914">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ v5)) * T(v6,w \ v5))) = a(x,y,z * ((u * (v5 / w)) * v6))
    ]]></literal>
    <justification jstring="[para(12402(a,1),27913(a,1,3,2))].">
      <j1 rule="para" parents="12402 27913"/>
    </justification>
  </clause>

  <clause id="27915">
    <literal><![CDATA[
      a(x,y,z * ((u * (w / v5)) * v6)) = a(x,y,z * ((u * (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[hyper(26977,a,27914,a),flip(a)].">
      <j1 rule="hyper" parents="26977 27914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27917">
    <literal><![CDATA[
      a(x,y,z * (((u * (w / u)) * u) * v5)) = a(x,y,z * ((w * (w / (u \ w))) * v5))
    ]]></literal>
    <justification jstring="[para(5823(a,2),27915(a,2,3,2,1)),flip(a)].">
      <j1 rule="para" parents="5823 27915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27918">
    <literal><![CDATA[
      a(x,y,z * (((u * (w / u)) * u) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[para(74(a,1),27917(a,2,3,2,1,2))].">
      <j1 rule="para" parents="74 27917"/>
    </justification>
  </clause>

  <clause id="27920">
    <literal><![CDATA[
      a(x,y,z * (u * L(w / v5,v5,v5))) = a(x,y,z * ((w * v5) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27210,a(flip),b,27918,a)].">
      <j1 rule="hyper" parents="60 27210 27918"/>
    </justification>
  </clause>

  <clause id="27921">
    <literal><![CDATA[
      a(R(x,x,y * (z \ (u \ 1))) * (y * (z \ u)),w,v5) = a(x \ (y * (z \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,2966,a(flip),b,27518,a),flip(a)].">
      <j1 rule="hyper" parents="370 2966 27518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27922">
    <literal><![CDATA[
      a(R(x,x,y * (z \ u)) * (y * (z \ u)),w,v5) = a(x \ (y * (z \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(27484(a,1),27921(a,1,1,1))].">
      <j1 rule="para" parents="27484 27921"/>
    </justification>
  </clause>

  <clause id="27923">
    <literal><![CDATA[
      a((1 / x) \ (y * (z \ u)),w,v5) = a(x \ (y * (z \ (u \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(1961(a,1),27922(a,1,1))].">
      <j1 rule="para" parents="1961 27922"/>
    </justification>
  </clause>

  <clause id="27924">
    <literal><![CDATA[
      a(x \ (y * (z \ (u \ 1))),w,v5) = a(x \ (y * (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26595,a,27923,a),flip(a)].">
      <j1 rule="hyper" parents="26595 27923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27926">
    <literal><![CDATA[
      L(x,y,R(1 / z,z,(u * w) * v5) \ (v5 * (u * w))) = L(x,y,z * (v5 * (T(u,v6) * w)))
    ]]></literal>
    <justification jstring="[para(27483(a,1),27754(a,1,3,1))].">
      <j1 rule="para" parents="27483 27754"/>
    </justification>
  </clause>

  <clause id="27927">
    <literal><![CDATA[
      L(x,y,z * (u * (T(w,v5) * v6))) = L(x,y,z * (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(27439(a,1),27926(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27439 27926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27929">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 / v6)))) = a(x,y,z * (u \ (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(2784(a,1),27910(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2784 27910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27930">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w / v5) * v6))) = a(x,y,z * (u \ (v6 * (v5 \ w))))
    ]]></literal>
    <justification jstring="[hyper(27152,a,27929,a)].">
      <j1 rule="hyper" parents="27152 27929"/>
    </justification>
  </clause>

  <clause id="27931">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 \ 1)))) = a(x,y,z * (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27217,a(flip),b,27930,a),flip(a)].">
      <j1 rule="hyper" parents="60 27217 27930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27932">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ 1))) * v5) = a(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(26965,a,27931,a)].">
      <j1 rule="hyper" parents="26965 27931"/>
    </justification>
  </clause>

  <clause id="27933">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ R(z,u,w))) * y) = R(z,x,y) \ R(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(27745,a,25632,a),flip(a)].">
      <j1 rule="hyper" parents="27745 25632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27934">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u * w),u,w) = R(x,u,w) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(25309,a,27933,a)].">
      <j1 rule="hyper" parents="25309 27933"/>
    </justification>
  </clause>

  <clause id="27936">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(23944(a,1),27934(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23944 27934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27937">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (R(x,u,x \ R(x,y,z)) \ R(R(x,u,x \ R(x,y,z)),y,z)) = a(x \ R(x,y,z),u,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,27936,a,b,11446,a)].">
      <j1 rule="hyper" parents="125 27936 11446"/>
    </justification>
  </clause>

  <clause id="27940">
    <literal><![CDATA[
      (x \ y) * (x * R(x \ ((x \ y) \ z),u,w)) = y * R((x * (x \ y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(12083(a,1),25681(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12083 25681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27941">
    <literal><![CDATA[
      (x \ y) * (x * R(x \ ((x \ y) \ z),u,w)) = y * R(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),27940(a,2,2,1,1))].">
      <j1 rule="para" parents="5 27940"/>
    </justification>
  </clause>

  <clause id="27942">
    <literal><![CDATA[
      ((x \ y) * x) \ R((x \ y) * x,z,u) = y * R(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(2463,a,27941,a)].">
      <j1 rule="hyper" parents="2463 27941"/>
    </justification>
  </clause>

  <clause id="27944">
    <literal><![CDATA[
      ((x \ y) * x) \ R((x \ y) * x,z,u) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1987,a(flip),b,27942,a),flip(a)].">
      <j1 rule="hyper" parents="370 1987 27942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27945">
    <literal><![CDATA[
      (((x * x) \ y) * x) \ R((x \ ((x \ 1) * y)) * x,z,u) = ((x \ 1) * y) \ R((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(942(a,1),27944(a,1,1,1))].">
      <j1 rule="para" parents="942 27944"/>
    </justification>
  </clause>

  <clause id="27946">
    <literal><![CDATA[
      L((x * x) * (y / x),z,u) \ (((x * x) * y) / x) = L((1 / x) \ y,z,u) \ (x \ ((x * x) * y))
    ]]></literal>
    <justification jstring="[para(853(a,1),25799(a,1,1,1))].">
      <j1 rule="para" parents="853 25799"/>
    </justification>
  </clause>

  <clause id="27947">
    <literal><![CDATA[
      L(x,y,L(z * u,(z * u) / z,w) * (w * (1 / ((z * u) / z)))) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(3401(a,1),26315(a,1,3,1))].">
      <j1 rule="para" parents="3401 26315"/>
    </justification>
  </clause>

  <clause id="27948">
    <literal><![CDATA[
      L(x,y,L(z * u,u,w) * (w * (1 / ((z * u) / z)))) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(26017(a,1),27947(a,1,3,1))].">
      <j1 rule="para" parents="26017 27947"/>
    </justification>
  </clause>

  <clause id="27949">
    <literal><![CDATA[
      L(x,y,L(z * u,u,w) * (w * ((z * u) / z))) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(25989,a,27948,a)].">
      <j1 rule="hyper" parents="25989 27948"/>
    </justification>
  </clause>

  <clause id="27951">
    <literal><![CDATA[
      L(x,y,L(z * u,u,w) * (w * (z \ (z * u)))) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25970,a(flip),b,27949,a)].">
      <j1 rule="hyper" parents="60 25970 27949"/>
    </justification>
  </clause>

  <clause id="27952">
    <literal><![CDATA[
      L(x,y,L(z * u,u,w) * (w * u)) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),27951(a,1,3,2,2))].">
      <j1 rule="para" parents="4 27951"/>
    </justification>
  </clause>

  <clause id="27953">
    <literal><![CDATA[
      L(x,y,z * (u * (w * u))) = L(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(25274,a,27952,a)].">
      <j1 rule="hyper" parents="25274 27952"/>
    </justification>
  </clause>

  <clause id="27955">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3459,a(flip),b,27953,a)].">
      <j1 rule="hyper" parents="60 3459 27953"/>
    </justification>
  </clause>

  <clause id="27956">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3680,a(flip),b,27955,a),flip(a)].">
      <j1 rule="hyper" parents="370 3680 27955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27957">
    <literal><![CDATA[
      L(x,y,a(z \ u,z \ u,z)) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),27956(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="5 27956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27958">
    <literal><![CDATA[
      L(x,y,a(z,z * u,L(u,z,z))) = L(x,y,a(z * u,z * u,z))
    ]]></literal>
    <justification jstring="[para(3080(a,1),27956(a,1,3))].">
      <j1 rule="para" parents="3080 27956"/>
    </justification>
  </clause>

  <clause id="27959">
    <literal><![CDATA[
      L(x,y,a(z,u,u * z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(26888(a,1),27956(a,1,3))].">
      <j1 rule="para" parents="26888 27956"/>
    </justification>
  </clause>

  <clause id="27960">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,u)) = L(x,y,a(z,z,z \ u))
    ]]></literal>
    <justification jstring="[para(26889(a,1),27956(a,1,3))].">
      <j1 rule="para" parents="26889 27956"/>
    </justification>
  </clause>

  <clause id="27961">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * z) * (z \ u))) = L(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,2),27960(a,2,3)),flip(a)].">
      <j1 rule="para" parents="83 27960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27962">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,u)) = L(x,y,a(z,z,z * u))
    ]]></literal>
    <justification jstring="[para(19763(a,1),27960(a,2,3))].">
      <j1 rule="para" parents="19763 27960"/>
    </justification>
  </clause>

  <clause id="27963">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z \ 1) \ u)) = L(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[para(936(a,1),27961(a,1,3,2))].">
      <j1 rule="para" parents="936 27961"/>
    </justification>
  </clause>

  <clause id="27964">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(27963(a,1),4252(a,1))].">
      <j1 rule="para" parents="27963 4252"/>
    </justification>
  </clause>

  <clause id="27965">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,L((1 / y) \ 1,z,u)) = (y \ L(y,z,u)) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3798(a,1),26316(a,2,1))].">
      <j1 rule="para" parents="3798 26316"/>
    </justification>
  </clause>

  <clause id="27966">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,L(y,z,u)) = (y \ L(y,z,u)) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(77(a,1),27965(a,1,3,1))].">
      <j1 rule="para" parents="77 27965"/>
    </justification>
  </clause>

  <clause id="27967">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(u / (1 / x),x,L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(27966(a,1),2774(a,1))].">
      <j1 rule="para" parents="27966 2774"/>
    </justification>
  </clause>

  <clause id="27968">
    <literal><![CDATA[
      a(L(x * y,(x * y) / x,z) * (z * (1 / ((x * y) / x))),u,w) = a(z * L(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(3388(a,1),26670(a,1,1,1))].">
      <j1 rule="para" parents="3388 26670"/>
    </justification>
  </clause>

  <clause id="27969">
    <literal><![CDATA[
      a(L(x * y,y,z) * (z * (1 / ((x * y) / x))),u,w) = a(z * L(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(26017(a,1),27968(a,1,1,1))].">
      <j1 rule="para" parents="26017 27968"/>
    </justification>
  </clause>

  <clause id="27970">
    <literal><![CDATA[
      a(L(x * y,y,z) * (z * (((x * y) / x) \ 1)),u,w) = a(z * L(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26686,a,27969,a)].">
      <j1 rule="hyper" parents="26686 27969"/>
    </justification>
  </clause>

  <clause id="27972">
    <literal><![CDATA[
      a((x * ((y * z) / y)) * L(y * z,z,x),u,w) = a(x * L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26669,a,27970,a)].">
      <j1 rule="hyper" parents="26669 27970"/>
    </justification>
  </clause>

  <clause id="27973">
    <literal><![CDATA[
      a((x * (y \ (y * z))) * L(y * z,z,x),u,w) = a(x * L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26653,a(flip),b,27972,a)].">
      <j1 rule="hyper" parents="60 26653 27972"/>
    </justification>
  </clause>

  <clause id="27974">
    <literal><![CDATA[
      a((x * y) * L(z * y,y,x),u,w) = a(x * L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),27973(a,1,1,1,2))].">
      <j1 rule="para" parents="4 27973"/>
    </justification>
  </clause>

  <clause id="27976">
    <literal><![CDATA[
      a(x * (y * (z * y)),u,w) = a(x * L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(92(a,1),27974(a,1,1))].">
      <j1 rule="para" parents="92 27974"/>
    </justification>
  </clause>

  <clause id="27977">
    <literal><![CDATA[
      a(x * ((y * z) * z),u,w) = a(x * L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26548,a,27976,a)].">
      <j1 rule="hyper" parents="26548 27976"/>
    </justification>
  </clause>

  <clause id="27978">
    <literal><![CDATA[
      a((x \ y) * L(y,x,x),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(26856,a,27977,a),flip(a)].">
      <j1 rule="hyper" parents="26856 27977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27979">
    <literal><![CDATA[
      a((L(x \ 1,x,L(y,x,x)) \ L(y,x,x)) * z,u,w) = a(L(y * (1 / x),x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(3401(a,1),26762(a,1,1,1,1))].">
      <j1 rule="para" parents="3401 26762"/>
    </justification>
  </clause>

  <clause id="27980">
    <literal><![CDATA[
      L((L(x,y,z) * L(x \ 1,y,z)) \ u,w,v5) = (L(x,y,z) * L(x \ 1,y,z)) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(27641(a,1),27642(a,1,1))].">
      <j1 rule="para" parents="27641 27642"/>
    </justification>
  </clause>

  <clause id="27981">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((y \ L(y,u,w)) * (x * T(y,z))) = a(x,T(y,z),y * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(23710(a,1),27690(a,1,1,2))].">
      <j1 rule="para" parents="23710 27690"/>
    </justification>
  </clause>

  <clause id="27982">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((y \ L(y,u,w)) * (x * T(y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27981(a,2),26557(a,1))].">
      <j1 rule="para" parents="27981 26557"/>
    </justification>
  </clause>

  <clause id="27983">
    <literal><![CDATA[
      (((x * x) \ y) * x) \ R(((x * x) \ y) * x,z,u) = ((x \ 1) * y) \ R((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(942(a,1),27945(a,1,2,1,1))].">
      <j1 rule="para" parents="942 27945"/>
    </justification>
  </clause>

  <clause id="27984">
    <literal><![CDATA[
      (x * y) \ ((y * y) * R(((y * y) \ x) * y,z,u)) = ((y \ 1) * x) \ R((y \ 1) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1443,a,27983,a)].">
      <j1 rule="hyper" parents="1443 27983"/>
    </justification>
  </clause>

  <clause id="27985">
    <literal><![CDATA[
      (x * y) \ R((y * y) * (((y * y) \ x) * y),z,u) = ((y \ 1) * x) \ R((y \ 1) * x,z,u)
    ]]></literal>
    <justification jstring="[para(1853(a,2),27984(a,1,2))].">
      <j1 rule="para" parents="1853 27984"/>
    </justification>
  </clause>

  <clause id="27986">
    <literal><![CDATA[
      ((x \ 1) * y) \ R((x \ 1) * y,z,u) = (y * x) \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),27985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 27985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27988">
    <literal><![CDATA[
      L((x * x) * (y / x),z,u) \ ((x * x) * (y / x)) = L((1 / x) \ y,z,u) \ (x \ ((x * x) * y))
    ]]></literal>
    <justification jstring="[para(853(a,1),27946(a,1,2))].">
      <j1 rule="para" parents="853 27946"/>
    </justification>
  </clause>

  <clause id="27989">
    <literal><![CDATA[
      L(x / y,z,u) \ ((y * y) \ ((y * y) * (x / y))) = L((1 / y) \ x,z,u) \ (y \ ((y * y) * x))
    ]]></literal>
    <justification jstring="[hyper(3809,a,27988,a)].">
      <j1 rule="hyper" parents="3809 27988"/>
    </justification>
  </clause>

  <clause id="27990">
    <literal><![CDATA[
      L((1 / x) \ y,z,u) \ (x \ ((x * x) * y)) = L(y / x,z,u) \ (y / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),27989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 27989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27991">
    <literal><![CDATA[
      L((1 / x) \ y,z,u) \ (x \ ((x * x) * y)) = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,25797,a(flip),b,27990,a),flip(a)].">
      <j1 rule="hyper" parents="370 25797 27990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27993">
    <literal><![CDATA[
      L((1 / x) \ y,z,u) \ ((1 / x) \ y) = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(554(a,1),27991(a,1,2))].">
      <j1 rule="para" parents="554 27991"/>
    </justification>
  </clause>

  <clause id="27994">
    <literal><![CDATA[
      L(x \ L(y,x,x),z,u) \ (x \ L(y,x,x)) = L(x * y,z,u) \ ((1 / x) \ L(y,x,x))
    ]]></literal>
    <justification jstring="[para(581(a,1),27993(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="581 27993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27995">
    <literal><![CDATA[
      L((1 / x) \ y,x,x) \ ((1 / x) \ y) = ((1 / x) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(586(a,1),27993(a,2,1))].">
      <j1 rule="para" parents="586 27993"/>
    </justification>
  </clause>

  <clause id="27996">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((1 / x) \ y) = ((1 / x) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(3710(a,1),27995(a,1,1))].">
      <j1 rule="para" parents="3710 27995"/>
    </justification>
  </clause>

  <clause id="27997">
    <literal><![CDATA[
      L((x \ 1) * y,z,u) \ (x \ L(y,x,x)) = L(x * y,z,u) \ ((1 / x) \ L(y,x,x))
    ]]></literal>
    <justification jstring="[para(2072(a,1),27994(a,1,1,1))].">
      <j1 rule="para" parents="2072 27994"/>
    </justification>
  </clause>

  <clause id="27998">
    <literal><![CDATA[
      L(x * y,z,u) \ ((1 / x) \ L(y,x,x)) = L((x \ 1) * y,z,u) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2072(a,1),27997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2072 27997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27999">
    <literal><![CDATA[
      L((x \ 1) * y,z,u) \ ((x \ 1) * y) = L(x * y,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(581(a,1),27998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="581 27998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28000">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z) \ (z * u)) = a(x,y,(z \ 1) * (u * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(27999(a,1),4034(a,1,3))].">
      <j1 rule="para" parents="27999 4034"/>
    </justification>
  </clause>

  <clause id="28001">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * ((z \ 1) * u))) = a(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(14754(a,1),28000(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14754 28000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28002">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * u) = a(x,y,a(u,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(27168,a,28001,a)].">
      <j1 rule="hyper" parents="27168 28001"/>
    </justification>
  </clause>

  <clause id="28003">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,L(z,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27204,a(flip),b,28002,a),flip(a)].">
      <j1 rule="hyper" parents="60 27204 28002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28004">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,28003,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 28003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28005">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,4033,a(flip),b,28004,a),flip(a)].">
      <j1 rule="hyper" parents="370 4033 28004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28006">
    <literal><![CDATA[
      (x \ (((x \ L(x,y,z)) \ x) * u)) * (x \ L(x,y,z)) = L(u,x * (L(x,y,z) \ x),x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25381(a,1),25637(a,2,2))].">
      <j1 rule="para" parents="25381 25637"/>
    </justification>
  </clause>

  <clause id="28007">
    <literal><![CDATA[
      T((x * y) \ (x * L(y,z,u)),x \ (L(y,z,u) \ (y * x))) = (((x * y) \ (x * L(y,z,u))) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(24939,a,25808,a)].">
      <j1 rule="hyper" parents="24939 25808"/>
    </justification>
  </clause>

  <clause id="28008">
    <literal><![CDATA[
      L(x,y * ((T(z,u \ K(w,v5)) \ 1) \ (u \ K(w,v5))),v6) = L(x,y * (L(z,z,u \ K(w,v5)) * u),v6)
    ]]></literal>
    <justification jstring="[hyper(26270,a,26295,a)].">
      <j1 rule="hyper" parents="26270 26295"/>
    </justification>
  </clause>

  <clause id="28009">
    <literal><![CDATA[
      (x \ (((x \ L(x,y,z)) \ x) * u)) * (x \ L(x,y,z)) = L(u,x * (L(x,y,z) \ x),x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3862,a(flip),b,28006,a),flip(a)].">
      <j1 rule="hyper" parents="370 3862 28006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28010">
    <literal><![CDATA[
      T((x * y) \ (x * L(y,z,u)),x \ (y * (L(y,z,u) \ x))) = (((x * y) \ (x * L(y,z,u))) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2160(a,1),28007(a,1,2,2))].">
      <j1 rule="para" parents="2160 28007"/>
    </justification>
  </clause>

  <clause id="28011">
    <literal><![CDATA[
      (((x * y) \ (x * L(y,z,u))) \ 1) \ 1 = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(25641,a,28010,a),flip(a)].">
      <j1 rule="hyper" parents="25641 28010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28013">
    <literal><![CDATA[
      ((x \ (L(y,z,u) * (y \ x))) \ 1) \ 1 = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25332(a,1),28011(a,1,1,1))].">
      <j1 rule="para" parents="25332 28011"/>
    </justification>
  </clause>

  <clause id="28014">
    <literal><![CDATA[
      a(x \ (y \ (z \ (u * (T(T(w,u),v5) * v6)))),v7,v8) = a(x \ (y \ (z \ (u * (w * v6)))),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,26727,a(flip),b,26862,a),flip(a)].">
      <j1 rule="hyper" parents="60 26727 26862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28016">
    <literal><![CDATA[
      a(x \ (y \ (z \ (u * (T(w,v5) * v6)))),v7,v8) = a(x \ (y \ (z \ (u * (w * v6)))),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,27673,a(flip),b,28014,a)].">
      <j1 rule="hyper" parents="60 27673 28014"/>
    </justification>
  </clause>

  <clause id="28020">
    <literal><![CDATA[
      a(x,y,((((z * z) / (1 / u)) * w) * v5) * v6) = a(x,y,v6 * (v5 * (((u \ (z * z)) \ 1) * w)))
    ]]></literal>
    <justification jstring="[para(1652(a,1),27683(a,1,3,1,1,1))].">
      <j1 rule="para" parents="1652 27683"/>
    </justification>
  </clause>

  <clause id="28021">
    <literal><![CDATA[
      a(x,y,((((1 / z) \ (u * u)) * w) * v5) * v6) = a(x,y,v6 * (v5 * (((z \ (u * u)) \ 1) * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27021,a(flip),b,28020,a)].">
      <j1 rule="hyper" parents="60 27021 28020"/>
    </justification>
  </clause>

  <clause id="28022">
    <literal><![CDATA[
      a(x,y,z * (u * (((w \ (v5 * v5)) \ 1) * v6))) = a(x,y,(((w * (v5 * v5)) * v6) * u) * z)
    ]]></literal>
    <justification jstring="[para(516(a,1),28021(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="516 28021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28023">
    <literal><![CDATA[
      a(x,y,z * (u * (((w \ (v5 * v5)) \ 1) * v6))) = a(x,y,((w * ((v5 * v5) * v6)) * u) * z)
    ]]></literal>
    <justification jstring="[para(29(a,1),28022(a,2,3,1,1))].">
      <j1 rule="para" parents="29 28022"/>
    </justification>
  </clause>

  <clause id="28024">
    <literal><![CDATA[
      a(x,y,((z * ((u * u) * w)) * v5) * v6) = a(x,y,(v5 * (w * (z \ (u * u)))) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27186,a(flip),b,28023,a),flip(a)].">
      <j1 rule="hyper" parents="60 27186 28023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28025">
    <literal><![CDATA[
      a(x,y,((z * ((u * u) * w)) * v5) * v6) = a(x,y,(v5 * (w * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,27733,a(flip),b,28024,a),flip(a)].">
      <j1 rule="hyper" parents="370 27733 28024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28027">
    <literal><![CDATA[
      L(K(x,y) * z,u,u) \ L(K(x,y) * (z * w),u,u) = L(L(w,z,u \ K(x,y)),(u \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(25360(a,1),25446(a,1,2))].">
      <j1 rule="para" parents="25360 25446"/>
    </justification>
  </clause>

  <clause id="28028">
    <literal><![CDATA[
      L(x,y,y) \ (K(z,u) * L(K(u,z) * (x * w),y,y)) = L(L(w,x,y \ K(u,z)),(y \ K(u,z)) * x,y)
    ]]></literal>
    <justification jstring="[hyper(25750,a,28027,a)].">
      <j1 rule="hyper" parents="25750 28027"/>
    </justification>
  </clause>

  <clause id="28029">
    <literal><![CDATA[
      L(L(x,y,z \ K(u,w)),(z \ K(u,w)) * y,z) = L(y,z,z) \ L(y * x,z,z)
    ]]></literal>
    <justification jstring="[para(25741(a,1),28028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25741 28028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28031">
    <literal><![CDATA[
      L(L(x,y,z),(z \ K(u,w)) * y,z) = L(y,z,z) \ L(y * x,z,z)
    ]]></literal>
    <justification jstring="[para(25921(a,1),28029(a,1,1))].">
      <j1 rule="para" parents="25921 28029"/>
    </justification>
  </clause>

  <clause id="28032">
    <literal><![CDATA[
      L(x,y,y) \ L(x * z,y,y) = L(L(z,x,y),y * x,y)
    ]]></literal>
    <justification jstring="[hyper(26272,a,28031,a),flip(a)].">
      <j1 rule="hyper" parents="26272 28031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28034">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z \ (z \ u),w) * (w * (z \ ((1 / z) \ u)))) = L(x,y,w * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3723(a,1),25589(a,1,3,1))].">
      <j1 rule="para" parents="3723 25589"/>
    </justification>
  </clause>

  <clause id="28035">
    <literal><![CDATA[
      (L(x \ (1 * L(x,y,z)),u,w) / (x \ 1)) * L(x \ 1,u,w) = (x \ 1) \ L(L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(62(a,1),25894(a,1,1,1,1,2,2,1))].">
      <j1 rule="para" parents="62 25894"/>
    </justification>
  </clause>

  <clause id="28036">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,w * v5,v6) * (v6 * (w * (v5 \ 1))),v7) = a(x,v6 * ((w * (v5 \ K(y,z))) * u),v7)
    ]]></literal>
    <justification jstring="[para(3778(a,1),26675(a,1,2,1))].">
      <j1 rule="para" parents="3778 26675"/>
    </justification>
  </clause>

  <clause id="28037">
    <literal><![CDATA[
      a(x,K(y,z) * (L(u,w * v5,v6) * (v6 * (w * (v5 \ 1)))),v7) = a(x,v6 * ((w * (v5 \ K(y,z))) * u),v7)
    ]]></literal>
    <justification jstring="[para(25748(a,1),28036(a,1,2))].">
      <j1 rule="para" parents="25748 28036"/>
    </justification>
  </clause>

  <clause id="28038">
    <literal><![CDATA[
      a(x,L(y,z * u,w) * (w * (z * (u \ 1))),v5) = a(x,w * ((z * (u \ K(v6,v7))) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(26554,a,28037,a)].">
      <j1 rule="hyper" parents="26554 28037"/>
    </justification>
  </clause>

  <clause id="28040">
    <literal><![CDATA[
      a(x,L(y,z * u,w) * ((z * u) * w),v5) = a(x,w * ((z * (u \ K(v6,v7))) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26846,a(flip),b,28038,a)].">
      <j1 rule="hyper" parents="60 26846 28038"/>
    </justification>
  </clause>

  <clause id="28041">
    <literal><![CDATA[
      a(x,y * ((z * (u \ K(w,v5))) * v6),v7) = a(x,y * ((z * u) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(26766,a,28040,a),flip(a)].">
      <j1 rule="hyper" parents="26766 28040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28042">
    <literal><![CDATA[
      a(x,y * (z * (u * (w \ K(v5,v6)))),v7) = a(x,y * ((u * w) * z),v7)
    ]]></literal>
    <justification jstring="[hyper(26586,a,28041,a)].">
      <j1 rule="hyper" parents="26586 28041"/>
    </justification>
  </clause>

  <clause id="28043">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,(w * w) \ v5,(w * w) \ v5)) = a(x,y,z \ (v5 * ((u * (w \ 1)) * v5)))
    ]]></literal>
    <justification jstring="[hyper(370,a,3150,a(flip),b,27125,a),flip(a)].">
      <j1 rule="hyper" parents="370 3150 27125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28045">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,(w * w) \ v5,(w * w) \ v5)) = a(x,y,z \ L(u * (w \ 1),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,27123,a(flip),b,28043,a),flip(a)].">
      <j1 rule="hyper" parents="370 27123 28043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28046">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,(w * w) \ v5,v5)) = a(x,y,z \ L(u * (w \ 1),v5,v5))
    ]]></literal>
    <justification jstring="[para(3362(a,1),28045(a,1,3,2))].">
      <j1 rule="para" parents="3362 28045"/>
    </justification>
  </clause>

  <clause id="28048">
    <literal><![CDATA[
      a(x,y,z \ L(u * (w \ 1),v5,v5)) = a(x,y,z \ L(u * w,v5,v5))
    ]]></literal>
    <justification jstring="[para(3387(a,1),28046(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3387 28046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28050">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(1 / x,x,y),(y * x) * x) = ((y * x) * (x * (x \ 1))) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[para(24938(a,1),25215(a,1,2))].">
      <j1 rule="para" parents="24938 25215"/>
    </justification>
  </clause>

  <clause id="28051">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(1 / x,x,y),L(y,x,x)) = ((y * x) * (x * (x \ 1))) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(25980,a,28050,a)].">
      <j1 rule="hyper" parents="25980 28050"/>
    </justification>
  </clause>

  <clause id="28052">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(x,x,y),L(y,x,x)) = ((y * x) * (x * (x \ 1))) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(25283,a,28051,a)].">
      <j1 rule="hyper" parents="25283 28051"/>
    </justification>
  </clause>

  <clause id="28053">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(x,x,y),L(y,x,x)) = (y * x) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[para(67(a,1),28052(a,2,1))].">
      <j1 rule="para" parents="67 28052"/>
    </justification>
  </clause>

  <clause id="28055">
    <literal><![CDATA[
      T(L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10450(a,1),25563(a,1,1,2))].">
      <j1 rule="para" parents="10450 25563"/>
    </justification>
  </clause>

  <clause id="28056">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * L(((z * x) * y) \ (x * y),u,w)) = R(z,x,y) \ L(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(15(a,2),25656(a,2,2,1))].">
      <j1 rule="para" parents="15 25656"/>
    </justification>
  </clause>

  <clause id="28057">
    <literal><![CDATA[
      (x * y) \ (((z * x) * L((z * x) \ x,u,w)) * y) = R(z,x,y) \ L(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(2552(a,1),28056(a,1,2))].">
      <j1 rule="para" parents="2552 28056"/>
    </justification>
  </clause>

  <clause id="28058">
    <literal><![CDATA[
      (x * y) \ ((z * (x * L(x \ (z \ x),u,w))) * y) = R(z,x,y) \ L(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(1598(a,1),28057(a,1,2,1))].">
      <j1 rule="para" parents="1598 28057"/>
    </justification>
  </clause>

  <clause id="28059">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ L(z,u,w))) * y) = R(z,x,y) \ L(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(25319(a,1),28058(a,1,2,1))].">
      <j1 rule="para" parents="25319 28058"/>
    </justification>
  </clause>

  <clause id="28060">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / (u * w)) * K(w,w \ 1))) = K(x,z \ a(y,K(w \ 1,w),u * w))
    ]]></literal>
    <justification jstring="[para(6291(a,1),26328(a,1,2,2))].">
      <j1 rule="para" parents="6291 26328"/>
    </justification>
  </clause>

  <clause id="28061">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / T(u,w)) / ((1 / w) \ 1))) = K(x,z \ a(y,1 / (1 / w),T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(22336,a,26329,a)].">
      <j1 rule="hyper" parents="22336 26329"/>
    </justification>
  </clause>

  <clause id="28062">
    <literal><![CDATA[
      ((x * R(x \ y,z,u)) * ((y * w) / y)) \ ((x * R(x \ y,z,u)) * w) = K(w,T(x * R(x \ y,z,u),y))
    ]]></literal>
    <justification jstring="[para(27841(a,1),27846(a,1,2))].">
      <j1 rule="para" parents="27841 27846"/>
    </justification>
  </clause>

  <clause id="28063">
    <literal><![CDATA[
      K(x,T(y * R(y \ z,u,w),z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6380,a,28062,a),flip(a)].">
      <j1 rule="hyper" parents="6380 28062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28064">
    <literal><![CDATA[
      K(x,y * R(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(25705(a,1),28063(a,1,2))].">
      <j1 rule="para" parents="25705 28063"/>
    </justification>
  </clause>

  <clause id="28065">
    <literal><![CDATA[
      K(x,y * R(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),28064(a,1,2,2,1))].">
      <j1 rule="para" parents="4 28064"/>
    </justification>
  </clause>

  <clause id="28066">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,w)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),28064(a,1,2,2,1))].">
      <j1 rule="para" parents="17 28064"/>
    </justification>
  </clause>

  <clause id="28072">
    <literal><![CDATA[
      K(x,y * ((z * u) / w)) = K(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[para(708(a,1),28065(a,1,2,2))].">
      <j1 rule="para" parents="708 28065"/>
    </justification>
  </clause>

  <clause id="28074">
    <literal><![CDATA[
      K(x,R(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(274(a,1),28066(a,1,2))].">
      <j1 rule="para" parents="274 28066"/>
    </justification>
  </clause>

  <clause id="28079">
    <literal><![CDATA[
      K(x,y * (R(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),28074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 28074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28080">
    <literal><![CDATA[
      T(x,y * (R(y,z,u) \ w)) = x * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,28079,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 28079 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28081">
    <literal><![CDATA[
      T(x,y * (R(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5256,a,b,28080,a),flip(a)].">
      <j1 rule="hyper" parents="370 5256 28080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28082">
    <literal><![CDATA[
      T(x,(y * z) * u) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(210(a,1),28081(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="210 28081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28084">
    <literal><![CDATA[
      T(1 / (x * a(y,z,u)),a(y,z,u) * (x * w)) = T((x * a(y,z,u)) \ 1,(x * a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25294,a(flip),b,28082,a),flip(a)].">
      <j1 rule="hyper" parents="60 25294 28082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28085">
    <literal><![CDATA[
      T(x * K(y * z,x),y * (z * x)) = L(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,5498,a(flip),b,28082,a),flip(a)].">
      <j1 rule="hyper" parents="60 5498 28082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28090">
    <literal><![CDATA[
      K(x,R(y,z,T(u,z)) * (u / (w / z))) = K(x,y / ((w / T(u,z)) / z))
    ]]></literal>
    <justification jstring="[hyper(27540,a,28072,a),flip(a)].">
      <j1 rule="hyper" parents="27540 28072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28091">
    <literal><![CDATA[
      K(x,y / ((z / T(u,w)) / w)) = K(x,y * (u / (z / w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,28074,a(flip),b,28090,a),flip(a)].">
      <j1 rule="hyper" parents="60 28074 28090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28093">
    <literal><![CDATA[
      K(x,(y / ((z * (y * (u * (1 / (1 / w))))) / (u * w))) * K(w \ 1,w)) = K(x,z \ a(y,K(w \ 1,w),u * w))
    ]]></literal>
    <justification jstring="[para(25084(a,1),28060(a,1,2))].">
      <j1 rule="para" parents="25084 28060"/>
    </justification>
  </clause>

  <clause id="28094">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / T(u,w)) / w)) = K(x,z \ a(y,1 / (1 / w),T(u,w)))
    ]]></literal>
    <justification jstring="[para(77(a,1),28061(a,1,2,2,2))].">
      <j1 rule="para" parents="77 28061"/>
    </justification>
  </clause>

  <clause id="28095">
    <literal><![CDATA[
      K(x,y / (((z * (y * (u * (1 / (1 / w))))) / T(u,w)) / w)) = K(x,z \ a(y,w,T(u,w)))
    ]]></literal>
    <justification jstring="[para(26456(a,1),28094(a,2,2,2))].">
      <j1 rule="para" parents="26456 28094"/>
    </justification>
  </clause>

  <clause id="28096">
    <literal><![CDATA[
      K(x,y * (z / ((u * (y * (z * (1 / (1 / w))))) / w))) = K(x,u \ a(y,w,T(z,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,28091,a(flip),b,28095,a)].">
      <j1 rule="hyper" parents="60 28091 28095"/>
    </justification>
  </clause>

  <clause id="28098">
    <literal><![CDATA[
      K(x,y \ a(z,K(u \ 1,u),w * u)) = K(x,z / ((y * (z * (w * (1 / (1 / u))))) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(6051,a,28093,a),flip(a)].">
      <j1 rule="hyper" parents="6051 28093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28100">
    <literal><![CDATA[
      K(x,y / ((z * (y * (u * (1 / (1 / w))))) / (u * w))) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(23493(a,1),28098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23493 28098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28101">
    <literal><![CDATA[
      K(x,y * ((z * u) / (w * (y * (z * (1 / (1 / u))))))) = K(x,w \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,22641,a(flip),b,28100,a)].">
      <j1 rule="hyper" parents="60 22641 28100"/>
    </justification>
  </clause>

  <clause id="28103">
    <literal><![CDATA[
      K(x,y * (z / ((u * (y * (z * (1 / (1 / w))))) / w))) = K(x,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,28072,a(flip),b,28101,a)].">
      <j1 rule="hyper" parents="60 28072 28101"/>
    </justification>
  </clause>

  <clause id="28104">
    <literal><![CDATA[
      K(x,y \ a(z,u,T(w,u))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,28096,a(flip),b,28103,a)].">
      <j1 rule="hyper" parents="60 28096 28103"/>
    </justification>
  </clause>

  <clause id="28106">
    <literal><![CDATA[
      K(x,y \ a(z,u,w)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(262(a,1),28104(a,1,2,2,3))].">
      <j1 rule="para" parents="262 28104"/>
    </justification>
  </clause>

  <clause id="28107">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) = K(x,(1 / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(15228,a,28106,a)].">
      <j1 rule="hyper" parents="15228 28106"/>
    </justification>
  </clause>

  <clause id="28110">
    <literal><![CDATA[
      a(x,y,z) * K(u,u \ 1) = u * (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28106,a(flip),b,5765,a)].">
      <j1 rule="hyper" parents="129 28106 5765"/>
    </justification>
  </clause>

  <clause id="28112">
    <literal><![CDATA[
      K(x,x \ 1) * a(y,z,u) = x * (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(28106(a,1),7467(a,1,1))].">
      <j1 rule="para" parents="28106 7467"/>
    </justification>
  </clause>

  <clause id="28113">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(77(a,1),28107(a,2,2))].">
      <j1 rule="para" parents="77 28107"/>
    </justification>
  </clause>

  <clause id="28114">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(21736,a,28113,a)].">
      <j1 rule="hyper" parents="21736 28113"/>
    </justification>
  </clause>

  <clause id="28119">
    <literal><![CDATA[
      x * K(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,28113,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 28113 5230"/>
    </justification>
  </clause>

  <clause id="28121">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,28113,a(flip),b,5230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 28113 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28128">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) * v5) = K(x,w * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,25458,a(flip),b,28114,a)].">
      <j1 rule="hyper" parents="60 25458 28114"/>
    </justification>
  </clause>

  <clause id="28130">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5265,a,28119,a)].">
      <j1 rule="hyper" parents="5265 28119"/>
    </justification>
  </clause>

  <clause id="28131">
    <literal><![CDATA[
      (x * a(y,z,u)) * T(w,x) = w * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,28119,a(flip),b,5285,a)].">
      <j1 rule="hyper" parents="129 28119 5285"/>
    </justification>
  </clause>

  <clause id="28134">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(19340,a,28130,a)].">
      <j1 rule="hyper" parents="19340 28130"/>
    </justification>
  </clause>

  <clause id="28139">
    <literal><![CDATA[
      T(x,a(y,z,u) * a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,23540,a(flip),b,28130,a),flip(a)].">
      <j1 rule="hyper" parents="370 23540 28130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28142">
    <literal><![CDATA[
      T(x \ 1,x * a(y,z,u)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(370,a,955,a(flip),b,28130,a),flip(a)].">
      <j1 rule="hyper" parents="370 955 28130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28143">
    <literal><![CDATA[
      x * T(y,x * a(z,u,w)) = y * x
    ]]></literal>
    <justification jstring="[hyper(129,a,28130,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="129 28130 17"/>
    </justification>
  </clause>

  <clause id="28145">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,21731,a,b,28130,a)].">
      <j1 rule="hyper" parents="60 21731 28130"/>
    </justification>
  </clause>

  <clause id="28146">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28082,a(flip),b,28130,a)].">
      <j1 rule="hyper" parents="60 28082 28130"/>
    </justification>
  </clause>

  <clause id="28150">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = w * (T(x,w) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(28130(a,1),24121(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28130 24121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28151">
    <literal><![CDATA[
      T((a(x,y,z) * u) \ 1,u) = 1 / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(956,a,28134,a),flip(a)].">
      <j1 rule="hyper" parents="956 28134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28161">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a(flip),b,28134,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 28134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28162">
    <literal><![CDATA[
      T((x * a(y,z,u)) \ 1,(x * a(y,z,u)) \ w) = T(1 / (x * a(y,z,u)),x * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28084,a(flip),b,28134,a)].">
      <j1 rule="hyper" parents="60 28084 28134"/>
    </justification>
  </clause>

  <clause id="28164">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) \ x = K(w,x)
    ]]></literal>
    <justification jstring="[para(28134(a,2),5699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28134 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28168">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ w) = T(x,u \ ((y * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(25828,a,28145,a),flip(a)].">
      <j1 rule="hyper" parents="25828 28145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28169">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ v5)) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(23653,a,28145,a)].">
      <j1 rule="hyper" parents="23653 28145"/>
    </justification>
  </clause>

  <clause id="28174">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28145,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 28145 17"/>
    </justification>
  </clause>

  <clause id="28175">
    <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(28145(a,1),328(a,1,2))].">
      <j1 rule="para" parents="28145 328"/>
    </justification>
  </clause>

  <clause id="28176">
    <literal><![CDATA[
      T(x,a(y,z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ 1) = v5
    ]]></literal>
    <justification jstring="[para(28145(a,1),6530(a,1))].">
      <j1 rule="para" parents="28145 6530"/>
    </justification>
  </clause>

  <clause id="28177">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (a(z,u,w) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(28145(a,1),25561(a,1,2))].">
      <j1 rule="para" parents="28145 25561"/>
    </justification>
  </clause>

  <clause id="28178">
    <literal><![CDATA[
      x / (a(y,z,u) * a(w,v5,v6)) = (a(y,z,u) * a(w,v5,v6)) \ x
    ]]></literal>
    <justification jstring="[hyper(4977,a,28139,a),flip(a)].">
      <j1 rule="hyper" parents="4977 28139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28179">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(28121(a,2),5265(a,1))].">
      <j1 rule="para" parents="28121 5265"/>
    </justification>
  </clause>

  <clause id="28181">
    <literal><![CDATA[
      a(x,y,z) / (1 / u) = (u \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(28142(a,1),7583(a,1,2))].">
      <j1 rule="para" parents="28142 7583"/>
    </justification>
  </clause>

  <clause id="28182">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * w = w * ((a(y,z,u) * w) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,109,a(flip),b,28161,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 109 28161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28184">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(5710,a,28164,a)].">
      <j1 rule="hyper" parents="5710 28164"/>
    </justification>
  </clause>

  <clause id="28185">
    <literal><![CDATA[
      K(x * a(y,z,u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(19357,a,28184,a)].">
      <j1 rule="hyper" parents="19357 28184"/>
    </justification>
  </clause>

  <clause id="28186">
    <literal><![CDATA[
      x * K(a(y,z,u) * x,w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,28184,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 28184 5230"/>
    </justification>
  </clause>

  <clause id="28190">
    <literal><![CDATA[
      K(x \ a(y,z,u),w) = K(x \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(15221,a,28185,a)].">
      <j1 rule="hyper" parents="15221 28185"/>
    </justification>
  </clause>

  <clause id="28196">
    <literal><![CDATA[
      a(x,y,z) \ T(a(x,y,z) * u,w) = T(u,w)
    ]]></literal>
    <justification jstring="[hyper(15470,a,28186,a)].">
      <j1 rule="hyper" parents="15470 28186"/>
    </justification>
  </clause>

  <clause id="28197">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,28186,a(flip),b,15215,a),flip(a)].">
      <j1 rule="hyper" parents="129 28186 15215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28198">
    <literal><![CDATA[
      K(x \ a(y,z,u),x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1716,a(flip),b,28190,a),flip(a)].">
      <j1 rule="hyper" parents="370 1716 28190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28199">
    <literal><![CDATA[
      K(a(x,y,z) / u,u) = K(u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(5686,a,28198,a)].">
      <j1 rule="hyper" parents="5686 28198"/>
    </justification>
  </clause>

  <clause id="28200">
    <literal><![CDATA[
      T(x,(y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(82(a,1),28179(a,1,2))].">
      <j1 rule="para" parents="82 28179"/>
    </justification>
  </clause>

  <clause id="28201">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(21731(a,2),28179(a,1))].">
      <j1 rule="para" parents="21731 28179"/>
    </justification>
  </clause>

  <clause id="28202">
    <literal><![CDATA[
      T(x,y * ((y \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * u) = w
    ]]></literal>
    <justification jstring="[para(19671(a,1),28201(a,1,2))].">
      <j1 rule="para" parents="19671 28201"/>
    </justification>
  </clause>

  <clause id="28208">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(74(a,1),28181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 28181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28209">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ a(z,u,w)) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(28181(a,1),27475(a,1,3,1))].">
      <j1 rule="para" parents="28181 27475"/>
    </justification>
  </clause>

  <clause id="28210">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = T(u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23635,a,28196,a),flip(a)].">
      <j1 rule="hyper" parents="23635 28196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28212">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) = a(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),28196(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 28196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28214">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = T(x,w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(28196(a,1),4845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28196 4845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28215">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = a(y,z,u) * T(x,w)
    ]]></literal>
    <justification jstring="[para(23620(a,1),28197(a,1,1))].">
      <j1 rule="para" parents="23620 28197"/>
    </justification>
  </clause>

  <clause id="28216">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) / u) = (u \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,28208,a)].">
      <j1 rule="hyper" parents="221 28208"/>
    </justification>
  </clause>

  <clause id="28217">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,u) / x) = (x * x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28208,a(flip),b,973,a)].">
      <j1 rule="hyper" parents="129 28208 973"/>
    </justification>
  </clause>

  <clause id="28218">
    <literal><![CDATA[
      (((x \ 1) \ 1) * ((x \ 1) \ 1)) * (a(y,z,u) / x) = (((x \ 1) \ 1) \ 1) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28208,a(flip),b,940,a)].">
      <j1 rule="hyper" parents="129 28208 940"/>
    </justification>
  </clause>

  <clause id="28219">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1307(a,1),28208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 28208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28220">
    <literal><![CDATA[
      L(x,x,x) \ a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(1317(a,2),28208(a,1,1))].">
      <j1 rule="para" parents="1317 28208"/>
    </justification>
  </clause>

  <clause id="28223">
    <literal><![CDATA[
      T(a(x,y,z) * K(u,u \ w),w) = K(u,u \ w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(7469(a,1),28210(a,2,1))].">
      <j1 rule="para" parents="7469 28210"/>
    </justification>
  </clause>

  <clause id="28225">
    <literal><![CDATA[
      T(a(x,y,z) \ (u / w),w \ u) = a(x,y,z) \ (u / w)
    ]]></literal>
    <justification jstring="[para(288(a,1),28212(a,2,2))].">
      <j1 rule="para" parents="288 28212"/>
    </justification>
  </clause>

  <clause id="28227">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,w)) = (y * a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(129,a,28214,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="129 28214 17"/>
    </justification>
  </clause>

  <clause id="28228">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (y * a(z,u,w)) * x = v5
    ]]></literal>
    <justification jstring="[para(28214(a,1),328(a,1,2))].">
      <j1 rule="para" parents="28214 328"/>
    </justification>
  </clause>

  <clause id="28230">
    <literal><![CDATA[
      a(x,y,z) * T(u,(u * a(x,y,z)) \ ((u * a(x,y,z)) \ 1)) = ((u * a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(4669,a,28215,a),flip(a)].">
      <j1 rule="hyper" parents="4669 28215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28233">
    <literal><![CDATA[
      ((x \ a(y,z,u)) \ 1) \ 1 = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(74(a,1),28216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="74 28216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28235">
    <literal><![CDATA[
      (1 / (x \ 1)) * (((1 / x) \ a(y,z,u)) \ w) = (x \ 1) * ((a(y,z,u) / ((x \ 1) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(28219(a,1),7701(a,1,2,1))].">
      <j1 rule="para" parents="28219 7701"/>
    </justification>
  </clause>

  <clause id="28236">
    <literal><![CDATA[
      1 / (a(x,y,z) / u) = (u \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,28233,a)].">
      <j1 rule="hyper" parents="221 28233"/>
    </justification>
  </clause>

  <clause id="28237">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) \ u) = a(x,y,z) * (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28233,a(flip),b,3508,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 28233 3508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28238">
    <literal><![CDATA[
      1 / (x \ a(y,z,u)) = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[para(28233(a,1),1307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28233 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28239">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ 1 = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(28233(a,1),1312(a,1,1,1))].">
      <j1 rule="para" parents="28233 1312"/>
    </justification>
  </clause>

  <clause id="28240">
    <literal><![CDATA[
      ((x \ a(y,z,u)) \ 1) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) / x = w
    ]]></literal>
    <justification jstring="[para(28236(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="28236 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28243">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ a(y,z,u) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),28239(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 28239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28247">
    <literal><![CDATA[
      T(x,(y / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(407(a,1),28202(a,1,2,2))].">
      <j1 rule="para" parents="407 28202"/>
    </justification>
  </clause>

  <clause id="28250">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23804,a,28131,a)].">
      <j1 rule="hyper" parents="23804 28131"/>
    </justification>
  </clause>

  <clause id="28252">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ ((y * z) * w)) = T(x,u \ w)
    ]]></literal>
    <justification jstring="[para(4(a,1),28168(a,2,2,2))].">
      <j1 rule="para" parents="4 28168"/>
    </justification>
  </clause>

  <clause id="28253">
    <literal><![CDATA[
      (x * y) * L(a(z,u,w),x,y) = (x * a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(26235,a,28227,a)].">
      <j1 rule="hyper" parents="26235 28227"/>
    </justification>
  </clause>

  <clause id="28254">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 = v6 * (a(u,w,v5) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(24067,a,28250,a)].">
      <j1 rule="hyper" parents="24067 28250"/>
    </justification>
  </clause>

  <clause id="28255">
    <literal><![CDATA[
      T(x / (y * a(z,u,w)),y) = (a(z,u,w) * y) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,7,a(flip),b,28250,a),flip(a)].">
      <j1 rule="hyper" parents="125 7 28250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28256">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / x = a(z,u,w) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,28250,a(flip),b,6287,a)].">
      <j1 rule="hyper" parents="128 28250 6287"/>
    </justification>
  </clause>

  <clause id="28257">
    <literal><![CDATA[
      (x / y) * (y * a(z,u,w)) = (a(z,u,w) * y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(109(a,1),28250(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 28250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28258">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(24941,a,28252,a)].">
      <j1 rule="hyper" parents="24941 28252"/>
    </justification>
  </clause>

  <clause id="28260">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ (z \ w)) = T(x,z \ (L(y,v5,v6) \ w))
    ]]></literal>
    <justification jstring="[hyper(27747,a,28258,a),flip(a)].">
      <j1 rule="hyper" parents="27747 28258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28267">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,(w \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,6446,a,b,28258,a),flip(a)].">
      <j1 rule="hyper" parents="370 6446 28258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28269">
    <literal><![CDATA[
      T(x,y \ L(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25772,a(flip),b,28258,a),flip(a)].">
      <j1 rule="hyper" parents="60 25772 28258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28270">
    <literal><![CDATA[
      T(x,y \ (z \ ((z * u) * w))) = T(x,(u \ y) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25723,a(flip),b,28258,a)].">
      <j1 rule="hyper" parents="60 25723 28258"/>
    </justification>
  </clause>

  <clause id="28271">
    <literal><![CDATA[
      T(x,y \ T(z * y,z)) = T(x,y * (L(y,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14453,a(flip),b,28258,a),flip(a)].">
      <j1 rule="hyper" parents="60 14453 28258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28279">
    <literal><![CDATA[
      T(x,y * (z \ L(u,w,v5))) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,25227,a(flip),b,28269,a)].">
      <j1 rule="hyper" parents="60 25227 28269"/>
    </justification>
  </clause>

  <clause id="28280">
    <literal><![CDATA[
      T(x,y \ ((z * u) \ w)) = T(x,y \ (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(344(a,1),28269(a,1,2,2))].">
      <j1 rule="para" parents="344 28269"/>
    </justification>
  </clause>

  <clause id="28281">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (z \ L(u,w,v5))) = T(x,(z \ L(u,w,v5)) * y)
    ]]></literal>
    <justification jstring="[para(28269(a,1),12600(a,1,2,1))].">
      <j1 rule="para" parents="28269 12600"/>
    </justification>
  </clause>

  <clause id="28283">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(28267(a,2),6462(a,1))].">
      <j1 rule="para" parents="28267 6462"/>
    </justification>
  </clause>

  <clause id="28286">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(23276(a,2),28283(a,1))].">
      <j1 rule="para" parents="23276 28283"/>
    </justification>
  </clause>

  <clause id="28288">
    <literal><![CDATA[
      T(x,y * (z \ L(u,w,v5))) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,25227,a(flip),b,28279,a),flip(a)].">
      <j1 rule="hyper" parents="370 25227 28279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28291">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ w)) / x = w / (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,28255,a)].">
      <j1 rule="hyper" parents="316 28255"/>
    </justification>
  </clause>

  <clause id="28292">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) = R(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,1141,a,b,28255,a),flip(a)].">
      <j1 rule="hyper" parents="60 1141 28255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28293">
    <literal><![CDATA[
      (x / (y * a(z,u,w))) * y = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,28255,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 28255 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28295">
    <literal><![CDATA[
      T(x,y \ (z \ ((z * u) * w))) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,22308,a(flip),b,28270,a),flip(a)].">
      <j1 rule="hyper" parents="370 22308 28270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28299">
    <literal><![CDATA[
      T(x,y \ ((z / u) \ w)) = T(x,(y \ u) * (z \ w))
    ]]></literal>
    <justification jstring="[para(351(a,1),28295(a,1,2,2,2))].">
      <j1 rule="para" parents="351 28295"/>
    </justification>
  </clause>

  <clause id="28300">
    <literal><![CDATA[
      L(x \ a(y,z,u),x * a(y,z,u),x \ a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) / x = w
    ]]></literal>
    <justification jstring="[para(14601(a,2),28240(a,1))].">
      <j1 rule="para" parents="14601 28240"/>
    </justification>
  </clause>

  <clause id="28301">
    <literal><![CDATA[
      (x * a(y,z,u)) * u = (x * u) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(14782(a,1),28253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14782 28253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28302">
    <literal><![CDATA[
      (1 / x) * a(y,z,x) = a(y,z,x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,75,a(flip),b,28301,a),flip(a)].">
      <j1 rule="hyper" parents="128 75 28301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28305">
    <literal><![CDATA[
      (x * (a(y,z,u) * u)) \ ((x * u) * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),u) = w
    ]]></literal>
    <justification jstring="[para(28301(a,1),1029(a,1,2))].">
      <j1 rule="para" parents="28301 1029"/>
    </justification>
  </clause>

  <clause id="28307">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,z * (L(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[para(5536(a,1),28271(a,1,2))].">
      <j1 rule="para" parents="5536 28271"/>
    </justification>
  </clause>

  <clause id="28308">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(24083,a,28307,a),flip(a)].">
      <j1 rule="hyper" parents="24083 28307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28315">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[para(28308(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="28308 5701"/>
    </justification>
  </clause>

  <clause id="28317">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,5701,a,b,28315,a),flip(a)].">
      <j1 rule="hyper" parents="370 5701 28315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28318">
    <literal><![CDATA[
      x * K(y * (L(y,z,u) \ x),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,28317,a,b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 28317 5230"/>
    </justification>
  </clause>

  <clause id="28321">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(x * (L(x,y,z) \ u),w)) = T(u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25041,a(flip),b,28318,a)].">
      <j1 rule="hyper" parents="60 25041 28318"/>
    </justification>
  </clause>

  <clause id="28324">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / x = a(y,z,u) * ((x * w) / x)
    ]]></literal>
    <justification jstring="[para(23620(a,2),28256(a,1,1,2))].">
      <j1 rule="para" parents="23620 28256"/>
    </justification>
  </clause>

  <clause id="28325">
    <literal><![CDATA[
      L((a(x,y,z) \ u) / w,w,a(x,y,z)) = u / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,1244,a,b,28291,a)].">
      <j1 rule="hyper" parents="60 1244 28291"/>
    </justification>
  </clause>

  <clause id="28327">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(28321(a,1),69(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28321 69"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28328">
    <literal><![CDATA[
      (a(x,y,z) * ((u * w) / u)) * K(v5,u) = (u * (a(x,y,z) * w)) / T(u,v5)
    ]]></literal>
    <justification jstring="[para(28324(a,1),5855(a,1,1))].">
      <j1 rule="para" parents="28324 5855"/>
    </justification>
  </clause>

  <clause id="28330">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      (w / u) * (a(x,y,z) \ u) = v5
    ]]></literal>
    <justification jstring="[para(109(a,1),28175(a,1,2))].">
      <j1 rule="para" parents="109 28175"/>
    </justification>
  </clause>

  <clause id="28331">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (L(y,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(18669,a,28260,a)].">
      <j1 rule="hyper" parents="18669 28260"/>
    </justification>
  </clause>

  <clause id="28332">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(22411,a,28331,a),flip(a)].">
      <j1 rule="hyper" parents="22411 28331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28334">
    <literal><![CDATA[
      T(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * (x \ u)) = T(L(1 / x,y,z) \ 1,x \ ((1 / x) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,22675,a(flip),b,28332,a)].">
      <j1 rule="hyper" parents="60 22675 28332"/>
    </justification>
  </clause>

  <clause id="28337">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ (u * w)) \ (u * w) = T(a(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(215,a,28177,a)].">
      <j1 rule="hyper" parents="215 28177"/>
    </justification>
  </clause>

  <clause id="28338">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(25788,a,28178,a)].">
      <j1 rule="hyper" parents="25788 28178"/>
    </justification>
  </clause>

  <clause id="28339">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(24129,a,28292,a),flip(a)].">
      <j1 rule="hyper" parents="24129 28292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28340">
    <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(28292(a,1),24129(a,1))].">
      <j1 rule="para" parents="28292 24129"/>
    </justification>
  </clause>

  <clause id="28341">
    <literal><![CDATA[
      L(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,14795,a(flip),b,28339,a),flip(a)].">
      <j1 rule="hyper" parents="60 14795 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28342">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),a(y,z,u)) = a(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,28339,a(flip),b,16504,a)].">
      <j1 rule="hyper" parents="125 28339 16504"/>
    </justification>
  </clause>

  <clause id="28343">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(28339(a,1),103(a,1,1))].">
      <j1 rule="para" parents="28339 103"/>
    </justification>
  </clause>

  <clause id="28344">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (R(y,z,z) * x) = R(y,z,z) * L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(28339(a,1),27526(a,2,2))].">
      <j1 rule="para" parents="28339 27526"/>
    </justification>
  </clause>

  <clause id="28345">
    <literal><![CDATA[
      L(x * y,z,a(x,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(60,a,27959,a(flip),b,28341,a)].">
      <j1 rule="hyper" parents="60 27959 28341"/>
    </justification>
  </clause>

  <clause id="28346">
    <literal><![CDATA[
      L(x * y,z,a(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(60,a,27956,a(flip),b,28341,a)].">
      <j1 rule="hyper" parents="60 27956 28341"/>
    </justification>
  </clause>

  <clause id="28347">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = a(x,y,z) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(129,a,28341,a(flip),b,14810,a(flip))].">
      <j1 rule="hyper" parents="129 28341 14810"/>
    </justification>
  </clause>

  <clause id="28348">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * z = a(x,y,z) \ z
    ]]></literal>
    <justification jstring="[hyper(125,a,28341,a(flip),b,3399,a),flip(a)].">
      <j1 rule="hyper" parents="125 28341 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28349">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28341(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28341 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28350">
    <literal><![CDATA[
      (a(x,y,z) * u) * z != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * (u * z) = w
    ]]></literal>
    <justification jstring="[para(28341(a,1),336(a,1,2))].">
      <j1 rule="para" parents="28341 336"/>
    </justification>
  </clause>

  <clause id="28351">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != L(w,v5,v6)
    ]]></literal>
    <literal><![CDATA[
      L(w,v5,v6) = x
    ]]></literal>
    <justification jstring="[para(28341(a,1),166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28341 166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28352">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,x)) = L(x,u,a(w,v5,x)) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28341(a,1),10440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28341 10440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28353">
    <literal><![CDATA[
      T(1 / a(x,x,y),a(x,x,y) * (x * y)) = (a(x,x,y) * (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(28345(a,1),583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28345 583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28354">
    <literal><![CDATA[
      R(a(x,x,y),z,L(y * x,z,a(x,x,y))) = (a(x,x,y) * (z * (y * x))) / (z * (y * x))
    ]]></literal>
    <justification jstring="[para(28346(a,1),623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28346 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28355">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (z * u)) \ ((a(x,y,z) \ z) * u) = a(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(28348(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28348 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28356">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (v5 * w)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w * (a(z,u,w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(28347(a,1),24037(a,1,3))].">
      <j1 rule="para" parents="28347 24037"/>
    </justification>
  </clause>

  <clause id="28357">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (v5 * w)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (v5 * a(z,u,w))) = v6
    ]]></literal>
    <justification jstring="[para(28347(a,1),27033(a,1,3))].">
      <j1 rule="para" parents="28347 27033"/>
    </justification>
  </clause>

  <clause id="28358">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) \ 1 = a(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,14176,a,b,28342,a)].">
      <j1 rule="hyper" parents="60 14176 28342"/>
    </justification>
  </clause>

  <clause id="28359">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23796,a,28343,a)].">
      <j1 rule="hyper" parents="23796 28343"/>
    </justification>
  </clause>

  <clause id="28360">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,28359,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 28359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28361">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,23620,a,b,28359,a)].">
      <j1 rule="hyper" parents="128 23620 28359"/>
    </justification>
  </clause>

  <clause id="28362">
    <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(28360(a,1),293(a,1,1)),flip(b)].">
      <j1 rule="para" parents="28360 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28363">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,x) * v5) = a(u,w,x) * (L(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[para(28349(a,1),28360(a,1,1))].">
      <j1 rule="para" parents="28349 28360"/>
    </justification>
  </clause>

  <clause id="28364">
    <literal><![CDATA[
      (a(x,y,z) * (u * L(z,w,v5))) / (a(x,y,z) * L(z,w,v5)) = L(u,a(x,y,z),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,27890,a(flip),b,28361,a),flip(a)].">
      <j1 rule="hyper" parents="370 27890 28361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28365">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(370,a,28227,a(flip),b,28150,a),flip(a)].">
      <j1 rule="hyper" parents="370 28227 28150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28367">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (w * a(x,y,z)) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(128,a,23642,a,b,28365,a)].">
      <j1 rule="hyper" parents="128 23642 28365"/>
    </justification>
  </clause>

  <clause id="28368">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27602,a(flip),b,28367,a)].">
      <j1 rule="hyper" parents="60 27602 28367"/>
    </justification>
  </clause>

  <clause id="28369">
    <literal><![CDATA[
      L(x / a(y,z,u),a(y,z,u),x \ w) \ w = a(y,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(28368(a,1),673(a,1,1))].">
      <j1 rule="para" parents="28368 673"/>
    </justification>
  </clause>

  <clause id="28370">
    <literal><![CDATA[
      L(x * (y * z),a(x,y,z),((x * y) * z) \ u) \ u = ((x * (y * z)) \ ((x * y) * z)) * (((x * y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(28368(a,1),1402(a,1,1))].">
      <j1 rule="para" parents="28368 1402"/>
    </justification>
  </clause>

  <clause id="28371">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) * u = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(28368(a,1),24105(a,1,1))].">
      <j1 rule="para" parents="28368 24105"/>
    </justification>
  </clause>

  <clause id="28372">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ ((a(y,z,u) * x) * L(w,a(y,z,u),x)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28368(a,1),25559(a,1,2,2))].">
      <j1 rule="para" parents="28368 25559"/>
    </justification>
  </clause>

  <clause id="28373">
    <literal><![CDATA[
      R(x,y,(z \ a(z,u,w)) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(27461,a,28209,a)].">
      <j1 rule="hyper" parents="27461 28209"/>
    </justification>
  </clause>

  <clause id="28374">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (z \ u)) = T(x,(z \ L(u,w,v5)) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28288,a(flip),b,28281,a)].">
      <j1 rule="hyper" parents="60 28288 28281"/>
    </justification>
  </clause>

  <clause id="28375">
    <literal><![CDATA[
      T(x,(y \ L(z,u,w)) * v5) = T(x,(y \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(12606,a,28374,a),flip(a)].">
      <j1 rule="hyper" parents="12606 28374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28377">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ (u / L(z,w,v5)))) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(60,a,25384,a(flip),b,28375,a),flip(a)].">
      <j1 rule="hyper" parents="60 25384 28375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28379">
    <literal><![CDATA[
      T(x,y \ (z / L(u,w,v5))) = T(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25221,a(flip),b,28377,a)].">
      <j1 rule="hyper" parents="60 25221 28377"/>
    </justification>
  </clause>

  <clause id="28381">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(28338(a,2),23805(a,1))].">
      <j1 rule="para" parents="28338 23805"/>
    </justification>
  </clause>

  <clause id="28382">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,x)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28341(a,1),28352(a,2,1))].">
      <j1 rule="para" parents="28341 28352"/>
    </justification>
  </clause>

  <clause id="28383">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,x)) = (L(x,y,z) \ (x * (x \ L(x,y,z)))) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(28382(a,1),4046(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28382 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28384">
    <literal><![CDATA[
      L((x \ y) * (y \ x),z,a(u,w,1 / (y \ x))) = (1 / (y \ x)) \ L(1 / (y \ x),y \ x,x)
    ]]></literal>
    <justification jstring="[para(3434(a,1),28382(a,1,1))].">
      <j1 rule="para" parents="3434 28382"/>
    </justification>
  </clause>

  <clause id="28385">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),u \ w) \ w = a(x,y,z) * (u \ w)
    ]]></literal>
    <justification jstring="[para(23572(a,1),28369(a,1,1,1))].">
      <j1 rule="para" parents="23572 28369"/>
    </justification>
  </clause>

  <clause id="28386">
    <literal><![CDATA[
      a(x,y,z) * (((u * w) / u) * K(v5,u)) = (u * (a(x,y,z) * w)) / T(u,v5)
    ]]></literal>
    <justification jstring="[hyper(23461,a,28328,a)].">
      <j1 rule="hyper" parents="23461 28328"/>
    </justification>
  </clause>

  <clause id="28387">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / T(x,v5) = a(y,z,u) * ((x * w) / T(x,v5))
    ]]></literal>
    <justification jstring="[para(5855(a,1),28386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5855 28386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28388">
    <literal><![CDATA[
      T(a(x,x,y) \ 1,a(x,x,y) * (x * y)) = (a(x,x,y) * (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(23572(a,1),28353(a,1,1))].">
      <j1 rule="para" parents="23572 28353"/>
    </justification>
  </clause>

  <clause id="28389">
    <literal><![CDATA[
      (a(x,x,y) * (x * y)) \ (x * y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,23824,a(flip),b,28388,a),flip(a)].">
      <j1 rule="hyper" parents="60 23824 28388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28391">
    <literal><![CDATA[
      (a(x,y,z) * (z * u)) \ (((1 / a(x,y,z)) \ z) * u) = a(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,2676,a(flip),b,28355,a)].">
      <j1 rule="hyper" parents="60 2676 28355"/>
    </justification>
  </clause>

  <clause id="28392">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ (((1 / a(z,u,x)) \ x) * y) = a(a(z,u,x) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(24117(a,1),28391(a,1,1))].">
      <j1 rule="para" parents="24117 28391"/>
    </justification>
  </clause>

  <clause id="28393">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ (((a(z,u,x) \ 1) \ x) * y) = a(a(z,u,x) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(23572(a,1),28392(a,1,2,1,1))].">
      <j1 rule="para" parents="23572 28392"/>
    </justification>
  </clause>

  <clause id="28394">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ ((x * a(z,u,x)) * y) = a(a(z,u,x) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(25300(a,1),28393(a,1,2,1))].">
      <j1 rule="para" parents="25300 28393"/>
    </justification>
  </clause>

  <clause id="28395">
    <literal><![CDATA[
      a(a(x,y,z) \ 1,z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(24131,a,28394,a),flip(a)].">
      <j1 rule="hyper" parents="24131 28394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28396">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(2973,a,28395,a)].">
      <j1 rule="hyper" parents="2973 28395"/>
    </justification>
  </clause>

  <clause id="28397">
    <literal><![CDATA[
      T((x * a(y,z,u)) \ 1,a(y,z,u) \ (x \ w)) = T(1 / (x * a(y,z,u)),x * w)
    ]]></literal>
    <justification jstring="[hyper(24939,a,28162,a)].">
      <j1 rule="hyper" parents="24939 28162"/>
    </justification>
  </clause>

  <clause id="28401">
    <literal><![CDATA[
      T(1 / (x * a(y,z,u)),x * w) = T((x * a(y,z,u)) \ 1,x \ w)
    ]]></literal>
    <justification jstring="[hyper(28201,a,28397,a),flip(a)].">
      <j1 rule="hyper" parents="28201 28397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28403">
    <literal><![CDATA[
      T(1 / (L(x,x,x) * a(y,z,u)),L(x,x,x) * a(w,v5,v6)) = T((L(x,x,x) * a(y,z,u)) \ 1,a(w,v5,v6) / x)
    ]]></literal>
    <justification jstring="[para(28220(a,1),28401(a,2,2))].">
      <j1 rule="para" parents="28220 28401"/>
    </justification>
  </clause>

  <clause id="28404">
    <literal><![CDATA[
      ((x \ 1) \ (1 / (x \ 1))) * (a(y,z,u) / x) = (((x \ 1) \ 1) \ 1) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(1211(a,1),28218(a,1,1))].">
      <j1 rule="para" parents="1211 28218"/>
    </justification>
  </clause>

  <clause id="28405">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ 1) \ a(y,z,u) = ((x \ 1) \ x) * (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(74(a,1),28404(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="74 28404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28407">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ 1) \ a(y,z,u) = (x * x) * (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(311(a,1),28405(a,2,1))].">
      <j1 rule="para" parents="311 28405"/>
    </justification>
  </clause>

  <clause id="28408">
    <literal><![CDATA[
      (x * x) * (a(y,z,u) / x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(1307(a,1),28407(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 28407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28409">
    <literal><![CDATA[
      (1 / x) \ (a(y,z,u) / x) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,28408,a(flip),b,553,a),flip(a)].">
      <j1 rule="hyper" parents="125 28408 553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28411">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ (x * (T(a(y,z,u),x) * w)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12481(a,1),28372(a,1,2))].">
      <j1 rule="para" parents="12481 28372"/>
    </justification>
  </clause>

  <clause id="28412">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ (x * (a(y,z,u) * w)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(23518(a,1),28411(a,1,2,2,1))].">
      <j1 rule="para" parents="23518 28411"/>
    </justification>
  </clause>

  <clause id="28414">
    <literal><![CDATA[
      R(a(x,x,y),z,L(y * x,z,a(x,x,y))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,6,a(flip),b,28354,a),flip(a)].">
      <j1 rule="hyper" parents="370 6 28354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28416">
    <literal><![CDATA[
      R(a(x,x,y),z,y * x) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(28346(a,1),28414(a,1,3))].">
      <j1 rule="para" parents="28346 28414"/>
    </justification>
  </clause>

  <clause id="28417">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(27073,a,28416,a)].">
      <j1 rule="hyper" parents="27073 28416"/>
    </justification>
  </clause>

  <clause id="28419">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(1994,a,28417,a)].">
      <j1 rule="hyper" parents="1994 28417"/>
    </justification>
  </clause>

  <clause id="28420">
    <literal><![CDATA[
      x * a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(156,a,28417,a)].">
      <j1 rule="hyper" parents="156 28417"/>
    </justification>
  </clause>

  <clause id="28421">
    <literal><![CDATA[
      a(x,x,y) * x = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,23634,a,b,28417,a)].">
      <j1 rule="hyper" parents="35 23634 28417"/>
    </justification>
  </clause>

  <clause id="28422">
    <literal><![CDATA[
      a(x,x,y) / x = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,28417,a(flip),b,1990,a(flip))].">
      <j1 rule="hyper" parents="128 28417 1990"/>
    </justification>
  </clause>

  <clause id="28423">
    <literal><![CDATA[
      (1 / x) \ a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28417,a(flip),b,2012,a)].">
      <j1 rule="hyper" parents="125 28417 2012"/>
    </justification>
  </clause>

  <clause id="28424">
    <literal><![CDATA[
      R(x \ 1,x,y) = x \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28417,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="125 28417 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28425">
    <literal><![CDATA[
      (x / (y * x)) \ a(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(125,a,28417,a(flip),b,1990,a(flip))].">
      <j1 rule="hyper" parents="125 28417 1990"/>
    </justification>
  </clause>

  <clause id="28426">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,L(x,y,z),u),y,z) = a(L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(24(a,1),28417(a,1,2))].">
      <j1 rule="para" parents="24 28417"/>
    </justification>
  </clause>

  <clause id="28428">
    <literal><![CDATA[
      R(L(a(x,x,y),z,u),L(x,z,u),y * x) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(28417(a,1),27371(a,1,1,1))].">
      <j1 rule="para" parents="28417 27371"/>
    </justification>
  </clause>

  <clause id="28429">
    <literal><![CDATA[
      x \ L(x,x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(28339(a,1),28417(a,1,2))].">
      <j1 rule="para" parents="28339 28417"/>
    </justification>
  </clause>

  <clause id="28432">
    <literal><![CDATA[
      a(x / y,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),28419(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 28419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28433">
    <literal><![CDATA[
      (a(x,x,y) / x) \ y = x * y
    ]]></literal>
    <justification jstring="[para(28419(a,1),211(a,1,1,1))].">
      <j1 rule="para" parents="28419 211"/>
    </justification>
  </clause>

  <clause id="28435">
    <literal><![CDATA[
      L(x,y,(y * z) \ z) * a(y,y,z) = (z / (y * z)) * (y * x)
    ]]></literal>
    <justification jstring="[para(28419(a,1),24917(a,1,2))].">
      <j1 rule="para" parents="28419 24917"/>
    </justification>
  </clause>

  <clause id="28436">
    <literal><![CDATA[
      a(x,y,z * (u * (w / (u * w)))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(28419(a,1),27031(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="28419 27031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28437">
    <literal><![CDATA[
      ((((x / (y * x)) / a(y,y,x)) \ 1) \ 1) \ (x / (y * x)) = (x / (y * x)) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(28425(a,1),4488(a,2,2,1,1))].">
      <j1 rule="para" parents="28425 4488"/>
    </justification>
  </clause>

  <clause id="28438">
    <literal><![CDATA[
      L(x * y,a(x,x,y) / x,a(x,x,y) / x) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[para(28433(a,1),586(a,1,1))].">
      <j1 rule="para" parents="28433 586"/>
    </justification>
  </clause>

  <clause id="28439">
    <literal><![CDATA[
      x \ a(x,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(60,a,2786,a(flip),b,28424,a),flip(a)].">
      <j1 rule="hyper" parents="60 2786 28424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28440">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(129,a,2786,a(flip),b,28424,a(flip))].">
      <j1 rule="hyper" parents="129 2786 28424"/>
    </justification>
  </clause>

  <clause id="28441">
    <literal><![CDATA[
      (x \ a(x,x,y)) * y = x \ y
    ]]></literal>
    <justification jstring="[para(28424(a,1),2784(a,1,1))].">
      <j1 rule="para" parents="28424 2784"/>
    </justification>
  </clause>

  <clause id="28442">
    <literal><![CDATA[
      x * (y \ a(y,y,x)) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(28424(a,1),6157(a,1,2))].">
      <j1 rule="para" parents="28424 6157"/>
    </justification>
  </clause>

  <clause id="28444">
    <literal><![CDATA[
      a(x,y * (z * (u \ (z \ u))),w) = a(x,y * a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(28440(a,1),26625(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28440 26625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28445">
    <literal><![CDATA[
      a(x,y,(((z \ u) / u) * z) * w) = a(x,y,w * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(28440(a,1),27031(a,2,3,2))].">
      <j1 rule="para" parents="28440 27031"/>
    </justification>
  </clause>

  <clause id="28446">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) \ a(L(L(x,y,z),u,w),L(L(x,y,z),u,w),x)) * x = x / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,12744,a,b,28441,a),flip(a)].">
      <j1 rule="hyper" parents="370 12744 28441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28447">
    <literal><![CDATA[
      R(x,y \ a(y,y,z),z) * (y \ z) = (x * (y \ a(y,y,z))) * z
    ]]></literal>
    <justification jstring="[hyper(129,a,28441,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="129 28441 210"/>
    </justification>
  </clause>

  <clause id="28448">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x * (y \ a(y,y,z))) * z) = a(x,y \ a(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(28441(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28441 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28449">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u \ a(u,u,z))) = R(x,y,(u \ a(u,u,z)) * (u \ z))
    ]]></literal>
    <justification jstring="[para(28441(a,1),2756(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="28441 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28450">
    <literal><![CDATA[
      L(x,y * ((z \ a(z,z,u \ K(w,v5))) * u),v6) = L(x,y * (z \ (u \ K(w,v5))),v6)
    ]]></literal>
    <justification jstring="[para(28441(a,1),26291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28441 26291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28451">
    <literal><![CDATA[
      a(x / y,y \ x,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(26559,a,28432,a)].">
      <j1 rule="hyper" parents="26559 28432"/>
    </justification>
  </clause>

  <clause id="28452">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(26516,a,28451,a)].">
      <j1 rule="hyper" parents="26516 28451"/>
    </justification>
  </clause>

  <clause id="28453">
    <literal><![CDATA[
      ((1 / (x / y)) * x) \ y = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,12460,a(flip),b,28452,a)].">
      <j1 rule="hyper" parents="60 12460 28452"/>
    </justification>
  </clause>

  <clause id="28454">
    <literal><![CDATA[
      L(x,y,(z / u) * (u / z)) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[para(28452(a,1),27957(a,1,3))].">
      <j1 rule="para" parents="28452 27957"/>
    </justification>
  </clause>

  <clause id="28456">
    <literal><![CDATA[
      L(x,y,(z / u) * (z \ u)) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(25949,a,28454,a)].">
      <j1 rule="hyper" parents="25949 28454"/>
    </justification>
  </clause>

  <clause id="28457">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(28456(a,1),25945(a,1))].">
      <j1 rule="para" parents="28456 25945"/>
    </justification>
  </clause>

  <clause id="28458">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) * u) * w) = a(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(27006,a,28445,a)].">
      <j1 rule="hyper" parents="27006 28445"/>
    </justification>
  </clause>

  <clause id="28459">
    <literal><![CDATA[
      L(R(a(x,x,y),L(x,z,u),y * x),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,28428,a)].">
      <j1 rule="hyper" parents="60 24 28428"/>
    </justification>
  </clause>

  <clause id="28460">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) * a(y,y,z) = (z / (y * z)) * (y * x)
    ]]></literal>
    <justification jstring="[para(27631(a,1),28435(a,1,1))].">
      <j1 rule="para" parents="27631 28435"/>
    </justification>
  </clause>

  <clause id="28461">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(28416(a,1),28459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28416 28459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28463">
    <literal><![CDATA[
      R(x,y * a(y,y,z),z) * (y \ z) = (x * (y \ a(y,y,z))) * z
    ]]></literal>
    <justification jstring="[para(27473(a,1),28447(a,1,1))].">
      <j1 rule="para" parents="27473 28447"/>
    </justification>
  </clause>

  <clause id="28464">
    <literal><![CDATA[
      R(x,R(y,y,z),z) * (y \ z) = (x * (y \ a(y,y,z))) * z
    ]]></literal>
    <justification jstring="[para(28420(a,1),28463(a,1,1,2))].">
      <j1 rule="para" parents="28420 28463"/>
    </justification>
  </clause>

  <clause id="28465">
    <literal><![CDATA[
      L(x \ R(x,L(x,y,z),u),y,z) = a(L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7813,a,28426,a)].">
      <j1 rule="hyper" parents="7813 28426"/>
    </justification>
  </clause>

  <clause id="28466">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x * (y \ a(y,y,z))) * z) = a(x,y * a(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,19690,a(flip),b,28448,a),flip(a)].">
      <j1 rule="hyper" parents="370 19690 28448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28467">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x * (y \ a(y,y,z))) * z) = a(x,R(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(28420(a,1),28466(a,2,2))].">
      <j1 rule="para" parents="28420 28466"/>
    </justification>
  </clause>

  <clause id="28468">
    <literal><![CDATA[
      L(x * y,a(x,x,y) / x,x \ a(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(24038,a,28438,a)].">
      <j1 rule="hyper" parents="24038 28438"/>
    </justification>
  </clause>

  <clause id="28469">
    <literal><![CDATA[
      L(x * y,a(x,x,y) / x,x * a(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(25440,a,28468,a)].">
      <j1 rule="hyper" parents="25440 28468"/>
    </justification>
  </clause>

  <clause id="28470">
    <literal><![CDATA[
      L(x * y,a(x,x,y) / x,R(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[para(28420(a,1),28469(a,1,3))].">
      <j1 rule="para" parents="28420 28469"/>
    </justification>
  </clause>

  <clause id="28471">
    <literal><![CDATA[
      L(x * y,a(x,x,y) / x,L(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(27280,a,28470,a)].">
      <j1 rule="hyper" parents="27280 28470"/>
    </justification>
  </clause>

  <clause id="28472">
    <literal><![CDATA[
      L(x * y,x \ a(x,x,y),L(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(26067,a,28471,a)].">
      <j1 rule="hyper" parents="26067 28471"/>
    </justification>
  </clause>

  <clause id="28473">
    <literal><![CDATA[
      L(x * y,x * a(x,x,y),L(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(26243,a,28472,a)].">
      <j1 rule="hyper" parents="26243 28472"/>
    </justification>
  </clause>

  <clause id="28474">
    <literal><![CDATA[
      L(x * y,R(x,x,y),L(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[para(28420(a,1),28473(a,1,2))].">
      <j1 rule="para" parents="28420 28473"/>
    </justification>
  </clause>

  <clause id="28475">
    <literal><![CDATA[
      L(x * y,L(x,x,y),L(x,x,y)) = (1 / (a(x,x,y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(27479,a,28474,a)].">
      <j1 rule="hyper" parents="27479 28474"/>
    </justification>
  </clause>

  <clause id="28476">
    <literal><![CDATA[
      L(x,y * (z \ (u \ K(w,v5))),v6) = L(x,y * ((z \ a(z,z,u)) * u),v6)
    ]]></literal>
    <justification jstring="[para(27035(a,1),28450(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="27035 28450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28478">
    <literal><![CDATA[
      L(x,y * (z \ (u \ K(w,v5))),v6) = L(x,y * (z \ u),v6)
    ]]></literal>
    <justification jstring="[para(28441(a,1),28476(a,2,2,2))].">
      <j1 rule="para" parents="28441 28476"/>
    </justification>
  </clause>

  <clause id="28479">
    <literal><![CDATA[
      L(x,y * ((T(z,u \ K(w,v5)) \ 1) \ u),v6) = L(x,y * (L(z,z,u \ K(w,v5)) * u),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,28008,a(flip),b,28478,a),flip(a)].">
      <j1 rule="hyper" parents="60 28008 28478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28480">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u \ a(u,u,z))) = R(x,y,(u * a(u,u,z)) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,28373,a(flip),b,28449,a),flip(a)].">
      <j1 rule="hyper" parents="370 28373 28449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28481">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u \ a(u,u,z))) = R(x,y,R(u,u,z) * (u \ z))
    ]]></literal>
    <justification jstring="[para(28420(a,1),28480(a,2,3,1))].">
      <j1 rule="para" parents="28420 28480"/>
    </justification>
  </clause>

  <clause id="28482">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u \ a(u,u,z))) = R(x,y,u \ ((1 / u) \ z))
    ]]></literal>
    <justification jstring="[para(1980(a,1),28481(a,2,3))].">
      <j1 rule="para" parents="1980 28481"/>
    </justification>
  </clause>

  <clause id="28483">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u \ a(u,u,z))) = R(x,y,u \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27485,a(flip),b,28482,a),flip(a)].">
      <j1 rule="hyper" parents="370 27485 28482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28484">
    <literal><![CDATA[
      R(x,y,L(z,u \ a(u,u,z),u * a(u,u,z))) = R(x,y,u \ (u \ z))
    ]]></literal>
    <justification jstring="[para(19691(a,1),28483(a,1,3))].">
      <j1 rule="para" parents="19691 28483"/>
    </justification>
  </clause>

  <clause id="28485">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(u,w,v5),a(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(28364(a,1),28362(a,1))].">
      <j1 rule="para" parents="28364 28362"/>
    </justification>
  </clause>

  <clause id="28486">
    <literal><![CDATA[
      (((a(x,x,y) \ (y / (x * y))) \ 1) \ 1) \ (y / (x * y)) = (y / (x * y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(23572(a,1),28437(a,1,1,1,1))].">
      <j1 rule="para" parents="23572 28437"/>
    </justification>
  </clause>

  <clause id="28487">
    <literal><![CDATA[
      L(x,y * (L(z,z,u \ K(w,v5)) * u),v6) = L(x,(T(z,u \ K(w,v5)) \ u) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(26096,a,28479,a),flip(a)].">
      <j1 rule="hyper" parents="26096 28479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28489">
    <literal><![CDATA[
      L(x,y * (L(z,z,u \ K(w,v5)) * u),v6) = L(x,(z \ u) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26033,a(flip),b,28487,a),flip(a)].">
      <j1 rule="hyper" parents="370 26033 28487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28491">
    <literal><![CDATA[
      L(x,y * (L(z,z,u) * u),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[para(25921(a,1),28489(a,1,2,2,1))].">
      <j1 rule="para" parents="25921 28489"/>
    </justification>
  </clause>

  <clause id="28492">
    <literal><![CDATA[
      a(x,y,z) * T(u,(u * a(x,y,z)) \ (a(x,y,z) \ (u \ 1))) = ((u * a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(28280(a,1),28230(a,1,2))].">
      <j1 rule="para" parents="28280 28230"/>
    </justification>
  </clause>

  <clause id="28493">
    <literal><![CDATA[
      (x \ 1) * ((a(y,z,u) / ((x \ 1) \ 1)) \ w) = x * (((1 / x) \ a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(401,a,28235,a),flip(a)].">
      <j1 rule="hyper" parents="401 28235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28495">
    <literal><![CDATA[
      (x \ 1) * (((1 / (x \ 1)) \ a(y,z,u)) \ w) = x * (((1 / x) \ a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(28219(a,1),28493(a,1,2,1))].">
      <j1 rule="para" parents="28219 28493"/>
    </justification>
  </clause>

  <clause id="28496">
    <literal><![CDATA[
      (x \ 1) * ((x \ a(y,z,u)) \ w) = x * (((1 / x) \ a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(74(a,1),28495(a,1,2,1,1))].">
      <j1 rule="para" parents="74 28495"/>
    </justification>
  </clause>

  <clause id="28498">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,x)) = 1 * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(295(a,1),28383(a,2,1))].">
      <j1 rule="para" parents="295 28383"/>
    </justification>
  </clause>

  <clause id="28499">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,x)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,28498,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 28498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28502">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (a(u,w,x) \ 1) = a(u,w,x) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(125,a,28499,a(flip),b,23820,a),flip(a)].">
      <j1 rule="hyper" parents="125 28499 23820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28503">
    <literal><![CDATA[
      a(x,y,z) * T(u,(u * a(x,y,z)) \ (u \ 1)) = ((u * a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(28169(a,1),28492(a,1,2))].">
      <j1 rule="para" parents="28169 28492"/>
    </justification>
  </clause>

  <clause id="28504">
    <literal><![CDATA[
      a(x,y,z) * T(u,a(x,y,z) \ (u \ (u \ 1))) = ((u * a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11045(a,1),28503(a,1,2))].">
      <j1 rule="para" parents="11045 28503"/>
    </justification>
  </clause>

  <clause id="28506">
    <literal><![CDATA[
      a(x,y,z) * T(u,u \ (u \ 1)) = ((u * a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(28145(a,1),28504(a,1,2))].">
      <j1 rule="para" parents="28145 28504"/>
    </justification>
  </clause>

  <clause id="28507">
    <literal><![CDATA[
      ((x * a(y,z,u)) \ 1) \ 1 = a(y,z,u) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4666(a,1),28506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4666 28506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28509">
    <literal><![CDATA[
      (a(x,y,z) * ((u \ 1) \ 1)) \ 1 = 1 / (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28507(a,1),1307(a,1,1))].">
      <j1 rule="para" parents="28507 1307"/>
    </justification>
  </clause>

  <clause id="28510">
    <literal><![CDATA[
      (a(x,y,z) * ((1 / u) \ 1)) \ 1 = 1 / (L(u,u,u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(1327(a,1),28509(a,1,1,2,1))].">
      <j1 rule="para" parents="1327 28509"/>
    </justification>
  </clause>

  <clause id="28511">
    <literal><![CDATA[
      1 / (L(x,x,x) * a(y,z,u)) = (a(y,z,u) * x) \ 1
    ]]></literal>
    <justification jstring="[para(77(a,1),28510(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="77 28510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28513">
    <literal><![CDATA[
      L((x \ y) * (y \ x),z,a(u,w,y \ x)) = (1 / (y \ x)) \ L(1 / (y \ x),y \ x,x)
    ]]></literal>
    <justification jstring="[para(3078(a,1),28384(a,1,3))].">
      <j1 rule="para" parents="3078 28384"/>
    </justification>
  </clause>

  <clause id="28514">
    <literal><![CDATA[
      L((x \ y) * (y \ x),z,a(u,w,y \ x)) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3434,a(flip),b,28513,a),flip(a)].">
      <j1 rule="hyper" parents="370 3434 28513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28515">
    <literal><![CDATA[
      ((x * (y \ z)) * (z \ y)) / ((y \ z) * (z \ y)) = a(x,y \ z,z \ y) * x
    ]]></literal>
    <justification jstring="[para(28514(a,1),19672(a,1,2))].">
      <j1 rule="para" parents="28514 19672"/>
    </justification>
  </clause>

  <clause id="28516">
    <literal><![CDATA[
      a(x,y \ z,z \ y) * x = R(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(693,a,28515,a),flip(a)].">
      <j1 rule="hyper" parents="693 28515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28518">
    <literal><![CDATA[
      T(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * (x \ u)) = T(L(1 / x,y,z) \ 1,(x \ x) * (1 \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,28299,a(flip),b,28334,a),flip(a)].">
      <j1 rule="hyper" parents="370 28299 28334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28519">
    <literal><![CDATA[
      T(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * (x \ u)) = T(L(1 / x,y,z) \ 1,1 * (1 \ u))
    ]]></literal>
    <justification jstring="[para(63(a,1),28518(a,2,2,1))].">
      <j1 rule="para" parents="63 28518"/>
    </justification>
  </clause>

  <clause id="28520">
    <literal><![CDATA[
      T(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * (x \ u)) = T(L(1 / x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),28519(a,2,2))].">
      <j1 rule="para" parents="5 28519"/>
    </justification>
  </clause>

  <clause id="28522">
    <literal><![CDATA[
      T(L(x \ 1,y,z) \ 1,x \ (x \ u)) = T(L(1 / x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(28286,a,28520,a)].">
      <j1 rule="hyper" parents="28286 28520"/>
    </justification>
  </clause>

  <clause id="28524">
    <literal><![CDATA[
      T(L(L(x,y,z) \ 1,u,w) \ 1,L(x,y,z) \ (1 / L(x,y,z))) = T(L(1 / L(x,y,z),u,w) \ 1,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(6791(a,1),28522(a,1,2,2))].">
      <j1 rule="para" parents="6791 28522"/>
    </justification>
  </clause>

  <clause id="28525">
    <literal><![CDATA[
      L(x * (y * z),a(x,y,z),((x * y) * z) \ u) \ u = a(x,y,z) * (((x * y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,2),28370(a,2,1))].">
      <j1 rule="para" parents="9 28370"/>
    </justification>
  </clause>

  <clause id="28526">
    <literal><![CDATA[
      L(x * (y * a(z,u,w)),a(x,y,a(z,u,w)),a(a(z,u,w),x,y)) \ ((x * a(z,u,w)) * y) = a(x,y,a(z,u,w)) * (((x * y) * a(z,u,w)) \ ((x * a(z,u,w)) * y))
    ]]></literal>
    <justification jstring="[para(25840(a,1),28525(a,1,1,3))].">
      <j1 rule="para" parents="25840 28525"/>
    </justification>
  </clause>

  <clause id="28527">
    <literal><![CDATA[
      T((L(x,x,x) * a(y,z,u)) \ 1,a(w,v5,v6) / x) = T((a(y,z,u) * x) \ 1,L(x,x,x) * a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(28511(a,1),28403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28511 28403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28528">
    <literal><![CDATA[
      T((L(x,x,x) * a(y,z,u)) \ 1,a(w,v5,v6) / x) = T((a(y,z,u) * x) \ 1,L(x,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,28130,a(flip),b,28527,a),flip(a)].">
      <j1 rule="hyper" parents="370 28130 28527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28530">
    <literal><![CDATA[
      T((L(x,x,x) * a(y,z,u)) \ 1,a(w,v5,v6) / x) = T((a(y,z,u) * x) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,23594,a(flip),b,28528,a),flip(a)].">
      <j1 rule="hyper" parents="370 23594 28528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28532">
    <literal><![CDATA[
      T((L(x,x,x) * a(y,z,u)) \ 1,a(w,v5,v6) / x) = 1 / (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,28151,a(flip),b,28530,a),flip(a)].">
      <j1 rule="hyper" parents="370 28151 28530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28533">
    <literal><![CDATA[
      T((L(x,x,x) * a(y,z,u)) \ 1,x \ 1) = 1 / (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(28176,a,28532,a)].">
      <j1 rule="hyper" parents="28176 28532"/>
    </justification>
  </clause>

  <clause id="28534">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) \ (x * R(x \ (((x \ y) \ 1) \ 1),z,u)) = (x * (y \ x)) \ R(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(3492(a,1),25794(a,2,2,1))].">
      <j1 rule="para" parents="3492 25794"/>
    </justification>
  </clause>

  <clause id="28535">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (x * R(x \ ((x \ y) \ 1),z,u)) = (x * (y \ x)) \ R(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27863,a(flip),b,28534,a)].">
      <j1 rule="hyper" parents="60 27863 28534"/>
    </justification>
  </clause>

  <clause id="28536">
    <literal><![CDATA[
      (x * (y \ x)) \ R(x * (y \ x),z,u) = (x \ y) \ (x * R(x \ (x \ y),z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27863,a(flip),b,28535,a),flip(a)].">
      <j1 rule="hyper" parents="60 27863 28535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28537">
    <literal><![CDATA[
      (x * (y \ x)) \ R(x * (y \ x),z,u) = (x \ y) \ (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2147(a,1),28536(a,2,2))].">
      <j1 rule="para" parents="2147 28536"/>
    </justification>
  </clause>

  <clause id="28538">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,(u * w) \ ((v5 * w) * u)) \ L(v5,w,u)) = L(x,y,((u * w) \ ((v5 * w) * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,23573,a(flip),b,26314,a),flip(a)].">
      <j1 rule="hyper" parents="370 23573 26314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28540">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,L(u,w,v5)) \ L(u,w,v5)) = L(x,y,((v5 * w) \ ((u * w) * v5)) * z)
    ]]></literal>
    <justification jstring="[para(27282(a,1),28538(a,1,3,1))].">
      <j1 rule="para" parents="27282 28538"/>
    </justification>
  </clause>

  <clause id="28541">
    <literal><![CDATA[
      L(x,y,T(L(z,u,w) * v5,v5 \ 1)) = L(x,y,((w * u) \ ((z * u) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(6487(a,1),28540(a,1,3))].">
      <j1 rule="para" parents="6487 28540"/>
    </justification>
  </clause>

  <clause id="28542">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * z)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(w,u,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(28541(a,1),23612(a,1))].">
      <j1 rule="para" parents="28541 23612"/>
    </justification>
  </clause>

  <clause id="28543">
    <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(26359(a,1),28542(a,1))].">
      <j1 rule="para" parents="26359 28542"/>
    </justification>
  </clause>

  <clause id="28544">
    <literal><![CDATA[
      T(L(L(x,y,z) \ 1,u,w) \ 1,x \ (1 / L(x,y,z))) = T(L(1 / L(x,y,z),u,w) \ 1,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(28283,a,28524,a)].">
      <j1 rule="hyper" parents="28283 28524"/>
    </justification>
  </clause>

  <clause id="28546">
    <literal><![CDATA[
      T(L(1 / L(x,y,z),u,w) \ 1,K(x,x \ 1)) = T(L(L(x,y,z) \ 1,u,w) \ 1,x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(60,a,28379,a(flip),b,28544,a),flip(a)].">
      <j1 rule="hyper" parents="60 28379 28544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28548">
    <literal><![CDATA[
      T(L(1 / L(x,y,z),u,w) \ 1,K(x,x \ 1)) = T(L(L(x,y,z) \ 1,u,w) \ 1,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,4658,a(flip),b,28546,a),flip(a)].">
      <j1 rule="hyper" parents="370 4658 28546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28549">
    <literal><![CDATA[
      T(L(L(x,y,z) \ 1,u,w) \ 1,x \ (x \ 1)) = L(1 / L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(4357,a,28548,a),flip(a)].">
      <j1 rule="hyper" parents="4357 28548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28551">
    <literal><![CDATA[
      L(x,T(y,z),y \ L(y,u,w)) * ((y \ L(y,u,w)) * T(y,z)) = (y \ L(y,u,w)) * (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(23839(a,1),25368(a,2,2))].">
      <j1 rule="para" parents="23839 25368"/>
    </justification>
  </clause>

  <clause id="28553">
    <literal><![CDATA[
      L(x,T(y,z),y * L(y,u,w)) * ((y \ L(y,u,w)) * T(y,z)) = (y \ L(y,u,w)) * (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(3862(a,1),28551(a,1,1))].">
      <j1 rule="para" parents="3862 28551"/>
    </justification>
  </clause>

  <clause id="28556">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * ((y \ L(y,z,u)) * T(y,w)) = (y \ L(y,z,u)) * (x * T(y,w))
    ]]></literal>
    <justification jstring="[para(26015(a,1),28553(a,1,1))].">
      <j1 rule="para" parents="26015 28553"/>
    </justification>
  </clause>

  <clause id="28558">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * L(T(y,w),z,u) = (y \ L(y,z,u)) * (x * T(y,w))
    ]]></literal>
    <justification jstring="[para(25143(a,1),28556(a,1,2))].">
      <j1 rule="para" parents="25143 28556"/>
    </justification>
  </clause>

  <clause id="28559">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(y,w) = (y \ L(y,z,u)) * (x * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27577,a(flip),b,28558,a)].">
      <j1 rule="hyper" parents="60 27577 28558"/>
    </justification>
  </clause>

  <clause id="28560">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) \ ((y \ L(y,u,w)) * (x * T(y,z))) = a(x,y * L(y,u,w),y)
    ]]></literal>
    <justification jstring="[para(28559(a,1),27810(a,1,2))].">
      <j1 rule="para" parents="28559 27810"/>
    </justification>
  </clause>

  <clause id="28561">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(27982,a,28560,a),flip(a)].">
      <j1 rule="hyper" parents="27982 28560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28563">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3883,a,28561,a)].">
      <j1 rule="hyper" parents="3883 28561"/>
    </justification>
  </clause>

  <clause id="28564">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3861,a,b,28563,a),flip(a)].">
      <j1 rule="hyper" parents="370 3861 28563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28565">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * (y \ L(y,z,u))) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,83,a,b,28564,a)].">
      <j1 rule="hyper" parents="370 83 28564"/>
    </justification>
  </clause>

  <clause id="28566">
    <literal><![CDATA[
      (x * ((y \ L(y,z,u)) * y)) \ ((x * y) * (y \ L(y,z,u))) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3838(a,2),28565(a,1,1,2))].">
      <j1 rule="para" parents="3838 28565"/>
    </justification>
  </clause>

  <clause id="28567">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * y = (x * y) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(157,a,28566,a)].">
      <j1 rule="hyper" parents="157 28566"/>
    </justification>
  </clause>

  <clause id="28568">
    <literal><![CDATA[
      (x * ((x \ y) \ L(x \ y,z,u))) * (x \ y) = y * ((x \ y) \ L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,171,a(flip),b,28567,a),flip(a)].">
      <j1 rule="hyper" parents="370 171 28567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28569">
    <literal><![CDATA[
      ((x * y) * (y \ L(y,z,u))) / L(y,z,u) = R(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(28567(a,1),3843(a,1,1))].">
      <j1 rule="para" parents="28567 3843"/>
    </justification>
  </clause>

  <clause id="28570">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = R(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1050,a,28569,a),flip(a)].">
      <j1 rule="hyper" parents="1050 28569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28571">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) = R(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(25598,a,28570,a)].">
      <j1 rule="hyper" parents="25598 28570"/>
    </justification>
  </clause>

  <clause id="28572">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(25324,a,28571,a),flip(a)].">
      <j1 rule="hyper" parents="25324 28571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28573">
    <literal><![CDATA[
      R(x,y,y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3857,a,28572,a)].">
      <j1 rule="hyper" parents="3857 28572"/>
    </justification>
  </clause>

  <clause id="28574">
    <literal><![CDATA[
      R(x,y,L(y,z,u) \ y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,14763,a,b,28573,a)].">
      <j1 rule="hyper" parents="60 14763 28573"/>
    </justification>
  </clause>

  <clause id="28575">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * L(x,y,z)) = x / (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,4154,a(flip),b,28574,a),flip(a)].">
      <j1 rule="hyper" parents="60 4154 28574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28576">
    <literal><![CDATA[
      x / (L(1 / x,y,z) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27702,a(flip),b,28575,a),flip(a)].">
      <j1 rule="hyper" parents="60 27702 28575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28578">
    <literal><![CDATA[
      (x * (x \ (y * L(y \ x,z,u)))) * (x \ y) = y * ((x \ y) \ L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(3823(a,1),28568(a,1,1,2))].">
      <j1 rule="para" parents="3823 28568"/>
    </justification>
  </clause>

  <clause id="28579">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (y \ x) = x * ((y \ x) \ L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(755,a,28578,a)].">
      <j1 rule="hyper" parents="755 28578"/>
    </justification>
  </clause>

  <clause id="28581">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (y \ x) = x * (y \ (x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[para(3823(a,1),28579(a,2,2))].">
      <j1 rule="para" parents="3823 28579"/>
    </justification>
  </clause>

  <clause id="28582">
    <literal><![CDATA[
      x \ (((x * x) * L((x * x) \ y,z,u)) * (y \ (x * x))) = (1 / x) \ (y \ ((x * x) * L((x * x) \ y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(125,a,28581,a,b,553,a)].">
      <j1 rule="hyper" parents="125 28581 553"/>
    </justification>
  </clause>

  <clause id="28584">
    <literal><![CDATA[
      (1 / x) \ (y \ ((x * x) * L((x * x) \ y,z,u))) = x \ (L(y,z,u) * (y \ (x * x)))
    ]]></literal>
    <justification jstring="[para(3806(a,1),28582(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3806 28582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28586">
    <literal><![CDATA[
      (1 / x) \ (y \ ((x * x) * L((x * x) \ y,z,u))) = x \ (y * L(y \ (x * x),z,u))
    ]]></literal>
    <justification jstring="[para(4125(a,1),28584(a,2,2))].">
      <j1 rule="para" parents="4125 28584"/>
    </justification>
  </clause>

  <clause id="28587">
    <literal><![CDATA[
      (1 / x) \ (y \ ((x * x) * L((x * x) \ y,z,u))) = (x \ y) * L((x \ y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1834,a(flip),b,28586,a),flip(a)].">
      <j1 rule="hyper" parents="370 1834 28586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28588">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3806(a,1),28587(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3806 28587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28589">
    <literal><![CDATA[
      (1 / x) \ (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(25857,a,28588,a),flip(a)].">
      <j1 rule="hyper" parents="25857 28588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28592">
    <literal><![CDATA[
      ((1 / x) \ y) * L((x \ y) \ (x \ 1),z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3836,a,b,28589,a)].">
      <j1 rule="hyper" parents="60 3836 28589"/>
    </justification>
  </clause>

  <clause id="28593">
    <literal><![CDATA[
      (x / L(x,y,z)) \ L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14697,a(flip),b,28589,a),flip(a)].">
      <j1 rule="hyper" parents="60 14697 28589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28594">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(3938(a,1),28593(a,1,1))].">
      <j1 rule="para" parents="3938 28593"/>
    </justification>
  </clause>

  <clause id="28595">
    <literal><![CDATA[
      a(x,y,L(L((z \ u) \ (z \ 1),w,v5),(z \ 1) \ u,v6) * (v6 * ((1 / z) \ u))) = a(x,y,v6 * ((u / z) \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(28592(a,1),27086(a,2,3,2))].">
      <j1 rule="para" parents="28592 27086"/>
    </justification>
  </clause>

  <clause id="28596">
    <literal><![CDATA[
      a(x * ((R(y,z,u) \ ((R(y,z,u) \ 1) \ w)) * L(y,z,u)),v5,v6) = a(x * ((R(y,z,u) \ 1) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26598,a(flip),b,27343,a),flip(a)].">
      <j1 rule="hyper" parents="370 26598 27343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28598">
    <literal><![CDATA[
      a(x * ((R(y,z,u) \ ((R(y,z,u) \ 1) \ w)) * L(y,z,u)),v5,v6) = a((R(y,z,u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26424,a(flip),b,28596,a),flip(a)].">
      <j1 rule="hyper" parents="370 26424 28596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28599">
    <literal><![CDATA[
      a(x,y,(((((z * u) * w) / (z * u)) * u) \ ((z * u) * w)) * v5) = a(x,y,R(z,u,((z * u) * w) / (z * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(27524,a,27366,a)].">
      <j1 rule="hyper" parents="27524 27366"/>
    </justification>
  </clause>

  <clause id="28600">
    <literal><![CDATA[
      a(x,y,R(z,u,((z * u) * w) / (z * u)) * v5) = a(x,y,((w * u) \ (w * (z * u))) * v5)
    ]]></literal>
    <justification jstring="[para(25805(a,1),28599(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="25805 28599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28601">
    <literal><![CDATA[
      a(x,y,R(z,u,((z * u) * w) / (z * u)) * v5) = a(x,y,L(T(z,u),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(270(a,1),28600(a,2,3,1))].">
      <j1 rule="para" parents="270 28600"/>
    </justification>
  </clause>

  <clause id="28602">
    <literal><![CDATA[
      a(x,y,R(z,u,((z * u) * w) / (z * u)) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26908,a(flip),b,28601,a),flip(a)].">
      <j1 rule="hyper" parents="370 26908 28601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28604">
    <literal><![CDATA[
      a(x,y,R(z,u,(z * u) \ ((z * u) * w)) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(24056(a,1),28602(a,1,3,1))].">
      <j1 rule="para" parents="24056 28602"/>
    </justification>
  </clause>

  <clause id="28605">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),28604(a,1,3,1,3))].">
      <j1 rule="para" parents="4 28604"/>
    </justification>
  </clause>

  <clause id="28606">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * (v5 * v6)) = a(x,y,L(z,u,w) * (v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(26976,a,28605,a)].">
      <j1 rule="hyper" parents="26976 28605"/>
    </justification>
  </clause>

  <clause id="28607">
    <literal><![CDATA[
      a(x,y,L((z * u) \ ((z * u) \ w),v5,v6) * (z * u)) = a(x,y,(z * u) \ R(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,27049,a(flip),b,28606,a),flip(a)].">
      <j1 rule="hyper" parents="60 27049 28606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28608">
    <literal><![CDATA[
      a(x,y,(z * u) \ R(w,v5,v6)) = a(x,y,(z * u) \ L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(26995,a,28607,a),flip(a)].">
      <j1 rule="hyper" parents="26995 28607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28610">
    <literal><![CDATA[
      a(x,y,L(L((z \ u) \ (z \ 1),w,v5),z \ u,v6) * (v6 * ((1 / z) \ u))) = a(x,y,v6 * ((u / z) \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(3392(a,1),28595(a,1,3,1))].">
      <j1 rule="para" parents="3392 28595"/>
    </justification>
  </clause>

  <clause id="28611">
    <literal><![CDATA[
      a(x,y,L(L((z \ u) \ (z \ 1),w,v5),z \ u,v6) * (v6 * ((z \ 1) \ u))) = a(x,y,v6 * ((u / z) \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(27203,a,28610,a)].">
      <j1 rule="hyper" parents="27203 28610"/>
    </justification>
  </clause>

  <clause id="28612">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) * L(L((z \ u) \ (z \ 1),v5,v6),z \ u,w)) = a(x,y,w * ((u / z) \ L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(27243,a,28611,a)].">
      <j1 rule="hyper" parents="27243 28611"/>
    </justification>
  </clause>

  <clause id="28613">
    <literal><![CDATA[
      a(x,y,z * (T(u \ w,z) * L((u \ w) \ (u \ 1),v5,v6))) = a(x,y,z * ((w / u) \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(12481(a,1),28612(a,1,3))].">
      <j1 rule="para" parents="12481 28612"/>
    </justification>
  </clause>

  <clause id="28614">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * L((u \ w) \ (u \ 1),v5,v6))) = a(x,y,z * ((w / u) \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(27092,a,28613,a)].">
      <j1 rule="hyper" parents="27092 28613"/>
    </justification>
  </clause>

  <clause id="28615">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(w \ 1,v5,v6)))) = a(x,y,z * ((w / u) \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(2521(a,1),28614(a,1,3,2))].">
      <j1 rule="para" parents="2521 28614"/>
    </justification>
  </clause>

  <clause id="28616">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ L(u,v5,v6))) = a(x,y,z * (w \ (u \ L(u,v5,v6))))
    ]]></literal>
    <justification jstring="[para(3816(a,1),28615(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3816 28615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28617">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ L(u,v5,v6))) = a(x,y,z * (w \ (u * L(u,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(370,a,27218,a(flip),b,28616,a),flip(a)].">
      <j1 rule="hyper" parents="370 27218 28616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28618">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ L(w,v5,v6))) = a(x,y,z * (u \ (w * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(27094,a,28617,a)].">
      <j1 rule="hyper" parents="27094 28617"/>
    </justification>
  </clause>

  <clause id="28619">
    <literal><![CDATA[
      (L(R(K(x,y) * z,u,w),v5,v6) \ L(K(x,y) * z,v5,v6)) \ 1 = L(z,v5,v6) \ (K(y,x) * R(L(K(x,y) * z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(24(a,1),25766(a,1,1,1))].">
      <j1 rule="para" parents="24 25766"/>
    </justification>
  </clause>

  <clause id="28620">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ (K(v5,v6) * L(K(v6,v5) * x,u,w))) \ 1 = L(x,u,w) \ (K(v5,v6) * R(L(K(v6,v5) * x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(25768(a,1),28619(a,1,1))].">
      <j1 rule="para" parents="25768 28619"/>
    </justification>
  </clause>

  <clause id="28621">
    <literal><![CDATA[
      L(x,y,z) \ (K(u,w) * R(L(K(w,u) * x,y,z),v5,v6)) = (L(R(x,v5,v6),y,z) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(25741(a,1),28620(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25741 28620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28622">
    <literal><![CDATA[
      L(x,y,z) \ (K(u,w) * L(R(K(w,u) * x,v5,v6),y,z)) = (L(R(x,v5,v6),y,z) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(24(a,1),28621(a,1,2,2))].">
      <j1 rule="para" parents="24 28621"/>
    </justification>
  </clause>

  <clause id="28624">
    <literal><![CDATA[
      L(x,y,z) \ L(K(u,w) * R(K(w,u) * x,v5,v6),y,z) = (L(R(x,v5,v6),y,z) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(25728(a,2),28622(a,1,2))].">
      <j1 rule="para" parents="25728 28622"/>
    </justification>
  </clause>

  <clause id="28625">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) \ 1 = L(x,u,w) \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4193(a,1),28624(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4193 28624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28626">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) \ 1 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,7812,a(flip),b,28625,a),flip(a)].">
      <j1 rule="hyper" parents="370 7812 28625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28628">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = R(z * K(y,x),y,x) \ L(R(z * K(y,x),y,x),u,w)
    ]]></literal>
    <justification jstring="[para(25688(a,1),25700(a,2,2,1))].">
      <j1 rule="para" parents="25688 25700"/>
    </justification>
  </clause>

  <clause id="28629">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = (R(z * K(y,x),y,x) \ L(R(z,y,x),u,w)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,25756,a(flip),b,28628,a),flip(a)].">
      <j1 rule="hyper" parents="370 25756 28628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28630">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = (K(x,y) * (R(z,y,x) \ L(R(z,y,x),u,w))) * K(y,x)
    ]]></literal>
    <justification jstring="[para(25696(a,1),28629(a,2,1))].">
      <j1 rule="para" parents="25696 28629"/>
    </justification>
  </clause>

  <clause id="28631">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = K(x,y) * ((R(z,y,x) \ L(R(z,y,x),u,w)) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,23481,a(flip),b,28630,a),flip(a)].">
      <j1 rule="hyper" parents="370 23481 28630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28632">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = K(x,y) * (R(z,y,x) * L(R(z,y,x) \ K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(25739(a,1),28631(a,2,2))].">
      <j1 rule="para" parents="25739 28631"/>
    </justification>
  </clause>

  <clause id="28633">
    <literal><![CDATA[
      (x * y) \ (((z * y) * x) * L(((z * y) * x) \ (x * y),u,w)) = R(z,y,x) \ L(R(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,25764,a(flip),b,28632,a),flip(a)].">
      <j1 rule="hyper" parents="370 25764 28632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28635">
    <literal><![CDATA[
      (x * y) \ (x * ((z * y) * L((z * y) \ y,u,w))) = R(z,y,x) \ L(R(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(25761(a,1),28633(a,1,2))].">
      <j1 rule="para" parents="25761 28633"/>
    </justification>
  </clause>

  <clause id="28636">
    <literal><![CDATA[
      (x * y) \ (x * (z * (y * L(y \ (z \ y),u,w)))) = R(z,y,x) \ L(R(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(1598(a,1),28635(a,1,2,2))].">
      <j1 rule="para" parents="1598 28635"/>
    </justification>
  </clause>

  <clause id="28637">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(z,u,w)))) = R(z,y,x) \ L(R(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(25319(a,1),28636(a,1,2,2))].">
      <j1 rule="para" parents="25319 28636"/>
    </justification>
  </clause>

  <clause id="28638">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(629,a,28637,a),flip(a)].">
      <j1 rule="hyper" parents="629 28637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28639">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(28637(a,1),629(a,1))].">
      <j1 rule="para" parents="28637 629"/>
    </justification>
  </clause>

  <clause id="28640">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ L(z,u,w))) * y) = L(z \ L(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28059,a,b,28638,a)].">
      <j1 rule="hyper" parents="60 28059 28638"/>
    </justification>
  </clause>

  <clause id="28641">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * R(x,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(R(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(28638(a,1),3847(a,1,1))].">
      <j1 rule="para" parents="28638 3847"/>
    </justification>
  </clause>

  <clause id="28642">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(28638(a,1),9916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28638 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28643">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      L(R(x,u,w),y,z) \ R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(28638(a,1),9929(a,1,1))].">
      <j1 rule="para" parents="28638 9929"/>
    </justification>
  </clause>

  <clause id="28644">
    <literal><![CDATA[
      R(T(x \ L(x,y,z),u * w),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(25322,a,28640,a)].">
      <j1 rule="hyper" parents="25322 28640"/>
    </justification>
  </clause>

  <clause id="28645">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23790(a,1),28644(a,1,1))].">
      <j1 rule="para" parents="23790 28644"/>
    </justification>
  </clause>

  <clause id="28646">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x \ L(x,y,z),u,u) = a(x \ L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,28645,a(flip),b,16504,a)].">
      <j1 rule="hyper" parents="125 28645 16504"/>
    </justification>
  </clause>

  <clause id="28647">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w))) = L(R((x \ L(x,y,z)) \ 1,u,w),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(28645(a,1),4176(a,1,2,2,2))].">
      <j1 rule="para" parents="28645 4176"/>
    </justification>
  </clause>

  <clause id="28649">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ L(z,u,w))) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      L(z \ L(z,u,w),x,y) = v5
    ]]></literal>
    <justification jstring="[para(28059(a,2),28639(a,1))].">
      <j1 rule="para" parents="28059 28639"/>
    </justification>
  </clause>

  <clause id="28650">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u)) \ 1 = a(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14176,a,b,28646,a)].">
      <j1 rule="hyper" parents="60 14176 28646"/>
    </justification>
  </clause>

  <clause id="28651">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) \ 1 = a(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(3861(a,1),28650(a,1,1))].">
      <j1 rule="para" parents="3861 28650"/>
    </justification>
  </clause>

  <clause id="28652">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w)))) = L(R((x \ L(x,y,z)) \ 1,u,w),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3823(a,1),28647(a,1,2,2))].">
      <j1 rule="para" parents="3823 28647"/>
    </justification>
  </clause>

  <clause id="28653">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * (x \ L(L(x,y,z) \ x,u,w)))) = L(R((x \ L(x,y,z)) \ 1,u,w),x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2156(a,1),28652(a,1,2,2))].">
      <j1 rule="para" parents="2156 28652"/>
    </justification>
  </clause>

  <clause id="28654">
    <literal><![CDATA[
      L(R((x \ L(x,y,z)) \ 1,u,w),x,x * L(x,y,z)) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(337,a,28653,a),flip(a)].">
      <j1 rule="hyper" parents="337 28653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28656">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),x,x * L(x,y,z)) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(9916(a,1),28654(a,1,1,1))].">
      <j1 rule="para" parents="9916 28654"/>
    </justification>
  </clause>

  <clause id="28657">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,10261,a(flip),b,28656,a)].">
      <j1 rule="hyper" parents="60 10261 28656"/>
    </justification>
  </clause>

  <clause id="28658">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x * L(x,y,z),u) = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,25845,a(flip),b,28657,a),flip(a)].">
      <j1 rule="hyper" parents="60 25845 28657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28659">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ L(x,y,z),L(x * L(x,u,w),y,z),v5) = v5 \ ((L(x,y,z) \ L(L(x,y,z),u,w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(26358,a,28658,a)].">
      <j1 rule="hyper" parents="26358 28658"/>
    </justification>
  </clause>

  <clause id="28660">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,(((v5 \ v6) * v5) \ 1) \ ((w * u) \ ((z * u) * w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26882,a(flip),b,27367,a),flip(a)].">
      <j1 rule="hyper" parents="370 26882 27367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28661">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,(((v5 \ v6) * v5) \ 1) \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27368,a(flip),b,28660,a),flip(a)].">
      <j1 rule="hyper" parents="370 27368 28660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28662">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,((v5 \ v6) * v5) \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3082,a(flip),b,28661,a),flip(a)].">
      <j1 rule="hyper" parents="370 3082 28661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28663">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,((v5 \ v6) * v5) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,28608,a(flip),b,28662,a),flip(a)].">
      <j1 rule="hyper" parents="370 28608 28662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28664">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,(w * u) \ ((z * u) * w))) = a(x,y,v6 \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,26900,a(flip),b,28663,a),flip(a)].">
      <j1 rule="hyper" parents="370 26900 28663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28666">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L((v5 \ v6) * v5,v6,L(z,u,w))) = a(x,y,v6 \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(27282(a,1),28664(a,1,3,2))].">
      <j1 rule="para" parents="27282 28664"/>
    </justification>
  </clause>

  <clause id="28667">
    <literal><![CDATA[
      a(x,y,L(z,z,L(u,w,v5)) * R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,27060,a(flip),b,28666,a)].">
      <j1 rule="hyper" parents="60 27060 28666"/>
    </justification>
  </clause>

  <clause id="28668">
    <literal><![CDATA[
      a(x,y,R(z,u,w) / (T(v5,z) \ 1)) = a(x,y,v5 \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(27291(a,1),28667(a,1,3))].">
      <j1 rule="para" parents="27291 28667"/>
    </justification>
  </clause>

  <clause id="28669">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ 1) \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26970,a,28668,a)].">
      <j1 rule="hyper" parents="26970 28668"/>
    </justification>
  </clause>

  <clause id="28670">
    <literal><![CDATA[
      a(x,y,T(z,u) \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(3116,a,28669,a)].">
      <j1 rule="hyper" parents="3116 28669"/>
    </justification>
  </clause>

  <clause id="28671">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26979,a,28670,a)].">
      <j1 rule="hyper" parents="26979 28670"/>
    </justification>
  </clause>

  <clause id="28673">
    <literal><![CDATA[
      a(x,y,x \ R(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,14686,a(flip),b,28671,a),flip(a)].">
      <j1 rule="hyper" parents="370 14686 28671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28674">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3861,a(flip),b,28671,a),flip(a)].">
      <j1 rule="hyper" parents="370 3861 28671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28675">
    <literal><![CDATA[
      a(x,y,z \ L(u * (w \ 1),w,w)) = a(x,y,z \ L(w * u,w,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27309,a,b,28671,a)].">
      <j1 rule="hyper" parents="60 27309 28671"/>
    </justification>
  </clause>

  <clause id="28676">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,u * (z \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(673(a,1),28671(a,1,3)),flip(a)].">
      <j1 rule="para" parents="673 28671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28677">
    <literal><![CDATA[
      a(x,y,z \ R(L(u,z,z),w,v5)) = a(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2085(a,1),28671(a,2,3))].">
      <j1 rule="para" parents="2085 28671"/>
    </justification>
  </clause>

  <clause id="28678">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,28673,a)].">
      <j1 rule="hyper" parents="49 28673"/>
    </justification>
  </clause>

  <clause id="28679">
    <literal><![CDATA[
      x \ R(x,y \ x,y) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(25472,a,28678,a),flip(a)].">
      <j1 rule="hyper" parents="25472 28678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28680">
    <literal><![CDATA[
      (x * y) * (x \ R(x,z,u)) = x * (y * (x \ R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(129,a,28678,a(flip),b,14810,a(flip))].">
      <j1 rule="hyper" parents="129 28678 14810"/>
    </justification>
  </clause>

  <clause id="28681">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) != x \ w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(28678(a,2),44(a,1))].">
      <j1 rule="para" parents="28678 44"/>
    </justification>
  </clause>

  <clause id="28682">
    <literal><![CDATA[
      (x * y) * L(x \ R(x,z,u),w,v5) = x * (y * L(x \ R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(28678(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="28678 528"/>
    </justification>
  </clause>

  <clause id="28683">
    <literal><![CDATA[
      L(a(x,x,y),z,x) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[para(28417(a,1),28678(a,1,1))].">
      <j1 rule="para" parents="28417 28678"/>
    </justification>
  </clause>

  <clause id="28684">
    <literal><![CDATA[
      L(a(x,x,y),z,x) != x \ u
    ]]></literal>
    <literal><![CDATA[
      R(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(28683(a,2),44(a,1))].">
      <j1 rule="para" parents="28683 44"/>
    </justification>
  </clause>

  <clause id="28685">
    <literal><![CDATA[
      x * a(x,y \ x,y) = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(156,a,28679,a)].">
      <j1 rule="hyper" parents="156 28679"/>
    </justification>
  </clause>

  <clause id="28686">
    <literal><![CDATA[
      a(x,y \ x,y) * x = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,23634,a,b,28679,a)].">
      <j1 rule="hyper" parents="35 23634 28679"/>
    </justification>
  </clause>

  <clause id="28687">
    <literal><![CDATA[
      R(x,y \ (x \ 1),y) = x * a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,27497,a,b,28685,a)].">
      <j1 rule="hyper" parents="370 27497 28685"/>
    </justification>
  </clause>

  <clause id="28688">
    <literal><![CDATA[
      R(x,(x \ 1) / y,y) = x * a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(27478,a,28687,a)].">
      <j1 rule="hyper" parents="27478 28687"/>
    </justification>
  </clause>

  <clause id="28689">
    <literal><![CDATA[
      (1 / x) \ a(x,y \ x,y) = R(x,(x \ 1) / y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,19685,a,b,28688,a)].">
      <j1 rule="hyper" parents="370 19685 28688"/>
    </justification>
  </clause>

  <clause id="28690">
    <literal><![CDATA[
      a(x,y \ x,y) / (x \ 1) = R(x,(x \ 1) / y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28219,a,b,28689,a)].">
      <j1 rule="hyper" parents="60 28219 28689"/>
    </justification>
  </clause>

  <clause id="28691">
    <literal><![CDATA[
      (x * ((x \ 1) / y)) * y = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,105,a,b,28690,a)].">
      <j1 rule="hyper" parents="34 105 28690"/>
    </justification>
  </clause>

  <clause id="28692">
    <literal><![CDATA[
      a(((x * ((x \ 1) / y)) * (y \ 1)) * z,u,w) = a(a(x,y \ x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(28691(a,1),26630(a,2,1,1))].">
      <j1 rule="para" parents="28691 26630"/>
    </justification>
  </clause>

  <clause id="28693">
    <literal><![CDATA[
      R(x,y,x \ R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(27499,a,28680,a)].">
      <j1 rule="hyper" parents="27499 28680"/>
    </justification>
  </clause>

  <clause id="28694">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ R(R(x,u,x \ R(x,y,z)),y,z)) = a(x \ R(x,y,z),u,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(28693(a,1),27937(a,1,2,1))].">
      <j1 rule="para" parents="28693 27937"/>
    </justification>
  </clause>

  <clause id="28695">
    <literal><![CDATA[
      a(x,y,z \ L(R(u,w,v5),z,z)) = a(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(24(a,1),28677(a,1,3,2))].">
      <j1 rule="para" parents="24 28677"/>
    </justification>
  </clause>

  <clause id="28696">
    <literal><![CDATA[
      a(x,y,(z \ 1) * R(u,w,v5)) = a(x,y,(z \ 1) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2072(a,1),28695(a,1,3))].">
      <j1 rule="para" parents="2072 28695"/>
    </justification>
  </clause>

  <clause id="28697">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(u,w,v5)) = a(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(27068,a,28696,a),flip(a)].">
      <j1 rule="hyper" parents="27068 28696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28698">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) = a(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(27068,a,28697,a),flip(a)].">
      <j1 rule="hyper" parents="27068 28697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28699">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(28697(a,1),27068(a,1))].">
      <j1 rule="para" parents="28697 27068"/>
    </justification>
  </clause>

  <clause id="28700">
    <literal><![CDATA[
      a(x,y,(z * u) * R(L(w,u,z),v5,v6)) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(528(a,1),28698(a,2,3))].">
      <j1 rule="para" parents="528 28698"/>
    </justification>
  </clause>

  <clause id="28701">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,v5,v6))) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(529(a,1),28700(a,1,3))].">
      <j1 rule="para" parents="529 28700"/>
    </justification>
  </clause>

  <clause id="28702">
    <literal><![CDATA[
      a(x,y,L(z,R(u,w,v5),v6) * (v6 * L(u,w,v5))) = a(x,y,v6 * (R(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(26967,a,28701,a),flip(a)].">
      <j1 rule="hyper" parents="26967 28701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28703">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),(u * w) * z,(u * w) * z)) = a(x,y,((u * w) * z) * ((u * w) * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(16506,a,28701,a)].">
      <j1 rule="hyper" parents="16506 28701"/>
    </justification>
  </clause>

  <clause id="28704">
    <literal><![CDATA[
      a(x,y,R(z,z,u * R(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,(1 / z) \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(1961(a,1),28701(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1961 28701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28705">
    <literal><![CDATA[
      a(x,y,z * ((R(u,w,v5) \ ((R(u,w,v5) \ 1) \ v6)) * L(u,w,v5))) = a(x,y,z * ((R(u,w,v5) \ 1) \ T(v6,R(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(2874(a,1),28701(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2874 28701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28706">
    <literal><![CDATA[
      a(x,y,R(z,R(u,w,v5),v6) * (v6 * L(u,w,v5))) = a(x,y,(z * R(u,w,v5)) * T(v6,R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(12402(a,1),28701(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12402 28701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28707">
    <literal><![CDATA[
      R(x,y,L(x \ R(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(27499,a,28682,a)].">
      <j1 rule="hyper" parents="27499 28682"/>
    </justification>
  </clause>

  <clause id="28708">
    <literal><![CDATA[
      R(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(16534(a,2),28707(a,1,3))].">
      <j1 rule="para" parents="16534 28707"/>
    </justification>
  </clause>

  <clause id="28709">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(28340,a,28708,a)].">
      <j1 rule="hyper" parents="28340 28708"/>
    </justification>
  </clause>

  <clause id="28710">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[para(28708(a,1),103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28708 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28711">
    <literal><![CDATA[
      x \ (y * a(x,z,u)) = (x \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(28708(a,1),675(a,1,1))].">
      <j1 rule="para" parents="28708 675"/>
    </justification>
  </clause>

  <clause id="28712">
    <literal><![CDATA[
      x * (y * a(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) * a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(28708(a,1),327(a,1,1))].">
      <j1 rule="para" parents="28708 327"/>
    </justification>
  </clause>

  <clause id="28713">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,w,v5) = L(x,y,z) * (u * a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(28708(a,1),688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28708 688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28715">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(28708(a,1),1026(a,1,1))].">
      <j1 rule="para" parents="28708 1026"/>
    </justification>
  </clause>

  <clause id="28716">
    <literal><![CDATA[
      x * a(y,y,y \ x) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(28708(a,1),3335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28708 3335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28717">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = z * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28708(a,1),27614(a,1,1))].">
      <j1 rule="para" parents="28708 27614"/>
    </justification>
  </clause>

  <clause id="28718">
    <literal><![CDATA[
      L(x,y,a(L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(166,a,28709,a)].">
      <j1 rule="hyper" parents="166 28709"/>
    </justification>
  </clause>

  <clause id="28719">
    <literal><![CDATA[
      (x * a(y,z,u)) * y = (x * y) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,28709,a(flip),b,25786,a)].">
      <j1 rule="hyper" parents="129 28709 25786"/>
    </justification>
  </clause>

  <clause id="28720">
    <literal><![CDATA[
      L(L(x,y,z),u,a(x,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28709(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28709 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28721">
    <literal><![CDATA[
      a(x,y,z) * (1 / x) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(28709(a,1),497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28709 497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28722">
    <literal><![CDATA[
      a(x,y,z) \ (u * x) = (a(x,y,z) \ u) * x
    ]]></literal>
    <justification jstring="[para(28709(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="28709 617"/>
    </justification>
  </clause>

  <clause id="28723">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != L(z,v5,v6)
    ]]></literal>
    <literal><![CDATA[
      L(z,v5,v6) = x
    ]]></literal>
    <justification jstring="[para(28709(a,1),166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28709 166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28724">
    <literal><![CDATA[
      (x * a(y,z,u)) * y = a(y,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(28709(a,1),23651(a,1,2))].">
      <j1 rule="para" parents="28709 23651"/>
    </justification>
  </clause>

  <clause id="28725">
    <literal><![CDATA[
      L(L(1 / x,y,z),u,a(x,w,v5)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2957(a,1),28720(a,1,3))].">
      <j1 rule="para" parents="2957 28720"/>
    </justification>
  </clause>

  <clause id="28726">
    <literal><![CDATA[
      (1 / x) * a(x,y,z) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(23637,a,28721,a)].">
      <j1 rule="hyper" parents="23637 28721"/>
    </justification>
  </clause>

  <clause id="28727">
    <literal><![CDATA[
      a(x,x,y) \ (y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(125,a,28422,a(flip),b,28721,a)].">
      <j1 rule="hyper" parents="125 28422 28721"/>
    </justification>
  </clause>

  <clause id="28728">
    <literal><![CDATA[
      (((1 / x) \ 1) \ 1) \ (y / (x * y)) = (y / (x * y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(28727(a,1),28486(a,1,1,1,1))].">
      <j1 rule="para" parents="28727 28486"/>
    </justification>
  </clause>

  <clause id="28729">
    <literal><![CDATA[
      (x \ 1) * (x \ (a(x,y,z) * u)) = (x \ (a(x,y,z) / x)) * u
    ]]></literal>
    <justification jstring="[para(28726(a,1),2109(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28726 2109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28730">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(778,a,28715,a),flip(a)].">
      <j1 rule="hyper" parents="778 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28731">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(776,a,28715,a)].">
      <j1 rule="hyper" parents="776 28715"/>
    </justification>
  </clause>

  <clause id="28732">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(719,a,28715,a),flip(a)].">
      <j1 rule="hyper" parents="719 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28733">
    <literal><![CDATA[
      (x * L(y,x,z)) * a(z,x,L(y,x,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(630,a,28715,a),flip(a)].">
      <j1 rule="hyper" parents="630 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28734">
    <literal><![CDATA[
      (x * y) * a(x,x,y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(597,a,28715,a),flip(a)].">
      <j1 rule="hyper" parents="597 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28735">
    <literal><![CDATA[
      x * ((y * z) * a(x,y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(156,a,28715,a)].">
      <j1 rule="hyper" parents="156 28715"/>
    </justification>
  </clause>

  <clause id="28736">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,28715,a,b,28301,a)].">
      <j1 rule="hyper" parents="128 28715 28301"/>
    </justification>
  </clause>

  <clause id="28737">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (z \ ((z * x) * y)) = y * a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28715,a,b,28343,a)].">
      <j1 rule="hyper" parents="125 28715 28343"/>
    </justification>
  </clause>

  <clause id="28738">
    <literal><![CDATA[
      (x * y) \ (z \ ((z * y) * x)) = K(y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,28715,a,b,12078,a)].">
      <j1 rule="hyper" parents="125 28715 12078"/>
    </justification>
  </clause>

  <clause id="28739">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x \ y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),28715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28745">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = ((x \ 1) * u) * a(L(x,y,z),x \ 1,u)
    ]]></literal>
    <justification jstring="[para(1771(a,1),28715(a,1,2,1))].">
      <j1 rule="para" parents="1771 28715"/>
    </justification>
  </clause>

  <clause id="28746">
    <literal><![CDATA[
      (L(x,x,y) * z) * a(y,L(x,x,y),z) = y \ ((y / (x \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(2480(a,1),28715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2480 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28747">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(L(x,y,z) \ x,L(x,y,z),u) = (L(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(3932(a,1),28715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3932 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28748">
    <literal><![CDATA[
      (x * L(y,z,x)) * a(z,x,L(y,z,x)) = z \ (x * (T(z,x) * y))
    ]]></literal>
    <justification jstring="[para(12481(a,1),28715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12481 28715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28749">
    <literal><![CDATA[
      ((x * y) * z) \ ((u \ ((u * x) * y)) * z) = R(a(u,x,y),x * y,z)
    ]]></literal>
    <justification jstring="[para(28715(a,2),25826(a,1,2,1))].">
      <j1 rule="para" parents="28715 25826"/>
    </justification>
  </clause>

  <clause id="28750">
    <literal><![CDATA[
      ((x \ 1) * y) * a(x,x,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(129,a,28731,a(flip),b,2113,a)].">
      <j1 rule="hyper" parents="129 28731 2113"/>
    </justification>
  </clause>

  <clause id="28751">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ ((1 / (1 / ((x * y) / x))) \ (x * y))
    ]]></literal>
    <justification jstring="[para(12651(a,1),28731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12651 28731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28753">
    <literal><![CDATA[
      x * a(y,y,x * y) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(26930(a,1),28716(a,1,2))].">
      <j1 rule="para" parents="26930 28716"/>
    </justification>
  </clause>

  <clause id="28754">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ (y * z)) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),28732(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 28732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28757">
    <literal><![CDATA[
      a(x,y,z) * ((u * w) * a(a(x,y,z),u,w)) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(370,a,23642,a(flip),b,28735,a),flip(a)].">
      <j1 rule="hyper" parents="370 23642 28735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28758">
    <literal><![CDATA[
      a(x,y * ((z * u) * a(y \ 1,z,u)),w) = a(x,((y \ 1) * z) * u,w)
    ]]></literal>
    <justification jstring="[para(28735(a,1),3061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28735 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28759">
    <literal><![CDATA[
      x * ((y * ((z \ u) \ u)) * a(x,y,z)) = (x * y) * ((z \ u) \ u)
    ]]></literal>
    <justification jstring="[para(26883(a,1),28735(a,1,2,2))].">
      <j1 rule="para" parents="26883 28735"/>
    </justification>
  </clause>

  <clause id="28760">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,28736,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 28736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28761">
    <literal><![CDATA[
      a(x,y,z) = y \ ((x \ ((x * y) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,28736,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="125 28736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28762">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = a(z,u,w) * (y * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,28736,a(flip),b,23572,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 28736 23572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28763">
    <literal><![CDATA[
      x * a(R(K(y,z) * u,w,v5),R(K(y,z) * u,w,v5),x * R(K(y,z) * u,w,v5)) = R(u,w,v5) \ (K(z,y) * ((R(K(y,z) * u,w,v5) \ 1) \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,25682,a(flip),b,28753,a),flip(a)].">
      <j1 rule="hyper" parents="370 25682 28753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28765">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) * u,w,a(x,y,z)) = ((a(x,y,z) * u) * w) / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28760(a,1),28325(a,1,1))].">
      <j1 rule="para" parents="28760 28325"/>
    </justification>
  </clause>

  <clause id="28768">
    <literal><![CDATA[
      a((x \ 1) \ ((y \ ((y * x) * z)) / z),u,w) = a(a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(28761(a,2),2959(a,2,1))].">
      <j1 rule="para" parents="28761 2959"/>
    </justification>
  </clause>

  <clause id="28769">
    <literal><![CDATA[
      L(x,y,z \ ((u \ ((u * (z \ 1)) * w)) / w)) = L(x,y,a(u,z \ 1,w))
    ]]></literal>
    <justification jstring="[para(28761(a,2),3371(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28761 3371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28770">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((x \ ((L(1 / x,y,z) \ 1) * u)) / u) = a(x,L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(3864(a,2),28761(a,2,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3864 28761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28771">
    <literal><![CDATA[
      x \ (((y * z) \ ((y * z) * R(x,y,z))) / a(x,y,z)) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16503(a,1),28761(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16503 28761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28772">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26234,a,28710,a)].">
      <j1 rule="hyper" parents="26234 28710"/>
    </justification>
  </clause>

  <clause id="28773">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23794,a,28710,a)].">
      <j1 rule="hyper" parents="23794 28710"/>
    </justification>
  </clause>

  <clause id="28774">
    <literal><![CDATA[
      x * ((x \ y) * a(x,z,u)) = y * a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(755,a,28710,a),flip(a)].">
      <j1 rule="hyper" parents="755 28710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28775">
    <literal><![CDATA[
      x * (y * a(x,x,y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,28734,a(flip),b,28710,a),flip(a)].">
      <j1 rule="hyper" parents="60 28734 28710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28776">
    <literal><![CDATA[
      a(x,y,a(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,28710,a(flip),b,19675,a),flip(a)].">
      <j1 rule="hyper" parents="126 28710 19675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28777">
    <literal><![CDATA[
      x \ ((1 / x) \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28734,a(flip),b,28710,a(flip))].">
      <j1 rule="hyper" parents="125 28734 28710"/>
    </justification>
  </clause>

  <clause id="28778">
    <literal><![CDATA[
      (a(x,y,z) * x) \ (x * (u * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28710(a,1),24122(a,1,2))].">
      <j1 rule="para" parents="28710 24122"/>
    </justification>
  </clause>

  <clause id="28779">
    <literal><![CDATA[
      (x * (y * a(x,z,u))) * u = ((x * y) * u) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(28710(a,1),28301(a,1,1))].">
      <j1 rule="para" parents="28710 28301"/>
    </justification>
  </clause>

  <clause id="28780">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,25781,a(flip),b,28772,a),flip(a)].">
      <j1 rule="hyper" parents="370 25781 28772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28782">
    <literal><![CDATA[
      L(x,y,z) != a(z,u,w)
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(28772(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="28772 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28783">
    <literal><![CDATA[
      (x * y) / a(x,z,u) = x * (y / a(x,z,u))
    ]]></literal>
    <justification jstring="[para(28772(a,1),727(a,1,2))].">
      <j1 rule="para" parents="28772 727"/>
    </justification>
  </clause>

  <clause id="28784">
    <literal><![CDATA[
      (x * y) * a(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * a(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(28772(a,1),336(a,1,2))].">
      <j1 rule="para" parents="28772 336"/>
    </justification>
  </clause>

  <clause id="28785">
    <literal><![CDATA[
      ((x \ 1) * y) * a(x,z,u) = (x \ 1) * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[para(28772(a,1),1502(a,1,2))].">
      <j1 rule="para" parents="28772 1502"/>
    </justification>
  </clause>

  <clause id="28786">
    <literal><![CDATA[
      (x * y) * L(a(x,z,u),w,v5) = x * (y * L(a(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(28772(a,1),528(a,1,2,1))].">
      <j1 rule="para" parents="28772 528"/>
    </justification>
  </clause>

  <clause id="28788">
    <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(28772(a,1),13469(a,1,2,2))].">
      <j1 rule="para" parents="28772 13469"/>
    </justification>
  </clause>

  <clause id="28789">
    <literal><![CDATA[
      L(K(x,y) * a(z,u,w),v5,z) = K(x,y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(28772(a,1),25728(a,2,2))].">
      <j1 rule="para" parents="28772 25728"/>
    </justification>
  </clause>

  <clause id="28790">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(589,a,28775,a(flip))].">
      <j1 rule="hyper" parents="589 28775"/>
    </justification>
  </clause>

  <clause id="28791">
    <literal><![CDATA[
      L(a(x,x,y) * y,x,x) = y
    ]]></literal>
    <justification jstring="[hyper(25255,a,28790,a)].">
      <j1 rule="hyper" parents="25255 28790"/>
    </justification>
  </clause>

  <clause id="28792">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,28790,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 28790 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28793">
    <literal><![CDATA[
      a(x,x,(x \ 1) * y) * ((x \ 1) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2124,a,28791,a),flip(a)].">
      <j1 rule="hyper" parents="2124 28791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28794">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) / y = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,28777,a,b,23620,a)].">
      <j1 rule="hyper" parents="128 28777 23620"/>
    </justification>
  </clause>

  <clause id="28795">
    <literal><![CDATA[
      ((x * y) * (z * a(y,y,z))) / ((1 / y) \ z) = R(x,y,y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(28777(a,1),102(a,1,1,2))].">
      <j1 rule="para" parents="28777 102"/>
    </justification>
  </clause>

  <clause id="28796">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ y = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(28777(a,2),14796(a,1,1))].">
      <j1 rule="para" parents="28777 14796"/>
    </justification>
  </clause>

  <clause id="28797">
    <literal><![CDATA[
      L(x,y,z * (u * (T(w,v5) * a(v6,v6,w)))) = L(x,y,z * (u * (v6 \ ((1 / v6) \ w))))
    ]]></literal>
    <justification jstring="[para(28777(a,2),27927(a,2,3,2,2))].">
      <j1 rule="para" parents="28777 27927"/>
    </justification>
  </clause>

  <clause id="28798">
    <literal><![CDATA[
      x \ (a(x,y,z) * u) = (x \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24100,a,28711,a)].">
      <j1 rule="hyper" parents="24100 28711"/>
    </justification>
  </clause>

  <clause id="28800">
    <literal><![CDATA[
      (x * (a(y,z,u) * y)) \ ((x * y) * a(y,z,u)) = a(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28719,a(flip),b,82,a)].">
      <j1 rule="hyper" parents="125 28719 82"/>
    </justification>
  </clause>

  <clause id="28804">
    <literal><![CDATA[
      L(x,y,z) * (x \ (y * z)) = (a(z,y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(26721,a,28722,a)].">
      <j1 rule="hyper" parents="26721 28722"/>
    </justification>
  </clause>

  <clause id="28805">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * x) * z = x * ((x \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[para(28722(a,1),26420(a,1,1))].">
      <j1 rule="para" parents="28722 26420"/>
    </justification>
  </clause>

  <clause id="28806">
    <literal><![CDATA[
      (x * a(y,z,u)) * y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) * a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(28724(a,2),23637(a,1))].">
      <j1 rule="para" parents="28724 23637"/>
    </justification>
  </clause>

  <clause id="28807">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = x * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,16518,a,b,28773,a)].">
      <j1 rule="hyper" parents="60 16518 28773"/>
    </justification>
  </clause>

  <clause id="28808">
    <literal><![CDATA[
      (x * (y * a(x,z,u))) \ ((a(x,z,u) * x) * y) = a(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(28773(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28773 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28809">
    <literal><![CDATA[
      L(x,y,z) * (u * (w * a(u,v5,x))) = a(u,v5,x) * (L(x,y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(28773(a,1),28363(a,1,2))].">
      <j1 rule="para" parents="28773 28363"/>
    </justification>
  </clause>

  <clause id="28810">
    <literal><![CDATA[
      (x * (y * a(x,x,y))) \ (x * y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(28773(a,1),28389(a,1,1))].">
      <j1 rule="para" parents="28773 28389"/>
    </justification>
  </clause>

  <clause id="28811">
    <literal><![CDATA[
      a(x,(y \ 1) * ((y \ z) * a(y,u,w)),v5) = a(x,z * a(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(28774(a,1),3061(a,2,2))].">
      <j1 rule="para" parents="28774 3061"/>
    </justification>
  </clause>

  <clause id="28812">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23639,a,28783,a)].">
      <j1 rule="hyper" parents="23639 28783"/>
    </justification>
  </clause>

  <clause id="28813">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),28812(a,2,2))].">
      <j1 rule="para" parents="23572 28812"/>
    </justification>
  </clause>

  <clause id="28814">
    <literal><![CDATA[
      (x * (y * z)) / z = x * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(25779,a,28813,a)].">
      <j1 rule="hyper" parents="25779 28813"/>
    </justification>
  </clause>

  <clause id="28815">
    <literal><![CDATA[
      a(x,y,y) \ y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(25776,a,28813,a),flip(a)].">
      <j1 rule="hyper" parents="25776 28813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28816">
    <literal><![CDATA[
      (x / y) * (a(x / y,z,u) \ y) = a(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(7(a,1),28813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 28813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28817">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) != x * w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(28813(a,2),40(a,1))].">
      <j1 rule="para" parents="28813 40"/>
    </justification>
  </clause>

  <clause id="28818">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(28813(a,1),25780(a,1,1))].">
      <j1 rule="para" parents="28813 25780"/>
    </justification>
  </clause>

  <clause id="28819">
    <literal><![CDATA[
      L(x,x,y) \ x = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3939,a,b,28815,a)].">
      <j1 rule="hyper" parents="36 3939 28815"/>
    </justification>
  </clause>

  <clause id="28820">
    <literal><![CDATA[
      a(x,y,y) \ 1 = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,28815,a(flip),b,25393,a),flip(a)].">
      <j1 rule="hyper" parents="125 28815 25393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28821">
    <literal><![CDATA[
      L(x,x,L(y,z,x)) = a(y,x,x) \ x
    ]]></literal>
    <justification jstring="[para(16548(a,1),28815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16548 28815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28822">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,9933,a(flip),b,28819,a)].">
      <j1 rule="hyper" parents="60 9933 28819"/>
    </justification>
  </clause>

  <clause id="28823">
    <literal><![CDATA[
      ((x * y) \ x) \ (y \ 1) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4084,a(flip),b,28819,a)].">
      <j1 rule="hyper" parents="60 4084 28819"/>
    </justification>
  </clause>

  <clause id="28824">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = x * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,28819,a(flip),b,3865,a),flip(a)].">
      <j1 rule="hyper" parents="129 28819 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28825">
    <literal><![CDATA[
      a(x,y,y) / y = 1 / L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,28819,a(flip),b,3954,a)].">
      <j1 rule="hyper" parents="128 28819 3954"/>
    </justification>
  </clause>

  <clause id="28826">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(28819(a,1),3892(a,2,2))].">
      <j1 rule="para" parents="28819 3892"/>
    </justification>
  </clause>

  <clause id="28828">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ L(w,w,v5)))) = a(x,y,(u \ a(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[para(28820(a,1),27084(a,1,3,2,2))].">
      <j1 rule="para" parents="28820 27084"/>
    </justification>
  </clause>

  <clause id="28829">
    <literal><![CDATA[
      L(x,x,L(y,z,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28815,a(flip),b,28821,a),flip(a)].">
      <j1 rule="hyper" parents="370 28815 28821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28832">
    <literal><![CDATA[
      x * ((y * x) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,23619,a,b,28822,a),flip(a)].">
      <j1 rule="hyper" parents="36 23619 28822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28833">
    <literal><![CDATA[
      (x * (y \ x)) / (y * ((y \ x) * (y \ x))) = ((y * (y \ x)) \ y) \ ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,19667,a,b,28823,a)].">
      <j1 rule="hyper" parents="370 19667 28823"/>
    </justification>
  </clause>

  <clause id="28834">
    <literal><![CDATA[
      (((x * y) * (1 / y)) \ (x * (1 / y))) \ (((y \ 1) \ 1) \ 1) = a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1520(a,1),28823(a,1,1,1))].">
      <j1 rule="para" parents="1520 28823"/>
    </justification>
  </clause>

  <clause id="28835">
    <literal><![CDATA[
      x \ ((y \ (y / x)) \ 1) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(719,a,28826,a)].">
      <j1 rule="hyper" parents="719 28826"/>
    </justification>
  </clause>

  <clause id="28836">
    <literal><![CDATA[
      (x \ ((x * y) * y)) / y = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,28736,a,b,28826,a)].">
      <j1 rule="hyper" parents="370 28736 28826"/>
    </justification>
  </clause>

  <clause id="28837">
    <literal><![CDATA[
      L(((x \ (x / y)) \ 1) \ z,y * a(x,y,y),x \ (x / y)) = 1 \ ((x \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[para(28826(a,1),656(a,1,2))].">
      <j1 rule="para" parents="28826 656"/>
    </justification>
  </clause>

  <clause id="28839">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(12093,a,28832,a)].">
      <j1 rule="hyper" parents="12093 28832"/>
    </justification>
  </clause>

  <clause id="28840">
    <literal><![CDATA[
      a(x,x \ y,x \ y) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),28832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 28832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28841">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ (y * (((x * y) \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,(x * y) \ x,y) = u
    ]]></literal>
    <justification jstring="[para(28832(a,1),629(a,1,1))].">
      <j1 rule="para" parents="28832 629"/>
    </justification>
  </clause>

  <clause id="28842">
    <literal><![CDATA[
      a(x,y * (((z * u) \ z) * u),w) = a(x,y * (a(z,u,u) \ 1),w)
    ]]></literal>
    <justification jstring="[para(28832(a,1),26495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28832 26495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28843">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ u) * w)) = a(x,y,(a(u,w,w) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(28832(a,1),27031(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="28832 27031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28844">
    <literal><![CDATA[
      L(a(x,y,y),y,((x \ (x / y)) \ 1) \ z) = ((z / ((x \ (x / y)) \ 1)) * y) \ z
    ]]></literal>
    <justification jstring="[para(28835(a,1),24911(a,1,1))].">
      <j1 rule="para" parents="28835 24911"/>
    </justification>
  </clause>

  <clause id="28845">
    <literal><![CDATA[
      a((x \ (y \ (y / x))) * z,u,w) = a(a(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(28835(a,1),26631(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28835 26631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28846">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = a(y,x,x) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,28824,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 28824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28847">
    <literal><![CDATA[
      x * a(y,y \ x,y \ x) = y * (L(1 / (y \ x),y \ x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,28824,a,b,28711,a),flip(a)].">
      <j1 rule="hyper" parents="129 28824 28711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28848">
    <literal><![CDATA[
      (x * (a(x,y,L(z,z,y)) \ y)) * L(z,z,y) = x * (y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2480(a,1),28818(a,2,2))].">
      <j1 rule="para" parents="2480 28818"/>
    </justification>
  </clause>

  <clause id="28849">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (x * (y * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(28818(a,1),25786(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28818 25786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28850">
    <literal><![CDATA[
      K(x,(a(y,z,x) \ z) * y) * ((x * y) \ (y * (z * x))) = L(a(y,z,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(28818(a,1),25993(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="28818 25993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28851">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,(u * y) \ (y * (z * u)),w)
    ]]></literal>
    <justification jstring="[para(28818(a,1),26037(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28818 26037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28852">
    <literal><![CDATA[
      ((x * (y / z)) * (a(x * (z \ y),u,w) \ u)) * w = (x * (y / z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(26438(a,1),28818(a,1,1,2,1))].">
      <j1 rule="para" parents="26438 28818"/>
    </justification>
  </clause>

  <clause id="28853">
    <literal><![CDATA[
      (x * (a(x,y,z \ u) \ y)) * (u / z) = x * (y * (u / z))
    ]]></literal>
    <justification jstring="[para(26882(a,1),28818(a,1,1,2,1))].">
      <j1 rule="para" parents="26882 28818"/>
    </justification>
  </clause>

  <clause id="28854">
    <literal><![CDATA[
      (x * (a(x,y,z * u) \ y)) * (u * z) = x * (y * (u * z))
    ]]></literal>
    <justification jstring="[para(26888(a,1),28818(a,1,1,2,1))].">
      <j1 rule="para" parents="26888 28818"/>
    </justification>
  </clause>

  <clause id="28855">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * T(y,x) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,12691,a,b,28839,a)].">
      <j1 rule="hyper" parents="60 12691 28839"/>
    </justification>
  </clause>

  <clause id="28856">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) * y = x \ ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(155,a,28836,a)].">
      <j1 rule="hyper" parents="155 28836"/>
    </justification>
  </clause>

  <clause id="28857">
    <literal><![CDATA[
      L(x \ (((y \ (y / x)) \ 1) \ z),x,y \ (y / x)) = (y \ ((y * x) * x)) \ z
    ]]></literal>
    <justification jstring="[para(28856(a,1),1501(a,2,1))].">
      <j1 rule="para" parents="28856 1501"/>
    </justification>
  </clause>

  <clause id="28858">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(x \ ((x * y) * T(z,y)),x) = (z * (y * a(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(28717(a,1),353(a,2,1))].">
      <j1 rule="para" parents="28717 353"/>
    </justification>
  </clause>

  <clause id="28859">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(23998,a,28730,a)].">
      <j1 rule="hyper" parents="23998 28730"/>
    </justification>
  </clause>

  <clause id="28860">
    <literal><![CDATA[
      (x * a(y,x,L(z,x,y))) \ (x * z) = L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,28733,a(flip),b,28301,a)].">
      <j1 rule="hyper" parents="125 28733 28301"/>
    </justification>
  </clause>

  <clause id="28862">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) / (a(x,x \ y,x \ y) \ 1) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,527,a,b,28739,a)].">
      <j1 rule="hyper" parents="60 527 28739"/>
    </justification>
  </clause>

  <clause id="28863">
    <literal><![CDATA[
      (L(x,x,y) * z) * a(R(y,x,x),R(y,x,x) \ (y * x),z) = R(y,x,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(3730(a,1),28739(a,1,1,1))].">
      <j1 rule="para" parents="3730 28739"/>
    </justification>
  </clause>

  <clause id="28864">
    <literal><![CDATA[
      T(x,y * (z \ (u * w))) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(28739(a,1),28146(a,1,2,2))].">
      <j1 rule="para" parents="28739 28146"/>
    </justification>
  </clause>

  <clause id="28865">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) \ (u \ (w * z))) = a(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(28754(a,1),26899(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28754 26899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28866">
    <literal><![CDATA[
      (1 / T(x,y)) \ L(1 / T(x,y),x,y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,12513,a,b,28855,a)].">
      <j1 rule="hyper" parents="60 12513 28855"/>
    </justification>
  </clause>

  <clause id="28867">
    <literal><![CDATA[
      (a(x,y,L(z,y,x)) * y) \ (y * z) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(23816,a,28860,a)].">
      <j1 rule="hyper" parents="23816 28860"/>
    </justification>
  </clause>

  <clause id="28868">
    <literal><![CDATA[
      T(a(x,y,L(z,y,x)) * y,z) = L(z,y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(28867(a,1),28337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28867 28337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28869">
    <literal><![CDATA[
      L(L(1 / x,1 / x,L(y,z,1 / x)),u,a(x,w,v5)) = L(1 / x,1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28829,a(flip),b,28725,a),flip(a)].">
      <j1 rule="hyper" parents="370 28829 28725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28870">
    <literal><![CDATA[
      L(a(x,y,z),u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(28780(a,2),25782(a,1))].">
      <j1 rule="para" parents="28780 25782"/>
    </justification>
  </clause>

  <clause id="28871">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(28775(a,1),28810(a,1,1))].">
      <j1 rule="para" parents="28775 28810"/>
    </justification>
  </clause>

  <clause id="28872">
    <literal><![CDATA[
      (x \ y) \ ((x \ 1) * y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,2142,a(flip),b,28871,a)].">
      <j1 rule="hyper" parents="60 2142 28871"/>
    </justification>
  </clause>

  <clause id="28873">
    <literal><![CDATA[
      L(K(x,y) * a(z,x,y),y * x,z) = (z * (y * x)) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(28738(a,1),344(a,1,1))].">
      <j1 rule="para" parents="28738 344"/>
    </justification>
  </clause>

  <clause id="28875">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * x) != v6
    ]]></literal>
    <literal><![CDATA[
      x * (a(u,w,v5) * a(x,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(24142(a,2),28784(a,1))].">
      <j1 rule="para" parents="24142 28784"/>
    </justification>
  </clause>

  <clause id="28876">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * x) * z = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),28805(a,2,2,1))].">
      <j1 rule="para" parents="17 28805"/>
    </justification>
  </clause>

  <clause id="28877">
    <literal><![CDATA[
      a((((a(x,y,z * u) \ y) * x) * (u * z)) \ w,v5,v6) = a((x * (T(y,x) * (z * u))) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(28876(a,1),26799(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28876 26799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28878">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) * z != w
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * a(z,u,x) = w
    ]]></literal>
    <justification jstring="[para(14786(a,1),28806(a,1,1))].">
      <j1 rule="para" parents="14786 28806"/>
    </justification>
  </clause>

  <clause id="28879">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * y = z * (L(z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(25564,a,28868,a),flip(a)].">
      <j1 rule="hyper" parents="25564 28868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28880">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = y \ (z * (L(z,y,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(125,a,28879,a(flip),b,23620,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="125 28879 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28882">
    <literal><![CDATA[
      ((x * a(y,z,u)) * u) \ (y \ (((y * x) * u) * a(y,z,u))) = a(y,x * a(y,z,u),u)
    ]]></literal>
    <justification jstring="[para(28779(a,1),28732(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="28779 28732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28883">
    <literal><![CDATA[
      (x \ 1) * (T(y,x \ 1) * a(x,z,u)) = (y * (x \ 1)) * a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(756,a,28785,a),flip(a)].">
      <j1 rule="hyper" parents="756 28785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28884">
    <literal><![CDATA[
      ((x \ 1) * a(x,y,z)) * z = (x \ 1) * (z * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,28301,a,b,28785,a)].">
      <j1 rule="hyper" parents="60 28301 28785"/>
    </justification>
  </clause>

  <clause id="28885">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) * a(x,z,u) = x * ((x \ 1) * (y * a(x,z,u)))
    ]]></literal>
    <justification jstring="[para(28785(a,1),28710(a,2,2))].">
      <j1 rule="para" parents="28785 28710"/>
    </justification>
  </clause>

  <clause id="28886">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (R(y,z,z) * x) = y * (x * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,28344,a,b,28807,a)].">
      <j1 rule="hyper" parents="60 28344 28807"/>
    </justification>
  </clause>

  <clause id="28887">
    <literal><![CDATA[
      (x / y) * (a(x / y,z,u) \ y) = a(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(26376(a,1),28816(a,2,1))].">
      <j1 rule="para" parents="26376 28816"/>
    </justification>
  </clause>

  <clause id="28888">
    <literal><![CDATA[
      (1 / T(x,y)) \ (y \ (T(y,x) / x)) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(12488(a,1),28866(a,1,2))].">
      <j1 rule="para" parents="12488 28866"/>
    </justification>
  </clause>

  <clause id="28889">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (T(x,y) / y)) = T(y,x) \ (a(x,y,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,28888,a(flip),b,28775,a),flip(a)].">
      <j1 rule="hyper" parents="125 28888 28775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28891">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,z,y)) = (x \ a(x,z,y)) * y
    ]]></literal>
    <justification jstring="[para(19684(a,1),28884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19684 28884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28892">
    <literal><![CDATA[
      (a(x \ y,x,z) \ y) * z = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(28887(a,1),28818(a,1,1))].">
      <j1 rule="para" parents="28887 28818"/>
    </justification>
  </clause>

  <clause id="28893">
    <literal><![CDATA[
      (a(x \ (y \ x),x * y,z) \ x) * z = (x / (x * y)) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(26783(a,1),28892(a,1,1,1))].">
      <j1 rule="para" parents="26783 28892"/>
    </justification>
  </clause>

  <clause id="28894">
    <literal><![CDATA[
      (a(a(x,x,y),x,z) \ R(x,x,y)) * z = (R(x,x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(28417(a,1),28892(a,1,1,1,1))].">
      <j1 rule="para" parents="28417 28892"/>
    </justification>
  </clause>

  <clause id="28895">
    <literal><![CDATA[
      L(x,1 / (y * x),a(y,x,1 / (y * x))) \ (y \ K(y * x,(y * x) \ 1)) = (1 / (y * x)) * a(y,x,1 / (y * x))
    ]]></literal>
    <justification jstring="[para(1709(a,2),28737(a,1,2,2))].">
      <j1 rule="para" parents="1709 28737"/>
    </justification>
  </clause>

  <clause id="28896">
    <literal><![CDATA[
      L(x,a(y,z,x),a(z,x,a(y,z,x))) \ (z \ (y \ ((y * z) * x))) = a(y,z,x) * a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(28715(a,2),28737(a,1,2,2))].">
      <j1 rule="para" parents="28715 28737"/>
    </justification>
  </clause>

  <clause id="28897">
    <literal><![CDATA[
      L(x,(1 / y) * L(z,y,y),u) = L(x,((y \ 1) \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(28793(a,1),14183(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28793 14183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28898">
    <literal><![CDATA[
      a((x \ (y \ (x \ y))) * z,u,w) = a(a(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26772,a(flip),b,28845,a)].">
      <j1 rule="hyper" parents="60 26772 28845"/>
    </justification>
  </clause>

  <clause id="28899">
    <literal><![CDATA[
      a(x,((y * (a(y,z,u \ w) \ z)) * (u \ w)) * v5,v6) = a(x,(y * (z * (w / u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28853(a,1),26657(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28853 26657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28900">
    <literal><![CDATA[
      L(x,(1 / y) * L(z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26029,a(flip),b,28897,a),flip(a)].">
      <j1 rule="hyper" parents="370 26029 28897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28902">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(2086(a,2),28900(a,1,2))].">
      <j1 rule="para" parents="2086 28900"/>
    </justification>
  </clause>

  <clause id="28903">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(27498,a,28902,a)].">
      <j1 rule="hyper" parents="27498 28902"/>
    </justification>
  </clause>

  <clause id="28904">
    <literal><![CDATA[
      L(x,L((1 / y) * z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(27514,a,28903,a)].">
      <j1 rule="hyper" parents="27514 28903"/>
    </justification>
  </clause>

  <clause id="28905">
    <literal><![CDATA[
      L(x,y \ (y \ z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),28903(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 28903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28906">
    <literal><![CDATA[
      L(x,y,L(z \ 1,L(u,z,z),w) * (w * (z \ ((1 / z) \ u)))) = L(x,y,w * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(28905(a,1),28034(a,1,3,1))].">
      <j1 rule="para" parents="28905 28034"/>
    </justification>
  </clause>

  <clause id="28907">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),1 / z,1 / z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27608,a,b,28904,a)].">
      <j1 rule="hyper" parents="60 27608 28904"/>
    </justification>
  </clause>

  <clause id="28908">
    <literal><![CDATA[
      a((((x \ y) * x) \ ((z * y) \ T(K(x,x \ y) * z,y))) * u,w,v5) = a(a(z * y,(x \ y) * x,(x \ y) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25292(a,2),28898(a,1,1,1,2,2))].">
      <j1 rule="para" parents="25292 28898"/>
    </justification>
  </clause>

  <clause id="28909">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),z,z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(3400(a,1),28907(a,1,2))].">
      <j1 rule="para" parents="3400 28907"/>
    </justification>
  </clause>

  <clause id="28910">
    <literal><![CDATA[
      L(x,L(y * z,z,z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(26305,a,28909,a)].">
      <j1 rule="hyper" parents="26305 28909"/>
    </justification>
  </clause>

  <clause id="28911">
    <literal><![CDATA[
      L(x,L(y,z,z) * z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26339,a(flip),b,28910,a)].">
      <j1 rule="hyper" parents="60 26339 28910"/>
    </justification>
  </clause>

  <clause id="28912">
    <literal><![CDATA[
      L(x,L(y,z \ y,z \ y),u) = L(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),28910(a,1,2,1))].">
      <j1 rule="para" parents="5 28910"/>
    </justification>
  </clause>

  <clause id="28913">
    <literal><![CDATA[
      L(x,y * ((1 / y) * L(z,(1 / y) * z,(1 / y) * z)),u) = L(x,((1 / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(4285(a,1),28910(a,1,2))].">
      <j1 rule="para" parents="4285 28910"/>
    </justification>
  </clause>

  <clause id="28914">
    <literal><![CDATA[
      L(x,L(L(y,z,z),y * z,y * z),u) = L(x,(y * z) \ (1 / ((y * z) / y)),u)
    ]]></literal>
    <justification jstring="[para(12651(a,1),28910(a,1,2,1))].">
      <j1 rule="para" parents="12651 28910"/>
    </justification>
  </clause>

  <clause id="28915">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26234,a,28713,a)].">
      <j1 rule="hyper" parents="26234 28713"/>
    </justification>
  </clause>

  <clause id="28916">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (u * a(x,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(28915(a,1),336(a,1,2))].">
      <j1 rule="para" parents="28915 336"/>
    </justification>
  </clause>

  <clause id="28917">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * a(x,z,u)) = (x \ (a(x,z,u) / x)) * y
    ]]></literal>
    <justification jstring="[para(28798(a,1),28729(a,1,2))].">
      <j1 rule="para" parents="28798 28729"/>
    </justification>
  </clause>

  <clause id="28918">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(26342,a,28778,a)].">
      <j1 rule="hyper" parents="26342 28778"/>
    </justification>
  </clause>

  <clause id="28919">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(28778(a,1),26342(a,1))].">
      <j1 rule="para" parents="28778 26342"/>
    </justification>
  </clause>

  <clause id="28920">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,a(x,y,z)) = (x * a(x,y,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,28918,a),flip(a)].">
      <j1 rule="hyper" parents="60 94 28918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28921">
    <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(28786(a,1),13469(a,1,2))].">
      <j1 rule="para" parents="28786 13469"/>
    </justification>
  </clause>

  <clause id="28922">
    <literal><![CDATA[
      x * (((y \ 1) \ (1 / (y \ 1))) * a(x,(y \ 1) \ 1,y)) = (x * ((y \ 1) \ 1)) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1211(a,1),28759(a,1,2,1))].">
      <j1 rule="para" parents="1211 28759"/>
    </justification>
  </clause>

  <clause id="28923">
    <literal><![CDATA[
      a((x \ 1) \ (y \ (z \ ((z * x) * y))),u,w) = a(a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26550,a,28768,a)].">
      <j1 rule="hyper" parents="26550 28768"/>
    </justification>
  </clause>

  <clause id="28924">
    <literal><![CDATA[
      a(x,y * (((z * u) \ z) * u),w) = a(x,a(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26483,a(flip),b,28842,a),flip(a)].">
      <j1 rule="hyper" parents="370 26483 28842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28925">
    <literal><![CDATA[
      a(x,y * (z * (u \ (u / z))),w) = a(x,a(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[para(3763(a,1),28924(a,1,2,2))].">
      <j1 rule="para" parents="3763 28924"/>
    </justification>
  </clause>

  <clause id="28926">
    <literal><![CDATA[
      a(x,y * (z * (u \ (z \ u))),w) = a(x,a(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27801,a(flip),b,28925,a)].">
      <j1 rule="hyper" parents="60 27801 28925"/>
    </justification>
  </clause>

  <clause id="28927">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = a(x,u * a(z,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28444,a(flip),b,28926,a),flip(a)].">
      <j1 rule="hyper" parents="60 28444 28926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28928">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ u) * w)) = a(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3109,a(flip),b,28843,a),flip(a)].">
      <j1 rule="hyper" parents="370 3109 28843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28929">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * u) * w) = a(x,y,a(z,u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(26965,a,28928,a)].">
      <j1 rule="hyper" parents="26965 28928"/>
    </justification>
  </clause>

  <clause id="28930">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) * u) * w) = a(x,y,a(z,u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27560,a(flip),b,28929,a)].">
      <j1 rule="hyper" parents="60 27560 28929"/>
    </justification>
  </clause>

  <clause id="28931">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,28458,a(flip),b,28930,a),flip(a)].">
      <j1 rule="hyper" parents="60 28458 28930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28932">
    <literal><![CDATA[
      a(x,y,z * a(u,w,w)) = a(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(26965,a,28931,a)].">
      <j1 rule="hyper" parents="26965 28931"/>
    </justification>
  </clause>

  <clause id="28933">
    <literal><![CDATA[
      (x / (y * x)) * ((y \ 1) \ 1) = (y \ 1) \ (x / (y * x))
    ]]></literal>
    <justification jstring="[para(77(a,1),28728(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 28728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28935">
    <literal><![CDATA[
      a(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(26353,a,28808,a),flip(a)].">
      <j1 rule="hyper" parents="26353 28808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28936">
    <literal><![CDATA[
      a(a(x,y,z),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(28808(a,1),26353(a,1))].">
      <j1 rule="para" parents="28808 26353"/>
    </justification>
  </clause>

  <clause id="28937">
    <literal><![CDATA[
      a(x,(y \ (a(y,z,u) / y)) * w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(28917(a,1),28811(a,1,2))].">
      <j1 rule="para" parents="28917 28811"/>
    </justification>
  </clause>

  <clause id="28938">
    <literal><![CDATA[
      a(x,(y \ (y \ a(y,z,u))) * w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26776,a(flip),b,28937,a)].">
      <j1 rule="hyper" parents="60 26776 28937"/>
    </justification>
  </clause>

  <clause id="28939">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(w,w,v5)))) = a(x,y,(u \ a(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27218,a(flip),b,28828,a)].">
      <j1 rule="hyper" parents="60 27218 28828"/>
    </justification>
  </clause>

  <clause id="28940">
    <literal><![CDATA[
      x * a(y,y \ x,y \ x) = y * (T(x \ y,y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(1055(a,1),28847(a,2,2,1))].">
      <j1 rule="para" parents="1055 28847"/>
    </justification>
  </clause>

  <clause id="28941">
    <literal><![CDATA[
      x * a(y,y \ x,y \ x) = y * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(3516(a,1),28940(a,2,2))].">
      <j1 rule="para" parents="3516 28940"/>
    </justification>
  </clause>

  <clause id="28942">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27509,a(flip),b,28851,a),flip(a)].">
      <j1 rule="hyper" parents="370 27509 28851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28943">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * y) = K(z,y) * a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28789,a(flip),b,28873,a),flip(a)].">
      <j1 rule="hyper" parents="60 28789 28873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28944">
    <literal><![CDATA[
      K(x,a(y,z,x)) * a(u,x,a(y,z,x)) = a(u,a(y,z,x),x)
    ]]></literal>
    <justification jstring="[hyper(28305,a,28943,a),flip(a)].">
      <j1 rule="hyper" parents="28305 28943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28946">
    <literal><![CDATA[
      K(x,a(x,y,z)) * a(u,x,a(x,y,z)) = a(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28800,a(flip),b,28943,a),flip(a)].">
      <j1 rule="hyper" parents="60 28800 28943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28947">
    <literal><![CDATA[
      L(x,K(y,z * y) * a(z,y,z * y),u) = L(x,z * ((z * y) * y),u)
    ]]></literal>
    <justification jstring="[para(28943(a,1),26087(a,1,2))].">
      <j1 rule="para" parents="28943 26087"/>
    </justification>
  </clause>

  <clause id="28948">
    <literal><![CDATA[
      a(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23542,a,28944,a),flip(a)].">
      <j1 rule="hyper" parents="23542 28944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28951">
    <literal><![CDATA[
      L(x,y,a(z,x,a(u,w,x))) = x
    ]]></literal>
    <justification jstring="[para(28948(a,1),28341(a,1,3))].">
      <j1 rule="para" parents="28948 28341"/>
    </justification>
  </clause>

  <clause id="28952">
    <literal><![CDATA[
      a(x,a(y,z,u),y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23542,a,28946,a),flip(a)].">
      <j1 rule="hyper" parents="23542 28946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28954">
    <literal><![CDATA[
      (x * a(y,z,u)) * (y \ 1) = (x * (y \ 1)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(28228,a,28883,a)].">
      <j1 rule="hyper" parents="28228 28883"/>
    </justification>
  </clause>

  <clause id="28955">
    <literal><![CDATA[
      ((x * (y \ 1)) * a(y,z,u)) / (y \ a(y,z,u)) = R(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(28954(a,1),26318(a,1,1))].">
      <j1 rule="para" parents="28954 26318"/>
    </justification>
  </clause>

  <clause id="28956">
    <literal><![CDATA[
      x * ((x \ 1) * (y * a(x,z,u))) = L(y,x,x) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2074(a,1),28885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2074 28885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28957">
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) = L(x,y,y) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2079,a,28956,a)].">
      <j1 rule="hyper" parents="2079 28956"/>
    </justification>
  </clause>

  <clause id="28958">
    <literal><![CDATA[
      L(x,y,y) * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) = w
    ]]></literal>
    <justification jstring="[para(28956(a,1),2079(a,1))].">
      <j1 rule="para" parents="28956 2079"/>
    </justification>
  </clause>

  <clause id="28960">
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) = a(y,z,u) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,28957,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 28957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28961">
    <literal><![CDATA[
      x \ L(x * a(y,z,u),y,y) = L(x,y,y) * (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,28957,a,b,2157,a)].">
      <j1 rule="hyper" parents="125 28957 2157"/>
    </justification>
  </clause>

  <clause id="28962">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,w,v5),u,u) = L(L(x,u,u),y,z) * a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,1),28957(a,2,1))].">
      <j1 rule="para" parents="25 28957"/>
    </justification>
  </clause>

  <clause id="28963">
    <literal><![CDATA[
      L((a(x,y,z) \ u) * a(x,y,z),x,x) * (u \ a(x,y,z)) = a(x,y,z) * (u \ (a(x,y,z) * L(a(x,y,z) \ u,x,x)))
    ]]></literal>
    <justification jstring="[para(28960(a,2),28581(a,1,1))].">
      <j1 rule="para" parents="28960 28581"/>
    </justification>
  </clause>

  <clause id="28964">
    <literal><![CDATA[
      L(x,y,y) * (x \ a(y,z,u)) = x * L(x \ a(y,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(3960,a,28961,a),flip(a)].">
      <j1 rule="hyper" parents="3960 28961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28966">
    <literal><![CDATA[
      (a(x,a(x,x,y),z) \ R(x,x,y)) * z = (R(x,x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(28935(a,1),28894(a,1,1,1))].">
      <j1 rule="para" parents="28935 28894"/>
    </justification>
  </clause>

  <clause id="28967">
    <literal><![CDATA[
      R((x * (y \ 1)) / (y \ 1),y,a(y,z,u)) = R(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(19780,a,28955,a)].">
      <j1 rule="hyper" parents="19780 28955"/>
    </justification>
  </clause>

  <clause id="28968">
    <literal><![CDATA[
      R(x,a(y,z,u),y) = R(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),28967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 28967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28969">
    <literal><![CDATA[
      R(a(x,y,y) \ z,x,a(x,y,y)) = (z * x) / R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,24108,a(flip),b,28968,a),flip(a)].">
      <j1 rule="hyper" parents="60 24108 28968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28970">
    <literal><![CDATA[
      L(a(x,y,y) \ z,x,a(x,y,y)) = (z * x) / R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(28340,a,28969,a)].">
      <j1 rule="hyper" parents="28340 28969"/>
    </justification>
  </clause>

  <clause id="28971">
    <literal><![CDATA[
      (x * a(x,y,y)) \ (x * z) = (z * x) / R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28920,a(flip),b,28970,a)].">
      <j1 rule="hyper" parents="60 28920 28970"/>
    </justification>
  </clause>

  <clause id="28972">
    <literal><![CDATA[
      (x * y) / R(y,z,z) = R(y,z,z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(16504(a,1),28971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16504 28971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28974">
    <literal><![CDATA[
      R(x,y,y) \ (x * (y \ 1)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,7003,a(flip),b,28972,a),flip(a)].">
      <j1 rule="hyper" parents="60 7003 28972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28975">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,u,x),u,u) = x * L(x \ L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,10444,a(flip),b,28962,a),flip(a)].">
      <j1 rule="hyper" parents="370 10444 28962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28976">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z) * a(u,u,x),u,u) = a(u,u,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(28975(a,2),14178(a,1,2))].">
      <j1 rule="para" parents="28975 14178"/>
    </justification>
  </clause>

  <clause id="28977">
    <literal><![CDATA[
      (a(x,a(x,x,y),z) \ R(x,x,y)) * z = (x \ R(x,x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(2014(a,1),28966(a,2,1))].">
      <j1 rule="para" parents="2014 28966"/>
    </justification>
  </clause>

  <clause id="28978">
    <literal><![CDATA[
      (a(x,a(x,x,y),z) \ R(x,x,y)) * z = a(x,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(28417(a,1),28977(a,2,1))].">
      <j1 rule="para" parents="28417 28977"/>
    </justification>
  </clause>

  <clause id="28979">
    <literal><![CDATA[
      (a(x,a(x,x,y),z) \ R(x,x,y)) * z = x * (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,28773,a(flip),b,28978,a),flip(a)].">
      <j1 rule="hyper" parents="370 28773 28978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28980">
    <literal><![CDATA[
      a(x,y * ((z * u) * a(y,z,u)),w) = a(x,((y \ 1) * z) * u,w)
    ]]></literal>
    <justification jstring="[para(2962(a,1),28758(a,1,2,2,2))].">
      <j1 rule="para" parents="2962 28758"/>
    </justification>
  </clause>

  <clause id="28981">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(28735(a,1),28980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28735 28980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28982">
    <literal><![CDATA[
      a(x,(y * z) * (u \ a(u,u,(y \ 1) * z)),w) = a(x,u \ T((y \ 1) * z,u \ 1),w)
    ]]></literal>
    <justification jstring="[para(28442(a,1),28981(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28442 28981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28983">
    <literal><![CDATA[
      L(x,y,z \ ((u \ ((u * (z \ 1)) * w)) / w)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(3050(a,1),28769(a,2,3))].">
      <j1 rule="para" parents="3050 28769"/>
    </justification>
  </clause>

  <clause id="28984">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w \ ((w * (z \ 1)) * u)))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(25954,a,28983,a)].">
      <j1 rule="hyper" parents="25954 28983"/>
    </justification>
  </clause>

  <clause id="28985">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) / ((x \ y) * (y \ x)) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[para(28840(a,1),28862(a,1,2))].">
      <j1 rule="para" parents="28840 28862"/>
    </justification>
  </clause>

  <clause id="28986">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((x \ y) * (x \ y)) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(9866,a,28985,a)].">
      <j1 rule="hyper" parents="9866 28985"/>
    </justification>
  </clause>

  <clause id="28987">
    <literal><![CDATA[
      L((x \ y) \ (y \ x),x \ y,y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(822,a,28986,a)].">
      <j1 rule="hyper" parents="822 28986"/>
    </justification>
  </clause>

  <clause id="28988">
    <literal><![CDATA[
      L(x,y * ((y * z) * z),u) = L(x,a(y,z,y * z),u)
    ]]></literal>
    <justification jstring="[hyper(26008,a,28947,a),flip(a)].">
      <j1 rule="hyper" parents="26008 28947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28989">
    <literal><![CDATA[
      L(x,a(y,z,y * z),u) = L(x,y * R(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(26277,a,28988,a),flip(a)].">
      <j1 rule="hyper" parents="26277 28988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28991">
    <literal><![CDATA[
      L(x,a(y,z,y * z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,16523,a(flip),b,28989,a),flip(a)].">
      <j1 rule="hyper" parents="370 16523 28989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28992">
    <literal><![CDATA[
      ((x * y) * (z * a(y,y,z))) / ((1 / y) \ z) = R(x,y,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27485,a(flip),b,28795,a),flip(a)].">
      <j1 rule="hyper" parents="370 27485 28795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28993">
    <literal><![CDATA[
      ((x * (y / x)) * (a(y,z,u) \ z)) * u = (x * (y / x)) * (z * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),28852(a,1,1,2,1,1))].">
      <j1 rule="para" parents="5 28852"/>
    </justification>
  </clause>

  <clause id="28994">
    <literal><![CDATA[
      L(x \ (((y \ (y / x)) \ 1) \ z),x,y \ (x \ y)) = (y \ ((y * x) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(25954,a,28857,a)].">
      <j1 rule="hyper" parents="25954 28857"/>
    </justification>
  </clause>

  <clause id="28995">
    <literal><![CDATA[
      L(L(1 / x,1 / x,L(y,z,x)),u,a(x,w,v5)) = L(1 / x,1 / x,y)
    ]]></literal>
    <justification jstring="[para(1488(a,1),28869(a,1,1,3))].">
      <j1 rule="para" parents="1488 28869"/>
    </justification>
  </clause>

  <clause id="28996">
    <literal><![CDATA[
      L(L(1 / x,x,L(y,z,x)),u,a(x,w,v5)) = L(1 / x,1 / x,y)
    ]]></literal>
    <justification jstring="[para(3388(a,1),28995(a,1,1))].">
      <j1 rule="para" parents="3388 28995"/>
    </justification>
  </clause>

  <clause id="28997">
    <literal><![CDATA[
      L(1 / x,x,L(y,z,x)) = L(1 / x,1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(28351,a,28996,a),flip(a)].">
      <j1 rule="hyper" parents="28351 28996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28998">
    <literal><![CDATA[
      L(1 / x,x,L(y,z,x)) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3388,a(flip),b,28997,a),flip(a)].">
      <j1 rule="hyper" parents="370 3388 28997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28999">
    <literal><![CDATA[
      L(x * y,y,y) \ L(x,y,y) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,26338,a,b,28998,a)].">
      <j1 rule="hyper" parents="60 26338 28998"/>
    </justification>
  </clause>

  <clause id="29001">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,v5),v6) * (v6 * L(u,w,v5))) = a(x,y,v6 * (R(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[para(27410(a,1),28702(a,1,3,1))].">
      <j1 rule="para" parents="27410 28702"/>
    </justification>
  </clause>

  <clause id="29002">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = ((x \ 1) * u) * a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(3050(a,1),28745(a,2,2))].">
      <j1 rule="para" parents="3050 28745"/>
    </justification>
  </clause>

  <clause id="29003">
    <literal><![CDATA[
      x \ (R(x,y,z) / a(x,y,z)) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),28771(a,1,2,1))].">
      <j1 rule="para" parents="4 28771"/>
    </justification>
  </clause>

  <clause id="29005">
    <literal><![CDATA[
      x \ (a(x,y,z) \ R(x,y,z)) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23572(a,1),29003(a,1,2))].">
      <j1 rule="para" parents="23572 29003"/>
    </justification>
  </clause>

  <clause id="29006">
    <literal><![CDATA[
      x * a(y * z,x,a(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(29005(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="29005 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29007">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = (z * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(82(a,1),28788(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 28788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29008">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,4,a(flip),b,29007,a),flip(a)].">
      <j1 rule="hyper" parents="370 4 29007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29009">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,4,a(flip),b,29007,a),flip(a)].">
      <j1 rule="hyper" parents="125 4 29007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29011">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = (x \ x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(29008(a,1),4046(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29008 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29013">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,194,a(flip),b,29011,a),flip(a)].">
      <j1 rule="hyper" parents="370 194 29011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29015">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,z)) = L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,29013,a(flip),b,10440,a)].">
      <j1 rule="hyper" parents="129 29013 10440"/>
    </justification>
  </clause>

  <clause id="29017">
    <literal><![CDATA[
      L(x,y,z) * L(x,u,z) = x * L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,29015,a(flip),b,2156,a),flip(a)].">
      <j1 rule="hyper" parents="129 29015 2156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29018">
    <literal><![CDATA[
      L(x,y,z) * L(x \ 1,u,z) = x \ L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,29015,a(flip),b,3825,a),flip(a)].">
      <j1 rule="hyper" parents="125 29015 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29019">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ x = 1 / L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(29015(a,1),2184(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29015 2184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29020">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(29015(a,1),2989(a,1,1))].">
      <j1 rule="para" parents="29015 2989"/>
    </justification>
  </clause>

  <clause id="29021">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(29015(a,1),3068(a,1,2))].">
      <j1 rule="para" parents="29015 3068"/>
    </justification>
  </clause>

  <clause id="29022">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29015(a,1),3132(a,1,3))].">
      <j1 rule="para" parents="29015 3132"/>
    </justification>
  </clause>

  <clause id="29023">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u) \ w,v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(29015(a,1),3594(a,1,2,1))].">
      <j1 rule="para" parents="29015 3594"/>
    </justification>
  </clause>

  <clause id="29024">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29015(a,1),7798(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29015 7798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29025">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) \ x) = L(L(x,y,z),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(29015(a,1),12813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29015 12813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29026">
    <literal><![CDATA[
      L(x,y,z * L(L(u,w,v5),w,v5)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(29015(a,1),14703(a,1,3,2))].">
      <j1 rule="para" parents="29015 14703"/>
    </justification>
  </clause>

  <clause id="29027">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ L(L(x,y,z) * (x \ L(x,y,z)),u,w) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(29015(a,1),16357(a,1,1))].">
      <j1 rule="para" parents="29015 16357"/>
    </justification>
  </clause>

  <clause id="29028">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (L(x,y,z) \ u) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29015(a,1),25373(a,1,1))].">
      <j1 rule="para" parents="29015 25373"/>
    </justification>
  </clause>

  <clause id="29029">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ R(L(L(x,y,z),y,z),u,w),L(L(x,y,z),y,z),w * u) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(25243,a,29020,a)].">
      <j1 rule="hyper" parents="25243 29020"/>
    </justification>
  </clause>

  <clause id="29030">
    <literal><![CDATA[
      a(L((1 / x) * y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),29020(a,1,1,1))].">
      <j1 rule="para" parents="586 29020"/>
    </justification>
  </clause>

  <clause id="29031">
    <literal><![CDATA[
      a(L(((1 / x) * y) \ 1,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(1491(a,1),29020(a,1,1,1))].">
      <j1 rule="para" parents="1491 29020"/>
    </justification>
  </clause>

  <clause id="29032">
    <literal><![CDATA[
      a(L(L(L(x,y,z),y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(112(a,2),29020(a,1,1))].">
      <j1 rule="para" parents="112 29020"/>
    </justification>
  </clause>

  <clause id="29033">
    <literal><![CDATA[
      a(x,L((1 / y) * z,y,y),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),29021(a,1,2,1))].">
      <j1 rule="para" parents="586 29021"/>
    </justification>
  </clause>

  <clause id="29034">
    <literal><![CDATA[
      a(x,L(L(L(y,z,u),z,u),w,v5),v6) = a(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(112(a,2),29021(a,1,2))].">
      <j1 rule="para" parents="112 29021"/>
    </justification>
  </clause>

  <clause id="29035">
    <literal><![CDATA[
      a(x,y,z) = y \ (L(z,y,x) * (L(L(z,y,x),y,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,28880,a(flip),b,29022,a),flip(a)].">
      <j1 rule="hyper" parents="60 28880 29022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29036">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,u \ (z \ w))
    ]]></literal>
    <justification jstring="[para(344(a,1),29022(a,1,3,1))].">
      <j1 rule="para" parents="344 29022"/>
    </justification>
  </clause>

  <clause id="29037">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3975,a(flip),b,29030,a)].">
      <j1 rule="hyper" parents="60 3975 29030"/>
    </justification>
  </clause>

  <clause id="29038">
    <literal><![CDATA[
      a(x \ (x \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),29037(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29039">
    <literal><![CDATA[
      a(x \ (R(x,y,z) * (x \ u)),w,v5) = a(L(R(x,y,z) * u,x,x),w,v5)
    ]]></literal>
    <justification jstring="[para(1954(a,1),29037(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1954 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29040">
    <literal><![CDATA[
      a(L(R(x,y,z) * u,R(x,y,z),L(x,y,z)),w,v5) = a(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(27279(a,1),29037(a,1,1))].">
      <j1 rule="para" parents="27279 29037"/>
    </justification>
  </clause>

  <clause id="29041">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(26590,a,29033,a)].">
      <j1 rule="hyper" parents="26590 29033"/>
    </justification>
  </clause>

  <clause id="29042">
    <literal><![CDATA[
      a(x,L(y * z,z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26651,a,b,29041,a)].">
      <j1 rule="hyper" parents="60 26651 29041"/>
    </justification>
  </clause>

  <clause id="29043">
    <literal><![CDATA[
      L(x,y,z) \ ((x * L(L(x,y,z),y,z)) * u) = (1 / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(29017(a,1),554(a,1,2,1))].">
      <j1 rule="para" parents="29017 554"/>
    </justification>
  </clause>

  <clause id="29044">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u) \ 1,w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3401,a(flip),b,29023,a),flip(a)].">
      <j1 rule="hyper" parents="370 3401 29023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29045">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(3530,a,29044,a)].">
      <j1 rule="hyper" parents="3530 29044"/>
    </justification>
  </clause>

  <clause id="29046">
    <literal><![CDATA[
      a(L((1 / x) * y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3869,a(flip),b,29031,a)].">
      <j1 rule="hyper" parents="60 3869 29031"/>
    </justification>
  </clause>

  <clause id="29047">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3975,a(flip),b,29046,a)].">
      <j1 rule="hyper" parents="60 3975 29046"/>
    </justification>
  </clause>

  <clause id="29048">
    <literal><![CDATA[
      a(x,y,z \ (z \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(27012,a,29036,a),flip(a)].">
      <j1 rule="hyper" parents="27012 29036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29049">
    <literal><![CDATA[
      a(x,y,L(z \ u,w \ z,w)) = a(x,y,(w \ z) \ (w \ u))
    ]]></literal>
    <justification jstring="[para(5(a,1),29036(a,1,3,1,1))].">
      <j1 rule="para" parents="5 29036"/>
    </justification>
  </clause>

  <clause id="29050">
    <literal><![CDATA[
      a(x,y,L(T(z * u,K(u,w)) \ v5,T(z,T(u,w)),u)) = a(x,y,T(z,T(u,w)) \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(8487(a,2),29036(a,1,3,1,1))].">
      <j1 rule="para" parents="8487 29036"/>
    </justification>
  </clause>

  <clause id="29051">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),29048(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4 29048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29052">
    <literal><![CDATA[
      a(x,y,L(z,z / u,z / u)) = a(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(77(a,1),29048(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="77 29048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29053">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ u),w,v5)) = a(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(3914(a,2),29048(a,1,3))].">
      <j1 rule="para" parents="3914 29048"/>
    </justification>
  </clause>

  <clause id="29054">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(26996,a,29051,a)].">
      <j1 rule="hyper" parents="26996 29051"/>
    </justification>
  </clause>

  <clause id="29055">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) * v5,R(z,u,w),L(z,u,w))) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(27279(a,1),29051(a,1,3))].">
      <j1 rule="para" parents="27279 29051"/>
    </justification>
  </clause>

  <clause id="29056">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(27089,a,29054,a)].">
      <j1 rule="hyper" parents="27089 29054"/>
    </justification>
  </clause>

  <clause id="29057">
    <literal><![CDATA[
      a(x,y,z * L(u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(26965,a,29056,a)].">
      <j1 rule="hyper" parents="26965 29056"/>
    </justification>
  </clause>

  <clause id="29058">
    <literal><![CDATA[
      a(x,y,L(z,z / u,u \ z)) = a(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(24012(a,1),29052(a,1,3))].">
      <j1 rule="para" parents="24012 29052"/>
    </justification>
  </clause>

  <clause id="29059">
    <literal><![CDATA[
      a(x,y,L(z,u \ z,u \ z)) = a(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(26018(a,1),29058(a,1,3))].">
      <j1 rule="para" parents="26018 29058"/>
    </justification>
  </clause>

  <clause id="29060">
    <literal><![CDATA[
      R(x,y \ L(L(y,z,u),z,u),w) = x
    ]]></literal>
    <justification jstring="[para(29018(a,1),14705(a,1,2))].">
      <j1 rule="para" parents="29018 14705"/>
    </justification>
  </clause>

  <clause id="29061">
    <literal><![CDATA[
      L(x,y,z \ L(L(z,u,w),v5,w)) = L(x,y,L(z,u,w) * L(z,v5,w))
    ]]></literal>
    <justification jstring="[para(29018(a,1),25833(a,1,3))].">
      <j1 rule="para" parents="29018 25833"/>
    </justification>
  </clause>

  <clause id="29062">
    <literal><![CDATA[
      x \ (L(L(x,y,z),y,z) * u) = (x \ L(L(x,y,z),y,z)) * u
    ]]></literal>
    <justification jstring="[para(29060(a,1),675(a,1,1))].">
      <j1 rule="para" parents="29060 675"/>
    </justification>
  </clause>

  <clause id="29063">
    <literal><![CDATA[
      (L(x,y,z) * L(T(x,u),y,z)) \ x = 1 / L(L(T(x,u),y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(25548,a,29019,a)].">
      <j1 rule="hyper" parents="25548 29019"/>
    </justification>
  </clause>

  <clause id="29064">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ 1,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(29025(a,1),3915(a,1,1))].">
      <j1 rule="para" parents="29025 3915"/>
    </justification>
  </clause>

  <clause id="29065">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29025(a,1),12815(a,1,3))].">
      <j1 rule="para" parents="29025 12815"/>
    </justification>
  </clause>

  <clause id="29066">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5),w,v5) \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(29025(a,1),15785(a,1,3,2))].">
      <j1 rule="para" parents="29025 15785"/>
    </justification>
  </clause>

  <clause id="29067">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3522,a,29065,a)].">
      <j1 rule="hyper" parents="3522 29065"/>
    </justification>
  </clause>

  <clause id="29068">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),v5,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,14799,a(flip),b,29067,a),flip(a)].">
      <j1 rule="hyper" parents="60 14799 29067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29069">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3962,a(flip),b,29067,a)].">
      <j1 rule="hyper" parents="60 3962 29067"/>
    </justification>
  </clause>

  <clause id="29070">
    <literal><![CDATA[
      L(x,y,L(((1 / z) * u) \ 1,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(1491(a,1),29067(a,1,3,1))].">
      <j1 rule="para" parents="1491 29067"/>
    </justification>
  </clause>

  <clause id="29071">
    <literal><![CDATA[
      L(x,y,L(L(L(z,u,w),u,w),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(112(a,2),29067(a,1,3))].">
      <j1 rule="para" parents="112 29067"/>
    </justification>
  </clause>

  <clause id="29072">
    <literal><![CDATA[
      L(x,y,(1 / z) * L(L(z * u,w,v5),v6,v7)) = L(x,y,z \ L(L(z \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(4124(a,1),29069(a,1,3))].">
      <j1 rule="para" parents="4124 29069"/>
    </justification>
  </clause>

  <clause id="29073">
    <literal><![CDATA[
      L(L(L(x \ L(x,y,z),u,w),u,w) \ 1,u,w) = 1 / L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,25162,a,b,29064,a),flip(a)].">
      <j1 rule="hyper" parents="370 25162 29064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29074">
    <literal><![CDATA[
      L((L(L(x,y,z),y,z) \ 1) \ R(L(L(x,y,z),y,z) \ 1,L(x,y,z) \ 1,u),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),28465(a,1,1,2,2))].">
      <j1 rule="para" parents="29064 28465"/>
    </justification>
  </clause>

  <clause id="29075">
    <literal><![CDATA[
      L(x,y,L((1 / z) * u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(25266,a,29070,a)].">
      <j1 rule="hyper" parents="25266 29070"/>
    </justification>
  </clause>

  <clause id="29076">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3979,a(flip),b,29075,a)].">
      <j1 rule="hyper" parents="60 3979 29075"/>
    </justification>
  </clause>

  <clause id="29077">
    <literal><![CDATA[
      L(x,y,L(z * u,z,u)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(25275,a,29076,a)].">
      <j1 rule="hyper" parents="25275 29076"/>
    </justification>
  </clause>

  <clause id="29078">
    <literal><![CDATA[
      L(x,L(L(L(y,z,u),z,u),w,v5),L(L(L(y,z,u),z,u),w,v5)) = a(L(y,w,v5),L(L(L(y,z,u),z,u),w,v5),x) \ x
    ]]></literal>
    <justification jstring="[para(29032(a,1),3943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29032 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29079">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w) * v5) = a(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(26991,a,29066,a)].">
      <j1 rule="hyper" parents="26991 29066"/>
    </justification>
  </clause>

  <clause id="29080">
    <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(4(a,1),29053(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="4 29053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29081">
    <literal><![CDATA[
      a(x,x,L(x \ y,z,u)) = a(x,x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,19761,a(flip),b,29080,a),flip(a)].">
      <j1 rule="hyper" parents="60 19761 29080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29082">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),T(u * K(z,u),w),T(u * K(z,u),w))) = a(x,y,L(T(u * K(z,u),w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(5320(a,1),29080(a,1,3,1,1))].">
      <j1 rule="para" parents="5320 29080"/>
    </justification>
  </clause>

  <clause id="29083">
    <literal><![CDATA[
      L((x \ L(L(x,y,z),y,z)) * u,1,w) = x \ (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,634,a,b,29062,a)].">
      <j1 rule="hyper" parents="370 634 29062"/>
    </justification>
  </clause>

  <clause id="29084">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) * u = L(L(x,y,z),y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,10604,a(flip),b,29062,a),flip(a)].">
      <j1 rule="hyper" parents="60 10604 29062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29085">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,69,a(flip),b,29084,a)].">
      <j1 rule="hyper" parents="125 69 29084"/>
    </justification>
  </clause>

  <clause id="29086">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) * (x \ u)) * L(w,u,x \ L(L(x,y,z),y,z)) = (x \ L(L(x,y,z),y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(29084(a,1),92(a,1,1))].">
      <j1 rule="para" parents="29084 92"/>
    </justification>
  </clause>

  <clause id="29087">
    <literal><![CDATA[
      L((x * (L(L(x,y,z),y,z) \ u)) \ w,(x \ L(L(x,y,z),y,z)) \ u,x \ L(L(x,y,z),y,z)) = u \ ((x \ L(L(x,y,z),y,z)) * w)
    ]]></literal>
    <justification jstring="[para(29085(a,1),656(a,1,1,1))].">
      <j1 rule="para" parents="29085 656"/>
    </justification>
  </clause>

  <clause id="29088">
    <literal><![CDATA[
      L((L(x,y,z) * L(x \ 1,y,z)) \ u,w,v5) = x * (L(L(x,y,z),y,z) \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,27980,a,b,29024,a)].">
      <j1 rule="hyper" parents="60 27980 29024"/>
    </justification>
  </clause>

  <clause id="29089">
    <literal><![CDATA[
      x \ ((L(y,z,u) * L(y \ 1,z,u)) \ w) = y * (L(L(y,z,u),z,u) \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27831,a(flip),b,29024,a)].">
      <j1 rule="hyper" parents="60 27831 29024"/>
    </justification>
  </clause>

  <clause id="29090">
    <literal><![CDATA[
      L(x,y,z) \ (L(x \ 1,y,z) \ x) = x * (L(L(x,y,z),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,27651,a(flip),b,29024,a)].">
      <j1 rule="hyper" parents="60 27651 29024"/>
    </justification>
  </clause>

  <clause id="29091">
    <literal><![CDATA[
      a(x * (L(L(x,y,z),y,z) \ u),w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(29024(a,1),14706(a,1,1))].">
      <j1 rule="para" parents="29024 14706"/>
    </justification>
  </clause>

  <clause id="29092">
    <literal><![CDATA[
      a(x,y,z * (L(L(z,u,w),u,w) \ v5)) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(29024(a,1),14707(a,1,3))].">
      <j1 rule="para" parents="29024 14707"/>
    </justification>
  </clause>

  <clause id="29093">
    <literal><![CDATA[
      x * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = (y * (L(L(y,z,u),z,u) \ x)) * w
    ]]></literal>
    <justification jstring="[para(29024(a,1),27852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29024 27852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29094">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) * (x \ u),w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(69(a,1),29091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="69 29091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29095">
    <literal><![CDATA[
      L(x \ 1,y,z) \ ((x \ 1) * (L(L(x \ 1,y,z),y,z) * a(x,u,w))) = (1 / L(x \ 1,y,z)) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[para(28785(a,1),29043(a,1,2))].">
      <j1 rule="para" parents="28785 29043"/>
    </justification>
  </clause>

  <clause id="29096">
    <literal><![CDATA[
      L(x,y,z \ L(L(z,u,w),v5,w)) = L(x,y,z * L(L(z,u,w),v5,w))
    ]]></literal>
    <justification jstring="[para(29017(a,1),29061(a,2,3))].">
      <j1 rule="para" parents="29017 29061"/>
    </justification>
  </clause>

  <clause id="29097">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * L(T(L(x \ R(x,y,z),u,w),v5),x,y * z)) \ L(x \ R(x,y,z),u,w) = 1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z)
    ]]></literal>
    <justification jstring="[para(16537(a,1),29063(a,1,1,1))].">
      <j1 rule="para" parents="16537 29063"/>
    </justification>
  </clause>

  <clause id="29098">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ x),y,z) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29090(a,1),4259(a,1,1))].">
      <j1 rule="para" parents="29090 4259"/>
    </justification>
  </clause>

  <clause id="29099">
    <literal><![CDATA[
      a(R(x,y,z) * (x \ (x \ u)),w,v5) = a(L(R(x,y,z) * u,x,x),w,v5)
    ]]></literal>
    <justification jstring="[para(1951(a,1),29039(a,1,1))].">
      <j1 rule="para" parents="1951 29039"/>
    </justification>
  </clause>

  <clause id="29100">
    <literal><![CDATA[
      L((x \ L(L(x,y,z),y,z)) * u,w \ w,v5) = x \ (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[para(63(a,2),29083(a,1,2))].">
      <j1 rule="para" parents="63 29083"/>
    </justification>
  </clause>

  <clause id="29101">
    <literal><![CDATA[
      a(L(x,y,z) * (x \ (x \ u)),w,v5) = a(L(R(x,y,z) * u,x,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27312,a(flip),b,29099,a)].">
      <j1 rule="hyper" parents="60 27312 29099"/>
    </justification>
  </clause>

  <clause id="29102">
    <literal><![CDATA[
      a(L(R(x,y,z) * u,L(x,y,z),L(x,y,z)),w,v5) = a(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(27410(a,1),29040(a,1,1))].">
      <j1 rule="para" parents="27410 29040"/>
    </justification>
  </clause>

  <clause id="29103">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) * v5,L(z,u,w),L(z,u,w))) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(27410(a,1),29055(a,1,3))].">
      <j1 rule="para" parents="27410 29055"/>
    </justification>
  </clause>

  <clause id="29104">
    <literal><![CDATA[
      L((x \ L(L(x,y,z),y,z)) * u,L(L(w,v5,v6),v5,v6) \ w,v7) = x \ (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29023,a,b,29100,a)].">
      <j1 rule="hyper" parents="60 29023 29100"/>
    </justification>
  </clause>

  <clause id="29105">
    <literal><![CDATA[
      (x * (y \ x)) / (y * ((y \ x) * (y \ x))) = (x \ y) \ ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),28833(a,2,1,1))].">
      <j1 rule="para" parents="5 28833"/>
    </justification>
  </clause>

  <clause id="29106">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) \ 1) = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,19759,a(flip),b,29105,a),flip(a)].">
      <j1 rule="hyper" parents="60 19759 29105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29108">
    <literal><![CDATA[
      L(a(x,y,y),y,(x \ (x / y)) \ z) = ((z / ((x \ (x / y)) \ 1)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(3576,a,28844,a)].">
      <j1 rule="hyper" parents="3576 28844"/>
    </justification>
  </clause>

  <clause id="29109">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z) * a(u,u,x),u,u) = a(u,u,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(4030(a,1),28976(a,2,1))].">
      <j1 rule="para" parents="4030 28976"/>
    </justification>
  </clause>

  <clause id="29110">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * v6)) = a(x,y,z * (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(26967,a,29001,a),flip(a)].">
      <j1 rule="hyper" parents="26967 29001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29111">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,(1 / z) \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(1961(a,1),29110(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1961 29110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29112">
    <literal><![CDATA[
      a(x,y,(z * (a(z,u,R(w,v5,v6) * v7) \ u)) * (L(w,v5,v6) * v7)) = a(x,y,z * (u * (R(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[para(28818(a,1),29110(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28818 29110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29113">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ L(L(L(x,y,z),y,z),u,w) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(29015(a,1),29027(a,1,2,1))].">
      <j1 rule="para" parents="29015 29027"/>
    </justification>
  </clause>

  <clause id="29114">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),y,z) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(10441,a,29113,a)].">
      <j1 rule="hyper" parents="10441 29113"/>
    </justification>
  </clause>

  <clause id="29115">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),u,w) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10440(a,1),29114(a,1,1))].">
      <j1 rule="para" parents="10440 29114"/>
    </justification>
  </clause>

  <clause id="29116">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,29115,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="125 29115 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29118">
    <literal><![CDATA[
      a(x,x,L(y \ L(y,z,u),x,x)) = (y \ L(y,z,u)) \ L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(29115(a,1),1362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29115 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29119">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,28589,a(flip),b,29116,a),flip(a)].">
      <j1 rule="hyper" parents="370 28589 29116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29120">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,u) \ 1,L(x \ L(x,y,z),u,u),u) = ((x / u) \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(29119(a,1),251(a,2,1))].">
      <j1 rule="para" parents="29119 251"/>
    </justification>
  </clause>

  <clause id="29121">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,w) = 1 / L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29115(a,1),29073(a,1,1,1))].">
      <j1 rule="para" parents="29115 29073"/>
    </justification>
  </clause>

  <clause id="29122">
    <literal><![CDATA[
      1 / L(x \ L(x,y,z),u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(9916(a,1),29121(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9916 29121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29124">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(25405,a,29122,a)].">
      <j1 rule="hyper" parents="25405 29122"/>
    </justification>
  </clause>

  <clause id="29125">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ 1 = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(215,a,29122,a)].">
      <j1 rule="hyper" parents="215 29122"/>
    </justification>
  </clause>

  <clause id="29126">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(28643,a,29124,a)].">
      <j1 rule="hyper" parents="28643 29124"/>
    </justification>
  </clause>

  <clause id="29127">
    <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(10448,a,29124,a)].">
      <j1 rule="hyper" parents="10448 29124"/>
    </justification>
  </clause>

  <clause id="29128">
    <literal><![CDATA[
      L((x \ y) \ L(x \ y,z,u),x \ y,x) \ 1 = y \ (x * (L(1 / (x \ y),z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,3890,a(flip),b,29124,a),flip(a)].">
      <j1 rule="hyper" parents="370 3890 29124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29129">
    <literal><![CDATA[
      1 / L(L(x,y,z) \ x,u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(221,a,29124,a)].">
      <j1 rule="hyper" parents="221 29124"/>
    </justification>
  </clause>

  <clause id="29130">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ x = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29124(a,1),27874(a,1,1))].">
      <j1 rule="para" parents="29124 27874"/>
    </justification>
  </clause>

  <clause id="29131">
    <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(29125(a,1),45(a,1))].">
      <j1 rule="para" parents="29125 45"/>
    </justification>
  </clause>

  <clause id="29132">
    <literal><![CDATA[
      L(x \ L(x,y,z),L(x,y,z),z * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2660(a,2),29125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2660 29125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29133">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(29129(a,1),388(a,1,1)),flip(b)].">
      <j1 rule="para" parents="29129 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29135">
    <literal><![CDATA[
      L(L(x,y,y) \ x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(29127(a,1),1364(a,1))].">
      <j1 rule="para" parents="29127 1364"/>
    </justification>
  </clause>

  <clause id="29136">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = v5 \ ((L(x,u,w) \ L(L(x,u,w),y,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(29127(a,1),28659(a,1,1))].">
      <j1 rule="para" parents="29127 28659"/>
    </justification>
  </clause>

  <clause id="29137">
    <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(1362(a,1),29135(a,1,1))].">
      <j1 rule="para" parents="1362 29135"/>
    </justification>
  </clause>

  <clause id="29138">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(29137,a,28772,a)].">
      <j1 rule="hyper" parents="29137 28772"/>
    </justification>
  </clause>

  <clause id="29139">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(29137,a,28461,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29137 28461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29140">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(29137,a,xx)].">
      <j1 rule="hyper" parents="29137"/>
    </justification>
  </clause>

  <clause id="29141">
    <literal><![CDATA[
      a(x,L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(28461(a,2),29137(a,1))].">
      <j1 rule="para" parents="28461 29137"/>
    </justification>
  </clause>

  <clause id="29142">
    <literal><![CDATA[
      a(x,x,y \ x) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(26985,a,29138,a),flip(a)].">
      <j1 rule="hyper" parents="26985 29138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29143">
    <literal><![CDATA[
      a(x,x,(x * y) \ (x * z)) = a(x,x,y \ z)
    ]]></literal>
    <justification jstring="[para(94(a,1),29138(a,1,3))].">
      <j1 rule="para" parents="94 29138"/>
    </justification>
  </clause>

  <clause id="29144">
    <literal><![CDATA[
      a(x,x,(x \ y) \ z) = a(x,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(656(a,1),29138(a,1,3)),flip(a)].">
      <j1 rule="para" parents="656 29138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29145">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,2548,a,b,29139,a)].">
      <j1 rule="hyper" parents="60 2548 29139"/>
    </justification>
  </clause>

  <clause id="29146">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(28709(a,1),29139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28709 29139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29147">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,L(y,z,u))) = (x \ a(x,L(x,z,u),y)) * y
    ]]></literal>
    <justification jstring="[para(29139(a,1),28891(a,1,2,2))].">
      <j1 rule="para" parents="29139 28891"/>
    </justification>
  </clause>

  <clause id="29148">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),z,u) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29022,a(flip),b,29140,a),flip(a)].">
      <j1 rule="hyper" parents="60 29022 29140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29149">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(29140(a,2),28870(a,1))].">
      <j1 rule="para" parents="29140 28870"/>
    </justification>
  </clause>

  <clause id="29150">
    <literal><![CDATA[
      a(L(x,y,z),L(L(x,u,w),u,w),v5) = a(x,x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29021,a,b,29145,a)].">
      <j1 rule="hyper" parents="60 29021 29145"/>
    </justification>
  </clause>

  <clause id="29151">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = ((x \ 1) * u) * a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(29145(a,1),29002(a,2,2))].">
      <j1 rule="para" parents="29145 29002"/>
    </justification>
  </clause>

  <clause id="29153">
    <literal><![CDATA[
      a(x,x,L(x \ y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(x * y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(29080(a,1),29149(a,1))].">
      <j1 rule="para" parents="29080 29149"/>
    </justification>
  </clause>

  <clause id="29154">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w) \ x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(10447(a,2),29133(a,1))].">
      <j1 rule="para" parents="10447 29133"/>
    </justification>
  </clause>

  <clause id="29155">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w) \ x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(28642(a,2),29133(a,1))].">
      <j1 rule="para" parents="28642 29133"/>
    </justification>
  </clause>

  <clause id="29156">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,L(y,z,u))) = (x \ a(x,x,L(y,z,u))) * y
    ]]></literal>
    <justification jstring="[para(29139(a,1),29147(a,2,1,2))].">
      <j1 rule="para" parents="29139 29147"/>
    </justification>
  </clause>

  <clause id="29157">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = (x \ 1) * (u * a(x,x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,28785,a(flip),b,29151,a),flip(a)].">
      <j1 rule="hyper" parents="370 28785 29151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29158">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * u) = (x \ a(x,x,L(u,y,z))) * u
    ]]></literal>
    <justification jstring="[hyper(370,a,29156,a(flip),b,29157,a),flip(a)].">
      <j1 rule="hyper" parents="370 29156 29157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29159">
    <literal><![CDATA[
      x * ((x \ a(x,x,L(y,z,u))) * y) = L(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(29158(a,1),4174(a,1,2))].">
      <j1 rule="para" parents="29158 4174"/>
    </justification>
  </clause>

  <clause id="29161">
    <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="[para(29024(a,1),29089(a,1,2))].">
      <j1 rule="para" parents="29024 29089"/>
    </justification>
  </clause>

  <clause id="29162">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (x \ u)) = L(L(x,y,z),y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(386,a,29161,a),flip(a)].">
      <j1 rule="hyper" parents="386 29161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29163">
    <literal><![CDATA[
      x / (L(y,z,u) * L(y \ 1,z,u)) = y * (L(L(y,z,u),z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(479,a,29093,a)].">
      <j1 rule="hyper" parents="479 29093"/>
    </justification>
  </clause>

  <clause id="29164">
    <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(29024(a,1),29093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29024 29093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29165">
    <literal><![CDATA[
      x / (y \ L(L(y,z,u),z,u)) = y * (L(L(y,z,u),z,u) \ x)
    ]]></literal>
    <justification jstring="[para(29018(a,1),29163(a,1,2))].">
      <j1 rule="para" parents="29018 29163"/>
    </justification>
  </clause>

  <clause id="29166">
    <literal><![CDATA[
      (x * (L(L(x,y,z),y,z) \ 1)) * u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,29164,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 29164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29167">
    <literal><![CDATA[
      ((x \ L(L(x,y,z),y,z)) \ 1) * u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29085(a,2),29166(a,1,1))].">
      <j1 rule="para" parents="29085 29166"/>
    </justification>
  </clause>

  <clause id="29168">
    <literal><![CDATA[
      a(((x \ L(L(x,y,z),y,z)) * u) * w,v5,v6) = a(w * (x * (L(L(x,y,z),y,z) \ u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(29167(a,1),26786(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29167 26786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29169">
    <literal><![CDATA[
      a(x,x,L(y \ L(y,z,u),x,x)) = a(x,x,y \ L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,14176,a,b,29118,a),flip(a)].">
      <j1 rule="hyper" parents="370 14176 29118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29170">
    <literal><![CDATA[
      a(x,x,L(y \ L(y,z,u),x,x)) = a(x,x,y * L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(3861(a,1),29169(a,2,1))].">
      <j1 rule="para" parents="3861 29169"/>
    </justification>
  </clause>

  <clause id="29171">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) \ 1 = a(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29149,a,29170,a),flip(a)].">
      <j1 rule="hyper" parents="29149 29170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29173">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) \ 1 = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3861,a(flip),b,29171,a),flip(a)].">
      <j1 rule="hyper" parents="370 3861 29171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29174">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z) * a(u,u,x),u,u) = a(u,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29109,a,b,29173,a)].">
      <j1 rule="hyper" parents="60 29109 29173"/>
    </justification>
  </clause>

  <clause id="29175">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,u) = a(u,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,28651,a(flip),b,29173,a)].">
      <j1 rule="hyper" parents="60 28651 29173"/>
    </justification>
  </clause>

  <clause id="29176">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * L(y,z,u),x,x) = w
    ]]></literal>
    <justification jstring="[para(29175(a,1),3859(a,1))].">
      <j1 rule="para" parents="29175 3859"/>
    </justification>
  </clause>

  <clause id="29177">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ a(u,u,x),u,u) = a(u,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3960,a,29174,a)].">
      <j1 rule="hyper" parents="3960 29174"/>
    </justification>
  </clause>

  <clause id="29178">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x * L(x,y,z),L(x,y,z),u) = (L(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(2998(a,1),28747(a,1,2))].">
      <j1 rule="para" parents="2998 28747"/>
    </justification>
  </clause>

  <clause id="29179">
    <literal><![CDATA[
      L(x,y,z * (u * T(a(w,w,v5) * v5,v6))) = L(x,y,z * (u * (w \ ((1 / w) \ v5))))
    ]]></literal>
    <justification jstring="[para(28210(a,2),28797(a,1,3,2,2))].">
      <j1 rule="para" parents="28210 28797"/>
    </justification>
  </clause>

  <clause id="29180">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(w * z) \ (z * (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(28850(a,1),25901(a,1,3))].">
      <j1 rule="para" parents="28850 25901"/>
    </justification>
  </clause>

  <clause id="29181">
    <literal><![CDATA[
      K(x,y * z) * ((x * z) \ (z * (y * x))) = L(a(z,y,x) \ y,z,x)
    ]]></literal>
    <justification jstring="[para(28128(a,1),28850(a,1,1))].">
      <j1 rule="para" parents="28128 28850"/>
    </justification>
  </clause>

  <clause id="29182">
    <literal><![CDATA[
      K(a(x,y,z),u * (z \ 1)) * ((z \ a(x,y,z)) \ ((z \ 1) * (u * a(x,y,z)))) = L(a(z \ 1,u,a(x,y,z)) \ u,z \ 1,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(24116(a,1),29181(a,1,2,1))].">
      <j1 rule="para" parents="24116 29181"/>
    </justification>
  </clause>

  <clause id="29183">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((w * z) * u)) * K(z,w * u)) = a(x,y,L(a(u,w,z) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(29181(a,1),27145(a,2,3))].">
      <j1 rule="para" parents="29181 27145"/>
    </justification>
  </clause>

  <clause id="29185">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K((x \ (x * y)) * T(z,y),x) = (z * (y * a(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(27711(a,1),28858(a,1,2))].">
      <j1 rule="para" parents="27711 28858"/>
    </justification>
  </clause>

  <clause id="29186">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ ((1 / w) \ v5)))) = L(x,y,z * (u * (a(w,w,v5) * v5)))
    ]]></literal>
    <justification jstring="[hyper(25951,a,29179,a),flip(a)].">
      <j1 rule="hyper" parents="25951 29179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29187">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(y * T(z,y),x) = (z * (y * a(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(4(a,1),29185(a,1,2,1,1))].">
      <j1 rule="para" parents="4 29185"/>
    </justification>
  </clause>

  <clause id="29188">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(z * y,x) = (z * (y * a(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),29187(a,1,2,1))].">
      <j1 rule="para" parents="107 29187"/>
    </justification>
  </clause>

  <clause id="29189">
    <literal><![CDATA[
      (x * y) * (T(z,y) * K(z * y,x)) = (z * (y * a(x,y,z))) * x
    ]]></literal>
    <justification jstring="[hyper(23461,a,29188,a)].">
      <j1 rule="hyper" parents="23461 29188"/>
    </justification>
  </clause>

  <clause id="29190">
    <literal><![CDATA[
      (x * (y * a(z,y,x))) * z = (z * y) * (y \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(15274(a,1),29189(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15274 29189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29191">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) = (z * y) * (y \ T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(28878,a,29190,a)].">
      <j1 rule="hyper" parents="28878 29190"/>
    </justification>
  </clause>

  <clause id="29192">
    <literal><![CDATA[
      (x * y) * R(z,y,x) = (z * y) * (y \ T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(25558,a,29191,a)].">
      <j1 rule="hyper" parents="25558 29191"/>
    </justification>
  </clause>

  <clause id="29193">
    <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(370,a,28367,a(flip),b,28765,a),flip(a)].">
      <j1 rule="hyper" parents="370 28367 28765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29194">
    <literal><![CDATA[
      a(a(x,y,z),x,u) * x = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(28723,a,29193,a),flip(a)].">
      <j1 rule="hyper" parents="28723 29193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29195">
    <literal><![CDATA[
      a(a(x,y,z),z,u) * z = L(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(28351,a,29193,a),flip(a)].">
      <j1 rule="hyper" parents="28351 29193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29196">
    <literal><![CDATA[
      T(L(a(a(x,y,z),u \ 1,w) * (u \ 1),w,a(x,y,z)) \ 1,u \ (u \ v5)) = T(L(1 / u,a(x,y,z),w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(29193(a,2),28522(a,1,1,1))].">
      <j1 rule="para" parents="29193 28522"/>
    </justification>
  </clause>

  <clause id="29197">
    <literal><![CDATA[
      (x * L(y,a(z,u,w),x)) * a(a(z,u,w),x,L(a(a(z,u,w),y,x) * y,x,a(z,u,w))) = x * (a(a(z,u,w),y,x) * y)
    ]]></literal>
    <justification jstring="[para(29193(a,1),28733(a,1,1,2))].">
      <j1 rule="para" parents="29193 28733"/>
    </justification>
  </clause>

  <clause id="29198">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * x = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(28935(a,1),29194(a,1,1))].">
      <j1 rule="para" parents="28935 29194"/>
    </justification>
  </clause>

  <clause id="29199">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[para(28396(a,1),29195(a,1,1))].">
      <j1 rule="para" parents="28396 29195"/>
    </justification>
  </clause>

  <clause id="29200">
    <literal><![CDATA[
      x \ L(x,a(x,y,z),u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(32,a,3838,a,b,29198,a)].">
      <j1 rule="hyper" parents="32 3838 29198"/>
    </justification>
  </clause>

  <clause id="29201">
    <literal><![CDATA[
      x \ L(x,a(y,z,x),u) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(32,a,3838,a,b,29199,a)].">
      <j1 rule="hyper" parents="32 3838 29199"/>
    </justification>
  </clause>

  <clause id="29202">
    <literal><![CDATA[
      (1 / x) \ a(y,a(z,u,y),w) = (y / x) \ L(y,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[para(29201(a,1),28589(a,1,2))].">
      <j1 rule="para" parents="29201 28589"/>
    </justification>
  </clause>

  <clause id="29203">
    <literal><![CDATA[
      L(((x \ (x / y)) \ 1) \ z,y * a(x,y,y),x \ (y \ x)) = 1 \ ((x \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(25954,a,28837,a)].">
      <j1 rule="hyper" parents="25954 28837"/>
    </justification>
  </clause>

  <clause id="29204">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = L(T(y,a(z,u,w)),a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,270,a(flip),b,28849,a),flip(a)].">
      <j1 rule="hyper" parents="370 270 28849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29205">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = L(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,23628,a(flip),b,29204,a),flip(a)].">
      <j1 rule="hyper" parents="370 23628 29204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29206">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ y = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(28723,a,29205,a),flip(a)].">
      <j1 rule="hyper" parents="28723 29205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29208">
    <literal><![CDATA[
      ((x * y) * a(z,u,y)) \ (z \ (((z * x) * y) * a(z,u,y))) = a(z,x * a(z,u,y),y)
    ]]></literal>
    <justification jstring="[para(28301(a,1),28882(a,1,1))].">
      <j1 rule="para" parents="28301 28882"/>
    </justification>
  </clause>

  <clause id="29209">
    <literal><![CDATA[
      L(x,y,(z \ 1) * L(L(z * u,w,v5),v6,v7)) = L(x,y,z \ L(L(z \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(25945,a,29072,a)].">
      <j1 rule="hyper" parents="25945 29072"/>
    </justification>
  </clause>

  <clause id="29210">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ u),w,v5) = x * (L(L(x,y,z),y,z) \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(29024(a,1),29088(a,1,1))].">
      <j1 rule="para" parents="29024 29088"/>
    </justification>
  </clause>

  <clause id="29211">
    <literal><![CDATA[
      a(x,y,R(T(z,u * w),u,w) * K(u,z * w)) = a(x,y,L(a(w,z,u) \ z,w,u))
    ]]></literal>
    <justification jstring="[para(880(a,1),29183(a,1,3,1))].">
      <j1 rule="para" parents="880 29183"/>
    </justification>
  </clause>

  <clause id="29212">
    <literal><![CDATA[
      a(x,y,R(T(z,u * w) * K(u,z * w),u,w)) = a(x,y,L(a(w,z,u) \ z,w,u))
    ]]></literal>
    <justification jstring="[para(25687(a,2),29211(a,1,3))].">
      <j1 rule="para" parents="25687 29211"/>
    </justification>
  </clause>

  <clause id="29213">
    <literal><![CDATA[
      a(x,y,L(T(z,u * w) * K(u,z * w),u,w)) = a(x,y,L(a(w,z,u) \ z,w,u))
    ]]></literal>
    <justification jstring="[hyper(27195,a,29212,a)].">
      <j1 rule="hyper" parents="27195 29212"/>
    </justification>
  </clause>

  <clause id="29214">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,z,w)) = a(x,y,L(T(u,w * z),w,z))
    ]]></literal>
    <justification jstring="[hyper(26982,a,29213,a),flip(a)].">
      <j1 rule="hyper" parents="26982 29213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29215">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,z,w)) = a(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26884,a(flip),b,29214,a),flip(a)].">
      <j1 rule="hyper" parents="370 26884 29214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29217">
    <literal><![CDATA[
      ((x * y) * a(z,u,y)) \ ((z \ ((z * x) * y)) * a(z,u,y)) = a(z,x * a(z,u,y),y)
    ]]></literal>
    <justification jstring="[para(28711(a,1),29208(a,1,2))].">
      <j1 rule="para" parents="28711 29208"/>
    </justification>
  </clause>

  <clause id="29218">
    <literal><![CDATA[
      L(x,y,z \ L(L(z \ u,w,v5),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(L(z * u,w,v5),v6,v7) * z) = v8
    ]]></literal>
    <justification jstring="[para(29209(a,1),25242(a,1))].">
      <j1 rule="para" parents="29209 25242"/>
    </justification>
  </clause>

  <clause id="29219">
    <literal><![CDATA[
      (L(x,x,y) * z) * a(R(y,x,x),L(x,x,y),z) = R(y,x,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(3730(a,1),28863(a,1,2,2))].">
      <j1 rule="para" parents="3730 28863"/>
    </justification>
  </clause>

  <clause id="29220">
    <literal><![CDATA[
      (L(x,x,y) * z) * a(L(y,x,x),L(x,x,y),z) = R(y,x,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(26613(a,1),29219(a,1,2))].">
      <j1 rule="para" parents="26613 29219"/>
    </justification>
  </clause>

  <clause id="29221">
    <literal><![CDATA[
      a(x,(y * (z * (u / w))) * v5,v6) = a(x,(y * (z * (w \ u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28818(a,1),28899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28818 28899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29222">
    <literal><![CDATA[
      L(x,y * ((1 / y) * L(z,(1 / y) * z,y * z)),u) = L(x,((1 / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(3369(a,1),28913(a,1,2,2,2))].">
      <j1 rule="para" parents="3369 28913"/>
    </justification>
  </clause>

  <clause id="29223">
    <literal><![CDATA[
      L(x,y * ((1 / y) * L(z,y * z,y * z)),u) = L(x,((1 / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(3389(a,1),29222(a,1,2,2,2))].">
      <j1 rule="para" parents="3389 29222"/>
    </justification>
  </clause>

  <clause id="29224">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(x,y,z)))) = L(z,y,x) * L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),28921(a,1,2,2))].">
      <j1 rule="para" parents="92 28921"/>
    </justification>
  </clause>

  <clause id="29225">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,y) = L(x * a(z,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(629,a,29224,a),flip(a)].">
      <j1 rule="hyper" parents="629 29224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29226">
    <literal><![CDATA[
      a(x,(y * z) * (u \ a(u,u,(y \ 1) * z)),w) = a(x,u \ ((y \ 1) * z),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26457,a(flip),b,28982,a),flip(a)].">
      <j1 rule="hyper" parents="370 26457 28982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29228">
    <literal><![CDATA[
      a(x,(y * z) * (u \ a(u,u,y * z)),w) = a(x,u \ ((y \ 1) * z),w)
    ]]></literal>
    <justification jstring="[para(3109(a,1),29226(a,1,2,2,2))].">
      <j1 rule="para" parents="3109 29226"/>
    </justification>
  </clause>

  <clause id="29229">
    <literal><![CDATA[
      a(x,y \ T(z * u,y \ 1),w) = a(x,y \ ((z \ 1) * u),w)
    ]]></literal>
    <justification jstring="[para(28442(a,1),29228(a,1,2))].">
      <j1 rule="para" parents="28442 29228"/>
    </justification>
  </clause>

  <clause id="29230">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) * u),w) = a(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(26562,a,29229,a),flip(a)].">
      <j1 rule="hyper" parents="26562 29229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29233">
    <literal><![CDATA[
      a(x,y,L(T(z * u,K(u,w)) \ v5,z,u)) = a(x,y,T(z,T(u,w)) \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(26015(a,1),29050(a,1,3))].">
      <j1 rule="para" parents="26015 29050"/>
    </justification>
  </clause>

  <clause id="29235">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,T(z,T(u,v5)) \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(27165,a,29233,a)].">
      <j1 rule="hyper" parents="27165 29233"/>
    </justification>
  </clause>

  <clause id="29236">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,26891,a(flip),b,29235,a),flip(a)].">
      <j1 rule="hyper" parents="370 26891 29235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29238">
    <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(29235(a,2),26979(a,1))].">
      <j1 rule="para" parents="29235 26979"/>
    </justification>
  </clause>

  <clause id="29240">
    <literal><![CDATA[
      x \ (y * (L(1 / (y \ x),z,u) \ 1)) = (x \ (y * L(y \ x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(656(a,1),29128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="656 29128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29241">
    <literal><![CDATA[
      x \ (y * (L(1 / (y \ x),z,u) \ 1)) = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(370,a,9926,a(flip),b,29240,a),flip(a)].">
      <j1 rule="hyper" parents="370 9926 29240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29243">
    <literal><![CDATA[
      a(x,y,R(z,z,u * R(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(370,a,3083,a(flip),b,28704,a),flip(a)].">
      <j1 rule="hyper" parents="370 3083 28704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29244">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,3083,a(flip),b,29111,a),flip(a)].">
      <j1 rule="hyper" parents="370 3083 29111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29245">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,u),L(x \ L(x,y,z),u,u),u) = ((x / u) \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(29124(a,1),29120(a,1,1))].">
      <j1 rule="para" parents="29124 29120"/>
    </justification>
  </clause>

  <clause id="29246">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,u),L(x * L(x,y,z),u,u),u) = ((x / u) \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(25893,a,29245,a)].">
      <j1 rule="hyper" parents="25893 29245"/>
    </justification>
  </clause>

  <clause id="29247">
    <literal><![CDATA[
      a((L(L(x,y,z),y,z) * (x \ u)) * w,v5,v6) = a(w * (x * (L(L(x,y,z),y,z) \ u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(29084(a,1),29168(a,1,1,1))].">
      <j1 rule="para" parents="29084 29168"/>
    </justification>
  </clause>

  <clause id="29248">
    <literal><![CDATA[
      a(x,y,R(z,R(u,w,v5),v6) * (v6 * L(u,w,v5))) = a(x,y,(z * R(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26885,a(flip),b,28706,a),flip(a)].">
      <j1 rule="hyper" parents="370 26885 28706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29250">
    <literal><![CDATA[
      a((((a(x,y,z * u) \ y) * x) * (u * z)) \ w,v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x * (y * (z * u))) \ w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(28877(a,2),26872(a,1))].">
      <j1 rule="para" parents="28877 26872"/>
    </justification>
  </clause>

  <clause id="29251">
    <literal><![CDATA[
      x * (((y \ 1) \ y) * a(x,(y \ 1) \ 1,y)) = (x * ((y \ 1) \ 1)) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(74(a,1),28922(a,1,2,1,2))].">
      <j1 rule="para" parents="74 28922"/>
    </justification>
  </clause>

  <clause id="29253">
    <literal><![CDATA[
      x * ((y * y) * a(x,(y \ 1) \ 1,y)) = (x * ((y \ 1) \ 1)) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(311(a,1),29251(a,1,2,1))].">
      <j1 rule="para" parents="311 29251"/>
    </justification>
  </clause>

  <clause id="29254">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * ((y \ 1) \ 1) = x * ((y * y) * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(3053(a,1),29253(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3053 29253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29255">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * ((y \ 1) \ 1) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,28735,a(flip),b,29254,a),flip(a)].">
      <j1 rule="hyper" parents="370 28735 29254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29256">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ R(L(L(x,y,z),y,z),u,w),x,w * u) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29045,a(flip),b,29029,a)].">
      <j1 rule="hyper" parents="60 29045 29029"/>
    </justification>
  </clause>

  <clause id="29258">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ L(R(L(x,y,z),u,w),y,z),x,w * u) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(24(a,1),29256(a,1,1,2))].">
      <j1 rule="para" parents="24 29256"/>
    </justification>
  </clause>

  <clause id="29259">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ L(L(R(x,u,w),y,z),y,z),x,w * u) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(24(a,1),29258(a,1,1,2,1))].">
      <j1 rule="para" parents="24 29258"/>
    </justification>
  </clause>

  <clause id="29260">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),u,w),x,z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(7816(a,1),29259(a,1,1))].">
      <j1 rule="para" parents="7816 29259"/>
    </justification>
  </clause>

  <clause id="29261">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24930,a,29260,a),flip(a)].">
      <j1 rule="hyper" parents="24930 29260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29262">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25271,a(flip),b,29260,a)].">
      <j1 rule="hyper" parents="60 25271 29260"/>
    </justification>
  </clause>

  <clause id="29263">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24930,a,29262,a),flip(a)].">
      <j1 rule="hyper" parents="24930 29262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29264">
    <literal><![CDATA[
      L(a(x,y,z),x,y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16538,a,29262,a),flip(a)].">
      <j1 rule="hyper" parents="16538 29262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29265">
    <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(125,a,29262,a(flip),b,29015,a)].">
      <j1 rule="hyper" parents="125 29262 29015"/>
    </justification>
  </clause>

  <clause id="29266">
    <literal><![CDATA[
      x * L(a(y,z,u),x,x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,29262,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="125 29262 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29267">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,v5)
    ]]></literal>
    <literal><![CDATA[
      L(a(u,w,v5),y,z) = x
    ]]></literal>
    <justification jstring="[para(29262(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="29262 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29268">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(29262(a,1),341(a,1,2,2))].">
      <j1 rule="para" parents="29262 341"/>
    </justification>
  </clause>

  <clause id="29269">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,w),x \ y,x) = x \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29262(a,1),617(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29262 617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29270">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(29262(a,1),29064(a,1,1,1))].">
      <j1 rule="para" parents="29262 29064"/>
    </justification>
  </clause>

  <clause id="29271">
    <literal><![CDATA[
      L(a(R(x,y,z),u,w),L(x,y,z),w * u) = R(x,y,z) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(27479,a,29263,a)].">
      <j1 rule="hyper" parents="27479 29263"/>
    </justification>
  </clause>

  <clause id="29272">
    <literal><![CDATA[
      L(a((1 / x) * y,z,u),(1 / x) * y,u * z) = ((1 / x) * y) \ L(R(x \ y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(592(a,2),29263(a,2,2))].">
      <j1 rule="para" parents="592 29263"/>
    </justification>
  </clause>

  <clause id="29273">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ a(x,y,z)) * (a(x,y,z) \ 1) = L(a(x,y,z),x,z * y) \ 1
    ]]></literal>
    <justification jstring="[para(29263(a,1),7784(a,1,1,1))].">
      <j1 rule="para" parents="29263 7784"/>
    </justification>
  </clause>

  <clause id="29274">
    <literal><![CDATA[
      L(a((x \ y) * z,u,w),(y / x) * z,w * u) = ((y / x) * z) \ R((y / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(26388(a,1),29263(a,1,1))].">
      <j1 rule="para" parents="26388 29263"/>
    </justification>
  </clause>

  <clause id="29275">
    <literal><![CDATA[
      L(a(L(x,y,y),z,u),y \ (y \ x),u * z) = (y \ (y \ x)) \ R(y \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(29038(a,1),29263(a,1,1))].">
      <j1 rule="para" parents="29038 29263"/>
    </justification>
  </clause>

  <clause id="29276">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),x,y * z) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29264(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29264 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29277">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,29266,a)].">
      <j1 rule="hyper" parents="135 29266"/>
    </justification>
  </clause>

  <clause id="29278">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),x,x) = w
    ]]></literal>
    <justification jstring="[para(29266(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="29266 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29279">
    <literal><![CDATA[
      x * L(y \ R(y,z,u),x,x) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,29261,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="125 29261 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29281">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ 1,u,w) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(29261(a,1),29064(a,1,1,1))].">
      <j1 rule="para" parents="29261 29064"/>
    </justification>
  </clause>

  <clause id="29282">
    <literal><![CDATA[
      L(a(x,y,z),u,(u * (a(x,y,z) \ 1)) \ 1) = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(25413,a,29270,a),flip(a)].">
      <j1 rule="hyper" parents="25413 29270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29283">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(14782(a,1),29270(a,2,1))].">
      <j1 rule="para" parents="14782 29270"/>
    </justification>
  </clause>

  <clause id="29284">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,L(z,w,v5)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(14799(a,1),29270(a,2,1))].">
      <j1 rule="para" parents="14799 29270"/>
    </justification>
  </clause>

  <clause id="29285">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = a(L(x,z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(16547(a,2),29270(a,2,1))].">
      <j1 rule="para" parents="16547 29270"/>
    </justification>
  </clause>

  <clause id="29286">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ 1 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29270(a,2),24112(a,1,1))].">
      <j1 rule="para" parents="29270 24112"/>
    </justification>
  </clause>

  <clause id="29288">
    <literal><![CDATA[
      (x * y) * (a(z,u,x) \ 1) = x * (y * (a(z,u,x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(129,a,29283,a(flip),b,14810,a(flip))].">
      <j1 rule="hyper" parents="129 29283 14810"/>
    </justification>
  </clause>

  <clause id="29290">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(z,u,w) = L(z,u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29284(a,1),23818(a,1,1))].">
      <j1 rule="para" parents="29284 23818"/>
    </justification>
  </clause>

  <clause id="29291">
    <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(60,a,24106,a,b,29286,a)].">
      <j1 rule="hyper" parents="60 24106 29286"/>
    </justification>
  </clause>

  <clause id="29292">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,u,a(x,y,z))) = u * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28762,a(flip),b,29268,a)].">
      <j1 rule="hyper" parents="60 28762 29268"/>
    </justification>
  </clause>

  <clause id="29293">
    <literal><![CDATA[
      (1 / x) \ (a(y,z,u) / x) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),x,x) = w
    ]]></literal>
    <justification jstring="[para(28409(a,2),29278(a,1))].">
      <j1 rule="para" parents="28409 29278"/>
    </justification>
  </clause>

  <clause id="29294">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ 1 = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(13549(a,1),29281(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13549 29281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29295">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) != v5 \ 1
    ]]></literal>
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(29294(a,1),45(a,1))].">
      <j1 rule="para" parents="29294 45"/>
    </justification>
  </clause>

  <clause id="29296">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(z,u,y) = L(a(z,u,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(25340,a,29292,a)].">
      <j1 rule="hyper" parents="25340 29292"/>
    </justification>
  </clause>

  <clause id="29297">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23999,a,29296,a)].">
      <j1 rule="hyper" parents="23999 29296"/>
    </justification>
  </clause>

  <clause id="29298">
    <literal><![CDATA[
      a(x,y,z) * a(u,z,a(x,y,z)) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(23794,a,29296,a)].">
      <j1 rule="hyper" parents="23794 29296"/>
    </justification>
  </clause>

  <clause id="29299">
    <literal><![CDATA[
      a(x,y,z) * a(u,z,a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),z,u) = w
    ]]></literal>
    <justification jstring="[para(29297(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="29297 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29300">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),L(a(x,y,z),u,w),w * u) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29265(a,1),2660(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29265 2660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29301">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x,z * y) = (x \ R(x,y,z)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29263(a,1),29265(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29263 29265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29302">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(x,y,z) \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(29263(a,1),29301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29263 29301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29303">
    <literal><![CDATA[
      L(a(R(x,y,z),u,w),L(x,y,z),w * u) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,27936,a(flip),b,29271,a),flip(a)].">
      <j1 rule="hyper" parents="370 27936 29271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29304">
    <literal><![CDATA[
      L(a(L(x,y,z),u,w),L(x,y,z),w * u) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(27318(a,1),29303(a,1,1))].">
      <j1 rule="para" parents="27318 29303"/>
    </justification>
  </clause>

  <clause id="29305">
    <literal><![CDATA[
      L(x,y,z) \ R(L(x,y,z),u,w) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29263,a(flip),b,29304,a)].">
      <j1 rule="hyper" parents="60 29263 29304"/>
    </justification>
  </clause>

  <clause id="29306">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(24(a,1),29305(a,1,2))].">
      <j1 rule="para" parents="24 29305"/>
    </justification>
  </clause>

  <clause id="29307">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(7813,a,29306,a),flip(a)].">
      <j1 rule="hyper" parents="7813 29306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29308">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y * z) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29307(a,1),16536(a,1,1))].">
      <j1 rule="para" parents="29307 16536"/>
    </justification>
  </clause>

  <clause id="29309">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,16537,a(flip),b,29308,a),flip(a)].">
      <j1 rule="hyper" parents="60 16537 29308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29310">
    <literal><![CDATA[
      ((1 / x) * a(y,z,u)) * x = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(25579,a,29309,a)].">
      <j1 rule="hyper" parents="25579 29309"/>
    </justification>
  </clause>

  <clause id="29311">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,a(x,y,z) \ u) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1124,a,29309,a),flip(a)].">
      <j1 rule="hyper" parents="1124 29309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29312">
    <literal><![CDATA[
      ((x * y) * z) \ ((u \ ((u * x) * y)) * z) = L(a(u,x,y),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28749,a,b,29309,a)].">
      <j1 rule="hyper" parents="60 28749 29309"/>
    </justification>
  </clause>

  <clause id="29313">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * ((a(x,y,z) * a(x,y,z)) \ v5) = R(a(x,y,z) \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(29309(a,1),2301(a,1,1))].">
      <j1 rule="para" parents="29309 2301"/>
    </justification>
  </clause>

  <clause id="29314">
    <literal><![CDATA[
      L(a(x,y,z),u,(a(x,y,z) * u) \ w) \ w = (u \ 1) * ((a(x,y,z) * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(29309(a,1),2815(a,1,1))].">
      <j1 rule="para" parents="29309 2815"/>
    </justification>
  </clause>

  <clause id="29315">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),a(x,y,z),u * w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29309(a,1),16534(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="29309 16534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29316">
    <literal><![CDATA[
      (x * R(x \ (a(y,z,u) \ x),w,v5)) * a(y,z,u) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(29309(a,1),25631(a,2,2,2))].">
      <j1 rule="para" parents="29309 25631"/>
    </justification>
  </clause>

  <clause id="29317">
    <literal><![CDATA[
      L(a(x,y,z),u,u) / u = (1 / u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(147,a,29310,a)].">
      <j1 rule="hyper" parents="147 29310"/>
    </justification>
  </clause>

  <clause id="29318">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,x) = L(a(y,z,u),x,x) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,586,a,b,29317,a)].">
      <j1 rule="hyper" parents="370 586 29317"/>
    </justification>
  </clause>

  <clause id="29319">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,x) != w / x
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),x,x) = w
    ]]></literal>
    <justification jstring="[para(29318(a,2),43(a,1))].">
      <j1 rule="para" parents="29318 43"/>
    </justification>
  </clause>

  <clause id="29320">
    <literal><![CDATA[
      L(a(x,y,z),y * z,a(x,u,z)) = a(x,y * a(x,u,z),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29217,a(flip),b,29312,a),flip(a)].">
      <j1 rule="hyper" parents="60 29217 29312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29321">
    <literal><![CDATA[
      (1 / (x / a(y,z,u))) * x = x * ((a(y,z,u) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,12454,a(flip),b,29311,a)].">
      <j1 rule="hyper" parents="60 12454 29311"/>
    </justification>
  </clause>

  <clause id="29322">
    <literal><![CDATA[
      (1 / (a(x,y,z) \ u)) * u = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(23572(a,1),29321(a,1,1,2))].">
      <j1 rule="para" parents="23572 29321"/>
    </justification>
  </clause>

  <clause id="29323">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ a(x,y,z),a(x,y,z),u * w) \ 1 = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29125,a,b,29315,a)].">
      <j1 rule="hyper" parents="60 29125 29315"/>
    </justification>
  </clause>

  <clause id="29324">
    <literal><![CDATA[
      L(a(x,y,z),u,u * (a(x,y,z) \ 1)) = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(3522,a,29282,a)].">
      <j1 rule="hyper" parents="3522 29282"/>
    </justification>
  </clause>

  <clause id="29325">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(25264,a,29324,a)].">
      <j1 rule="hyper" parents="25264 29324"/>
    </justification>
  </clause>

  <clause id="29326">
    <literal><![CDATA[
      (a(x,y,z) \ (x \ R(x,y,z))) * (a(x,y,z) \ 1) = L(a(x,y,z),x,z * y) \ 1
    ]]></literal>
    <justification jstring="[para(29302(a,1),29273(a,1,1))].">
      <j1 rule="para" parents="29302 29273"/>
    </justification>
  </clause>

  <clause id="29327">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),a(x,y,z),u * w) \ 1 = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29265(a,1),29323(a,1,1,1))].">
      <j1 rule="para" parents="29265 29323"/>
    </justification>
  </clause>

  <clause id="29328">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (x \ R(x,y,z)) = L(a(x,y,z),x,z * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(28381,a,29326,a)].">
      <j1 rule="hyper" parents="28381 29326"/>
    </justification>
  </clause>

  <clause id="29329">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(29263(a,1),29328(a,2,1))].">
      <j1 rule="para" parents="29263 29328"/>
    </justification>
  </clause>

  <clause id="29330">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29315(a,1),29327(a,1,1))].">
      <j1 rule="para" parents="29315 29327"/>
    </justification>
  </clause>

  <clause id="29332">
    <literal><![CDATA[
      L(a(L(x,y,y),z,u),L(x,y,y),u * z) = (y \ (y \ x)) \ R(y \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28905,a(flip),b,29275,a)].">
      <j1 rule="hyper" parents="60 28905 29275"/>
    </justification>
  </clause>

  <clause id="29333">
    <literal><![CDATA[
      (x \ (x \ y)) \ R(x \ (x \ y),z,u) = L(y,x,x) \ R(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29263,a(flip),b,29332,a),flip(a)].">
      <j1 rule="hyper" parents="60 29263 29332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29334">
    <literal><![CDATA[
      (x \ (x \ y)) \ R(x \ (x \ y),z,u) = L(y,x,x) \ L(R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(24(a,1),29333(a,2,2))].">
      <j1 rule="para" parents="24 29333"/>
    </justification>
  </clause>

  <clause id="29335">
    <literal><![CDATA[
      (x \ (x \ y)) \ R(x \ (x \ y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ R(y,z,u),x,x) = w
    ]]></literal>
    <justification jstring="[para(29334(a,2),7813(a,1))].">
      <j1 rule="para" parents="29334 7813"/>
    </justification>
  </clause>

  <clause id="29336">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,29132,a(flip),b,29300,a)].">
      <j1 rule="hyper" parents="60 29132 29300"/>
    </justification>
  </clause>

  <clause id="29337">
    <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(29336(a,1),24094(a,1,1))].">
      <j1 rule="para" parents="29336 24094"/>
    </justification>
  </clause>

  <clause id="29338">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(4028,a,29313,a),flip(a)].">
      <j1 rule="hyper" parents="4028 29313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29339">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = v6
    ]]></literal>
    <justification jstring="[para(29313(a,1),4032(a,1))].">
      <j1 rule="para" parents="29313 4032"/>
    </justification>
  </clause>

  <clause id="29340">
    <literal><![CDATA[
      L(a((x \ y) * z,u,w),(x \ y) * z,w * u) = ((y / x) * z) \ R((y / x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(26195,a,29274,a)].">
      <j1 rule="hyper" parents="26195 29274"/>
    </justification>
  </clause>

  <clause id="29341">
    <literal><![CDATA[
      ((x / y) * z) \ R((x / y) * z,u,w) = ((y \ x) * z) \ R((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29263,a(flip),b,29340,a),flip(a)].">
      <j1 rule="hyper" parents="60 29263 29340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29342">
    <literal><![CDATA[
      L(a(x * y,z,u),(1 / x) * y,u * z) = ((1 / x) * y) \ L(R(x \ y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(2958(a,1),29272(a,1,1))].">
      <j1 rule="para" parents="2958 29272"/>
    </justification>
  </clause>

  <clause id="29343">
    <literal><![CDATA[
      L(a(x * y,z,u),x * y,u * z) = ((1 / x) * y) \ L(R(x \ y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(4129,a,29342,a)].">
      <j1 rule="hyper" parents="4129 29342"/>
    </justification>
  </clause>

  <clause id="29344">
    <literal><![CDATA[
      ((1 / x) * y) \ L(R(x \ y,z,u),x,x) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29263,a(flip),b,29343,a),flip(a)].">
      <j1 rule="hyper" parents="60 29263 29343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29345">
    <literal><![CDATA[
      ((1 / x) * y) \ R((1 / x) * y,z,u) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(592(a,1),29344(a,1,2))].">
      <j1 rule="para" parents="592 29344"/>
    </justification>
  </clause>

  <clause id="29346">
    <literal><![CDATA[
      ((1 / (x / y)) * z) \ R((1 / (x / y)) * z,u,w) = ((y \ x) * z) \ R((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,29341,a(flip),b,29345,a),flip(a)].">
      <j1 rule="hyper" parents="370 29341 29345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29347">
    <literal><![CDATA[
      (((x / y) \ 1) * z) \ R(((x / y) \ 1) * z,u,w) = ((y \ x) * z) \ R((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29341,a(flip),b,29346,a)].">
      <j1 rule="hyper" parents="60 29341 29346"/>
    </justification>
  </clause>

  <clause id="29348">
    <literal><![CDATA[
      ((x \ y) * z) \ R((x \ y) * z,u,w) = (z * (y / x)) \ R(z * (y / x),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27986,a(flip),b,29347,a),flip(a)].">
      <j1 rule="hyper" parents="60 27986 29347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29349">
    <literal><![CDATA[
      ((x \ y) * z) \ R((x \ y) * z,u,w) = (z * (x \ y)) \ R(z * (x \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27837,a(flip),b,29348,a),flip(a)].">
      <j1 rule="hyper" parents="370 27837 29348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29350">
    <literal><![CDATA[
      ((x \ y) * y) \ R((x \ y) * y,z,u) = (y \ x) \ (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,28537,a(flip),b,29349,a),flip(a)].">
      <j1 rule="hyper" parents="370 28537 29349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29351">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ u = (x \ L(L(x,y,z),y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(1079,a,29104,a)].">
      <j1 rule="hyper" parents="1079 29104"/>
    </justification>
  </clause>

  <clause id="29352">
    <literal><![CDATA[
      R(x / (y \ L(L(y,z,u),z,u)),y \ L(L(y,z,u),z,u),x \ w) \ w = (L(L(y,z,u),z,u) \ y) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,673,a,b,29351,a)].">
      <j1 rule="hyper" parents="370 673 29351"/>
    </justification>
  </clause>

  <clause id="29353">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ u = L(L(x,y,z),y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,29084,a(flip),b,29351,a),flip(a)].">
      <j1 rule="hyper" parents="370 29084 29351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29354">
    <literal><![CDATA[
      L((x \ L(L(x,y,z),y,z)) * 1,L(L(x,y,z),y,z) \ x,u) = (u * (L(L(x,y,z),y,z) \ x)) \ u
    ]]></literal>
    <justification jstring="[para(29351(a,1),251(a,1,1))].">
      <j1 rule="para" parents="29351 251"/>
    </justification>
  </clause>

  <clause id="29355">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) * u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(781,a,29353,a)].">
      <j1 rule="hyper" parents="781 29353"/>
    </justification>
  </clause>

  <clause id="29356">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(28693(a,1),28694(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28693 28694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29357">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,63,a(flip),b,29356,a),flip(a)].">
      <j1 rule="hyper" parents="370 63 29356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29358">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,x * R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(27066,a,29357,a)].">
      <j1 rule="hyper" parents="27066 29357"/>
    </justification>
  </clause>

  <clause id="29360">
    <literal><![CDATA[
      a(x * R(x,y,z),u,x * R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(2980,a,29358,a)].">
      <j1 rule="hyper" parents="2980 29358"/>
    </justification>
  </clause>

  <clause id="29361">
    <literal><![CDATA[
      L(x * R(x,y,z),u,x * R(x,y,z)) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,29360,a)].">
      <j1 rule="hyper" parents="49 29360"/>
    </justification>
  </clause>

  <clause id="29362">
    <literal><![CDATA[
      T((x * R(x,y,z)) * u,x * R(x,y,z)) = u * (x * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(29361(a,1),5548(a,1,1,1))].">
      <j1 rule="para" parents="29361 5548"/>
    </justification>
  </clause>

  <clause id="29363">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),(u * w) * z,(u * w) * z)) = a(x,y,((u * w) * z) * (w * (T(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(12481(a,1),28703(a,2,3,2))].">
      <j1 rule="para" parents="12481 28703"/>
    </justification>
  </clause>

  <clause id="29364">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),(u * w) * z,(u * w) * z)) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27182,a(flip),b,29363,a),flip(a)].">
      <j1 rule="hyper" parents="370 27182 29363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29366">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,a(x,y,z)) = z \ (y \ (x \ ((x * y) * z)))
    ]]></literal>
    <justification jstring="[para(28951(a,1),28896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28951 28896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29367">
    <literal><![CDATA[
      x \ (y \ (z \ ((z * y) * x))) = L(a(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(29299,a,29366,a),flip(a)].">
      <j1 rule="hyper" parents="29299 29366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29368">
    <literal><![CDATA[
      L(x \ L(L(x,y,z),y,z),L(L(x,y,z),y,z) \ x,u) = (u * (L(L(x,y,z),y,z) \ x)) \ u
    ]]></literal>
    <justification jstring="[para(3(a,1),29354(a,1,1))].">
      <j1 rule="para" parents="3 29354"/>
    </justification>
  </clause>

  <clause id="29369">
    <literal><![CDATA[
      L(x \ L(L(x,y,z),y,z),x \ x,u) = (u * (L(L(x,y,z),y,z) \ x)) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,29023,a(flip),b,29368,a)].">
      <j1 rule="hyper" parents="60 29023 29368"/>
    </justification>
  </clause>

  <clause id="29371">
    <literal><![CDATA[
      (x * (L(L(y,z,u),z,u) \ y)) \ x = L(y \ L(L(y,z,u),z,u),1,x)
    ]]></literal>
    <justification jstring="[para(63(a,1),29369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="63 29369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29372">
    <literal><![CDATA[
      (x * (L(L(y,z,u),z,u) \ y)) \ x = y \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,634,a(flip),b,29371,a),flip(a)].">
      <j1 rule="hyper" parents="370 634 29371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29375">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ (((((x * y) / x) \ 1) \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(1313(a,1),28751(a,2,2,1))].">
      <j1 rule="para" parents="1313 28751"/>
    </justification>
  </clause>

  <clause id="29376">
    <literal><![CDATA[
      a(x,y,(z * (a(z,u,L(w,v5,v6) * v7) \ u)) * (L(w,v5,v6) * v7)) = a(x,y,z * (u * (R(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[para(28605(a,1),29112(a,1,3,1,2,1))].">
      <j1 rule="para" parents="28605 29112"/>
    </justification>
  </clause>

  <clause id="29377">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = v5 \ (L(x \ L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(10440(a,1),29136(a,2,2,1))].">
      <j1 rule="para" parents="10440 29136"/>
    </justification>
  </clause>

  <clause id="29378">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ ((x * y) * ((((x * y) \ x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(4488(a,1),29375(a,2,2))].">
      <j1 rule="para" parents="4488 29375"/>
    </justification>
  </clause>

  <clause id="29379">
    <literal><![CDATA[
      a(x,y,z * (u * (R(w,v5,v6) * v7))) = a(x,y,z * (u * (L(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[para(28818(a,1),29376(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28818 29376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29380">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w,v5,w) * v6))) = a(x,y,(u * (w * v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27247,a(flip),b,29379,a),flip(a)].">
      <j1 rule="hyper" parents="60 27247 29379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29381">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w \ (w \ v5),v6,v7) * w))) = a(x,y,(u * (w \ R(v5,v6,v7))) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27158,a(flip),b,29379,a),flip(a)].">
      <j1 rule="hyper" parents="60 27158 29379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29382">
    <literal><![CDATA[
      a(x,y,(z * (u \ R(w,v5,v6))) * v7) = a(x,y,(z * (u \ L(w,v5,v6))) * v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,27159,a(flip),b,29381,a),flip(a)].">
      <j1 rule="hyper" parents="60 27159 29381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29383">
    <literal><![CDATA[
      a(x,y,(z * (u \ L(w,v5,w))) * v6) = a(x,y,((u \ w) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27686,a(flip),b,29382,a),flip(a)].">
      <j1 rule="hyper" parents="60 27686 29382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29384">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ L(v5,v6,v5)))) = a(x,y,((w \ v5) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,29383,a)].">
      <j1 rule="hyper" parents="26965 29383"/>
    </justification>
  </clause>

  <clause id="29385">
    <literal><![CDATA[
      a(x,y,((z \ u) * R(w \ 1,w,z \ L(u,v5,u))) * v6) = a(x,y,v6 * (w \ (z \ L(u,v5,u))))
    ]]></literal>
    <justification jstring="[para(2784(a,1),29384(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2784 29384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29386">
    <literal><![CDATA[
      a(x,y,((z \ u) * R(w \ 1,w,z \ u)) * v5) = a(x,y,v5 * (w \ (z \ L(u,v6,u))))
    ]]></literal>
    <justification jstring="[para(27493(a,1),29385(a,1,3,1,2))].">
      <j1 rule="para" parents="27493 29385"/>
    </justification>
  </clause>

  <clause id="29387">
    <literal><![CDATA[
      a(x,y,(z \ T(u \ w,z \ 1)) * v5) = a(x,y,v5 * (z \ (u \ L(w,v6,w))))
    ]]></literal>
    <justification jstring="[para(6157(a,1),29386(a,1,3,1))].">
      <j1 rule="para" parents="6157 29386"/>
    </justification>
  </clause>

  <clause id="29389">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ L(v5,v6,v5)))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(27007,a,29387,a),flip(a)].">
      <j1 rule="hyper" parents="27007 29387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29392">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ (x * (y * (((y \ (x \ x)) \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[para(12767(a,1),29378(a,2,2))].">
      <j1 rule="para" parents="12767 29378"/>
    </justification>
  </clause>

  <clause id="29393">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ (x * (y * (((y \ 1) \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[para(63(a,1),29392(a,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="63 29392"/>
    </justification>
  </clause>

  <clause id="29395">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ (x * (y * (1 / y)))
    ]]></literal>
    <justification jstring="[para(1307(a,1),29393(a,2,2,2,2))].">
      <j1 rule="para" parents="1307 29393"/>
    </justification>
  </clause>

  <clause id="29396">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = L(x,y,y) \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1709(a,2),29395(a,2,2,2))].">
      <j1 rule="para" parents="1709 29395"/>
    </justification>
  </clause>

  <clause id="29397">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = (L(x,y,y) \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,23460,a(flip),b,29396,a),flip(a)].">
      <j1 rule="hyper" parents="370 23460 29396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29398">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = a(y,y,x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1362(a,1),29397(a,2,1))].">
      <j1 rule="para" parents="1362 29397"/>
    </justification>
  </clause>

  <clause id="29399">
    <literal><![CDATA[
      a(1 / ((x * y) / x),1 / ((x * y) / x),x * y) = y * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28110,a(flip),b,29398,a),flip(a)].">
      <j1 rule="hyper" parents="370 28110 29398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29400">
    <literal><![CDATA[
      a(1 / ((x * y) / x),(x * y) / x,x * y) = y * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(3055,a,29399,a)].">
      <j1 rule="hyper" parents="3055 29399"/>
    </justification>
  </clause>

  <clause id="29401">
    <literal><![CDATA[
      a(1 / ((x * y) / x),y,x * y) = y * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(26558,a,29400,a)].">
      <j1 rule="hyper" parents="26558 29400"/>
    </justification>
  </clause>

  <clause id="29402">
    <literal><![CDATA[
      a((x * y) / x,y,x * y) = y * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(2969,a,29401,a)].">
      <j1 rule="hyper" parents="2969 29401"/>
    </justification>
  </clause>

  <clause id="29404">
    <literal><![CDATA[
      a(x \ (x * y),y,x * y) = y * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(26516,a,29402,a)].">
      <j1 rule="hyper" parents="26516 29402"/>
    </justification>
  </clause>

  <clause id="29405">
    <literal><![CDATA[
      x * (a(x,x,y) / x) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),29404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 29404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29406">
    <literal><![CDATA[
      L(x,y,a(z,z,u * z)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(29405(a,1),24028(a,1,3))].">
      <j1 rule="para" parents="29405 24028"/>
    </justification>
  </clause>

  <clause id="29407">
    <literal><![CDATA[
      a(x,((y \ 1) * (a(y,y,z) / y)) * u,w) = a(x,a(y,y,z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(29405(a,1),28981(a,2,2,1))].">
      <j1 rule="para" parents="29405 28981"/>
    </justification>
  </clause>

  <clause id="29408">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(26888(a,1),29406(a,1,3))].">
      <j1 rule="para" parents="26888 29406"/>
    </justification>
  </clause>

  <clause id="29409">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27962,a,b,29408,a)].">
      <j1 rule="hyper" parents="60 27962 29408"/>
    </justification>
  </clause>

  <clause id="29410">
    <literal><![CDATA[
      L(x,y,(z \ u) * (z * u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(27964,a,29409,a)].">
      <j1 rule="hyper" parents="27964 29409"/>
    </justification>
  </clause>

  <clause id="29411">
    <literal><![CDATA[
      a(x,((y * y) \ a(y,y,z)) * u,w) = a(x,a(y,y,z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(28217(a,1),29407(a,1,2,1))].">
      <j1 rule="para" parents="28217 29407"/>
    </justification>
  </clause>

  <clause id="29412">
    <literal><![CDATA[
      a(x,(y \ (y \ a(y,y,z))) * u,w) = a(x,a(y,y,z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(19687(a,1),29411(a,1,2,1))].">
      <j1 rule="para" parents="19687 29411"/>
    </justification>
  </clause>

  <clause id="29413">
    <literal><![CDATA[
      a(x,a(y,y,z * y) * u,w) = a(x,u * a(y,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28938,a(flip),b,29412,a),flip(a)].">
      <j1 rule="hyper" parents="60 28938 29412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29414">
    <literal><![CDATA[
      (((x * y) * (y \ 1)) \ (x * (y \ 1))) \ (((y \ 1) \ 1) \ 1) = a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4703(a,1),28834(a,1,1))].">
      <j1 rule="para" parents="4703 28834"/>
    </justification>
  </clause>

  <clause id="29415">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) * (x \ u)) * L(w,u,x * L(L(x,y,z),y,z)) = (x \ L(L(x,y,z),y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(29096(a,1),29086(a,1,2))].">
      <j1 rule="para" parents="29096 29086"/>
    </justification>
  </clause>

  <clause id="29416">
    <literal><![CDATA[
      (R(x,y,y) \ (x * (y \ 1))) \ (((y \ 1) \ 1) \ 1) = a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1111(a,1),29414(a,1,1,1))].">
      <j1 rule="para" parents="1111 29414"/>
    </justification>
  </clause>

  <clause id="29417">
    <literal><![CDATA[
      a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1) = L(y \ 1,y,x) \ (((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(28974(a,1),29416(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28974 29416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29418">
    <literal><![CDATA[
      a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1) = L(y \ 1,y,x) \ (1 / y)
    ]]></literal>
    <justification jstring="[para(1307(a,1),29417(a,2,2))].">
      <j1 rule="para" parents="1307 29417"/>
    </justification>
  </clause>

  <clause id="29419">
    <literal><![CDATA[
      a(x * (1 / y),(y \ 1) \ 1,(y \ 1) \ 1) = y * (1 / L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,27533,a(flip),b,29418,a),flip(a)].">
      <j1 rule="hyper" parents="370 27533 29418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29420">
    <literal><![CDATA[
      a(x * (1 / y),(y \ 1) \ 1,y) = y * (1 / L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(26951,a,29419,a)].">
      <j1 rule="hyper" parents="26951 29419"/>
    </justification>
  </clause>

  <clause id="29421">
    <literal><![CDATA[
      a(x * (1 / y),y,y) = y * (1 / L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(26560,a,29420,a)].">
      <j1 rule="hyper" parents="26560 29420"/>
    </justification>
  </clause>

  <clause id="29423">
    <literal><![CDATA[
      x * (1 / L(x,x,y)) = a(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(3006,a,29421,a),flip(a)].">
      <j1 rule="hyper" parents="3006 29421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29424">
    <literal><![CDATA[
      x * (a(y,x,x) / x) = a(y * x,x,x)
    ]]></literal>
    <justification jstring="[para(28825(a,2),29423(a,1,2))].">
      <j1 rule="para" parents="28825 29423"/>
    </justification>
  </clause>

  <clause id="29425">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) * (x \ u)) * L(w,u,x * x) = (x \ L(L(x,y,z),y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(29026(a,1),29415(a,1,2))].">
      <j1 rule="para" parents="29026 29415"/>
    </justification>
  </clause>

  <clause id="29426">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) * (x \ u)) * w = (x \ L(L(x,y,z),y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(615(a,1),29425(a,1,2))].">
      <j1 rule="para" parents="615 29425"/>
    </justification>
  </clause>

  <clause id="29428">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) * (x \ u)) * w = L(L(x,y,z),y,z) * (x \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29084,a(flip),b,29426,a),flip(a)].">
      <j1 rule="hyper" parents="370 29084 29426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29429">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) * (x \ (u * w)),v5,v6) = a(w * (x * (L(L(x,y,z),y,z) \ u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(29428(a,1),29247(a,1,1))].">
      <j1 rule="para" parents="29428 29247"/>
    </justification>
  </clause>

  <clause id="29430">
    <literal><![CDATA[
      a(x * (y * (L(L(y,z,u),z,u) \ w)),v5,v6) = a(w * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,29094,a(flip),b,29429,a),flip(a)].">
      <j1 rule="hyper" parents="60 29094 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29432">
    <literal><![CDATA[
      a((x \ 1) * (y * (L(L(y,z,u),z,u) \ L(w,x,x))),v5,v6) = a(L(w * (1 / x),x,x),v5,v6)
    ]]></literal>
    <justification jstring="[para(4641(a,2),29430(a,2,1))].">
      <j1 rule="para" parents="4641 29430"/>
    </justification>
  </clause>

  <clause id="29433">
    <literal><![CDATA[
      a((x \ 1) * L(y * (L(L(y,z,u),z,u) \ w),x,x),v5,v6) = a(L(w * (1 / x),x,x),v5,v6)
    ]]></literal>
    <justification jstring="[para(29210(a,2),29432(a,1,1,2))].">
      <j1 rule="para" parents="29210 29432"/>
    </justification>
  </clause>

  <clause id="29434">
    <literal><![CDATA[
      a(L((1 / x) * (y * (L(L(y,z,u),z,u) \ w)),x,x),v5,v6) = a(L(w * (1 / x),x,x),v5,v6)
    ]]></literal>
    <justification jstring="[para(3712(a,2),29433(a,1,1))].">
      <j1 rule="para" parents="3712 29433"/>
    </justification>
  </clause>

  <clause id="29435">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y),z,u) = a(y \ (w * (L(L(w,v5,v6),v5,v6) \ x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29030,a(flip),b,29434,a),flip(a)].">
      <j1 rule="hyper" parents="60 29030 29434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29436">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y),z,u) = a(w * (L(L(w,v5,v6),v5,v6) \ (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[para(29161(a,1),29435(a,2,1))].">
      <j1 rule="para" parents="29161 29435"/>
    </justification>
  </clause>

  <clause id="29437">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (L(L(x \ 1,y,z),y,z) * a(x,u,w))) = (1 / L(x \ 1,y,z)) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(2194,a,29095,a)].">
      <j1 rule="hyper" parents="2194 29095"/>
    </justification>
  </clause>

  <clause id="29438">
    <literal><![CDATA[
      (x \ 1) * (L(L(x \ 1,y,z),y,z) * (L(x \ 1,y,z) \ a(x,u,w))) = (1 / L(x \ 1,y,z)) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[para(2156(a,1),29437(a,1,2))].">
      <j1 rule="para" parents="2156 29437"/>
    </justification>
  </clause>

  <clause id="29439">
    <literal><![CDATA[
      R(x * (L(L(x,y,z),y,z) \ u),x \ L(L(x,y,z),y,z),u \ w) \ w = (L(L(x,y,z),y,z) \ x) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(29165(a,1),29352(a,1,1,1))].">
      <j1 rule="para" parents="29165 29352"/>
    </justification>
  </clause>

  <clause id="29440">
    <literal><![CDATA[
      (x * (L(L(x,y,z),y,z) \ u)) \ w = (L(L(x,y,z),y,z) \ x) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(29060(a,1),29439(a,1,1))].">
      <j1 rule="para" parents="29060 29439"/>
    </justification>
  </clause>

  <clause id="29441">
    <literal><![CDATA[
      (x * (L(L(x,y,z),y,z) \ u)) \ w = L(L(x,y,z),y,z) * (x \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29353,a(flip),b,29440,a),flip(a)].">
      <j1 rule="hyper" parents="370 29353 29440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29443">
    <literal><![CDATA[
      T(L(a(a(x,y,z),u,w) * (u \ 1),w,a(x,y,z)) \ 1,u \ (u \ v5)) = T(L(1 / u,a(x,y,z),w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(3050(a,1),29196(a,1,1,1,1,1))].">
      <j1 rule="para" parents="3050 29196"/>
    </justification>
  </clause>

  <clause id="29444">
    <literal><![CDATA[
      a(x,y,z * ((R(u,w,v5) \ ((R(u,w,v5) \ 1) \ v6)) * L(u,w,v5))) = a(x,y,z * ((R(u,w,v5) \ 1) \ v6))
    ]]></literal>
    <justification jstring="[hyper(27091,a,28705,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="27091 28705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29445">
    <literal><![CDATA[
      a(x,y,z * ((R(u,w,v5) \ ((R(u,w,v5) \ 1) \ v6)) * L(u,w,v5))) = a(x,y,(R(u,w,v5) \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26928,a(flip),b,29444,a),flip(a)].">
      <j1 rule="hyper" parents="370 26928 29444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29446">
    <literal><![CDATA[
      L(x,1 / (y * x),a(y,x,y * x)) \ (y \ K(y * x,(y * x) \ 1)) = (1 / (y * x)) * a(y,x,1 / (y * x))
    ]]></literal>
    <justification jstring="[para(3078(a,1),28895(a,1,1,3))].">
      <j1 rule="para" parents="3078 28895"/>
    </justification>
  </clause>

  <clause id="29447">
    <literal><![CDATA[
      L(x,1 / (y * x),a(x,x,y)) \ (y \ K(y * x,(y * x) \ 1)) = (1 / (y * x)) * a(y,x,1 / (y * x))
    ]]></literal>
    <justification jstring="[para(27956(a,1),29446(a,1,1))].">
      <j1 rule="para" parents="27956 29446"/>
    </justification>
  </clause>

  <clause id="29448">
    <literal><![CDATA[
      (1 / (x * y)) * a(x,y,1 / (x * y)) = y \ (x \ K(x * y,(x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(28709(a,1),29447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28709 29447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29449">
    <literal><![CDATA[
      (1 / (x * y)) * a(x,y,1 / (x * y)) = y \ (x \ K(x * y,y \ (x \ 1)))
    ]]></literal>
    <justification jstring="[para(23393(a,1),29448(a,2,2,2))].">
      <j1 rule="para" parents="23393 29448"/>
    </justification>
  </clause>

  <clause id="29450">
    <literal><![CDATA[
      (1 / (x * y)) * a(x,y,1 / (x * y)) = y \ (x \ K(x \ y,y \ x))
    ]]></literal>
    <justification jstring="[para(6901(a,1),29449(a,2,2,2))].">
      <j1 rule="para" parents="6901 29449"/>
    </justification>
  </clause>

  <clause id="29451">
    <literal><![CDATA[
      (1 / (x * y)) * a(x,y,x * y) = y \ (x \ K(x \ y,y \ x))
    ]]></literal>
    <justification jstring="[para(3078(a,1),29450(a,1,2))].">
      <j1 rule="para" parents="3078 29450"/>
    </justification>
  </clause>

  <clause id="29452">
    <literal><![CDATA[
      x \ (y \ K(y \ x,x \ y)) = a(y,x,y * x) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28302,a(flip),b,29451,a),flip(a)].">
      <j1 rule="hyper" parents="60 28302 29451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29453">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),T(u * K(z,u),w),u * K(z,u))) = a(x,y,L(T(u * K(z,u),w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(23573(a,1),29082(a,1,3))].">
      <j1 rule="para" parents="23573 29082"/>
    </justification>
  </clause>

  <clause id="29456">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),T(u * K(z,u),w),u)) = a(x,y,L(T(u * K(z,u),w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(23574(a,1),29453(a,1,3))].">
      <j1 rule="para" parents="23574 29453"/>
    </justification>
  </clause>

  <clause id="29460">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),u * K(z,u),u)) = a(x,y,L(T(u * K(z,u),w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(26015(a,1),29456(a,1,3))].">
      <j1 rule="para" parents="26015 29456"/>
    </justification>
  </clause>

  <clause id="29462">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),u,u)) = a(x,y,L(T(u * K(z,u),w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(26028(a,1),29460(a,1,3))].">
      <j1 rule="para" parents="26028 29460"/>
    </justification>
  </clause>

  <clause id="29463">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),u,u)) = a(x,y,L((u * K(z,u)) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,26911,a(flip),b,29462,a),flip(a)].">
      <j1 rule="hyper" parents="370 26911 29462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29466">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),u,u)) = a(x,y,L(K(u,z) * (u \ z),v5,v6))
    ]]></literal>
    <justification jstring="[para(7846(a,1),29463(a,2,3,1))].">
      <j1 rule="para" parents="7846 29463"/>
    </justification>
  </clause>

  <clause id="29467">
    <literal><![CDATA[
      a(x,y,L(L(z * T(u,w),v5,v6),u,u)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u \ z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(29466(a,2),27008(a,1))].">
      <j1 rule="para" parents="29466 27008"/>
    </justification>
  </clause>

  <clause id="29468">
    <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(107(a,1),29467(a,1,3,1,1))].">
      <j1 rule="para" parents="107 29467"/>
    </justification>
  </clause>

  <clause id="29469">
    <literal><![CDATA[
      a(x,y,z) * (u \ (a(x,y,z) * L(a(x,y,z) \ u,x,x))) = L(u,x,x) * (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23621(a,1),28963(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23621 28963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29470">
    <literal><![CDATA[
      a(x,y,z) * (u \ (a(x,y,z) * L(a(x,y,z) \ u,x,x))) = u * L(u \ a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,28964,a(flip),b,29469,a),flip(a)].">
      <j1 rule="hyper" parents="370 28964 29469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29471">
    <literal><![CDATA[
      a(x,y,z) * (u \ L((a(x,y,z) \ u) * a(x,y,z),x,x)) = u * L(u \ a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(28960(a,2),29470(a,1,2,2))].">
      <j1 rule="para" parents="28960 29470"/>
    </justification>
  </clause>

  <clause id="29472">
    <literal><![CDATA[
      a(x,y,z) * (u \ L(u,x,x)) = u * L(u \ a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(23621(a,1),29471(a,1,2,2,1))].">
      <j1 rule="para" parents="23621 29471"/>
    </justification>
  </clause>

  <clause id="29473">
    <literal><![CDATA[
      (x * L(y,a(z,u,w),x)) * a(a(z,u,w),x,L(y,a(z,u,w),x)) = x * (a(a(z,u,w),y,x) * y)
    ]]></literal>
    <justification jstring="[para(29193(a,1),29197(a,1,2,3))].">
      <j1 rule="para" parents="29193 29197"/>
    </justification>
  </clause>

  <clause id="29474">
    <literal><![CDATA[
      a(x,y,z) \ (u * (T(a(x,y,z),u) * w)) = u * (a(a(x,y,z),w,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28748,a(flip),b,29473,a)].">
      <j1 rule="hyper" parents="60 28748 29473"/>
    </justification>
  </clause>

  <clause id="29475">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = u * (a(a(x,y,z),w,u) * w)
    ]]></literal>
    <justification jstring="[para(23518(a,1),29474(a,1,2,2,1))].">
      <j1 rule="para" parents="23518 29474"/>
    </justification>
  </clause>

  <clause id="29477">
    <literal><![CDATA[
      a((((x \ y) * x) \ ((z * y) \ (K(x,x \ y) * z))) * u,w,v5) = a(a(z * y,(x \ y) * x,(x \ y) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26698,a(flip),b,28908,a)].">
      <j1 rule="hyper" parents="60 26698 28908"/>
    </justification>
  </clause>

  <clause id="29479">
    <literal><![CDATA[
      a(a(x * y,(z \ y) * z,(z \ y) * z) * u,w,v5) = a((((z \ y) * z) \ ((x * y) \ x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26701,a(flip),b,29477,a),flip(a)].">
      <j1 rule="hyper" parents="60 26701 29477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29481">
    <literal><![CDATA[
      a(a(x * y,(z \ y) * z,(z \ y) * z) * u,w,v5) = a((((z \ y) * z) \ (x \ (y \ x))) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27557,a(flip),b,29479,a),flip(a)].">
      <j1 rule="hyper" parents="370 27557 29479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29482">
    <literal><![CDATA[
      a(a(x * y,(z \ y) * z,(z \ y) * z) * u,w,v5) = a((y \ (x \ (y \ x))) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26398,a(flip),b,29481,a),flip(a)].">
      <j1 rule="hyper" parents="370 26398 29481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29484">
    <literal><![CDATA[
      a(a(x * y,(z \ y) * z,(z \ y) * z) * u,w,v5) = a(a(x,y,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,28898,a(flip),b,29482,a),flip(a)].">
      <j1 rule="hyper" parents="370 28898 29482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29485">
    <literal><![CDATA[
      a(a(x * y,(z \ y) * z,y) * u,w,v5) = a(a(x,y,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(26889(a,1),29484(a,1,1,1))].">
      <j1 rule="para" parents="26889 29484"/>
    </justification>
  </clause>

  <clause id="29486">
    <literal><![CDATA[
      a(a(x * y,y,y) * z,u,w) = a(a(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(194(a,1),29485(a,1,1,1,2))].">
      <j1 rule="para" parents="194 29485"/>
    </justification>
  </clause>

  <clause id="29488">
    <literal><![CDATA[
      (a(x,y,z) * L(u,w,a(x,y,z))) \ (a(x,y,z) * (w * T(u,w * a(x,y,z)))) = L(w,a(x,y,z),L(u,w,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(23540(a,1),26344(a,1,2,2,1))].">
      <j1 rule="para" parents="23540 26344"/>
    </justification>
  </clause>

  <clause id="29489">
    <literal><![CDATA[
      (a(x,y,z) * L(u,w,a(x,y,z))) \ (a(x,y,z) * (u * w)) = L(w,a(x,y,z),L(u,w,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(28143(a,1),29488(a,1,2,2))].">
      <j1 rule="para" parents="28143 29488"/>
    </justification>
  </clause>

  <clause id="29491">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ (u * L(x \ L(x,y,z),x,x \ u)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,26006,a(flip),b,27804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 26006 27804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29492">
    <literal><![CDATA[
      L((L(x,y,z) * (x \ u)) \ u,w,x) = 1 * ((L(x,y,z) * (x \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(29491(a,1),27804(a,2,1))].">
      <j1 rule="para" parents="29491 27804"/>
    </justification>
  </clause>

  <clause id="29493">
    <literal><![CDATA[
      L((L(x,y,z) * (x \ u)) \ u,w,x) = (L(x,y,z) * (x \ u)) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,29492,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 29492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29494">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(123,a,29492,a(flip),b,27703,a(flip))].">
      <j1 rule="hyper" parents="123 29492 27703"/>
    </justification>
  </clause>

  <clause id="29498">
    <literal><![CDATA[
      L((x * L(y,z,u)) \ (x * y),w,y) = (L(y,z,u) * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(29494(a,1),29493(a,1,1))].">
      <j1 rule="para" parents="29494 29493"/>
    </justification>
  </clause>

  <clause id="29499">
    <literal><![CDATA[
      L((x * L(y,z,u)) \ (x * y),w,y) = (x * L(y,z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,29494,a(flip),b,29498,a),flip(a)].">
      <j1 rule="hyper" parents="370 29494 29498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29500">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (u * L(x,y,z)) \ (u * x) = w
    ]]></literal>
    <justification jstring="[para(29498(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="29498 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29501">
    <literal><![CDATA[
      L(x \ ((x / L(y,z,u)) * y),w,y) = ((x / L(y,z,u)) * L(y,z,u)) \ ((x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),29499(a,1,1,1))].">
      <j1 rule="para" parents="7 29499"/>
    </justification>
  </clause>

  <clause id="29502">
    <literal><![CDATA[
      L(x \ (y * (L(y,z,u) \ x)),w,y) = ((x / L(y,z,u)) * L(y,z,u)) \ ((x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(24078(a,1),29501(a,1,1,2))].">
      <j1 rule="para" parents="24078 29501"/>
    </justification>
  </clause>

  <clause id="29503">
    <literal><![CDATA[
      L(x \ (y * (L(y,z,u) \ x)),w,y) = x \ ((x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),29502(a,2,1))].">
      <j1 rule="para" parents="7 29502"/>
    </justification>
  </clause>

  <clause id="29504">
    <literal><![CDATA[
      L(x \ (y * (L(y,z,u) \ x)),w,y) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(24078(a,1),29503(a,2,2))].">
      <j1 rule="para" parents="24078 29503"/>
    </justification>
  </clause>

  <clause id="29505">
    <literal><![CDATA[
      (x \ y) \ (L(x,z,u) \ y) = y \ (x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(1079,a,29504,a)].">
      <j1 rule="hyper" parents="1079 29504"/>
    </justification>
  </clause>

  <clause id="29506">
    <literal><![CDATA[
      (x * y) \ (x * (x * (L(x,z,u) \ y))) = y \ (x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,94,a(flip),b,29504,a)].">
      <j1 rule="hyper" parents="60 94 29504"/>
    </justification>
  </clause>

  <clause id="29507">
    <literal><![CDATA[
      L((x * (L(L(x,y,z),y,z) \ u)) \ w,x * (L(L(x,y,z),y,z) \ u),x \ L(L(x,y,z),y,z)) = u \ ((x \ L(L(x,y,z),y,z)) * w)
    ]]></literal>
    <justification jstring="[para(29085(a,1),29087(a,1,2))].">
      <j1 rule="para" parents="29085 29087"/>
    </justification>
  </clause>

  <clause id="29508">
    <literal><![CDATA[
      L(a(x \ 1,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = 1 * ((x \ a(z,u,x)) \ ((x \ 1) * (y * a(z,u,x))))
    ]]></literal>
    <justification jstring="[hyper(60,a,23517,a(flip),b,29182,a),flip(a)].">
      <j1 rule="hyper" parents="60 23517 29182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29510">
    <literal><![CDATA[
      L(a(x \ 1,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = 1 * ((a(z,u,x) * x) \ (x * (y * a(z,u,x))))
    ]]></literal>
    <justification jstring="[para(26351(a,1),29508(a,2,2))].">
      <j1 rule="para" parents="26351 29508"/>
    </justification>
  </clause>

  <clause id="29511">
    <literal><![CDATA[
      x * a(R(K(y,z) * u,w,v5),R(K(y,z) * u,w,v5),x * R(u,w,v5)) = R(u,w,v5) \ (K(z,y) * ((R(K(y,z) * u,w,v5) \ 1) \ x))
    ]]></literal>
    <justification jstring="[para(27030(a,1),28763(a,1,2))].">
      <j1 rule="para" parents="27030 28763"/>
    </justification>
  </clause>

  <clause id="29513">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ (1 * R(1 \ L(L(x,y,z),y,z),L(x,y,z) \ 1,u)),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2514(a,1),29074(a,1,1))].">
      <j1 rule="para" parents="2514 29074"/>
    </justification>
  </clause>

  <clause id="29514">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ (1 * R(L(L(x,y,z),y,z),L(x,y,z) \ 1,u)),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(62(a,1),29513(a,1,1,2,2,1))].">
      <j1 rule="para" parents="62 29513"/>
    </justification>
  </clause>

  <clause id="29515">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ (1 * L(R(L(x,y,z),L(x,y,z) \ 1,u),y,z)),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(24(a,1),29514(a,1,1,2,2))].">
      <j1 rule="para" parents="24 29514"/>
    </justification>
  </clause>

  <clause id="29516">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ (1 * L(R(L(x,y,z),L(x,y,z),u),y,z)),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2759(a,1),29515(a,1,1,2,2,1))].">
      <j1 rule="para" parents="2759 29515"/>
    </justification>
  </clause>

  <clause id="29517">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ (1 * L(L(R(x,L(x,y,z),u),y,z),y,z)),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(24(a,1),29516(a,1,1,2,2,1))].">
      <j1 rule="para" parents="24 29516"/>
    </justification>
  </clause>

  <clause id="29518">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ L(L(R(x,L(x,y,z),u),y,z),y,z),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2(a,1),29517(a,1,1,2))].">
      <j1 rule="para" parents="2 29517"/>
    </justification>
  </clause>

  <clause id="29519">
    <literal><![CDATA[
      L(L(L(x \ R(x,L(x,y,z),u),y,z),y,z),y,z) = a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(7816(a,1),29518(a,1,1))].">
      <j1 rule="para" parents="7816 29518"/>
    </justification>
  </clause>

  <clause id="29520">
    <literal><![CDATA[
      a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u) = L(L(a(L(x,y,z),L(x,y,z),u),y,z),y,z)
    ]]></literal>
    <justification jstring="[para(28465(a,1),29519(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28465 29519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29521">
    <literal><![CDATA[
      a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u) = L(a(L(x,y,z),L(L(x,y,z),y,z),u),y,z)
    ]]></literal>
    <justification jstring="[para(28461(a,2),29520(a,2,1))].">
      <j1 rule="para" parents="28461 29520"/>
    </justification>
  </clause>

  <clause id="29522">
    <literal><![CDATA[
      a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u) = L(a(x,x,L(u,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(29150(a,1),29521(a,2,1))].">
      <j1 rule="para" parents="29150 29521"/>
    </justification>
  </clause>

  <clause id="29523">
    <literal><![CDATA[
      a(L(L(L(x,y,z),y,z) \ 1,y,z),L(L(L(x,y,z),y,z) \ 1,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,29148,a(flip),b,29522,a),flip(a)].">
      <j1 rule="hyper" parents="370 29148 29522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29526">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(L(L(x,y,z),y,z) \ 1,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),29523(a,1,1))].">
      <j1 rule="para" parents="29064 29523"/>
    </justification>
  </clause>

  <clause id="29527">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(x,y,z) \ 1,u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),29526(a,1,2))].">
      <j1 rule="para" parents="29064 29526"/>
    </justification>
  </clause>

  <clause id="29528">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(3058,a,29527,a)].">
      <j1 rule="hyper" parents="3058 29527"/>
    </justification>
  </clause>

  <clause id="29529">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(2973,a,29528,a)].">
      <j1 rule="hyper" parents="2973 29528"/>
    </justification>
  </clause>

  <clause id="29530">
    <literal><![CDATA[
      a(L(x,y,z),L(L(L(x,u,w),u,w),y,z),v5) = a(x,x,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29034,a,b,29529,a)].">
      <j1 rule="hyper" parents="60 29034 29529"/>
    </justification>
  </clause>

  <clause id="29531">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27502,a,b,29529,a)].">
      <j1 rule="hyper" parents="60 27502 29529"/>
    </justification>
  </clause>

  <clause id="29532">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,x,u) = (1 / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(129,a,29529,a(flip),b,28731,a)].">
      <j1 rule="hyper" parents="129 29529 28731"/>
    </justification>
  </clause>

  <clause id="29533">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) \ a(L(x,y,z),L(x,y,z),x)) * x = x / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29529(a,1),28446(a,1,1,2))].">
      <j1 rule="para" parents="29529 28446"/>
    </justification>
  </clause>

  <clause id="29534">
    <literal><![CDATA[
      L(x,y,z) * (u * a(x,x,u)) = (1 / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(29529(a,1),28775(a,1,2,2))].">
      <j1 rule="para" parents="29529 28775"/>
    </justification>
  </clause>

  <clause id="29536">
    <literal><![CDATA[
      (1 / L(x,y,a(x,z,u))) \ w = (x * w) * a(x,x,w)
    ]]></literal>
    <justification jstring="[para(28709(a,1),29532(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28709 29532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29537">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * (u * a(x \ 1,x \ 1,u))) = x * ((1 / L(x \ 1,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(29534(a,1),4027(a,2,2))].">
      <j1 rule="para" parents="29534 4027"/>
    </justification>
  </clause>

  <clause id="29538">
    <literal><![CDATA[
      (1 / L(x,y,a(x,z,u))) \ w = (1 / x) \ w
    ]]></literal>
    <justification jstring="[hyper(370,a,28734,a(flip),b,29536,a),flip(a)].">
      <j1 rule="hyper" parents="370 28734 29536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29539">
    <literal><![CDATA[
      (1 / L(x,y,a(x,z,u))) \ w = R(x,x,w) * w
    ]]></literal>
    <justification jstring="[hyper(370,a,1961,a,b,29538,a),flip(a)].">
      <j1 rule="hyper" parents="370 1961 29538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29540">
    <literal><![CDATA[
      (1 / L(x,a(x,y,z),z)) \ u = R(x,x,u) * u
    ]]></literal>
    <justification jstring="[para(26346(a,2),29539(a,1,1,2))].">
      <j1 rule="para" parents="26346 29539"/>
    </justification>
  </clause>

  <clause id="29541">
    <literal><![CDATA[
      (1 / L(x,a(x,y,z),z)) \ u = u * R(T(x,u),x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,274,a,b,29540,a),flip(a)].">
      <j1 rule="hyper" parents="370 274 29540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29542">
    <literal><![CDATA[
      L(x,L(L(L(y,z,u),z,u),w,v5),L(L(L(y,z,u),z,u),w,v5)) = a(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(29530(a,1),29078(a,2,1))].">
      <j1 rule="para" parents="29530 29078"/>
    </justification>
  </clause>

  <clause id="29543">
    <literal><![CDATA[
      L(x,L(L(L(y,z,u),z,u),w,v5),L(L(L(y,z,u),z,u),w,v5)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3943,a(flip),b,29542,a),flip(a)].">
      <j1 rule="hyper" parents="370 3943 29542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29545">
    <literal><![CDATA[
      L(x,L(L(L(y,z,u),z,u),w,v5),L(y,w,v5)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29071,a(flip),b,29543,a)].">
      <j1 rule="hyper" parents="60 29071 29543"/>
    </justification>
  </clause>

  <clause id="29547">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29045,a(flip),b,29545,a)].">
      <j1 rule="hyper" parents="60 29045 29545"/>
    </justification>
  </clause>

  <clause id="29548">
    <literal><![CDATA[
      L(x,a(y,z,u),L(y \ R(y,z,u),y,u * z)) = L(x,y \ R(y,z,u),y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(29260(a,1),29545(a,1,2))].">
      <j1 rule="para" parents="29260 29545"/>
    </justification>
  </clause>

  <clause id="29550">
    <literal><![CDATA[
      (1 / (a(x,x,y) / x)) * y = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28475,a(flip),b,29547,a)].">
      <j1 rule="hyper" parents="60 28475 29547"/>
    </justification>
  </clause>

  <clause id="29551">
    <literal><![CDATA[
      L(R((x \ 1) \ 1,y,z) \ u,x,x) = 1 \ ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27616,a(flip),b,29547,a),flip(a)].">
      <j1 rule="hyper" parents="60 27616 29547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29552">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x,x) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(125,a,29547,a(flip),b,2074,a)].">
      <j1 rule="hyper" parents="125 29547 2074"/>
    </justification>
  </clause>

  <clause id="29553">
    <literal><![CDATA[
      L(x,(1 / y) * z,L(y \ z,y,y)) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),29547(a,1,2))].">
      <j1 rule="para" parents="586 29547"/>
    </justification>
  </clause>

  <clause id="29554">
    <literal><![CDATA[
      L(x,(y * z) \ u,L(z \ (y \ u),z,y)) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),29547(a,1,2))].">
      <j1 rule="para" parents="344 29547"/>
    </justification>
  </clause>

  <clause id="29555">
    <literal><![CDATA[
      L(x,L(y \ (z * u),w,v5),L(L((z \ y) \ u,w,v5),z \ y,z)) = L(x,L((z \ y) \ u,w,v5),L((z \ y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(1078(a,1),29547(a,1,2))].">
      <j1 rule="para" parents="1078 29547"/>
    </justification>
  </clause>

  <clause id="29558">
    <literal><![CDATA[
      a(x,y * (z \ (z \ u)),w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(29547(a,1),27669(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29547 27669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29559">
    <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(29547(a,1),29051(a,1,3))].">
      <j1 rule="para" parents="29547 29051"/>
    </justification>
  </clause>

  <clause id="29560">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(v5,z,z)) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(29547(a,1),29057(a,1,3,2))].">
      <j1 rule="para" parents="29547 29057"/>
    </justification>
  </clause>

  <clause id="29561">
    <literal><![CDATA[
      a(L(R(x,y,z) * u,x,x),w,v5) = a(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(29547(a,1),29102(a,1,1))].">
      <j1 rule="para" parents="29547 29102"/>
    </justification>
  </clause>

  <clause id="29562">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) * v5,z,z)) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(29547(a,1),29103(a,1,3))].">
      <j1 rule="para" parents="29547 29103"/>
    </justification>
  </clause>

  <clause id="29564">
    <literal><![CDATA[
      ((x \ a(x,x,y)) \ 1) * y = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(28236(a,1),29550(a,1,1))].">
      <j1 rule="para" parents="28236 29550"/>
    </justification>
  </clause>

  <clause id="29565">
    <literal><![CDATA[
      L(x * y,x,x) = (R(x \ 1,x,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(28424(a,2),29564(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28424 29564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29566">
    <literal><![CDATA[
      L(x \ (1 / y),x \ y,x \ y) = (R((x \ y) \ 1,x \ y,y \ (1 / y)) \ 1) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1221(a,1),29565(a,1,1))].">
      <j1 rule="para" parents="1221 29565"/>
    </justification>
  </clause>

  <clause id="29567">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,u,u)) = a(x,y,z \ (R(u \ 1,u,w) * w))
    ]]></literal>
    <justification jstring="[para(29565(a,2),3158(a,1,3,2))].">
      <j1 rule="para" parents="29565 3158"/>
    </justification>
  </clause>

  <clause id="29568">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) \ w) = a(x,y,(R(z \ 1,z,u) * u) \ w)
    ]]></literal>
    <justification jstring="[para(29565(a,2),3159(a,1,3,1))].">
      <j1 rule="para" parents="29565 3159"/>
    </justification>
  </clause>

  <clause id="29569">
    <literal><![CDATA[
      a(x,y,z * (L(u * w,u,u) \ (u * w))) = a(x,y,z * ((u * w) * ((R(u \ 1,u,w) \ 1) * w)))
    ]]></literal>
    <justification jstring="[para(29565(a,1),15777(a,2,3,2,2))].">
      <j1 rule="para" parents="29565 15777"/>
    </justification>
  </clause>

  <clause id="29570">
    <literal><![CDATA[
      a(x \ L(y * z,y,y),u,w) = a(x \ (R(y \ 1,y,z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(29565(a,2),26716(a,1,1,2))].">
      <j1 rule="para" parents="29565 26716"/>
    </justification>
  </clause>

  <clause id="29571">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,w * ((R(u \ 1,u,z) \ 1) * z))
    ]]></literal>
    <justification jstring="[para(29565(a,1),27061(a,2,3,2))].">
      <j1 rule="para" parents="29565 27061"/>
    </justification>
  </clause>

  <clause id="29572">
    <literal><![CDATA[
      a(x,y * (z \ L(u * w,u,u)),v5) = a(x,y * (z \ (R(u \ 1,u,w) * w)),v5)
    ]]></literal>
    <justification jstring="[para(29565(a,2),27544(a,1,2,2,2))].">
      <j1 rule="para" parents="29565 27544"/>
    </justification>
  </clause>

  <clause id="29573">
    <literal><![CDATA[
      x * ((1 / x) * (L(x,y,z) \ u)) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,4244,a,b,29552,a)].">
      <j1 rule="hyper" parents="60 4244 29552"/>
    </justification>
  </clause>

  <clause id="29575">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = L(x,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(2082(a,1),29552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2082 29552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29576">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L(u,x,x) = (L(x \ 1,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(3407(a,1),29552(a,1,2))].">
      <j1 rule="para" parents="3407 29552"/>
    </justification>
  </clause>

  <clause id="29577">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ L(u,1 / x,1 / x)) = x \ ((L(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29552(a,1),4160(a,2,2))].">
      <j1 rule="para" parents="29552 4160"/>
    </justification>
  </clause>

  <clause id="29578">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29552(a,1),4245(a,2,2))].">
      <j1 rule="para" parents="29552 4245"/>
    </justification>
  </clause>

  <clause id="29579">
    <literal><![CDATA[
      a(x,y * L(z,y,y),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),29558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 29558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29581">
    <literal><![CDATA[
      a(x,(y * (z * (u \ w))) * L(v5,y * (z * (w / u)),y * (z * (w / u))),v6) = a(x,(y * (z * (w / u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,29221,a(flip),b,29579,a)].">
      <j1 rule="hyper" parents="60 29221 29579"/>
    </justification>
  </clause>

  <clause id="29582">
    <literal><![CDATA[
      a(x,y * L(z,y \ 1,y \ 1),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(3407(a,2),29579(a,1,2,2))].">
      <j1 rule="para" parents="3407 29579"/>
    </justification>
  </clause>

  <clause id="29583">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(1143,a,29573,a)].">
      <j1 rule="hyper" parents="1143 29573"/>
    </justification>
  </clause>

  <clause id="29584">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(125,a,29573,a(flip),b,951,a)].">
      <j1 rule="hyper" parents="125 29573 951"/>
    </justification>
  </clause>

  <clause id="29586">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,29575,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 29575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29587">
    <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(29575(a,2),2194(a,1))].">
      <j1 rule="para" parents="29575 2194"/>
    </justification>
  </clause>

  <clause id="29588">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(x,y,z) \ 1) \ u)) = (x \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(125,a,5,a(flip),b,29583,a),flip(a)].">
      <j1 rule="hyper" parents="125 5 29583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29589">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * (L(x \ 1,y,z) \ u)) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(4017(a,2),29583(a,1,2))].">
      <j1 rule="para" parents="4017 29583"/>
    </justification>
  </clause>

  <clause id="29590">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * y = (x \ 1) * R(y,x,x)
    ]]></literal>
    <justification jstring="[para(6538(a,1),29583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6538 29583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29591">
    <literal><![CDATA[
      R((1 / x) * y,x,x) = (L(x,x,y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,4538,a,b,29590,a)].">
      <j1 rule="hyper" parents="370 4538 29590"/>
    </justification>
  </clause>

  <clause id="29592">
    <literal><![CDATA[
      L(x,y * R((1 / z) * u,z,z),w) = L(x,y * (L(z,z,u) * u),w)
    ]]></literal>
    <justification jstring="[para(29591(a,2),27586(a,1,2,2))].">
      <j1 rule="para" parents="29591 27586"/>
    </justification>
  </clause>

  <clause id="29594">
    <literal><![CDATA[
      x \ ((L(1 / x,y,z) \ 1) * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4308,a(flip),b,29584,a)].">
      <j1 rule="hyper" parents="60 4308 29584"/>
    </justification>
  </clause>

  <clause id="29595">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x * x) * u) = x * (L(x,y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[para(939(a,1),29586(a,1,2))].">
      <j1 rule="para" parents="939 29586"/>
    </justification>
  </clause>

  <clause id="29596">
    <literal><![CDATA[
      a(L(x,y,z) * ((x \ 1) \ u),w,v5) = a(x * (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(29586(a,1),2968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29586 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29597">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * ((z \ 1) \ v5)) = a(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(29586(a,1),3109(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29586 3109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29598">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) \ u) / L(x,y,z) = ((x \ 1) \ u) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,29588,a(flip),b,24078,a),flip(a)].">
      <j1 rule="hyper" parents="128 29588 24078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29599">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ 1) \ u)) = (L(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(29588(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="29588 69"/>
    </justification>
  </clause>

  <clause id="29600">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((x * (L(x,y,z) \ u)) / u) = a(x,L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(29594(a,1),28770(a,1,2,1))].">
      <j1 rule="para" parents="29594 28770"/>
    </justification>
  </clause>

  <clause id="29601">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ T(u,L(x,y,z)) = T(((x \ 1) \ u) / x,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29598(a,1),25176(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29598 25176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29602">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ ((x \ 1) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),29599(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 29599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29603">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (L(x,y,z) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29028,a,b,29602,a)].">
      <j1 rule="hyper" parents="60 29028 29602"/>
    </justification>
  </clause>

  <clause id="29604">
    <literal><![CDATA[
      L(x,(1 / y) * z,y * z) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(3519,a,29553,a)].">
      <j1 rule="hyper" parents="3519 29553"/>
    </justification>
  </clause>

  <clause id="29605">
    <literal><![CDATA[
      L(x,y \ z,y \ z) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(4129,a,29604,a),flip(a)].">
      <j1 rule="hyper" parents="4129 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29606">
    <literal><![CDATA[
      L(x,y \ z,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,y * z) = u
    ]]></literal>
    <justification jstring="[para(29604(a,1),4129(a,1))].">
      <j1 rule="para" parents="29604 4129"/>
    </justification>
  </clause>

  <clause id="29607">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,x * y) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(790,a,29605,a),flip(a)].">
      <j1 rule="hyper" parents="790 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29608">
    <literal><![CDATA[
      L(L(x,y,z),x * u,x * u) = L((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12459,a(flip),b,29605,a),flip(a)].">
      <j1 rule="hyper" parents="60 12459 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29609">
    <literal><![CDATA[
      L(R(x,y,z),x * u,x * u) = R((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12458,a(flip),b,29605,a),flip(a)].">
      <j1 rule="hyper" parents="60 12458 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29610">
    <literal><![CDATA[
      L(x,x * y,x * y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,12454,a(flip),b,29605,a),flip(a)].">
      <j1 rule="hyper" parents="60 12454 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29611">
    <literal><![CDATA[
      L(x,y * z,y * z) \ x = a(y \ z,y \ z,x)
    ]]></literal>
    <justification jstring="[para(29605(a,1),1362(a,1,1))].">
      <j1 rule="para" parents="29605 1362"/>
    </justification>
  </clause>

  <clause id="29612">
    <literal><![CDATA[
      L(x,L((y \ z) * u,y * z,y * z),w) = L(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(29605(a,1),28903(a,1,2))].">
      <j1 rule="para" parents="29605 28903"/>
    </justification>
  </clause>

  <clause id="29613">
    <literal><![CDATA[
      L(x,L(y,z * y,z * y),u) = L(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(29605(a,1),28912(a,1,2))].">
      <j1 rule="para" parents="29605 28912"/>
    </justification>
  </clause>

  <clause id="29614">
    <literal><![CDATA[
      a(x,y,L((z \ u) * w,z * u,z * u)) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(29605(a,1),29051(a,1,3))].">
      <j1 rule="para" parents="29605 29051"/>
    </justification>
  </clause>

  <clause id="29615">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = a(x,y,(z / u) \ u)
    ]]></literal>
    <justification jstring="[para(29605(a,1),29059(a,1,3))].">
      <j1 rule="para" parents="29605 29059"/>
    </justification>
  </clause>

  <clause id="29616">
    <literal><![CDATA[
      L(x,y * x,x * y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(26186,a,29610,a)].">
      <j1 rule="hyper" parents="26186 29610"/>
    </justification>
  </clause>

  <clause id="29617">
    <literal><![CDATA[
      L(x,y * x,y * x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(26097,a,29610,a)].">
      <j1 rule="hyper" parents="26097 29610"/>
    </justification>
  </clause>

  <clause id="29618">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y) * y,L(x,x,y) * y) = (1 / (y * (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(3402(a,1),29610(a,2,1,2))].">
      <j1 rule="para" parents="3402 29610"/>
    </justification>
  </clause>

  <clause id="29619">
    <literal><![CDATA[
      L(L(x,y,z),u * x,u * x) = L((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(29617(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29617 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29620">
    <literal><![CDATA[
      a(x * y,x * y,1 / y) = ((1 / (x / y)) * x) \ y
    ]]></literal>
    <justification jstring="[para(29617(a,1),3090(a,2,1))].">
      <j1 rule="para" parents="29617 3090"/>
    </justification>
  </clause>

  <clause id="29621">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (K(w,v5) / u),K(w,v5) * (a(x,y,z) \ (1 / u))) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(22781(a,1),29617(a,1,2))].">
      <j1 rule="para" parents="22781 29617"/>
    </justification>
  </clause>

  <clause id="29622">
    <literal><![CDATA[
      a(x,y,L(z,u * z,L(u,z,z))) = a(x,y,(1 / (u / z)) * u)
    ]]></literal>
    <justification jstring="[para(29617(a,1),27118(a,2,3))].">
      <j1 rule="para" parents="29617 27118"/>
    </justification>
  </clause>

  <clause id="29623">
    <literal><![CDATA[
      a(x * (L(x,y,y) * y),z,u) = a((1 / (x / y)) * x,z,u)
    ]]></literal>
    <justification jstring="[para(29617(a,1),27337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29617 27337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29624">
    <literal><![CDATA[
      L(x,y * ((1 / y) * ((1 / (y / z)) * y)),u) = L(x,((1 / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(29617(a,1),29223(a,1,2,2,2))].">
      <j1 rule="para" parents="29617 29223"/>
    </justification>
  </clause>

  <clause id="29625">
    <literal><![CDATA[
      a(x \ y,x \ y,z) = a(x * y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1364,a,29611,a),flip(a)].">
      <j1 rule="hyper" parents="1364 29611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29626">
    <literal><![CDATA[
      L(x,y,a(z * u,z * u,z)) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[para(29625(a,1),27957(a,1,3))].">
      <j1 rule="para" parents="29625 27957"/>
    </justification>
  </clause>

  <clause id="29627">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x * a(z,u,x),x * a(z,u,x)) = (1 / (x \ a(z,u,x))) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(25842(a,1),29607(a,1,1))].">
      <j1 rule="para" parents="25842 29607"/>
    </justification>
  </clause>

  <clause id="29628">
    <literal><![CDATA[
      L(x,(1 / (y / z)) * y,u) = L(x,(y \ z) \ y,u)
    ]]></literal>
    <justification jstring="[para(29617(a,1),29613(a,1,2))].">
      <j1 rule="para" parents="29617 29613"/>
    </justification>
  </clause>

  <clause id="29629">
    <literal><![CDATA[
      L(x,(y \ z) \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * y,u) = w
    ]]></literal>
    <justification jstring="[para(29628(a,1),26269(a,1))].">
      <j1 rule="para" parents="29628 26269"/>
    </justification>
  </clause>

  <clause id="29630">
    <literal><![CDATA[
      a(x,y,(1 / (z / u)) * z) = a(x,y,(u / z) \ z)
    ]]></literal>
    <justification jstring="[para(29617(a,1),29615(a,1,3))].">
      <j1 rule="para" parents="29617 29615"/>
    </justification>
  </clause>

  <clause id="29631">
    <literal><![CDATA[
      a(x,y,(z / u) \ u) = a(x,y,(u / z) * u)
    ]]></literal>
    <justification jstring="[hyper(27009,a,29630,a),flip(a)].">
      <j1 rule="hyper" parents="27009 29630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29632">
    <literal><![CDATA[
      a(x,y,(z / u) \ u) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26896,a(flip),b,29631,a),flip(a)].">
      <j1 rule="hyper" parents="370 26896 29631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29633">
    <literal><![CDATA[
      a(x,y,(z \ u) \ z) = a(x,y,(u \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(26998,a,29632,a)].">
      <j1 rule="hyper" parents="26998 29632"/>
    </justification>
  </clause>

  <clause id="29634">
    <literal><![CDATA[
      a(x * y,x * y,1 / y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28453,a(flip),b,29620,a),flip(a)].">
      <j1 rule="hyper" parents="370 28453 29620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29635">
    <literal><![CDATA[
      a(x * y,x * y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3102,a,29634,a)].">
      <j1 rule="hyper" parents="3102 29634"/>
    </justification>
  </clause>

  <clause id="29636">
    <literal><![CDATA[
      L(x,y,a(z,z * u,L(u,z,z))) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27958,a,b,29626,a)].">
      <j1 rule="hyper" parents="60 27958 29626"/>
    </justification>
  </clause>

  <clause id="29637">
    <literal><![CDATA[
      a(x,x,L(x,y,z) \ u) = a(x,x,L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(29149,a,29559,a),flip(a)].">
      <j1 rule="hyper" parents="29149 29559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29639">
    <literal><![CDATA[
      a(x,y,L(R(z \ 1,u,w) * v5,z,z)) = a(x,y,R(z,u,w) \ ((z * z) \ v5))
    ]]></literal>
    <justification jstring="[para(2301(a,1),29562(a,1,3,1))].">
      <j1 rule="para" parents="2301 29562"/>
    </justification>
  </clause>

  <clause id="29641">
    <literal><![CDATA[
      a(x * ((L(x,y,z) \ 1) * u),w,v5) = a(x \ (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(29578(a,1),29037(a,1,1))].">
      <j1 rule="para" parents="29578 29037"/>
    </justification>
  </clause>

  <clause id="29642">
    <literal><![CDATA[
      a(x,y,z * ((L(z,u,w) \ 1) * v5)) = a(x,y,z \ (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(29578(a,1),29051(a,1,3))].">
      <j1 rule="para" parents="29578 29051"/>
    </justification>
  </clause>

  <clause id="29643">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),(a(x,y,z) \ u) * a(x,y,z),(a(x,y,z) \ u) * a(x,y,z)) = L((1 / (a(x,y,z) * (a(x,y,z) / u))) * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(28237(a,1),29608(a,2,1,1,2))].">
      <j1 rule="para" parents="28237 29608"/>
    </justification>
  </clause>

  <clause id="29644">
    <literal><![CDATA[
      L(x,L((1 / (y / z)) * y,y,y),u) = L(x,(z * y) \ (1 / ((z * y) / z)),u)
    ]]></literal>
    <justification jstring="[para(29608(a,1),28914(a,1,2))].">
      <j1 rule="para" parents="29608 28914"/>
    </justification>
  </clause>

  <clause id="29645">
    <literal><![CDATA[
      L(x,x * y,x * y) \ R((1 / (y / x)) * y,z,u) = L(x \ R(x,z,u),x * y,x * y)
    ]]></literal>
    <justification jstring="[para(29609(a,1),7812(a,1,2))].">
      <j1 rule="para" parents="29609 7812"/>
    </justification>
  </clause>

  <clause id="29646">
    <literal><![CDATA[
      L((1 / (x / y)) * x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / (x * y)) * (x * (y * y)) = z
    ]]></literal>
    <justification jstring="[para(29619(a,1),994(a,1))].">
      <j1 rule="para" parents="29619 994"/>
    </justification>
  </clause>

  <clause id="29647">
    <literal><![CDATA[
      a(x * (L(x,y,y) * y),z,u) = a((x / y) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,2958,a(flip),b,29623,a),flip(a)].">
      <j1 rule="hyper" parents="370 2958 29623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29648">
    <literal><![CDATA[
      a(x * (L(x,y,y) * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(29647(a,2),26524(a,1))].">
      <j1 rule="para" parents="29647 26524"/>
    </justification>
  </clause>

  <clause id="29649">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x * x) * u) = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(2160(a,1),29595(a,2,2))].">
      <j1 rule="para" parents="2160 29595"/>
    </justification>
  </clause>

  <clause id="29650">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (L(x,y,z) * (x \ (L(x,y,z) \ u))) = u \ (L(L(x,y,z),y,z) * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(29603(a,1),16187(a,1,2))].">
      <j1 rule="para" parents="29603 16187"/>
    </justification>
  </clause>

  <clause id="29651">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = a(x,y,z) * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(29262(a,1),29603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29262 29603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29652">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) * ((x \ 1) \ a(x,u,w))) = (1 / L(x \ 1,y,z)) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[para(29603(a,1),29438(a,1,2))].">
      <j1 rule="para" parents="29603 29438"/>
    </justification>
  </clause>

  <clause id="29653">
    <literal><![CDATA[
      a(x,y,L(z,u * z,L(u,z,z))) = a(x,y,(u / z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3079,a(flip),b,29622,a),flip(a)].">
      <j1 rule="hyper" parents="370 3079 29622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29654">
    <literal><![CDATA[
      a(x,y,L(z,u * z,L(u,z,z))) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26896,a(flip),b,29653,a),flip(a)].">
      <j1 rule="hyper" parents="370 26896 29653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29655">
    <literal><![CDATA[
      (L(x,y,z) \ (x * x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,573,a(flip),b,29649,a)].">
      <j1 rule="hyper" parents="60 573 29649"/>
    </justification>
  </clause>

  <clause id="29656">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(2160(a,1),29655(a,1,1))].">
      <j1 rule="para" parents="2160 29655"/>
    </justification>
  </clause>

  <clause id="29657">
    <literal><![CDATA[
      L(x,(y * (L(y,z,u) \ y)) \ y,y * (L(y,z,u) \ y)) = y * (L(y,z,u) \ (((y * (L(y,z,u) \ y)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(1060,a,29656,a)].">
      <j1 rule="hyper" parents="1060 29656"/>
    </justification>
  </clause>

  <clause id="29658">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ T(u,x * (L(x,y,z) \ x)))) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(328,a,29656,a),flip(a)].">
      <j1 rule="hyper" parents="328 29656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29660">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) * y) * ((x * y) \ (y * (y * (L(y,z,u) \ x)))) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(29656(a,1),25993(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="29656 25993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29661">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (L(a(x,y,z),u,w) \ v5)) = L(a(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(29291(a,1),29656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29291 29656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29662">
    <literal><![CDATA[
      L(R((x \ 1) \ 1,y,z) \ u,x,x) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(370,a,62,a(flip),b,29551,a),flip(a)].">
      <j1 rule="hyper" parents="370 62 29551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29664">
    <literal><![CDATA[
      (x \ 1) \ ((R(x,y,z) \ 1) * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29662(a,1),3255(a,1,2))].">
      <j1 rule="para" parents="29662 3255"/>
    </justification>
  </clause>

  <clause id="29665">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,u,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(2784(a,1),29567(a,2,3,2))].">
      <j1 rule="para" parents="2784 29567"/>
    </justification>
  </clause>

  <clause id="29666">
    <literal><![CDATA[
      a(x,y,z \ L(u * (w \ 1),w,w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,28675,a,b,29665,a)].">
      <j1 rule="hyper" parents="60 28675 29665"/>
    </justification>
  </clause>

  <clause id="29667">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,u,u))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27228,a(flip),b,29665,a)].">
      <j1 rule="hyper" parents="60 27228 29665"/>
    </justification>
  </clause>

  <clause id="29668">
    <literal><![CDATA[
      a(x,y,z \ (u \ (u \ w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),29665(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="5 29665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29669">
    <literal><![CDATA[
      a(x,y,z \ L(u * w,w,w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,28048,a(flip),b,29666,a)].">
      <j1 rule="hyper" parents="60 28048 29666"/>
    </justification>
  </clause>

  <clause id="29670">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) \ w) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(2784(a,1),29568(a,2,3,1))].">
      <j1 rule="para" parents="2784 29568"/>
    </justification>
  </clause>

  <clause id="29671">
    <literal><![CDATA[
      a(x \ L(y * z,y,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(2784(a,1),29570(a,2,1,2))].">
      <j1 rule="para" parents="2784 29570"/>
    </justification>
  </clause>

  <clause id="29672">
    <literal><![CDATA[
      a(x \ (y * L(z,y,y)),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26726,a(flip),b,29671,a)].">
      <j1 rule="hyper" parents="60 26726 29671"/>
    </justification>
  </clause>

  <clause id="29673">
    <literal><![CDATA[
      a(R(x,L(y,x,x),L(y,x,x)) \ (x \ y),z,u) = a(L(L(y,x,x),L(y,x,x),x),z,u)
    ]]></literal>
    <justification jstring="[para(3730(a,1),29672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3730 29672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29674">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ u,x,x) = (L(x \ 1,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,14141,a(flip),b,29589,a)].">
      <j1 rule="hyper" parents="60 14141 29589"/>
    </justification>
  </clause>

  <clause id="29675">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,29405,a(flip),b,29674,a),flip(a)].">
      <j1 rule="hyper" parents="370 29405 29674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29676">
    <literal><![CDATA[
      L(x,y * R((1 / z) * u,z,z),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,28491,a(flip),b,29592,a),flip(a)].">
      <j1 rule="hyper" parents="370 28491 29592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29677">
    <literal><![CDATA[
      L(x,(y \ (z * K(u,w))) * v5,v6) = L(x,v5 * ((y \ 1) * ((z * y) * y)),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27826,a(flip),b,29676,a),flip(a)].">
      <j1 rule="hyper" parents="60 27826 29676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29678">
    <literal><![CDATA[
      a(L(x,y,z) * (x \ u),w,v5) = a(x * (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26643,a,29596,a)].">
      <j1 rule="hyper" parents="26643 29596"/>
    </justification>
  </clause>

  <clause id="29679">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ (x \ u)),w,v5) = a(L(R(x,y,z) * u,x,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29101,a(flip),b,29678,a),flip(a)].">
      <j1 rule="hyper" parents="60 29101 29678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29680">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z,w,v5)) = a(x,y,z * (L(z,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(26936,a,29597,a)].">
      <j1 rule="hyper" parents="26936 29597"/>
    </justification>
  </clause>

  <clause id="29681">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (z \ v5)) = a(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(26965,a,29680,a)].">
      <j1 rule="hyper" parents="26965 29680"/>
    </justification>
  </clause>

  <clause id="29682">
    <literal><![CDATA[
      a(x \ (L(x,y,z) \ u),w,v5) = a((L(x,y,z) * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26786,a(flip),b,29641,a),flip(a)].">
      <j1 rule="hyper" parents="60 26786 29641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29683">
    <literal><![CDATA[
      a(x \ (L(x,y,z) \ u),w,v5) = a(x * (L(x,y,z) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,29682,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 29682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29684">
    <literal><![CDATA[
      a(x \ (L(x,y,z) \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (L(x,y,z) * u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(29682(a,2),26519(a,1))].">
      <j1 rule="para" parents="29682 26519"/>
    </justification>
  </clause>

  <clause id="29685">
    <literal><![CDATA[
      a(x,y,z \ (L(z,u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (L(z,u,w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(29642(a,1),27080(a,1))].">
      <j1 rule="para" parents="29642 27080"/>
    </justification>
  </clause>

  <clause id="29686">
    <literal><![CDATA[
      a(L(R(x,y,z) * u,x,x),w,v5) = a(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(2161(a,1),29679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2161 29679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29687">
    <literal><![CDATA[
      a(R(x,y,z) \ u,w,v5) = a(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29561,a(flip),b,29686,a)].">
      <j1 rule="hyper" parents="60 29561 29686"/>
    </justification>
  </clause>

  <clause id="29688">
    <literal><![CDATA[
      a(L(T(x,y * y),y,y) \ z,u,w) = a(((x * y) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26708,a(flip),b,29687,a),flip(a)].">
      <j1 rule="hyper" parents="60 26708 29687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29689">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,y) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(29688(a,1),26532(a,1))].">
      <j1 rule="para" parents="29688 26532"/>
    </justification>
  </clause>

  <clause id="29690">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,w * (R(u \ 1,u,z) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27079,a(flip),b,29571,a),flip(a)].">
      <j1 rule="hyper" parents="370 27079 29571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29691">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[para(2784(a,1),29690(a,2,3,2))].">
      <j1 rule="para" parents="2784 29690"/>
    </justification>
  </clause>

  <clause id="29692">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u \ (x * (L(x,y,z) \ u))) = a(x,L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(25643(a,1),29600(a,1,2))].">
      <j1 rule="para" parents="25643 29600"/>
    </justification>
  </clause>

  <clause id="29693">
    <literal><![CDATA[
      L(x,L(1 / (y / z),y,y) * y,u) = L(x,((1 / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(877(a,1),29624(a,1,2))].">
      <j1 rule="para" parents="877 29624"/>
    </justification>
  </clause>

  <clause id="29694">
    <literal><![CDATA[
      L(x,((1 / y) * z) \ y,u) = L(x,y \ (1 / (y / z)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28911,a(flip),b,29693,a),flip(a)].">
      <j1 rule="hyper" parents="60 28911 29693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29695">
    <literal><![CDATA[
      L(x,((1 / y) * z) \ y,u) = L(x,y \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3722,a(flip),b,29694,a),flip(a)].">
      <j1 rule="hyper" parents="370 3722 29694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29696">
    <literal><![CDATA[
      L(x,((1 / y) * z) \ y,u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26111,a(flip),b,29695,a),flip(a)].">
      <j1 rule="hyper" parents="370 26111 29695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29697">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3718,a(flip),b,29696,a)].">
      <j1 rule="hyper" parents="60 3718 29696"/>
    </justification>
  </clause>

  <clause id="29698">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * ((u * z) * z)),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[para(205(a,1),29677(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="205 29677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29699">
    <literal><![CDATA[
      L(x,y * (z * ((u * z) * z)),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27586,a(flip),b,29698,a)].">
      <j1 rule="hyper" parents="60 27586 29698"/>
    </justification>
  </clause>

  <clause id="29700">
    <literal><![CDATA[
      L(x,y * L(z * u,u,u),w) = L(x,(u \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27784,a(flip),b,29699,a)].">
      <j1 rule="hyper" parents="60 27784 29699"/>
    </justification>
  </clause>

  <clause id="29701">
    <literal><![CDATA[
      L(x,(y \ z) * x,x * L(z * y,y,y)) = (1 / (L(z * y,y,y) / x)) * L(z * y,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29610,a(flip),b,29700,a),flip(a)].">
      <j1 rule="hyper" parents="60 29610 29700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29702">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u \ (x * (L(x,y,z) \ u))) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3113,a(flip),b,29692,a),flip(a)].">
      <j1 rule="hyper" parents="370 3113 29692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29703">
    <literal><![CDATA[
      L(x,(y * z) \ u,(y * z) \ u) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(344(a,1),29554(a,1,3))].">
      <j1 rule="para" parents="344 29554"/>
    </justification>
  </clause>

  <clause id="29704">
    <literal><![CDATA[
      L(x,y \ (z \ u),y \ (z \ u)) = L(x,(z * y) * u,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(29606,a,29703,a),flip(a)].">
      <j1 rule="hyper" parents="29606 29703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29705">
    <literal><![CDATA[
      L(x,(y * z) * u,(y * z) * u) = L(x,z * (y \ u),z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(29606,a,29704,a),flip(a)].">
      <j1 rule="hyper" parents="29606 29704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29706">
    <literal><![CDATA[
      L(x,(y * z) * u,(y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * (y \ u),z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(29704(a,1),29606(a,1))].">
      <j1 rule="para" parents="29704 29606"/>
    </justification>
  </clause>

  <clause id="29707">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),w * (u \ z),w * (u \ z))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[para(29705(a,1),29364(a,1,3))].">
      <j1 rule="para" parents="29705 29364"/>
    </justification>
  </clause>

  <clause id="29708">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ T(u,L(x,y,z)) = (x \ ((x \ 1) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),29601(a,2,1))].">
      <j1 rule="para" parents="109 29601"/>
    </justification>
  </clause>

  <clause id="29710">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * L(x,z,u) = (L(x,z,u) \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(23594(a,1),29708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23594 29708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29712">
    <literal><![CDATA[
      a(x,y,L(R(z \ 1,u,w) * v5,z,z)) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,3146,a(flip),b,29639,a),flip(a)].">
      <j1 rule="hyper" parents="370 3146 29639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29714">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L(v5,z,z)) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27859,a(flip),b,29712,a)].">
      <j1 rule="hyper" parents="60 27859 29712"/>
    </justification>
  </clause>

  <clause id="29715">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(v5,z,z)) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,28605,a(flip),b,29714,a)].">
      <j1 rule="hyper" parents="60 28605 29714"/>
    </justification>
  </clause>

  <clause id="29716">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29560,a(flip),b,29715,a),flip(a)].">
      <j1 rule="hyper" parents="60 29560 29715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29717">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) * ((u \ 1) \ 1)) \ w) = a(x,y,L(u * z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(27099,a,29716,a)].">
      <j1 rule="hyper" parents="27099 29716"/>
    </justification>
  </clause>

  <clause id="29718">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) * ((u \ 1) \ 1)) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,29670,a(flip),b,29717,a),flip(a)].">
      <j1 rule="hyper" parents="370 29670 29717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29719">
    <literal><![CDATA[
      a(x,y,R(z * u,u,u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(1517(a,1),29718(a,1,3,1))].">
      <j1 rule="para" parents="1517 29718"/>
    </justification>
  </clause>

  <clause id="29720">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29716,a(flip),b,29719,a)].">
      <j1 rule="hyper" parents="60 29716 29719"/>
    </justification>
  </clause>

  <clause id="29721">
    <literal><![CDATA[
      L(x,(y * z) \ (1 / ((y * z) / y)),u) = L(x,z \ (1 / (z / y)),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28910,a(flip),b,29644,a),flip(a)].">
      <j1 rule="hyper" parents="60 28910 29644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29722">
    <literal><![CDATA[
      L(x,(y * z) \ (1 / ((y * z) / y)),u) = L(x,z \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3722,a(flip),b,29721,a),flip(a)].">
      <j1 rule="hyper" parents="370 3722 29721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29723">
    <literal><![CDATA[
      L(x,(y * z) \ (1 / ((y * z) / y)),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26111,a(flip),b,29722,a),flip(a)].">
      <j1 rule="hyper" parents="370 26111 29722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29724">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * z) / y),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(26215,a,29723,a)].">
      <j1 rule="hyper" parents="26215 29723"/>
    </justification>
  </clause>

  <clause id="29725">
    <literal><![CDATA[
      L(x,(y * z) \ (y \ (y * z)),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(26273,a,29724,a)].">
      <j1 rule="hyper" parents="26273 29724"/>
    </justification>
  </clause>

  <clause id="29726">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(4(a,1),29725(a,1,2,2))].">
      <j1 rule="para" parents="4 29725"/>
    </justification>
  </clause>

  <clause id="29727">
    <literal><![CDATA[
      a(x,y * (z \ L(u * w,u,u)),v5) = a(x,y * (z \ (u \ w)),v5)
    ]]></literal>
    <justification jstring="[para(2784(a,1),29572(a,2,2,2,2))].">
      <j1 rule="para" parents="2784 29572"/>
    </justification>
  </clause>

  <clause id="29728">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (L(a(x,y,z),u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v6
    ]]></literal>
    <justification jstring="[para(29651(a,1),2166(a,1,2))].">
      <j1 rule="para" parents="29651 2166"/>
    </justification>
  </clause>

  <clause id="29729">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (L(a(x,y,z),a(x,y,z),u) \ u)) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,28371,a(flip),b,29661,a),flip(a)].">
      <j1 rule="hyper" parents="370 28371 29661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29730">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) \ a(L(x,y,z),x,L(x,y,z))) * x = x / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2564(a,1),29533(a,1,1,2))].">
      <j1 rule="para" parents="2564 29533"/>
    </justification>
  </clause>

  <clause id="29732">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ L(u,x,x)) = x \ ((L(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3400(a,1),29577(a,1,2,2))].">
      <j1 rule="para" parents="3400 29577"/>
    </justification>
  </clause>

  <clause id="29733">
    <literal><![CDATA[
      (x \ y) \ L(z,y \ x,y \ x) = (L(1 / (y \ x),y \ x,x) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(4189,a,29732,a)].">
      <j1 rule="hyper" parents="4189 29732"/>
    </justification>
  </clause>

  <clause id="29734">
    <literal><![CDATA[
      (x \ y) \ L(z,y * x,y * x) = (L(1 / (y \ x),y \ x,x) \ 1) * z
    ]]></literal>
    <justification jstring="[para(29605(a,1),29733(a,1,2))].">
      <j1 rule="para" parents="29605 29733"/>
    </justification>
  </clause>

  <clause id="29735">
    <literal><![CDATA[
      (x \ y) \ L(z,y * x,y * x) = ((x \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(3418(a,1),29734(a,2,1,1))].">
      <j1 rule="para" parents="3418 29734"/>
    </justification>
  </clause>

  <clause id="29736">
    <literal><![CDATA[
      L(x,y * (z \ y),y * (z \ y)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(16286,a,29735,a),flip(a)].">
      <j1 rule="hyper" parents="16286 29735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29737">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ T(u,x))) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25347(a,1),29658(a,1,2,2,2))].">
      <j1 rule="para" parents="25347 29658"/>
    </justification>
  </clause>

  <clause id="29738">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(2197(a,1),29737(a,1,2))].">
      <j1 rule="para" parents="2197 29737"/>
    </justification>
  </clause>

  <clause id="29741">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) \ a(x,x,L(L(x,y,z),y,z))) * x = x / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29145(a,1),29730(a,1,1,2))].">
      <j1 rule="para" parents="29145 29730"/>
    </justification>
  </clause>

  <clause id="29742">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) \ K(x,x \ 1)) * x = x / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14194(a,1),29741(a,1,1,2))].">
      <j1 rule="para" parents="14194 29741"/>
    </justification>
  </clause>

  <clause id="29743">
    <literal><![CDATA[
      (1 / L(L(x,y,z),u,w)) * x = x / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(7216(a,1),29742(a,1,1))].">
      <j1 rule="para" parents="7216 29742"/>
    </justification>
  </clause>

  <clause id="29745">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ 1) = x / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25178,a(flip),b,29743,a)].">
      <j1 rule="hyper" parents="60 25178 29743"/>
    </justification>
  </clause>

  <clause id="29746">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ 1) = L(L(x,u,w),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,12744,a(flip),b,29745,a),flip(a)].">
      <j1 rule="hyper" parents="370 12744 29745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29747">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),v5,x) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) * (L(x \ R(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28678(a,1),29746(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="28678 29746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29748">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (u * (a(x,y,z) \ 1))) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(23630(a,1),29729(a,1,2,2))].">
      <j1 rule="para" parents="23630 29729"/>
    </justification>
  </clause>

  <clause id="29749">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),a(x,y,z)) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(23820(a,1),29748(a,1,2))].">
      <j1 rule="para" parents="23820 29748"/>
    </justification>
  </clause>

  <clause id="29750">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),a(y,z,u),a(y,z,u)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(125,a,23821,a(flip),b,29749,a),flip(a)].">
      <j1 rule="hyper" parents="125 23821 29749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29751">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),a(y,z,u),a(y,z,u)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (a(y,z,u) \ x) = v5
    ]]></literal>
    <justification jstring="[para(29750(a,2),719(a,1))].">
      <j1 rule="para" parents="29750 719"/>
    </justification>
  </clause>

  <clause id="29752">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * (u * a(x \ 1,x,u))) = x * ((1 / L(x \ 1,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(3050(a,1),29537(a,1,2,2,2))].">
      <j1 rule="para" parents="3050 29537"/>
    </justification>
  </clause>

  <clause id="29753">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * (u * a(x,x,u))) = x * ((1 / L(x \ 1,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(2962(a,1),29752(a,1,2,2,2))].">
      <j1 rule="para" parents="2962 29752"/>
    </justification>
  </clause>

  <clause id="29754">
    <literal><![CDATA[
      x * ((1 / L(x \ 1,y,z)) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(28792(a,1),29753(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28792 29753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29755">
    <literal><![CDATA[
      x * ((L(1 / x,y,z) \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5071(a,1),29754(a,1,2,1))].">
      <j1 rule="para" parents="5071 29754"/>
    </justification>
  </clause>

  <clause id="29756">
    <literal><![CDATA[
      x * ((a(y,x,x) * x) \ z) = L(x,x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(28846(a,1),29755(a,1,2,1))].">
      <j1 rule="para" parents="28846 29755"/>
    </justification>
  </clause>

  <clause id="29757">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y \ R(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25668,a(flip),b,29548,a),flip(a)].">
      <j1 rule="hyper" parents="60 25668 29548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29758">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y \ L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(27266,a,29757,a)].">
      <j1 rule="hyper" parents="27266 29757"/>
    </justification>
  </clause>

  <clause id="29759">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y * L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14694,a,29758,a)].">
      <j1 rule="hyper" parents="14694 29758"/>
    </justification>
  </clause>

  <clause id="29760">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,a(x,y,z),a(x,y,z)) = 1 \ ((R(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27278,a(flip),b,29759,a),flip(a)].">
      <j1 rule="hyper" parents="60 27278 29759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29761">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,a(x,y,z),a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(29760(a,2),190(a,1)),flip(b)].">
      <j1 rule="para" parents="29760 190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29762">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * u,x * u) = ((1 / (u / x)) * u) \ R((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(29610(a,1),29645(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29610 29645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29763">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * u,x * u) = ((x \ u) * u) \ R((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29346,a(flip),b,29762,a),flip(a)].">
      <j1 rule="hyper" parents="370 29346 29762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29764">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * u,x * u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,29350,a(flip),b,29763,a),flip(a)].">
      <j1 rule="hyper" parents="370 29350 29763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29765">
    <literal><![CDATA[
      ((x \ y) \ y) \ ((x \ y) \ R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,29736,a(flip),b,29764,a),flip(a)].">
      <j1 rule="hyper" parents="60 29736 29764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29766">
    <literal><![CDATA[
      x \ ((y / x) \ R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,8530,a(flip),b,29765,a)].">
      <j1 rule="hyper" parents="60 8530 29765"/>
    </justification>
  </clause>

  <clause id="29767">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ R(y,z,u)) = x * L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,29765,a(flip),b,7961,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 29765 7961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29768">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ R(y,z,u)) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,29279,a(flip),b,29767,a),flip(a)].">
      <j1 rule="hyper" parents="370 29279 29767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29769">
    <literal><![CDATA[
      (1 / x) \ (y \ R(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(8570,a,29768,a),flip(a)].">
      <j1 rule="hyper" parents="8570 29768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29770">
    <literal><![CDATA[
      (1 / x) \ a(y,y,z) = (y / x) \ R(y,y,z)
    ]]></literal>
    <justification jstring="[para(28417(a,1),29769(a,1,2))].">
      <j1 rule="para" parents="28417 29769"/>
    </justification>
  </clause>

  <clause id="29771">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ a(w,w,v5))) = a(x,y,z * ((w / u) \ R(w,w,v5)))
    ]]></literal>
    <justification jstring="[para(29770(a,1),27023(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29770 27023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29772">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ R(u,u,v5))) = a(x,y,(w \ a(u,u,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(26936,a,29771,a),flip(a)].">
      <j1 rule="hyper" parents="26936 29771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29773">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ R(w,w,v5))) = a(x,y,(u \ a(w,w,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(27094,a,29772,a)].">
      <j1 rule="hyper" parents="27094 29772"/>
    </justification>
  </clause>

  <clause id="29774">
    <literal><![CDATA[
      (1 / L(x \ 1,y,z)) \ a(x,u,w) = L(x \ 1,y,z) * a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(2166,a,29652,a),flip(a)].">
      <j1 rule="hyper" parents="2166 29652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29775">
    <literal><![CDATA[
      L(x \ (1 / y),x * y,x * y) = (R((x \ y) \ 1,x \ y,y \ (1 / y)) \ 1) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(29606,a,29566,a)].">
      <j1 rule="hyper" parents="29606 29566"/>
    </justification>
  </clause>

  <clause id="29776">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * ((R(u \ 1,u,w) \ 1) * w))) = a(x,y,z * a(u,u,u * w))
    ]]></literal>
    <justification jstring="[para(1362(a,1),29569(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1362 29569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29777">
    <literal><![CDATA[
      a(x,y,((z * u) * (u * R(z \ 1,z,u))) * w) = a(x,y,w * a(z,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27186,a(flip),b,29776,a)].">
      <j1 rule="hyper" parents="60 27186 29776"/>
    </justification>
  </clause>

  <clause id="29778">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ T(u,z \ 1))) * w) = a(x,y,w * a(z,z,z * u))
    ]]></literal>
    <justification jstring="[para(6157(a,1),29777(a,1,3,1,2))].">
      <j1 rule="para" parents="6157 29777"/>
    </justification>
  </clause>

  <clause id="29779">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ u)) * w) = a(x,y,w * a(z,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27128,a(flip),b,29778,a)].">
      <j1 rule="hyper" parents="60 27128 29778"/>
    </justification>
  </clause>

  <clause id="29781">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ y)) * ((x * y) \ (y * (y * (L(y,z,u) \ x)))) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(23873(a,1),29660(a,1,1,2))].">
      <j1 rule="para" parents="23873 29660"/>
    </justification>
  </clause>

  <clause id="29782">
    <literal><![CDATA[
      L(x \ (1 / y),x * y,x * y) = (((x \ y) \ 1) \ 1) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(699(a,1),29775(a,2,1,1))].">
      <j1 rule="para" parents="699 29775"/>
    </justification>
  </clause>

  <clause id="29784">
    <literal><![CDATA[
      L(x \ (1 / y),x * y,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ (y \ (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(29782(a,2),1462(a,1))].">
      <j1 rule="para" parents="29782 1462"/>
    </justification>
  </clause>

  <clause id="29785">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ (y * (y * (L(y,z,u) \ x)))) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(25881(a,1),29781(a,1,1))].">
      <j1 rule="para" parents="25881 29781"/>
    </justification>
  </clause>

  <clause id="29786">
    <literal><![CDATA[
      (x * y) \ (x * (x * (L(x,z,u) \ y))) = L(L(x,z,u) \ x,x,y)
    ]]></literal>
    <justification jstring="[hyper(12091,a,29785,a)].">
      <j1 rule="hyper" parents="12091 29785"/>
    </justification>
  </clause>

  <clause id="29788">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29506,a(flip),b,29786,a),flip(a)].">
      <j1 rule="hyper" parents="60 29506 29786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29789">
    <literal><![CDATA[
      x \ (y * (L(y,z,z) \ x)) = a(z,z,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(29135,a,29788,a),flip(a)].">
      <j1 rule="hyper" parents="29135 29788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29790">
    <literal><![CDATA[
      x \ ((x \ y) * (L(x \ y,z,u) \ x)) = y \ (x * (L(1 / (x \ y),z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(3895,a,29788,a),flip(a)].">
      <j1 rule="hyper" parents="3895 29788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29791">
    <literal><![CDATA[
      x * (L(y,z,x) \ y) = y * (L(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(129,a,29009,a(flip),b,29788,a(flip))].">
      <j1 rule="hyper" parents="129 29009 29788"/>
    </justification>
  </clause>

  <clause id="29792">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * K(u \ (x * (L(x,y,z) \ u)),u) = L(L(x,y,z) \ x,x,u) * u
    ]]></literal>
    <justification jstring="[para(29788(a,2),353(a,2,1))].">
      <j1 rule="para" parents="29788 353"/>
    </justification>
  </clause>

  <clause id="29793">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,u) = (u \ (x * (L(x,y,z) \ u))) * ((L(x,y,z) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(29788(a,1),1771(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29788 1771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29794">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ (L(y,z,u) \ y) = (L(y,z,u) \ y) * (L(L(y,z,u) \ y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(29788(a,1),2162(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29788 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29795">
    <literal><![CDATA[
      x \ (y * (L(y,z,z) \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,z,L(y,y,x)) = u
    ]]></literal>
    <justification jstring="[para(29788(a,1),29135(a,1))].">
      <j1 rule="para" parents="29788 29135"/>
    </justification>
  </clause>

  <clause id="29796">
    <literal><![CDATA[
      L(x \ y,z,x) \ (x \ y) = x \ (L(y / x,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,25657,a(flip),b,29791,a),flip(a)].">
      <j1 rule="hyper" parents="125 25657 29791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29797">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) * z = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,23634,a,b,29789,a)].">
      <j1 rule="hyper" parents="35 23634 29789"/>
    </justification>
  </clause>

  <clause id="29798">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) != u * z
    ]]></literal>
    <literal><![CDATA[
      a(y,y,L(x,x,z)) = u
    ]]></literal>
    <justification jstring="[para(29797(a,1),41(a,1))].">
      <j1 rule="para" parents="29797 41"/>
    </justification>
  </clause>

  <clause id="29799">
    <literal><![CDATA[
      L(x \ y,x,x) \ (x \ y) = x \ (y / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(12750(a,1),29796(a,2,2))].">
      <j1 rule="para" parents="12750 29796"/>
    </justification>
  </clause>

  <clause id="29800">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ y) = x \ (y / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(586(a,1),29799(a,1,1))].">
      <j1 rule="para" parents="586 29799"/>
    </justification>
  </clause>

  <clause id="29801">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((1 / x) \ y) = x \ (y / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,27996,a,b,29800,a)].">
      <j1 rule="hyper" parents="60 27996 29800"/>
    </justification>
  </clause>

  <clause id="29802">
    <literal><![CDATA[
      (x * y) \ ((x \ 1) \ y) = x \ (y / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,1274,a(flip),b,29800,a)].">
      <j1 rule="hyper" parents="60 1274 29800"/>
    </justification>
  </clause>

  <clause id="29803">
    <literal><![CDATA[
      (x \ 1) \ (y / ((1 / (x \ 1)) * y)) = (x * y) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),29800(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 29800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29804">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * y)) = (x * y) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(74(a,1),29803(a,1,2,2,1))].">
      <j1 rule="para" parents="74 29803"/>
    </justification>
  </clause>

  <clause id="29806">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * y)) = x \ (y / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,29802,a(flip),b,29804,a),flip(a)].">
      <j1 rule="hyper" parents="370 29802 29804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29807">
    <literal><![CDATA[
      x \ ((x \ y) * (L(x \ y,z,u) \ x)) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29241,a(flip),b,29790,a),flip(a)].">
      <j1 rule="hyper" parents="370 29241 29790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29808">
    <literal><![CDATA[
      L(x \ y,z,u) \ (x \ y) = y \ (L(x / y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(25657(a,1),29807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25657 29807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29809">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,25797,a,b,29808,a)].">
      <j1 rule="hyper" parents="60 25797 29808"/>
    </justification>
  </clause>

  <clause id="29810">
    <literal><![CDATA[
      x \ (L((y \ x) / x,z,u) \ (y \ x)) = L(y,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,25854,a(flip),b,29808,a),flip(a)].">
      <j1 rule="hyper" parents="60 25854 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29811">
    <literal><![CDATA[
      (x \ y) \ (L(y / (x \ y),z,u) \ y) = (y \ (L(x,z,u) * (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,9979,a(flip),b,29808,a),flip(a)].">
      <j1 rule="hyper" parents="60 9979 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29812">
    <literal><![CDATA[
      (x * y) \ (L(x / (x * y),z,u) \ x) = L(y,z,u) \ (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),29808(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29813">
    <literal><![CDATA[
      L((x \ ((1 / x) \ y)) \ y,z,u) \ ((x \ ((1 / x) \ y)) \ y) = y \ (L(a(x,x,y),z,u) \ (x \ ((1 / x) \ y)))
    ]]></literal>
    <justification jstring="[para(28794(a,1),29808(a,2,2,1,1))].">
      <j1 rule="para" parents="28794 29808"/>
    </justification>
  </clause>

  <clause id="29814">
    <literal><![CDATA[
      (x * y) \ (L(x / (x * y),z,u) \ x) = L(y,z,u) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),29812(a,2,2))].">
      <j1 rule="para" parents="4 29812"/>
    </justification>
  </clause>

  <clause id="29815">
    <literal><![CDATA[
      (x \ (L(y,z,u) * (y \ x))) \ 1 = (y \ x) \ (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),29811(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 29811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29817">
    <literal><![CDATA[
      (x \ (L(y,z,u) * (y \ x))) \ 1 = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29505,a(flip),b,29815,a),flip(a)].">
      <j1 rule="hyper" parents="370 29505 29815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29818">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ 1 = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(29817(a,1),28013(a,1,1))].">
      <j1 rule="para" parents="29817 28013"/>
    </justification>
  </clause>

  <clause id="29819">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ 1 = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,25332,a(flip),b,29818,a),flip(a)].">
      <j1 rule="hyper" parents="370 25332 29818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29820">
    <literal><![CDATA[
      (x * ((y * (L(y,z,u) \ x)) \ x)) \ x = (x \ (L(y,z,u) * (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(29819(a,1),3499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29819 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29821">
    <literal><![CDATA[
      (x * ((y * (L(y,z,u) \ x)) \ x)) \ x = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29817,a(flip),b,29820,a),flip(a)].">
      <j1 rule="hyper" parents="370 29817 29820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29822">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * K(x / L(x,y,z),u) = L(L(x,y,z) \ x,x,u) * u
    ]]></literal>
    <justification jstring="[para(25422(a,1),29792(a,1,2))].">
      <j1 rule="para" parents="25422 29792"/>
    </justification>
  </clause>

  <clause id="29823">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * K(L(x,y,z) \ x,u) = L(L(x,y,z) \ x,x,u) * u
    ]]></literal>
    <justification jstring="[para(3938(a,1),29822(a,1,2,1))].">
      <j1 rule="para" parents="3938 29822"/>
    </justification>
  </clause>

  <clause id="29824">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = (x * (L(x,y,z) \ u)) * 1
    ]]></literal>
    <justification jstring="[para(23516(a,1),29823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23516 29823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29825">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,29824,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 29824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29826">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(29824(a,2),143(a,1)),flip(b)].">
      <j1 rule="para" parents="29824 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29828">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ (L(L(x,y,z),y,z) \ 1),L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),29825(a,1,1,1,1))].">
      <j1 rule="para" parents="29064 29825"/>
    </justification>
  </clause>

  <clause id="29829">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,u) = (u \ (x * (L(x,y,z) \ u))) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(14170(a,1),29793(a,2,2))].">
      <j1 rule="para" parents="14170 29793"/>
    </justification>
  </clause>

  <clause id="29830">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ (L(y,z,u) \ y) = (L(y,z,u) \ y) * L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(29125(a,1),29794(a,2,2))].">
      <j1 rule="para" parents="29125 29794"/>
    </justification>
  </clause>

  <clause id="29831">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ (L(y,z,u) \ y) = y * (L(y,z,u) \ L(y \ L(y,z,u),y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,14880,a(flip),b,29830,a),flip(a)].">
      <j1 rule="hyper" parents="370 14880 29830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29832">
    <literal><![CDATA[
      x \ (L(L(y,z,u),z,u) * (L(y,z,u) \ x)) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(2155(a,1),29650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2155 29650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29834">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (x \ u) = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(29603(a,1),29832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29603 29832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29835">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ u = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,16189,a,b,29834,a)].">
      <j1 rule="hyper" parents="60 16189 29834"/>
    </justification>
  </clause>

  <clause id="29836">
    <literal><![CDATA[
      (x * (x \ (L(y,z,u) * (y \ x)))) \ x = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(29835(a,1),29821(a,1,1,2))].">
      <j1 rule="para" parents="29835 29821"/>
    </justification>
  </clause>

  <clause id="29837">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(404,a,29836,a)].">
      <j1 rule="hyper" parents="404 29836"/>
    </justification>
  </clause>

  <clause id="29838">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * y) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(29500,a,29837,a)].">
      <j1 rule="hyper" parents="29500 29837"/>
    </justification>
  </clause>

  <clause id="29840">
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) \ (a(y,z,u) * x) = a(y,z,u) \ (x * (L(x,y,y) \ a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28960(a,2),29838(a,1,1))].">
      <j1 rule="para" parents="28960 29838"/>
    </justification>
  </clause>

  <clause id="29841">
    <literal><![CDATA[
      a(x,y,z) \ (u * (L(u,x,x) \ a(x,y,z))) = K(a(x,y,z),u) * a(x,x,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,25629,a(flip),b,29840,a),flip(a)].">
      <j1 rule="hyper" parents="60 25629 29840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29842">
    <literal><![CDATA[
      a(x,y,z) \ (u * (L(u,x,x) \ a(x,y,z))) = a(x,x,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,23519,a(flip),b,29841,a),flip(a)].">
      <j1 rule="hyper" parents="370 23519 29841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29843">
    <literal><![CDATA[
      a(x,x,L(y,y,a(x,z,u))) = a(x,x,y * a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(29795,a,29842,a)].">
      <j1 rule="hyper" parents="29795 29842"/>
    </justification>
  </clause>

  <clause id="29845">
    <literal><![CDATA[
      a(x,x,y * a(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29146,a(flip),b,29843,a),flip(a)].">
      <j1 rule="hyper" parents="60 29146 29843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29846">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(26965,a,29845,a)].">
      <j1 rule="hyper" parents="26965 29845"/>
    </justification>
  </clause>

  <clause id="29848">
    <literal><![CDATA[
      a(x,x,x \ (y * z)) = a(x,x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(28739(a,1),29845(a,1,3))].">
      <j1 rule="para" parents="28739 29845"/>
    </justification>
  </clause>

  <clause id="29849">
    <literal><![CDATA[
      (a(x,x,y) / x) \ (a(x,z,u) * y) = x * (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(29846(a,1),28433(a,1,1,1))].">
      <j1 rule="para" parents="29846 28433"/>
    </justification>
  </clause>

  <clause id="29850">
    <literal><![CDATA[
      a(x,x,(x \ y) * z) = a(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(26993,a,29848,a),flip(a)].">
      <j1 rule="hyper" parents="26993 29848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29851">
    <literal><![CDATA[
      a(x,x,L((x \ y) * z,u,w)) = L(a(x,x,x * (y * z)),u,w)
    ]]></literal>
    <justification jstring="[para(29850(a,1),29140(a,2,1))].">
      <j1 rule="para" parents="29850 29140"/>
    </justification>
  </clause>

  <clause id="29852">
    <literal><![CDATA[
      a(x,x,L((x \ y) * z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(x * (y * z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29851(a,2),29137(a,1))].">
      <j1 rule="para" parents="29851 29137"/>
    </justification>
  </clause>

  <clause id="29853">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),v5,x) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) * L((x \ R(x,y,z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29281(a,2),29747(a,2,2))].">
      <j1 rule="para" parents="29281 29747"/>
    </justification>
  </clause>

  <clause id="29854">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),v5,x) \ (x \ R(x,y,z)) = x \ (R(x,y,z) * L(R(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,2520,a(flip),b,29853,a),flip(a)].">
      <j1 rule="hyper" parents="370 2520 29853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29855">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),v5,x) \ (x \ R(x,y,z)) = R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,1951,a(flip),b,29854,a),flip(a)].">
      <j1 rule="hyper" parents="370 1951 29854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29856">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ (x \ R(x,y,z)) = R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[para(614(a,1),29855(a,1,1))].">
      <j1 rule="para" parents="614 29855"/>
    </justification>
  </clause>

  <clause id="29857">
    <literal><![CDATA[
      (R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w))) \ (1 / (x \ R(x,y,z))) = L(1 / (x \ R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(29856(a,1),3988(a,1,1))].">
      <j1 rule="para" parents="29856 3988"/>
    </justification>
  </clause>

  <clause id="29858">
    <literal><![CDATA[
      (R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w))) \ ((x \ R(x,y,z)) \ 1) = L(1 / (x \ R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(23942(a,1),29857(a,1,2))].">
      <j1 rule="para" parents="23942 29857"/>
    </justification>
  </clause>

  <clause id="29859">
    <literal><![CDATA[
      (R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w))) \ (R(x,y,z) \ x) = L(1 / (x \ R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(13549(a,1),29858(a,1,2))].">
      <j1 rule="para" parents="13549 29858"/>
    </justification>
  </clause>

  <clause id="29860">
    <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(23942(a,1),29859(a,2,1))].">
      <j1 rule="para" parents="23942 29859"/>
    </justification>
  </clause>

  <clause id="29861">
    <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(13549(a,1),29860(a,2,1))].">
      <j1 rule="para" parents="13549 29860"/>
    </justification>
  </clause>

  <clause id="29862">
    <literal><![CDATA[
      a(x,(y * (z * (u \ w))) * L(v5,y * (z * (w / u)),y * (z * (u \ w))),v6) = a(x,(y * (z * (w / u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25970(a,1),29581(a,1,2,2))].">
      <j1 rule="para" parents="25970 29581"/>
    </justification>
  </clause>

  <clause id="29863">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x \ L(x,y,z),x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25310(a,1),29657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25310 29657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29864">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x \ L(x,y,z),x * (x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,25719,a(flip),b,29863,a),flip(a)].">
      <j1 rule="hyper" parents="370 25719 29863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29865">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x \ L(x,y,z),L(x * (x * x),y,z))
    ]]></literal>
    <justification jstring="[para(3905(a,2),29864(a,2,3))].">
      <j1 rule="para" parents="3905 29864"/>
    </justification>
  </clause>

  <clause id="29866">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x \ L(x,y,z),L(L(x,x,x),y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3980,a(flip),b,29865,a),flip(a)].">
      <j1 rule="hyper" parents="370 3980 29865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29867">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x \ L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14008,a(flip),b,29866,a),flip(a)].">
      <j1 rule="hyper" parents="370 14008 29866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29869">
    <literal><![CDATA[
      x * (L(x,y,z) \ (((x * (L(x,y,z) \ x)) \ x) * u)) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3863,a(flip),b,29867,a),flip(a)].">
      <j1 rule="hyper" parents="370 3863 29867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29870">
    <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="[para(25310(a,1),29869(a,1,2,2,1))].">
      <j1 rule="para" parents="25310 29869"/>
    </justification>
  </clause>

  <clause id="29871">
    <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(4175,a,29870,a),flip(a)].">
      <j1 rule="hyper" parents="4175 29870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29873">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * (L(x,y,z) \ x))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,26340,a,b,29871,a)].">
      <j1 rule="hyper" parents="60 26340 29871"/>
    </justification>
  </clause>

  <clause id="29874">
    <literal><![CDATA[
      L(x,a(y,y,z),L(z,y,y)) = L(x,z,z * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3968,a(flip),b,29871,a)].">
      <j1 rule="hyper" parents="60 3968 29871"/>
    </justification>
  </clause>

  <clause id="29875">
    <literal><![CDATA[
      L(x,(y \ z) * ((1 / y) * z),L(y \ z,y,y)) = L(x,y \ z,(y \ z) * L(y \ z,y,y))
    ]]></literal>
    <justification jstring="[para(586(a,1),29871(a,1,2,2))].">
      <j1 rule="para" parents="586 29871"/>
    </justification>
  </clause>

  <clause id="29876">
    <literal><![CDATA[
      L(x,a(y,y,z),L(z,y,y)) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3680,a(flip),b,29874,a),flip(a)].">
      <j1 rule="hyper" parents="370 3680 29874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29877">
    <literal><![CDATA[
      L(a(x,x,y) \ z,y,a(x,x,y)) = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(2436,a,29876,a),flip(a)].">
      <j1 rule="hyper" parents="2436 29876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29878">
    <literal><![CDATA[
      L(a(x,x,y) \ z,y,a(x,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(29876(a,1),2436(a,1))].">
      <j1 rule="para" parents="29876 2436"/>
    </justification>
  </clause>

  <clause id="29879">
    <literal><![CDATA[
      (a(x,x,y) * y) \ (y * z) = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26350,a(flip),b,29877,a)].">
      <j1 rule="hyper" parents="60 26350 29877"/>
    </justification>
  </clause>

  <clause id="29880">
    <literal><![CDATA[
      L(x,y,z * (u * (L(w,v5,v5) * (w \ w)))) = L(x,y,z * (u * (a(v5,v5,w) * w)))
    ]]></literal>
    <justification jstring="[para(29879(a,1),25846(a,1,3,2,2))].">
      <j1 rule="para" parents="29879 25846"/>
    </justification>
  </clause>

  <clause id="29881">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * (L(x,y,z) \ x))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2191,a,29873,a)].">
      <j1 rule="hyper" parents="2191 29873"/>
    </justification>
  </clause>

  <clause id="29882">
    <literal><![CDATA[
      L(x,y,z) * ((x \ u) * (L(x,y,z) \ x)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(14757(a,1),29881(a,1,2))].">
      <j1 rule="para" parents="14757 29881"/>
    </justification>
  </clause>

  <clause id="29883">
    <literal><![CDATA[
      L(x,y,z * (u * (a(w,w,v5) * v5))) = L(x,y,z * (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(195(a,1),29880(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="195 29880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29884">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ ((1 / w) \ v5)))) = L(x,y,z * (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,29186,a,b,29883,a)].">
      <j1 rule="hyper" parents="60 29186 29883"/>
    </justification>
  </clause>

  <clause id="29886">
    <literal><![CDATA[
      L(x,y,L(z \ 1,L(u,z,z),w) * (w * L(u,z,z))) = L(x,y,w * (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,28906,a(flip),b,29884,a),flip(a)].">
      <j1 rule="hyper" parents="60 28906 29884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29887">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * (w \ 1))) = L(x,y,z * (w \ T(u,w \ 1)))
    ]]></literal>
    <justification jstring="[hyper(25274,a,29886,a)].">
      <j1 rule="hyper" parents="25274 29886"/>
    </justification>
  </clause>

  <clause id="29888">
    <literal><![CDATA[
      L(x,y,z * L(u * (1 / w),w,w)) = L(x,y,z * (w \ T(u,w \ 1)))
    ]]></literal>
    <justification jstring="[para(4641(a,2),29887(a,1,3,2))].">
      <j1 rule="para" parents="4641 29887"/>
    </justification>
  </clause>

  <clause id="29889">
    <literal><![CDATA[
      L(x,y,z * L(u * w,w,w)) = L(x,y,z * (w \ T(u,w \ 1)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27527,a(flip),b,29888,a)].">
      <j1 rule="hyper" parents="60 27527 29888"/>
    </justification>
  </clause>

  <clause id="29890">
    <literal><![CDATA[
      L(x,y,z * L(u * w,w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(29889(a,2),25984(a,1))].">
      <j1 rule="para" parents="29889 25984"/>
    </justification>
  </clause>

  <clause id="29891">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * L(y \ z,y,y)) = L(x,(y \ z) * ((1 / y) * z),y * z)
    ]]></literal>
    <justification jstring="[hyper(3519,a,29875,a),flip(a)].">
      <j1 rule="hyper" parents="3519 29875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29892">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * L(y \ z,y,y)) = L(x,(y \ z) * (z * y),y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26282,a(flip),b,29891,a),flip(a)].">
      <j1 rule="hyper" parents="370 26282 29891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29893">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ ((x \ ((1 / x) \ y)) \ y) = y \ (L(a(x,x,y),z,u) \ (x \ ((1 / x) \ y)))
    ]]></literal>
    <justification jstring="[para(28796(a,1),29813(a,1,1,1))].">
      <j1 rule="para" parents="28796 29813"/>
    </justification>
  </clause>

  <clause id="29894">
    <literal><![CDATA[
      x \ (L(a(y,y,x),z,u) \ (y \ ((1 / y) \ x))) = L(a(y,y,x) \ 1,z,u) \ (a(y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(28796(a,1),29893(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28796 29893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29895">
    <literal><![CDATA[
      x \ (L(a(y,y,x),z,u) \ (y \ ((1 / y) \ x))) = 1 \ (L(a(y,y,x) / 1,z,u) \ a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29808,a(flip),b,29894,a),flip(a)].">
      <j1 rule="hyper" parents="370 29808 29894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29896">
    <literal><![CDATA[
      x \ (L(a(y,y,x),z,u) \ (y \ ((1 / y) \ x))) = 1 \ (L(a(y,y,x),z,u) \ a(y,y,x))
    ]]></literal>
    <justification jstring="[para(72(a,1),29895(a,2,2,1,1))].">
      <j1 rule="para" parents="72 29895"/>
    </justification>
  </clause>

  <clause id="29897">
    <literal><![CDATA[
      a(x,(y * (z * (u \ w))) * L(v5,y * (z * (u \ w)),y * (z * (u \ w))),v6) = a(x,(y * (z * (w / u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(26231(a,1),29862(a,1,2,2))].">
      <j1 rule="para" parents="26231 29862"/>
    </justification>
  </clause>

  <clause id="29898">
    <literal><![CDATA[
      a(x,(y * (z * (u / w))) \ v5,v6) = a(x,(y * (z * (w \ u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,29579,a(flip),b,29897,a),flip(a)].">
      <j1 rule="hyper" parents="60 29579 29897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29899">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * ((1 / w) \ v5))) \ v6,v7) = a(x,(y * ((K(u,z) / w) \ v5)) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,27670,a(flip),b,29898,a),flip(a)].">
      <j1 rule="hyper" parents="60 27670 29898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29900">
    <literal><![CDATA[
      a(x,(y * ((K(z,u) / w) \ v5)) \ v6,v7) = a(x,(y * ((1 / w) \ v5)) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26812,a,29899,a),flip(a)].">
      <j1 rule="hyper" parents="26812 29899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29902">
    <literal><![CDATA[
      a(x,(y * ((K(z,u) / w) \ v5)) \ v6,v7) = a(x,(y * ((w \ 1) \ v5)) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,26814,a(flip),b,29900,a),flip(a)].">
      <j1 rule="hyper" parents="370 26814 29900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29903">
    <literal><![CDATA[
      a(x,(y * ((K(z,u) / w) \ v5)) \ v6,v7) = a(x,((w \ v5) * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,27552,a(flip),b,29902,a),flip(a)].">
      <j1 rule="hyper" parents="370 27552 29902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29904">
    <literal><![CDATA[
      a(x,(y * ((z \ K(u,w)) \ v5)) \ v6,v7) = a(x,((z \ v5) * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26815,a,29903,a)].">
      <j1 rule="hyper" parents="26815 29903"/>
    </justification>
  </clause>

  <clause id="29905">
    <literal><![CDATA[
      L(x,L((y \ z) \ u,w,v5),L((y \ z) \ u,w,v5)) = L(x,L(z \ (y * u),w,v5),L(z \ (y * u),w,v5))
    ]]></literal>
    <justification jstring="[para(1078(a,1),29555(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1078 29555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29906">
    <literal><![CDATA[
      L(x,L((y \ z) \ u,w,v5),L((y \ z) \ u,w,v5)) = L(x,z \ (y * u),z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,29547,a(flip),b,29905,a),flip(a)].">
      <j1 rule="hyper" parents="370 29547 29905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29908">
    <literal><![CDATA[
      L(x,L((y \ z) \ u,w,v5),L((y \ z) \ u,w,v5)) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,29605,a(flip),b,29906,a),flip(a)].">
      <j1 rule="hyper" parents="370 29605 29906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29909">
    <literal><![CDATA[
      L(x,(y \ z) \ u,(y \ z) \ u) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14824,a,29908,a)].">
      <j1 rule="hyper" parents="14824 29908"/>
    </justification>
  </clause>

  <clause id="29910">
    <literal><![CDATA[
      L(x,(y \ z) * u,(y \ z) * u) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(29606,a,29909,a)].">
      <j1 rule="hyper" parents="29606 29909"/>
    </justification>
  </clause>

  <clause id="29911">
    <literal><![CDATA[
      L(x,(y \ z) * u,u * (y \ z)) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(24037,a,29910,a)].">
      <j1 rule="hyper" parents="24037 29910"/>
    </justification>
  </clause>

  <clause id="29912">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (K(w,v5) / u),a(x,y,z) \ (K(w,v5) / u)) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(22781(a,1),29621(a,1,3))].">
      <j1 rule="para" parents="22781 29621"/>
    </justification>
  </clause>

  <clause id="29913">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (K(w,v5) / u),a(x,y,z) \ (u \ K(w,v5))) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(25954,a,29912,a)].">
      <j1 rule="hyper" parents="25954 29912"/>
    </justification>
  </clause>

  <clause id="29914">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (K(w,v5) / u),a(x,y,z) \ u) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,25977,a(flip),b,29913,a)].">
      <j1 rule="hyper" parents="60 25977 29913"/>
    </justification>
  </clause>

  <clause id="29916">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),u,(a(x,y,z) \ u) * a(x,y,z)) = L((1 / (a(x,y,z) * (a(x,y,z) / u))) * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26191,a,29643,a)].">
      <j1 rule="hyper" parents="26191 29643"/>
    </justification>
  </clause>

  <clause id="29917">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),u,u) = L((1 / (a(x,y,z) * (a(x,y,z) / u))) * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(24979,a,29916,a)].">
      <j1 rule="hyper" parents="24979 29916"/>
    </justification>
  </clause>

  <clause id="29919">
    <literal><![CDATA[
      L(1 \ (L(x,y,z) * (L(L(x,y,z),y,z) \ 1)),L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29505(a,1),29828(a,1,1,1))].">
      <j1 rule="para" parents="29505 29828"/>
    </justification>
  </clause>

  <clause id="29920">
    <literal><![CDATA[
      L(1 \ (L(L(x,y,z),y,z) \ L(x,y,z)),L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2162(a,1),29919(a,1,1,1,2))].">
      <j1 rule="para" parents="2162 29919"/>
    </justification>
  </clause>

  <clause id="29921">
    <literal><![CDATA[
      L(1 \ L(L(x,y,z) \ x,y,z),L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29127(a,1),29920(a,1,1,1,2))].">
      <j1 rule="para" parents="29127 29920"/>
    </justification>
  </clause>

  <clause id="29922">
    <literal><![CDATA[
      L(1 \ (L(x,y,z) \ x),L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29009(a,1),29921(a,1,1,1,2))].">
      <j1 rule="para" parents="29009 29921"/>
    </justification>
  </clause>

  <clause id="29923">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(L(x,y,z),y,z) \ 1,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(62(a,1),29922(a,1,1,1))].">
      <j1 rule="para" parents="62 29922"/>
    </justification>
  </clause>

  <clause id="29925">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29044(a,1),29923(a,1,1))].">
      <j1 rule="para" parents="29044 29923"/>
    </justification>
  </clause>

  <clause id="29926">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ 1) * (L(L(L(x,y,z),y,z) \ 1,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(29826,a,29925,a),flip(a)].">
      <j1 rule="hyper" parents="29826 29925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29928">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ 1) * ((L(x,y,z) \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),29926(a,1,2,1))].">
      <j1 rule="para" parents="29064 29926"/>
    </justification>
  </clause>

  <clause id="29929">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(29587,a,29928,a)].">
      <j1 rule="hyper" parents="29587 29928"/>
    </justification>
  </clause>

  <clause id="29930">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) \ u)) = L(L(x,y,z),y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(2183,a,29929,a),flip(a)].">
      <j1 rule="hyper" parents="2183 29929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29932">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(29929(a,1),2183(a,1))].">
      <j1 rule="para" parents="29929 2183"/>
    </justification>
  </clause>

  <clause id="29933">
    <literal><![CDATA[
      a(x,y,z) = y \ (z * (L(z,y,x) \ y))
    ]]></literal>
    <justification jstring="[para(29929(a,1),29035(a,2,2))].">
      <j1 rule="para" parents="29929 29035"/>
    </justification>
  </clause>

  <clause id="29934">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,29788,a,b,29933,a),flip(a)].">
      <j1 rule="hyper" parents="370 29788 29933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29935">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29035,a,b,29933,a),flip(a)].">
      <j1 rule="hyper" parents="370 29035 29933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29936">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,x * L(x,y,z),u) \ (x * L(x,y,z))),x,L(x,y,z)) = a(u,x * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2391,a,b,29933,a)].">
      <j1 rule="hyper" parents="370 2391 29933"/>
    </justification>
  </clause>

  <clause id="29937">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,L(x,y,z),u) \ L(x,y,z))) = a(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,29933,a)].">
      <j1 rule="hyper" parents="370 2160 29933"/>
    </justification>
  </clause>

  <clause id="29938">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = y * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,29933,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="129 29933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29939">
    <literal><![CDATA[
      x \ (L(y / x,x,z) \ y) = a(z,x,x \ y)
    ]]></literal>
    <justification jstring="[para(25657(a,1),29933(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25657 29933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29940">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ x) * (x * L(x \ L(x,y,z),x,u))) = a(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29130(a,1),29933(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="29130 29933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29941">
    <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(29933(a,2),29829(a,2,1))].">
      <j1 rule="para" parents="29933 29829"/>
    </justification>
  </clause>

  <clause id="29942">
    <literal><![CDATA[
      a(x,y,y \ x) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(26985,a,29935,a),flip(a)].">
      <j1 rule="hyper" parents="26985 29935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29943">
    <literal><![CDATA[
      L(x,y,z) \ (a(z,y,L(x,y,z)) \ u) = a(z,y,x) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29935(a,1),25342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29935 25342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29944">
    <literal><![CDATA[
      a(x,y,z) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(29935(a,1),28859(a,1,1))].">
      <j1 rule="para" parents="29935 28859"/>
    </justification>
  </clause>

  <clause id="29945">
    <literal><![CDATA[
      L(x,y,z) = (y * a(z,y,x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(29935(a,1),28860(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29935 28860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29946">
    <literal><![CDATA[
      L(x,(y / z) \ (y * z),u) = L(x,a(y,z,y * z),u)
    ]]></literal>
    <justification jstring="[para(29942(a,1),26280(a,2,2))].">
      <j1 rule="para" parents="29942 26280"/>
    </justification>
  </clause>

  <clause id="29947">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * (z \ 1))) = a(x,y,a(u,z,u * z))
    ]]></literal>
    <justification jstring="[para(29942(a,1),27201(a,2,3))].">
      <j1 rule="para" parents="29942 27201"/>
    </justification>
  </clause>

  <clause id="29948">
    <literal><![CDATA[
      L(L(x,L(y,z,u),y) \ x,x,L(y,z,u)) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(29141,a,29934,a),flip(a)].">
      <j1 rule="hyper" parents="29141 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29949">
    <literal><![CDATA[
      L(L(x,y * L(y,z,u),y) \ x,x,y * L(y,z,u)) = a(y * L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(27655,a,29934,a),flip(a)].">
      <j1 rule="hyper" parents="27655 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29950">
    <literal><![CDATA[
      L(L(x,R(y,z,u),w) \ x,x,L(y,z,u)) = a(w,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,27279,a(flip),b,29934,a)].">
      <j1 rule="hyper" parents="370 27279 29934"/>
    </justification>
  </clause>

  <clause id="29951">
    <literal><![CDATA[
      L(L(x,x \ y,z) \ x,x,y) = a(z,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13239,a(flip),b,29934,a)].">
      <j1 rule="hyper" parents="370 13239 29934"/>
    </justification>
  </clause>

  <clause id="29952">
    <literal><![CDATA[
      L(L(x,a(y,z,u),y) \ x,x,a(y,z,u)) = a(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28935,a,b,29934,a),flip(a)].">
      <j1 rule="hyper" parents="60 28935 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29953">
    <literal><![CDATA[
      L(a(x,y,z),z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(29267,a,29934,a(flip))].">
      <j1 rule="hyper" parents="29267 29934"/>
    </justification>
  </clause>

  <clause id="29954">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,y) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(29934(a,2),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29934 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29955">
    <literal><![CDATA[
      L(x,y,z) != a(u,z,y)
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ y = x
    ]]></literal>
    <justification jstring="[para(29934(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="29934 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29956">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(1 / (L(x,y,z) \ x),x,y) \ 1) = a(z,y,x) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29934(a,2),3865(a,2,1))].">
      <j1 rule="para" parents="29934 3865"/>
    </justification>
  </clause>

  <clause id="29957">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) \ a(z,y,x) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29934(a,2),14177(a,1,2))].">
      <j1 rule="para" parents="29934 14177"/>
    </justification>
  </clause>

  <clause id="29958">
    <literal><![CDATA[
      L(L(x,y,a(z,u,y)) \ x,x,a(z,u,y)) = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(26346(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="26346 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29959">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) \ x,x,y) = a(L(z * L(z,u,w),z,w * u),y,x)
    ]]></literal>
    <justification jstring="[para(27375(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="27375 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29960">
    <literal><![CDATA[
      (1 / (L(x,y,z) \ x)) / L((L(x,y,z) \ x) \ 1,x,y) = (L(x,y,z) \ x) * (1 / a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29934(a,2),27534(a,2,2,2))].">
      <j1 rule="para" parents="29934 27534"/>
    </justification>
  </clause>

  <clause id="29961">
    <literal><![CDATA[
      L(L(x,L(y,z,u) * w,v5) \ x,x,R(y,z,u) * w) = a(v5,R(y,z,u) * w,x)
    ]]></literal>
    <justification jstring="[para(27781(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="27781 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29962">
    <literal><![CDATA[
      L(L(x,y,z \ u) \ x,x,y) = a(L(z * u,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(29077(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="29077 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29963">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(29934(a,2),29125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29934 29125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29964">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,u,w),y) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(29127(a,1),29934(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29127 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29965">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,z,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(29934(a,2),29225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29934 29225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29966">
    <literal><![CDATA[
      L(x,a(y,z,u),L(L(u,z,y) \ u,u,z)) = L(x,L(u,z,y) \ u,L(u,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(29934(a,2),29547(a,1,2))].">
      <j1 rule="para" parents="29934 29547"/>
    </justification>
  </clause>

  <clause id="29967">
    <literal><![CDATA[
      L(a(x,y,z * (u / w)),z * (w \ u),y) = L(z * (u / w),y,x) \ (z * (u / w))
    ]]></literal>
    <justification jstring="[hyper(26270,a,29953,a)].">
      <j1 rule="hyper" parents="26270 29953"/>
    </justification>
  </clause>

  <clause id="29968">
    <literal><![CDATA[
      x \ (y \ (z \ ((z * y) * x))) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,29367,a,b,29953,a)].">
      <j1 rule="hyper" parents="60 29367 29953"/>
    </justification>
  </clause>

  <clause id="29969">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,29953,a(flip),b,29298,a)].">
      <j1 rule="hyper" parents="125 29953 29298"/>
    </justification>
  </clause>

  <clause id="29971">
    <literal><![CDATA[
      L(x,x,y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * a(y,x,x) = u
    ]]></literal>
    <justification jstring="[para(29953(a,1),14784(a,1))].">
      <j1 rule="para" parents="29953 14784"/>
    </justification>
  </clause>

  <clause id="29972">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (y * x) = y * (x * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29953(a,1),23631(a,1,1))].">
      <j1 rule="para" parents="29953 23631"/>
    </justification>
  </clause>

  <clause id="29973">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),a(z,y,x),z) = (z \ R(z,y,x)) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[para(29263(a,1),29953(a,2,1))].">
      <j1 rule="para" parents="29263 29953"/>
    </justification>
  </clause>

  <clause id="29975">
    <literal><![CDATA[
      L(x,(L(y,z,u) * y) * z,(L(y,z,u) * y) * z) = L(x,z * a(u,z,y),y * (L(y,z,u) \ z))
    ]]></literal>
    <justification jstring="[para(29938(a,1),29705(a,2,2))].">
      <j1 rule="para" parents="29938 29705"/>
    </justification>
  </clause>

  <clause id="29976">
    <literal><![CDATA[
      L(x,y * a(z,y,y),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(29945(a,2),26087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29945 26087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29977">
    <literal><![CDATA[
      a(x,y,((z * a(u,z,z)) * w) * v5) = a(x,y,(L(z,z,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(29945(a,2),27199(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="29945 27199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29978">
    <literal><![CDATA[
      a(x,x,a(y,x,z) \ z) = a(x,x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(29945(a,2),29143(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29945 29143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29979">
    <literal><![CDATA[
      (x * a(L(y,z,u) \ w,x,v5)) \ (x * v5) = L(v5,x,R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(29687(a,1),29945(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="29687 29945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29980">
    <literal><![CDATA[
      L(x \ L(x,a(x,y,z),u),a(x,y,z),x) = a(u,a(x,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[hyper(28919,a,29963,a)].">
      <j1 rule="hyper" parents="28919 29963"/>
    </justification>
  </clause>

  <clause id="29981">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,x),u),a(y,z,x),x) = a(u,a(y,z,x),x) \ 1
    ]]></literal>
    <justification jstring="[hyper(26347,a,29963,a)].">
      <j1 rule="hyper" parents="26347 29963"/>
    </justification>
  </clause>

  <clause id="29982">
    <literal><![CDATA[
      L((x * L(x,y,z)) \ L(x * L(x,y,z),x,u),x,x * L(x,y,z)) = a(u,x,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(4173,a,29963,a)].">
      <j1 rule="hyper" parents="4173 29963"/>
    </justification>
  </clause>

  <clause id="29983">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29330,a(flip),b,29963,a),flip(a)].">
      <j1 rule="hyper" parents="370 29330 29963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29984">
    <literal><![CDATA[
      (x * a(y,x,x \ L(x,y,z))) \ (x * (x \ L(x,y,z))) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,29945,a(flip),b,29963,a)].">
      <j1 rule="hyper" parents="60 29945 29963"/>
    </justification>
  </clause>

  <clause id="29985">
    <literal><![CDATA[
      x * (T(y,x) * (y \ L(y,x,z))) = (y * x) * (a(z,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(129,a,29963,a(flip),b,12480,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 29963 12480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29986">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(29963(a,1),29115(a,1,1))].">
      <j1 rule="para" parents="29963 29115"/>
    </justification>
  </clause>

  <clause id="29987">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ (u \ (x * (L(x,y,z) \ u))),L(x,y,z) \ x,x) = a(u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(29788(a,1),29963(a,1,1,2))].">
      <j1 rule="para" parents="29788 29963"/>
    </justification>
  </clause>

  <clause id="29988">
    <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(29986(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29986 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29989">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,29810,a(flip),b,29939,a),flip(a)].">
      <j1 rule="hyper" parents="60 29810 29939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29990">
    <literal><![CDATA[
      (x * (1 / y)) \ (L(x / (x * (1 / y)),x * (1 / y),z) \ x) = a(z,x * (1 / y),L(y,y,x))
    ]]></literal>
    <justification jstring="[para(3398(a,2),29939(a,2,3))].">
      <j1 rule="para" parents="3398 29939"/>
    </justification>
  </clause>

  <clause id="29991">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,y \ (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(23998,a,29989,a),flip(a)].">
      <j1 rule="hyper" parents="23998 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29992">
    <literal><![CDATA[
      a(x,y,y \ ((z \ R(z,u,w)) \ y)) = R(z,u,w) * (z \ L(R(z,u,w) \ z,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29856,a(flip),b,29989,a),flip(a)].">
      <j1 rule="hyper" parents="370 29856 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29993">
    <literal><![CDATA[
      a(x,y,y \ ((z / u) \ y)) = z \ (L(u / z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,29809,a(flip),b,29989,a),flip(a)].">
      <j1 rule="hyper" parents="370 29809 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29994">
    <literal><![CDATA[
      a(x,y,y \ ((z \ u) \ y)) = u \ (L(z / u,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29808,a(flip),b,29989,a),flip(a)].">
      <j1 rule="hyper" parents="370 29808 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29995">
    <literal><![CDATA[
      a(x,y,y \ ((y \ (x \ z)) \ y)) = ((x * y) \ z) \ (y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(344(a,1),29989(a,2,1))].">
      <j1 rule="para" parents="344 29989"/>
    </justification>
  </clause>

  <clause id="29996">
    <literal><![CDATA[
      L(x * (1 / y),x,z) \ (x * (1 / y)) = a(z,x,x \ L(y,y,x))
    ]]></literal>
    <justification jstring="[para(3398(a,2),29989(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3398 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29997">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(29989(a,2),3941(a,1,1))].">
      <j1 rule="para" parents="29989 3941"/>
    </justification>
  </clause>

  <clause id="29998">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * L(z \ (u \ z),z,z)) = a(x,y,L(u,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(29989(a,1),4033(a,2,3))].">
      <j1 rule="para" parents="29989 4033"/>
    </justification>
  </clause>

  <clause id="29999">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ (w \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * L(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(29989(a,2),26988(a,1,3))].">
      <j1 rule="para" parents="29989 26988"/>
    </justification>
  </clause>

  <clause id="30000">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,v5) \ L(L(x,y,z) \ x,u,w) = a(v5,x,x \ (x * L(x \ L(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(29130(a,1),29989(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29130 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30001">
    <literal><![CDATA[
      L(((x \ (x / y)) \ 1) \ z,L(y,y,x),x \ (y \ x)) = 1 \ ((x \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29203,a(flip),b,29976,a),flip(a)].">
      <j1 rule="hyper" parents="60 29203 29976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30002">
    <literal><![CDATA[
      a(x,x,a(y,x,z) * z) = a(x,x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(27067,a,29978,a)].">
      <j1 rule="hyper" parents="27067 29978"/>
    </justification>
  </clause>

  <clause id="30003">
    <literal><![CDATA[
      L(x,x \ y,y) \ x = a(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(28782,a,29951,a),flip(a)].">
      <j1 rule="hyper" parents="28782 29951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30004">
    <literal><![CDATA[
      L(x,x \ y,y) \ x = (y * ((y \ 1) / x)) * x
    ]]></literal>
    <justification jstring="[hyper(370,a,28691,a,b,30003,a),flip(a)].">
      <j1 rule="hyper" parents="370 28691 30003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30005">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = L(1 / z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,3865,a,b,29968,a),flip(a)].">
      <j1 rule="hyper" parents="35 3865 29968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30006">
    <literal><![CDATA[
      1 / L(x,x \ y,y) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[hyper(3956,a,30004,a)].">
      <j1 rule="hyper" parents="3956 30004"/>
    </justification>
  </clause>

  <clause id="30007">
    <literal><![CDATA[
      T(x * ((x \ 1) / y),y) = L(y,y \ x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(275,a,30004,a(flip),b,2162,a)].">
      <j1 rule="hyper" parents="275 30004 2162"/>
    </justification>
  </clause>

  <clause id="30009">
    <literal><![CDATA[
      (1 / x) * (x / y) = x * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(12462,a,30006,a)].">
      <j1 rule="hyper" parents="12462 30006"/>
    </justification>
  </clause>

  <clause id="30010">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),y,y) = L(y,y \ x,x) \ 1
    ]]></literal>
    <justification jstring="[para(30006(a,1),5097(a,1,1))].">
      <j1 rule="para" parents="30006 5097"/>
    </justification>
  </clause>

  <clause id="30011">
    <literal><![CDATA[
      L(x \ (x / y),x,x) = x * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(988,a,30009,a)].">
      <j1 rule="hyper" parents="988 30009"/>
    </justification>
  </clause>

  <clause id="30012">
    <literal><![CDATA[
      (x * (y \ (x \ 1))) * ((y \ (x \ 1)) \ (x \ 1)) = ((1 / x) * (x / y)) * y
    ]]></literal>
    <justification jstring="[para(30009(a,2),6515(a,2,1))].">
      <j1 rule="para" parents="30009 6515"/>
    </justification>
  </clause>

  <clause id="30013">
    <literal><![CDATA[
      L(L(1 / x,x,y),y,y) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[para(3417(a,2),30011(a,1,1))].">
      <j1 rule="para" parents="3417 30011"/>
    </justification>
  </clause>

  <clause id="30014">
    <literal><![CDATA[
      L(1 / x,y,y) \ 1 = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(554(a,1),30005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="554 30005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30015">
    <literal><![CDATA[
      x \ (y \ ((y * x) * (L(z,u,w) \ z))) = L(z \ L(z,u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(9918(a,1),30005(a,2,1,1))].">
      <j1 rule="para" parents="9918 30005"/>
    </justification>
  </clause>

  <clause id="30016">
    <literal><![CDATA[
      L(1 / L(x,y,z),z,y) \ 1 = z \ (y \ (z * (T(y,z) * x)))
    ]]></literal>
    <justification jstring="[para(12481(a,1),30005(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12481 30005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30017">
    <literal><![CDATA[
      x \ ((x * y) * a(z,x,y)) = L(1 / y,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(28715(a,1),30005(a,1,2))].">
      <j1 rule="para" parents="28715 30005"/>
    </justification>
  </clause>

  <clause id="30018">
    <literal><![CDATA[
      x \ ((1 / x) \ (y \ 1)) = L(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(74(a,1),30014(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 30014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30019">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ 1 = L(y \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(30014(a,1),5068(a,1,1))].">
      <j1 rule="para" parents="30014 5068"/>
    </justification>
  </clause>

  <clause id="30020">
    <literal><![CDATA[
      L(1 / x,R(1 / y,z,u),R(1 / y,z,u)) \ 1 = R(1 / y,z,u) \ ((R(y \ 1,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(7106(a,1),30014(a,2,2,1))].">
      <j1 rule="para" parents="7106 30014"/>
    </justification>
  </clause>

  <clause id="30021">
    <literal><![CDATA[
      x * (L(y,x,x) \ 1) = (1 / x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,30018,a)].">
      <j1 rule="hyper" parents="156 30018"/>
    </justification>
  </clause>

  <clause id="30022">
    <literal><![CDATA[
      a(L(L(x,y,y) \ 1,y,z),u,w) = a((y * z) \ (z * ((1 / y) \ (x \ 1))),u,w)
    ]]></literal>
    <justification jstring="[para(30018(a,1),26770(a,1,1,1))].">
      <j1 rule="para" parents="30018 26770"/>
    </justification>
  </clause>

  <clause id="30023">
    <literal><![CDATA[
      L(L(x \ 1,y,y),(y \ 1) \ (y \ x),y \ x) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(30019(a,1),3584(a,1,1))].">
      <j1 rule="para" parents="30019 3584"/>
    </justification>
  </clause>

  <clause id="30024">
    <literal><![CDATA[
      (L(x,x \ y,y) \ 1) * (x \ K(x,y * ((y \ 1) / x))) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(30007(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="30007 7872"/>
    </justification>
  </clause>

  <clause id="30025">
    <literal><![CDATA[
      L(x,(y \ z) * (z * y),u) = L(x,a(z,y,z * y),u)
    ]]></literal>
    <justification jstring="[hyper(26281,a,29946,a)].">
      <j1 rule="hyper" parents="26281 29946"/>
    </justification>
  </clause>

  <clause id="30026">
    <literal><![CDATA[
      x \ (y \ ((y * x) * L(a(z,y,x),u,w))) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(823,a,29954,a)].">
      <j1 rule="hyper" parents="823 29954"/>
    </justification>
  </clause>

  <clause id="30027">
    <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(13239(a,1),29954(a,1,1))].">
      <j1 rule="para" parents="13239 29954"/>
    </justification>
  </clause>

  <clause id="30028">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,z)) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(28499(a,1),29954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28499 29954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30029">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29955,a,29983,a)].">
      <j1 rule="hyper" parents="29955 29983"/>
    </justification>
  </clause>

  <clause id="30030">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) = L(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(4080,a,30029,a),flip(a)].">
      <j1 rule="hyper" parents="4080 30029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30031">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) \ 1 = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(3893,a,30029,a)].">
      <j1 rule="hyper" parents="3893 30029"/>
    </justification>
  </clause>

  <clause id="30032">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ x) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,30029,a,b,xx)].">
      <j1 rule="hyper" parents="129 30029"/>
    </justification>
  </clause>

  <clause id="30033">
    <literal><![CDATA[
      L(x,y,a(z,u,u \ (w \ u))) \ x = x \ L(x,y,L(w,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(29989(a,1),30029(a,2,2,3))].">
      <j1 rule="para" parents="29989 30029"/>
    </justification>
  </clause>

  <clause id="30034">
    <literal><![CDATA[
      L((a(a(x,y,z),u,w) * u) \ 1,w,a(x,y,z)) = L(u,a(x,y,z),w) \ 1
    ]]></literal>
    <justification jstring="[para(29193(a,1),30030(a,2,1))].">
      <j1 rule="para" parents="29193 30030"/>
    </justification>
  </clause>

  <clause id="30035">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) = 1 / L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(221,a,30031,a),flip(a)].">
      <j1 rule="hyper" parents="221 30031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30036">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(30031(a,1),29755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30031 29755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30039">
    <literal><![CDATA[
      L(x,(y \ z) * (z * y),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,28991,a(flip),b,30025,a),flip(a)].">
      <j1 rule="hyper" parents="370 28991 30025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30040">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * L(y \ z,y,y)) = L(x,a(z,y,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29892,a,b,30039,a)].">
      <j1 rule="hyper" parents="60 29892 30039"/>
    </justification>
  </clause>

  <clause id="30041">
    <literal><![CDATA[
      L(x,a(y,y,y \ z),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,26283,a,b,30039,a)].">
      <j1 rule="hyper" parents="60 26283 30039"/>
    </justification>
  </clause>

  <clause id="30042">
    <literal><![CDATA[
      L(x,a(y,y,y * z),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(19763(a,1),30041(a,1,2))].">
      <j1 rule="para" parents="19763 30041"/>
    </justification>
  </clause>

  <clause id="30043">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29934,a,b,30028,a),flip(a)].">
      <j1 rule="hyper" parents="370 29934 30028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30044">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(30028(a,1),639(a,1)),flip(b)].">
      <j1 rule="para" parents="30028 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30045">
    <literal><![CDATA[
      a(x,y * a(x,z,u),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29320,a(flip),b,30043,a)].">
      <j1 rule="hyper" parents="60 29320 30043"/>
    </justification>
  </clause>

  <clause id="30047">
    <literal><![CDATA[
      a(L(x * y,x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(29962(a,1),30044(a,1))].">
      <j1 rule="para" parents="29962 30044"/>
    </justification>
  </clause>

  <clause id="30048">
    <literal><![CDATA[
      a(x,y,y \ ((K(z,u) / u) \ y)) = K(z,u) \ (L(T(u,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5698(a,2),29993(a,2,2,1,1))].">
      <j1 rule="para" parents="5698 29993"/>
    </justification>
  </clause>

  <clause id="30049">
    <literal><![CDATA[
      a(x,y,y \ ((z \ L(z,u,w)) \ y)) = L(z,u,w) \ (L(L(z,u,w) \ z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(3938(a,1),29994(a,2,2,1,1))].">
      <j1 rule="para" parents="3938 29994"/>
    </justification>
  </clause>

  <clause id="30050">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * (z \ 1))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,28005,a(flip),b,29947,a),flip(a)].">
      <j1 rule="hyper" parents="370 28005 29947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30051">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27042,a(flip),b,30050,a)].">
      <j1 rule="hyper" parents="60 27042 30050"/>
    </justification>
  </clause>

  <clause id="30052">
    <literal><![CDATA[
      a(x,y,(z \ u) * (z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27192,a(flip),b,30051,a)].">
      <j1 rule="hyper" parents="60 27192 30051"/>
    </justification>
  </clause>

  <clause id="30053">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) = (u * w) \ ((u * (z \ L(z,y,x))) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,28640,a,b,29988,a),flip(a)].">
      <j1 rule="hyper" parents="370 28640 29988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30054">
    <literal><![CDATA[
      L(a(x,y,z),z,z \ u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29954,a(flip),b,30027,a),flip(a)].">
      <j1 rule="hyper" parents="60 29954 30027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30055">
    <literal><![CDATA[
      L(a(x,y,z),z,u * z) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(24975,a,30054,a),flip(a)].">
      <j1 rule="hyper" parents="24975 30054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30056">
    <literal><![CDATA[
      L(x / (L(y,z,u) \ x),z,u) \ w = y * (L(y,z,u) \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(74(a,2),29930(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="74 29930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30057">
    <literal><![CDATA[
      L(L(x,y,L(y,z,u)) \ x,x,L(y,z,u)) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(2390(a,1),29948(a,1,1,1))].">
      <j1 rule="para" parents="2390 29948"/>
    </justification>
  </clause>

  <clause id="30058">
    <literal><![CDATA[
      L(L(x,L(y,z,u),w) \ x,x,L(y,z,u)) = a(w,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(27410(a,1),29950(a,1,1,1))].">
      <j1 rule="para" parents="27410 29950"/>
    </justification>
  </clause>

  <clause id="30059">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) \ x,x,a(y,z,u)) = a(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(28918(a,1),29952(a,1,1,1))].">
      <j1 rule="para" parents="28918 29952"/>
    </justification>
  </clause>

  <clause id="30060">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) \ x = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,29009,a(flip),b,29958,a)].">
      <j1 rule="hyper" parents="60 29009 29958"/>
    </justification>
  </clause>

  <clause id="30062">
    <literal><![CDATA[
      x * a(y,a(z,u,y),x) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,30060,a(flip),b,30029,a(flip))].">
      <j1 rule="hyper" parents="129 30060 30029"/>
    </justification>
  </clause>

  <clause id="30063">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,L(x,u,w),y),u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25,a,b,29964,a)].">
      <j1 rule="hyper" parents="60 25 29964"/>
    </justification>
  </clause>

  <clause id="30064">
    <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(60,a,14767,a(flip),b,29964,a)].">
      <j1 rule="hyper" parents="60 14767 29964"/>
    </justification>
  </clause>

  <clause id="30065">
    <literal><![CDATA[
      L(L(L(x,x,y) \ x,z,u),x,L(x,z,u)) = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,2390,a(flip),b,29964,a)].">
      <j1 rule="hyper" parents="60 2390 29964"/>
    </justification>
  </clause>

  <clause id="30066">
    <literal><![CDATA[
      x * (T(y,x) * (y \ L(y,x,z))) = y * (x * (a(z,x,y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(370,a,29288,a(flip),b,29985,a),flip(a)].">
      <j1 rule="hyper" parents="370 29288 29985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30067">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,29929,a(flip),b,30036,a),flip(a)].">
      <j1 rule="hyper" parents="32 29929 30036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30068">
    <literal><![CDATA[
      L(a(x,y,z) * (a(x,y,z) * (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="[hyper(4101,a,30067,a),flip(a)].">
      <j1 rule="hyper" parents="4101 30067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30069">
    <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(2095,a,30067,a),flip(a)].">
      <j1 rule="hyper" parents="2095 30067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30070">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = L(x,v5,a(v6 * v6,v7,v8))
    ]]></literal>
    <justification jstring="[hyper(370,a,647,a,b,30067,a),flip(a)].">
      <j1 rule="hyper" parents="370 647 30067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30072">
    <literal><![CDATA[
      (x * L(y,x,a(z,u,w))) * a(z,u,w) = (x * a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(129,a,30067,a(flip),b,25786,a),flip(a)].">
      <j1 rule="hyper" parents="129 30067 25786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30073">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != L(v5,v6,v7)
    ]]></literal>
    <literal><![CDATA[
      L(L(v5,y,a(z,u,w)),v6,v7) = x
    ]]></literal>
    <justification jstring="[para(30067(a,1),166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30067 166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30074">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ x = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29009,a(flip),b,30057,a)].">
      <j1 rule="hyper" parents="60 29009 30057"/>
    </justification>
  </clause>

  <clause id="30076">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ y = L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,23619,a,b,30074,a)].">
      <j1 rule="hyper" parents="36 23619 30074"/>
    </justification>
  </clause>

  <clause id="30079">
    <literal><![CDATA[
      a(x,R(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(30044,a,30058,a),flip(a)].">
      <j1 rule="hyper" parents="30044 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30080">
    <literal><![CDATA[
      a(x,R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(30058(a,1),30044(a,1))].">
      <j1 rule="para" parents="30058 30044"/>
    </justification>
  </clause>

  <clause id="30081">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(26579,a,30079,a),flip(a)].">
      <j1 rule="hyper" parents="26579 30079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30083">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x * (y \ a(y,y,z))) * z) = a(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28467,a,b,30079,a)].">
      <j1 rule="hyper" parents="60 28467 30079"/>
    </justification>
  </clause>

  <clause id="30085">
    <literal><![CDATA[
      x * a(R(K(y,z) * u,w,v5),L(K(y,z) * u,w,v5),x * R(u,w,v5)) = R(u,w,v5) \ (K(z,y) * ((R(K(y,z) * u,w,v5) \ 1) \ x))
    ]]></literal>
    <justification jstring="[para(30079(a,1),29511(a,1,2))].">
      <j1 rule="para" parents="30079 29511"/>
    </justification>
  </clause>

  <clause id="30086">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(251(a,1),30081(a,1,2))].">
      <j1 rule="para" parents="251 30081"/>
    </justification>
  </clause>

  <clause id="30087">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ x = a(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(28782,a,30059,a),flip(a)].">
      <j1 rule="hyper" parents="28782 30059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30088">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ x = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,28935,a(flip),b,30087,a),flip(a)].">
      <j1 rule="hyper" parents="370 28935 30087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30090">
    <literal><![CDATA[
      x \ L(x,y,a(y,z,u)) = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,30029,a(flip),b,30088,a)].">
      <j1 rule="hyper" parents="60 30029 30088"/>
    </justification>
  </clause>

  <clause id="30091">
    <literal><![CDATA[
      L(L(a(x,y,y),z,u),y,L(y,z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(28819(a,1),30065(a,1,1,1))].">
      <j1 rule="para" parents="28819 30065"/>
    </justification>
  </clause>

  <clause id="30092">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(14789,a,30091,a)].">
      <j1 rule="hyper" parents="14789 30091"/>
    </justification>
  </clause>

  <clause id="30093">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,16547,a,b,30092,a)].">
      <j1 rule="hyper" parents="370 16547 30092"/>
    </justification>
  </clause>

  <clause id="30094">
    <literal><![CDATA[
      a(x,y,L(y,y,(x \ (x / y)) \ z)) = ((z / ((x \ (x / y)) \ 1)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(370,a,29108,a(flip),b,30092,a),flip(a)].">
      <j1 rule="hyper" parents="370 29108 30092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30095">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),z,u) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(29267,a,30092,a(flip))].">
      <j1 rule="hyper" parents="29267 30092"/>
    </justification>
  </clause>

  <clause id="30097">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(30093(a,1),28815(a,1,1))].">
      <j1 rule="para" parents="30093 28815"/>
    </justification>
  </clause>

  <clause id="30099">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,w)
    ]]></literal>
    <literal><![CDATA[
      a(u,w,L(w,y,z)) = x
    ]]></literal>
    <justification jstring="[para(30095(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="30095 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30100">
    <literal><![CDATA[
      L(a(L(x,y,z),u,u) \ 1,u,u) = u \ (a(x,u,L(u,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(30097(a,2),29986(a,2,2))].">
      <j1 rule="para" parents="30097 29986"/>
    </justification>
  </clause>

  <clause id="30101">
    <literal><![CDATA[
      x * (K(y,x) * L(y,x,z)) = y * (x * (a(z,x,y) \ 1))
    ]]></literal>
    <justification jstring="[para(7860(a,1),30066(a,1,2))].">
      <j1 rule="para" parents="7860 30066"/>
    </justification>
  </clause>

  <clause id="30102">
    <literal><![CDATA[
      x * L(T(y,x),x,z) = y * (x * (a(z,x,y) \ 1))
    ]]></literal>
    <justification jstring="[para(12351(a,1),30101(a,1,2))].">
      <j1 rule="para" parents="12351 30101"/>
    </justification>
  </clause>

  <clause id="30103">
    <literal><![CDATA[
      x * (y * (a(z,y,x) \ 1)) = L(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(489,a,30102,a),flip(a)].">
      <j1 rule="hyper" parents="489 30102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30104">
    <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(30070(a,2),640(a,1))].">
      <j1 rule="para" parents="30070 640"/>
    </justification>
  </clause>

  <clause id="30106">
    <literal><![CDATA[
      L(x / (y * a(z,u,w)),y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(z,u,w) \ x) / y = v5
    ]]></literal>
    <justification jstring="[para(28325(a,1),30104(a,1,1))].">
      <j1 rule="para" parents="28325 30104"/>
    </justification>
  </clause>

  <clause id="30109">
    <literal><![CDATA[
      ((x * y) \ z) \ (y \ (x \ z)) = a(x,y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(27100,a,29995,a),flip(a)].">
      <j1 rule="hyper" parents="27100 29995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30110">
    <literal><![CDATA[
      (1 / (x * y)) \ (y \ (x \ K(x * y,(x * y) \ 1))) = a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(1712(a,1),30109(a,1,1))].">
      <j1 rule="para" parents="1712 30109"/>
    </justification>
  </clause>

  <clause id="30111">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(x,y,z)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ ((a(x,y,z) \ 1) \ u) = v5
    ]]></literal>
    <justification jstring="[para(30069(a,2),719(a,1))].">
      <j1 rule="para" parents="30069 719"/>
    </justification>
  </clause>

  <clause id="30112">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),a(x,y,z) * u) = ((a(x,y,z) \ 1) \ u) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(30069(a,1),1362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30069 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30113">
    <literal><![CDATA[
      L(L(a(x,y,y) \ 1,z,u),y,y) = y \ (a(x,y,L(y,z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(29285(a,2),30100(a,1,1))].">
      <j1 rule="para" parents="29285 30100"/>
    </justification>
  </clause>

  <clause id="30114">
    <literal><![CDATA[
      x \ (a(y,x,L(x,z,u)) \ x) = L(x \ L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29988,a(flip),b,30113,a),flip(a)].">
      <j1 rule="hyper" parents="60 29988 30113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30115">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = x \ L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(30097(a,1),30114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30097 30114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30116">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29945,a,b,29979,a),flip(a)].">
      <j1 rule="hyper" parents="60 29945 29979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30117">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),a(x,y,z),x) = a(u,a(x,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[para(29200(a,1),29980(a,1,1))].">
      <j1 rule="para" parents="29200 29980"/>
    </justification>
  </clause>

  <clause id="30118">
    <literal><![CDATA[
      a(x,a(y,z,u),y) \ 1 = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(28870,a,30117,a),flip(a)].">
      <j1 rule="hyper" parents="28870 30117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30120">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ 1 = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28952(a,1),30118(a,1,1))].">
      <j1 rule="para" parents="28952 30118"/>
    </justification>
  </clause>

  <clause id="30121">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(29337,a,30120,a),flip(a)].">
      <j1 rule="hyper" parents="29337 30120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30122">
    <literal><![CDATA[
      x * a(y,x,a(x,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(129,a,30121,a(flip),b,29200,a)].">
      <j1 rule="hyper" parents="129 30121 29200"/>
    </justification>
  </clause>

  <clause id="30123">
    <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(30121(a,2),26519(a,1))].">
      <j1 rule="para" parents="30121 26519"/>
    </justification>
  </clause>

  <clause id="30124">
    <literal><![CDATA[
      L(x,a(x,y,z),y * z) = a(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29006,a,30122,a),flip(a)].">
      <j1 rule="hyper" parents="29006 30122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30125">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,y,z) \ x) = L(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,27617,a,b,30124,a)].">
      <j1 rule="hyper" parents="370 27617 30124"/>
    </justification>
  </clause>

  <clause id="30126">
    <literal><![CDATA[
      L(x,a(x,y,z),y * z) \ R(x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(30124(a,2),23619(a,1,1))].">
      <j1 rule="para" parents="30124 23619"/>
    </justification>
  </clause>

  <clause id="30127">
    <literal><![CDATA[
      L(a(x,a(y,z,x),u),a(y,z,x),x) = a(u,a(y,z,x),x) \ 1
    ]]></literal>
    <justification jstring="[para(29201(a,1),29981(a,1,1))].">
      <j1 rule="para" parents="29201 29981"/>
    </justification>
  </clause>

  <clause id="30128">
    <literal><![CDATA[
      a(x,a(y,z,u),u) \ 1 = a(u,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(28870,a,30127,a),flip(a)].">
      <j1 rule="hyper" parents="28870 30127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30130">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ 1 = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(28948(a,1),30128(a,1,1))].">
      <j1 rule="para" parents="28948 30128"/>
    </justification>
  </clause>

  <clause id="30131">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(29337,a,30130,a),flip(a)].">
      <j1 rule="hyper" parents="29337 30130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30132">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,a(z,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(129,a,30131,a(flip),b,29201,a)].">
      <j1 rule="hyper" parents="129 30131 29201"/>
    </justification>
  </clause>

  <clause id="30133">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * w = w * a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,30131,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 30131 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30134">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = L(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(30131(a,1),29199(a,1,1))].">
      <j1 rule="para" parents="30131 29199"/>
    </justification>
  </clause>

  <clause id="30135">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(30131(a,1),30062(a,1,2))].">
      <j1 rule="para" parents="30131 30062"/>
    </justification>
  </clause>

  <clause id="30137">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,u \ (w \ u))) = x \ L(x,y,L(w,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,30029,a(flip),b,30033,a)].">
      <j1 rule="hyper" parents="60 30029 30033"/>
    </justification>
  </clause>

  <clause id="30138">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * ((1 / y) * z)) = L(x,a(z,y,y),y * z)
    ]]></literal>
    <justification jstring="[para(586(a,1),30040(a,1,3,2))].">
      <j1 rule="para" parents="586 30040"/>
    </justification>
  </clause>

  <clause id="30139">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * ((y \ 1) * z)) = L(x,a(z,y,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(25985,a,30138,a)].">
      <j1 rule="hyper" parents="25985 30138"/>
    </justification>
  </clause>

  <clause id="30140">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * (y * z)) = L(x,a(z,y,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25836,a(flip),b,30139,a)].">
      <j1 rule="hyper" parents="60 25836 30139"/>
    </justification>
  </clause>

  <clause id="30141">
    <literal><![CDATA[
      L(x,a(y,z,z),z * y) = L(x,z \ y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,29410,a(flip),b,30140,a),flip(a)].">
      <j1 rule="hyper" parents="60 29410 30140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30142">
    <literal><![CDATA[
      a(x,y,y \ ((K(z,u) / u) \ y)) = K(u,z) * (L(T(u,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,7506,a(flip),b,30048,a),flip(a)].">
      <j1 rule="hyper" parents="370 7506 30048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30143">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,u \ (w \ u))) = x \ L(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[para(3483(a,1),30137(a,2,2))].">
      <j1 rule="para" parents="3483 30137"/>
    </justification>
  </clause>

  <clause id="30144">
    <literal><![CDATA[
      a(x,y,y \ ((K(z,u) / u) \ y)) = L(u,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,25547,a(flip),b,30142,a),flip(a)].">
      <j1 rule="hyper" parents="370 25547 30142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30146">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,27255,a(flip),b,30144,a)].">
      <j1 rule="hyper" parents="60 27255 30144"/>
    </justification>
  </clause>

  <clause id="30147">
    <literal><![CDATA[
      (x * ((L(y,z,x) \ y) \ z)) * L(y,y,z) = x * (z / (y \ 1))
    ]]></literal>
    <justification jstring="[para(30146(a,1),28848(a,1,1,2,1))].">
      <j1 rule="para" parents="30146 28848"/>
    </justification>
  </clause>

  <clause id="30148">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ u) = L(z,y,x) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29935(a,1),29943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29935 29943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30149">
    <literal><![CDATA[
      L(x,y,z) * a(y,x,a(z,y,x)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,29969,a(flip),b,30148,a(flip))].">
      <j1 rule="hyper" parents="129 29969 30148"/>
    </justification>
  </clause>

  <clause id="30150">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,L(x,y,z),u) \ L(x,y,z))) = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,2564,a(flip),b,29937,a),flip(a)].">
      <j1 rule="hyper" parents="370 2564 29937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30151">
    <literal><![CDATA[
      a(L(x * L(x,y,z),x,z * y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(29959(a,1),30044(a,1))].">
      <j1 rule="para" parents="29959 30044"/>
    </justification>
  </clause>

  <clause id="30152">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z,a(z,y,x)) = (z \ R(z,y,x)) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28918,a(flip),b,29973,a)].">
      <j1 rule="hyper" parents="60 28918 29973"/>
    </justification>
  </clause>

  <clause id="30153">
    <literal><![CDATA[
      (x * a(y,x,x * L(x,y,z))) \ (x * (x \ L(x,y,z))) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(3861(a,1),29984(a,1,1,2))].">
      <j1 rule="para" parents="3861 29984"/>
    </justification>
  </clause>

  <clause id="30154">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * ((1 / z) * (u \ z))) = a(x,y,L(u,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(586(a,1),29998(a,1,3,2))].">
      <j1 rule="para" parents="586 29998"/>
    </justification>
  </clause>

  <clause id="30155">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (z * (u \ z))) = a(x,y,L(u,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(27173,a,30154,a)].">
      <j1 rule="hyper" parents="27173 30154"/>
    </justification>
  </clause>

  <clause id="30156">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (z * (u \ z))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(1362(a,1),30155(a,2,3))].">
      <j1 rule="para" parents="1362 30155"/>
    </justification>
  </clause>

  <clause id="30157">
    <literal><![CDATA[
      a(x,y,a(z,z,u \ z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30052,a(flip),b,30156,a)].">
      <j1 rule="hyper" parents="60 30052 30156"/>
    </justification>
  </clause>

  <clause id="30158">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(29142(a,1),30157(a,1,3))].">
      <j1 rule="para" parents="29142 30157"/>
    </justification>
  </clause>

  <clause id="30159">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),z * (L(z,u,w) \ v5))) = a(x,y,a(L(z,u,w),L(z,u,w),z \ v5))
    ]]></literal>
    <justification jstring="[para(29681(a,1),30158(a,1,3))].">
      <j1 rule="para" parents="29681 30158"/>
    </justification>
  </clause>

  <clause id="30160">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) != v5
    ]]></literal>
    <literal><![CDATA[
      L(z \ L(z,y,x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(30053(a,2),28649(a,1))].">
      <j1 rule="para" parents="30053 28649"/>
    </justification>
  </clause>

  <clause id="30161">
    <literal><![CDATA[
      L(x / (L(y,z,u) \ x),z,u) \ w = (y \ 1) \ ((L(y,z,u) \ 1) * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29584,a,b,30056,a),flip(a)].">
      <j1 rule="hyper" parents="370 29584 30056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30162">
    <literal><![CDATA[
      a(x,y,L(y,y,(x \ (x / y)) \ z)) = ((z / (y * a(x,y,y))) * y) \ z
    ]]></literal>
    <justification jstring="[para(28826(a,1),30094(a,2,1,1,2))].">
      <j1 rule="para" parents="28826 30094"/>
    </justification>
  </clause>

  <clause id="30163">
    <literal><![CDATA[
      a(x,y,L(y,y,(x \ (x / y)) \ z)) = (y * ((a(x,y,y) * y) \ z)) \ z
    ]]></literal>
    <justification jstring="[para(28293(a,1),30162(a,2,1))].">
      <j1 rule="para" parents="28293 30162"/>
    </justification>
  </clause>

  <clause id="30164">
    <literal><![CDATA[
      a(x,y,L(y,y,(x \ (x / y)) \ z)) = (L(y,y,x) * (y \ z)) \ z
    ]]></literal>
    <justification jstring="[para(29756(a,1),30163(a,2,1))].">
      <j1 rule="para" parents="29756 30163"/>
    </justification>
  </clause>

  <clause id="30165">
    <literal><![CDATA[
      a(x,y,L(y,y,(x \ (x / y)) \ z)) = z \ (y * (L(y,y,x) \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,29837,a(flip),b,30164,a),flip(a)].">
      <j1 rule="hyper" parents="370 29837 30164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30166">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4264,a,30150,a)].">
      <j1 rule="hyper" parents="4264 30150"/>
    </justification>
  </clause>

  <clause id="30168">
    <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(30166(a,1),30064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30166 30064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30169">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,30095,a(flip),b,30168,a),flip(a)].">
      <j1 rule="hyper" parents="370 30095 30168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30170">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),z,u) = a(x,L(y,w,v5),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,30095,a,b,30169,a)].">
      <j1 rule="hyper" parents="370 30095 30169"/>
    </justification>
  </clause>

  <clause id="30171">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = a(x,y,y) * x
    ]]></literal>
    <justification jstring="[para(30169(a,1),16508(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30169 16508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30172">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,16508,a(flip),b,30171,a),flip(a)].">
      <j1 rule="hyper" parents="370 16508 30171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30173">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = w
    ]]></literal>
    <justification jstring="[para(30171(a,2),16526(a,1))].">
      <j1 rule="para" parents="30171 16526"/>
    </justification>
  </clause>

  <clause id="30174">
    <literal><![CDATA[
      R(x,(1 / y) * z,L(y \ z,y,y)) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),30172(a,1,2))].">
      <j1 rule="para" parents="586 30172"/>
    </justification>
  </clause>

  <clause id="30175">
    <literal><![CDATA[
      R((1 / L(x,y,z)) * u,L(x,y,z),L(x,y,z)) = (L(x,y,z) \ 1) * R(u,x,x)
    ]]></literal>
    <justification jstring="[para(30172(a,1),4538(a,2,2))].">
      <j1 rule="para" parents="30172 4538"/>
    </justification>
  </clause>

  <clause id="30176">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w)) = x \ R(x,(y \ 1) \ z,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(30172(a,1),16520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30172 16520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30177">
    <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(30099,a,30170,a)].">
      <j1 rule="hyper" parents="30099 30170"/>
    </justification>
  </clause>

  <clause id="30178">
    <literal><![CDATA[
      R(x,(1 / y) * z,(1 / y) * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(586(a,1),30174(a,1,3))].">
      <j1 rule="para" parents="586 30174"/>
    </justification>
  </clause>

  <clause id="30179">
    <literal><![CDATA[
      R(x,(1 / y) * z,y * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(2808,a,30178,a)].">
      <j1 rule="hyper" parents="2808 30178"/>
    </justification>
  </clause>

  <clause id="30180">
    <literal><![CDATA[
      R(x,y \ z,y \ z) = R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27468,a(flip),b,30179,a),flip(a)].">
      <j1 rule="hyper" parents="60 27468 30179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30181">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(14783,a,30152,a),flip(a)].">
      <j1 rule="hyper" parents="14783 30152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30183">
    <literal><![CDATA[
      a(x,y,z) \ (x \ R(x,y,z)) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29302,a(flip),b,30181,a)].">
      <j1 rule="hyper" parents="60 29302 30181"/>
    </justification>
  </clause>

  <clause id="30184">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) * ((z \ R(z,y,x)) \ 1) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(30183(a,1),27876(a,1,1))].">
      <j1 rule="para" parents="30183 27876"/>
    </justification>
  </clause>

  <clause id="30185">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) * (R(z,y,x) \ z) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(13549(a,1),30184(a,1,2))].">
      <j1 rule="para" parents="13549 30184"/>
    </justification>
  </clause>

  <clause id="30186">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = (a(z,y,x) \ 1) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[para(29963(a,1),29957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29963 29957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30187">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,311,a(flip),b,30186,a),flip(a)].">
      <j1 rule="hyper" parents="370 311 30186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30188">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) \ x)) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,27649,a(flip),b,30187,a)].">
      <j1 rule="hyper" parents="60 27649 30187"/>
    </justification>
  </clause>

  <clause id="30189">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(29932,a,30188,a)].">
      <j1 rule="hyper" parents="29932 30188"/>
    </justification>
  </clause>

  <clause id="30190">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (a(z,y,x) * a(z,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(129,a,30188,a(flip),b,29930,a(flip))].">
      <j1 rule="hyper" parents="129 30188 29930"/>
    </justification>
  </clause>

  <clause id="30192">
    <literal><![CDATA[
      L(x * (a(y,z,x) * a(y,z,x)),z,y) = x * (L(x,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(30189(a,1),29098(a,1,1,2))].">
      <j1 rule="para" parents="30189 29098"/>
    </justification>
  </clause>

  <clause id="30193">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = L(L(z,y,x),y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[para(30189(a,1),29353(a,1,1))].">
      <j1 rule="para" parents="30189 29353"/>
    </justification>
  </clause>

  <clause id="30194">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(30189(a,1),29355(a,1,1))].">
      <j1 rule="para" parents="30189 29355"/>
    </justification>
  </clause>

  <clause id="30195">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) \ x = u \ L(L(u,z,y),z,y)
    ]]></literal>
    <justification jstring="[para(30189(a,1),29372(a,1,1,2))].">
      <j1 rule="para" parents="30189 29372"/>
    </justification>
  </clause>

  <clause id="30196">
    <literal><![CDATA[
      L(L(x,y,z) * (a(z,y,x) * a(z,y,x)),y,z) = x
    ]]></literal>
    <justification jstring="[hyper(4040,a,30190,a)].">
      <j1 rule="hyper" parents="4040 30190"/>
    </justification>
  </clause>

  <clause id="30198">
    <literal><![CDATA[
      L(L(x * (a(y,z,x) * a(y,z,x)),z,y),z,y) = x
    ]]></literal>
    <justification jstring="[para(3874(a,2),30196(a,1,1))].">
      <j1 rule="para" parents="3874 30196"/>
    </justification>
  </clause>

  <clause id="30199">
    <literal><![CDATA[
      L(L(x * (a(y,z,x) * a(y,z,x)),u,w),z,y) = L(x * (L(x,z,y) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(30192(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30192 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30200">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[para(30192(a,1),30198(a,1,1))].">
      <j1 rule="para" parents="30192 30198"/>
    </justification>
  </clause>

  <clause id="30201">
    <literal><![CDATA[
      L((x \ (x / y)) \ 1,y,x) = y
    ]]></literal>
    <justification jstring="[para(3892(a,2),30200(a,1,1))].">
      <j1 rule="para" parents="3892 30200"/>
    </justification>
  </clause>

  <clause id="30202">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,(y * (L(y,z,u) \ y)) * y,y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(30200(a,1),4170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30200 4170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30203">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (L((x \ (x / y)) \ 1,y,x) \ z) = y \ (((x \ (x / y)) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(30201(a,1),2178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30201 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30204">
    <literal><![CDATA[
      L(x,(y \ (y / z)) \ 1,L((y \ (y / z)) \ 1,z,y)) = L(x,z,(y \ (y / z)) \ 1)
    ]]></literal>
    <justification jstring="[para(30201(a,1),2390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30201 2390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30205">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (x \ (u \ a(z,y,x))) = u \ (a(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,21727,a(flip),b,30193,a),flip(a)].">
      <j1 rule="hyper" parents="60 21727 30193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30206">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) * (x \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(30193(a,1),2954(a,1,1))].">
      <j1 rule="para" parents="30193 2954"/>
    </justification>
  </clause>

  <clause id="30207">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(195(a,1),30206(a,1,1))].">
      <j1 rule="para" parents="195 30206"/>
    </justification>
  </clause>

  <clause id="30208">
    <literal><![CDATA[
      a(x * (y * (L(L(y,z,u),z,u) \ w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w * x,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(29429(a,1),30206(a,1))].">
      <j1 rule="para" parents="29429 30206"/>
    </justification>
  </clause>

  <clause id="30210">
    <literal><![CDATA[
      a(L((x * y) \ z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ (x \ z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(344(a,1),30207(a,1,1,1))].">
      <j1 rule="para" parents="344 30207"/>
    </justification>
  </clause>

  <clause id="30211">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ 1) \ u) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,21755,a,b,30194,a)].">
      <j1 rule="hyper" parents="60 21755 30194"/>
    </justification>
  </clause>

  <clause id="30212">
    <literal><![CDATA[
      a(x * (L(L(x,y,z),y,z) \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(30194(a,1),2975(a,1,1))].">
      <j1 rule="para" parents="30194 2975"/>
    </justification>
  </clause>

  <clause id="30213">
    <literal><![CDATA[
      a(x,y,z * (L(L(z,u,w),u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v5) = v6
    ]]></literal>
    <justification jstring="[para(30194(a,1),3075(a,1,3))].">
      <j1 rule="para" parents="30194 3075"/>
    </justification>
  </clause>

  <clause id="30214">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(29436(a,2),30212(a,1))].">
      <j1 rule="para" parents="29436 30212"/>
    </justification>
  </clause>

  <clause id="30215">
    <literal><![CDATA[
      a(L(x * y,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(27888(a,1),30214(a,1))].">
      <j1 rule="para" parents="27888 30214"/>
    </justification>
  </clause>

  <clause id="30216">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ v5) = v6
    ]]></literal>
    <justification jstring="[para(29162(a,1),30213(a,1,3))].">
      <j1 rule="para" parents="29162 30213"/>
    </justification>
  </clause>

  <clause id="30217">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ 1) = z \ L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(607,a,30195,a)].">
      <j1 rule="hyper" parents="607 30195"/>
    </justification>
  </clause>

  <clause id="30218">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ ((a(z,y,x) \ 1) * u) = x \ (a(z,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(832,a,30211,a),flip(a)].">
      <j1 rule="hyper" parents="832 30211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30219">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ ((a(z,y,x) \ 1) * u) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,24136,a(flip),b,30218,a),flip(a)].">
      <j1 rule="hyper" parents="370 24136 30218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30220">
    <literal><![CDATA[
      L(L(x,y,y * L(y,z,u)) \ x,x,y * L(y,z,u)) = a(y * L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(4170(a,1),29949(a,1,1,1))].">
      <j1 rule="para" parents="4170 29949"/>
    </justification>
  </clause>

  <clause id="30222">
    <literal><![CDATA[
      L(L(x,L(y,z,u) * w,v5) \ x,x,L(y,z,u) * w) = a(v5,R(y,z,u) * w,x)
    ]]></literal>
    <justification jstring="[hyper(28543,a,29961,a)].">
      <j1 rule="hyper" parents="28543 29961"/>
    </justification>
  </clause>

  <clause id="30223">
    <literal><![CDATA[
      a(L(L(x,y,y),y,z),u,w) = a((y * z) \ (z * ((1 / y) \ (x \ 1))),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3869,a(flip),b,30022,a)].">
      <j1 rule="hyper" parents="60 3869 30022"/>
    </justification>
  </clause>

  <clause id="30224">
    <literal><![CDATA[
      a(L(L(x,y,y),y,z),u,w) = a((y * z) \ (z * ((1 / y) \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27924,a(flip),b,30223,a),flip(a)].">
      <j1 rule="hyper" parents="370 27924 30223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30225">
    <literal><![CDATA[
      a(L(L(x,y,y),y,z),u,w) = a((y * z) \ (z * (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26777,a(flip),b,30224,a),flip(a)].">
      <j1 rule="hyper" parents="370 26777 30224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30226">
    <literal><![CDATA[
      L(L(x \ 1,y,y),y \ (y \ x),y \ x) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(3545,a,30023,a)].">
      <j1 rule="hyper" parents="3545 30023"/>
    </justification>
  </clause>

  <clause id="30227">
    <literal><![CDATA[
      L(L(x \ 1,y,y),L(x,y,y),y \ x) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,28905,a(flip),b,30226,a)].">
      <j1 rule="hyper" parents="60 28905 30226"/>
    </justification>
  </clause>

  <clause id="30228">
    <literal><![CDATA[
      R((1 / L(x,y,z)) * u,x,x) = (L(x,y,z) \ 1) * R(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(30173,a,30175,a)].">
      <j1 rule="hyper" parents="30173 30175"/>
    </justification>
  </clause>

  <clause id="30230">
    <literal><![CDATA[
      x * R((1 / L(y,z,u)) * ((L(y,z,u) \ 1) \ (x \ 1)),y,y) = (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y)
    ]]></literal>
    <justification jstring="[para(30228(a,2),2461(a,1,2))].">
      <j1 rule="para" parents="30228 2461"/>
    </justification>
  </clause>

  <clause id="30231">
    <literal><![CDATA[
      L(L((a(x,y,z) * a(x,y,z)) * z,u,w),y,x) = L(z * (L(z,y,x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(28254(a,2),30199(a,1,1,1))].">
      <j1 rule="para" parents="28254 30199"/>
    </justification>
  </clause>

  <clause id="30232">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) \ x = a(y * L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(28782,a,30220,a),flip(a)].">
      <j1 rule="hyper" parents="28782 30220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30233">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) \ x = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,27654,a(flip),b,30232,a),flip(a)].">
      <j1 rule="hyper" parents="370 27654 30232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30235">
    <literal><![CDATA[
      a(x,R(y,z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(30044,a,30222,a),flip(a)].">
      <j1 rule="hyper" parents="30044 30222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30236">
    <literal><![CDATA[
      a(x,R(R(y,z,u),w,v5) * (z * u),v6) = a(x,(L(y,w,v5) * z) * u,v6)
    ]]></literal>
    <justification jstring="[para(688(a,1),30235(a,2,2))].">
      <j1 rule="para" parents="688 30235"/>
    </justification>
  </clause>

  <clause id="30237">
    <literal><![CDATA[
      a(x,T(y * R(z,u,w),K(R(z,u,w),v5)),v6) = a(x,L(z,u,w) * T(y,T(R(z,u,w),v5)),v6)
    ]]></literal>
    <justification jstring="[para(8487(a,2),30235(a,1,2))].">
      <j1 rule="para" parents="8487 30235"/>
    </justification>
  </clause>

  <clause id="30238">
    <literal><![CDATA[
      a(x,(R(y,z,u) * w) * v5,v6) = a(x,(L(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(689(a,1),30236(a,1,2))].">
      <j1 rule="para" parents="689 30236"/>
    </justification>
  </clause>

  <clause id="30239">
    <literal><![CDATA[
      a(x,(L(y,z,u) * L(w,w,R(y,z,u))) * v5,v6) = a(x,(R(y,z,u) / (w \ 1)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2480(a,1),30238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2480 30238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30240">
    <literal><![CDATA[
      L((a(x,y,z) * a(x,y,z)) * L(z,u,w),y,x) = L(z * (L(z,y,x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(3782(a,1),30231(a,1,1))].">
      <j1 rule="para" parents="3782 30231"/>
    </justification>
  </clause>

  <clause id="30241">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * L(L(z,u,w),y,x) = L(z * (L(z,y,x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3782,a(flip),b,30240,a)].">
      <j1 rule="hyper" parents="60 3782 30240"/>
    </justification>
  </clause>

  <clause id="30242">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (L(x,y,z) \ x)) * L(L(x,u,w),y,z) = L(x * (L(x,y,z) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(30187(a,2),30241(a,1,1))].">
      <j1 rule="para" parents="30187 30241"/>
    </justification>
  </clause>

  <clause id="30243">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ x) * (x * L(x \ L(x,y,z),x,u))) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,4030,a(flip),b,29940,a),flip(a)].">
      <j1 rule="hyper" parents="370 4030 29940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30244">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(29934(a,2),29966(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29934 29966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30245">
    <literal><![CDATA[
      L(a(x,y,z * (u \ w)),z * (u \ w),y) = L(z * (w / u),y,x) \ (z * (w / u))
    ]]></literal>
    <justification jstring="[para(26939(a,1),29967(a,1,1))].">
      <j1 rule="para" parents="26939 29967"/>
    </justification>
  </clause>

  <clause id="30246">
    <literal><![CDATA[
      a(x,y,y \ ((z \ L(z,u,w)) \ y)) = L(z,u,w) \ (z * L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[para(29130(a,1),30049(a,2,2))].">
      <j1 rule="para" parents="29130 30049"/>
    </justification>
  </clause>

  <clause id="30247">
    <literal><![CDATA[
      L(x,(y \ (y / z)) \ 1,L((y \ (y / z)) \ 1,z,y)) = L(x,z,y \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,1492,a(flip),b,30204,a),flip(a)].">
      <j1 rule="hyper" parents="370 1492 30204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30248">
    <literal><![CDATA[
      L(x,(y \ (y / z)) \ 1,L((y \ (y / z)) \ 1,z,y)) = L(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,25927,a(flip),b,30247,a),flip(a)].">
      <j1 rule="hyper" parents="370 25927 30247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30249">
    <literal><![CDATA[
      L(x,(y \ (y / z)) \ 1,z) = L(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(30201(a,1),30248(a,1,3))].">
      <j1 rule="para" parents="30201 30248"/>
    </justification>
  </clause>

  <clause id="30250">
    <literal><![CDATA[
      L(x,y \ (y / z),z) = L(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(3530,a,30249,a)].">
      <j1 rule="hyper" parents="3530 30249"/>
    </justification>
  </clause>

  <clause id="30251">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(26273,a,30250,a)].">
      <j1 rule="hyper" parents="26273 30250"/>
    </justification>
  </clause>

  <clause id="30252">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) * (y * ((y \ z) / z)) = y * (((y \ z) / z) * x)
    ]]></literal>
    <justification jstring="[para(30251(a,1),26084(a,1,1))].">
      <j1 rule="para" parents="30251 26084"/>
    </justification>
  </clause>

  <clause id="30253">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) * a(y,y,z) = y * (((y \ z) / z) * x)
    ]]></literal>
    <justification jstring="[para(28440(a,1),30252(a,1,2))].">
      <j1 rule="para" parents="28440 30252"/>
    </justification>
  </clause>

  <clause id="30254">
    <literal><![CDATA[
      (x / (y * x)) * (y * z) = y * (((y \ x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28460,a(flip),b,30253,a)].">
      <j1 rule="hyper" parents="60 28460 30253"/>
    </justification>
  </clause>

  <clause id="30255">
    <literal><![CDATA[
      x \ (y / ((1 / x) * y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(125,a,1083,a(flip),b,30254,a(flip))].">
      <j1 rule="hyper" parents="125 1083 30254"/>
    </justification>
  </clause>

  <clause id="30256">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,29806,a,b,30255,a)].">
      <j1 rule="hyper" parents="60 29806 30255"/>
    </justification>
  </clause>

  <clause id="30257">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((1 / x) \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,29801,a,b,30255,a)].">
      <j1 rule="hyper" parents="60 29801 30255"/>
    </justification>
  </clause>

  <clause id="30258">
    <literal><![CDATA[
      (x / (y * x)) * ((y \ 1) \ 1) = ((y \ x) / x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,28933,a,b,30256,a)].">
      <j1 rule="hyper" parents="60 28933 30256"/>
    </justification>
  </clause>

  <clause id="30259">
    <literal><![CDATA[
      ((x \ y) / y) * x = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(2008,a,30258,a),flip(a)].">
      <j1 rule="hyper" parents="2008 30258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30261">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((1 / x) \ y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,30259,a(flip),b,30257,a),flip(a)].">
      <j1 rule="hyper" parents="370 30259 30257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30262">
    <literal><![CDATA[
      a(x,y,z * (((1 / u) \ w) * L((1 / u) \ w,u,u))) = a(x,y,z * (u * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(30261(a,1),15796(a,2,3,2))].">
      <j1 rule="para" parents="30261 15796"/>
    </justification>
  </clause>

  <clause id="30263">
    <literal><![CDATA[
      x \ (x * (L(x \ L(x,y,z),x,u) * (L(x,y,z) \ x))) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25167(a,1),30243(a,1,2))].">
      <j1 rule="para" parents="25167 30243"/>
    </justification>
  </clause>

  <clause id="30264">
    <literal><![CDATA[
      L(x * (y / z),u,w) \ (x * (y / z)) = L(x * (z \ y),u,w) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,29953,a(flip),b,30245,a),flip(a)].">
      <j1 rule="hyper" parents="60 29953 30245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30265">
    <literal><![CDATA[
      L(x * (y \ 1),x,z) \ (x * (y \ 1)) = a(z,x,x \ L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29996,a(flip),b,30264,a),flip(a)].">
      <j1 rule="hyper" parents="60 29996 30264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30266">
    <literal><![CDATA[
      a(x,y,y \ L(z,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y * z,y,x) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(30265(a,1),27880(a,1))].">
      <j1 rule="para" parents="30265 27880"/>
    </justification>
  </clause>

  <clause id="30267">
    <literal><![CDATA[
      a(x,y,y \ ((z \ L(z,u,w)) \ y)) = z * (L(z,u,w) \ L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,2160,a(flip),b,30246,a),flip(a)].">
      <j1 rule="hyper" parents="370 2160 30246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30268">
    <literal><![CDATA[
      x \ (x * (x * (L(x,y,z) \ L(x \ L(x,y,z),x,u)))) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25304(a,1),30263(a,1,2,2))].">
      <j1 rule="para" parents="25304 30263"/>
    </justification>
  </clause>

  <clause id="30269">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x \ L(x,y,z),x,u)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(386,a,30268,a)].">
      <j1 rule="hyper" parents="386 30268"/>
    </justification>
  </clause>

  <clause id="30270">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ x,x,u)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(14871(a,1),30268(a,1,2))].">
      <j1 rule="para" parents="14871 30268"/>
    </justification>
  </clause>

  <clause id="30271">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) \ (L(y,z,u) \ y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29831,a,b,30269,a)].">
      <j1 rule="hyper" parents="60 29831 30269"/>
    </justification>
  </clause>

  <clause id="30273">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ x,x,x \ u)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13239(a,2),30270(a,1,2,2))].">
      <j1 rule="para" parents="13239 30270"/>
    </justification>
  </clause>

  <clause id="30274">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,z,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(29933(a,2),30271(a,1,1))].">
      <j1 rule="para" parents="29933 30271"/>
    </justification>
  </clause>

  <clause id="30275">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,29969,a(flip),b,30274,a),flip(a)].">
      <j1 rule="hyper" parents="60 29969 30274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30276">
    <literal><![CDATA[
      (x * a(y,x,a(z,y,x))) \ (x * (x * L(x,y,z))) = L(x * L(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[para(30275(a,1),29945(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="30275 29945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30277">
    <literal><![CDATA[
      (x * a(y,x,a(z,y,x))) \ (x * (x \ L(x,y,z))) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(30275(a,1),30153(a,1,1,2))].">
      <j1 rule="para" parents="30275 30153"/>
    </justification>
  </clause>

  <clause id="30278">
    <literal><![CDATA[
      (x * a(y,x,a(z,y,x))) \ L(x,y,z) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(5(a,1),30277(a,1,2))].">
      <j1 rule="para" parents="5 30277"/>
    </justification>
  </clause>

  <clause id="30280">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ L(x,z,y) = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[para(30132(a,1),30278(a,1,1))].">
      <j1 rule="para" parents="30132 30278"/>
    </justification>
  </clause>

  <clause id="30281">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) = a(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30270,a(flip),b,30273,a)].">
      <j1 rule="hyper" parents="60 30270 30273"/>
    </justification>
  </clause>

  <clause id="30282">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ (x * (x * L(x,z,y))) = L(x * L(x,z,y),x,z)
    ]]></literal>
    <justification jstring="[para(30132(a,1),30276(a,1,1))].">
      <j1 rule="para" parents="30132 30276"/>
    </justification>
  </clause>

  <clause id="30283">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ L(x * (x * x),z,y) = L(x * L(x,z,y),x,z)
    ]]></literal>
    <justification jstring="[para(3905(a,2),30282(a,1,2))].">
      <j1 rule="para" parents="3905 30282"/>
    </justification>
  </clause>

  <clause id="30284">
    <literal><![CDATA[
      (L(x,a(y,z,x),z) \ L(x,z,y)) * (x * x) = L(x * L(x,z,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(3902,a,30283,a)].">
      <j1 rule="hyper" parents="3902 30283"/>
    </justification>
  </clause>

  <clause id="30285">
    <literal><![CDATA[
      L(x * L(x,y,z),x,y) = (a(z,y,x) \ 1) * (x * x)
    ]]></literal>
    <justification jstring="[para(30280(a,1),30284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30280 30284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30286">
    <literal><![CDATA[
      L(x * L(x,y,z),x,y) = a(z,y,x) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,519,a(flip),b,30285,a),flip(a)].">
      <j1 rule="hyper" parents="370 519 30285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30287">
    <literal><![CDATA[
      L(x * L(x,y,z),x,y) = x * (a(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,25338,a(flip),b,30286,a),flip(a)].">
      <j1 rule="hyper" parents="370 25338 30286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30288">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),a(x,y,z) * u) = (a(x,y,z) \ u) \ ((1 / a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1264,a(flip),b,30112,a),flip(a)].">
      <j1 rule="hyper" parents="370 1264 30112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30289">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3866,a,30161,a)].">
      <j1 rule="hyper" parents="3866 30161"/>
    </justification>
  </clause>

  <clause id="30290">
    <literal><![CDATA[
      L(x * y,y,x) \ 1 = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(747,a,30289,a),flip(a)].">
      <j1 rule="hyper" parents="747 30289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30292">
    <literal><![CDATA[
      L(L(L(x,y,z) \ 1,u,w),y,z) = L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(30289(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30289 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30294">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(30289(a,2),45(a,1))].">
      <j1 rule="para" parents="30289 45"/>
    </justification>
  </clause>

  <clause id="30301">
    <literal><![CDATA[
      (x * y) * (y \ (x \ 1)) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,30290,a(flip),b,14765,a)].">
      <j1 rule="hyper" parents="129 30290 14765"/>
    </justification>
  </clause>

  <clause id="30302">
    <literal><![CDATA[
      a(x,y \ (x \ 1),x * (y \ (x \ 1))) = ((1 / x) * (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,30012,a(flip),b,30301,a),flip(a)].">
      <j1 rule="hyper" parents="60 30012 30301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30303">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ 1,u,w) = L(L(x,u,w) \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(30292(a,1),30289(a,1,1,1))].">
      <j1 rule="para" parents="30292 30289"/>
    </justification>
  </clause>

  <clause id="30304">
    <literal><![CDATA[
      T(L(L(x \ 1,y,z) \ 1,u,w),x \ (x \ 1)) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(30303(a,2),28549(a,1,1))].">
      <j1 rule="para" parents="30303 28549"/>
    </justification>
  </clause>

  <clause id="30305">
    <literal><![CDATA[
      a(x,y \ (x \ 1),(y \ x) * x) = ((1 / x) * (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,27084,a(flip),b,30302,a)].">
      <j1 rule="hyper" parents="60 27084 30302"/>
    </justification>
  </clause>

  <clause id="30306">
    <literal><![CDATA[
      a(x,y \ x,(y \ x) * x) = ((1 / x) * (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,3112,a(flip),b,30305,a)].">
      <j1 rule="hyper" parents="60 3112 30305"/>
    </justification>
  </clause>

  <clause id="30307">
    <literal><![CDATA[
      a(x,y \ x,(y \ x) * x) = (x * ((x \ 1) / y)) * y
    ]]></literal>
    <justification jstring="[para(30009(a,1),30306(a,2,1))].">
      <j1 rule="para" parents="30009 30306"/>
    </justification>
  </clause>

  <clause id="30308">
    <literal><![CDATA[
      a(x,y \ x,(y \ x) * x) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28691,a(flip),b,30307,a),flip(a)].">
      <j1 rule="hyper" parents="370 28691 30307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30309">
    <literal><![CDATA[
      L(x,y,a(z \ u,z \ u,u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(30308(a,1),27959(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30308 27959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30310">
    <literal><![CDATA[
      L(x,y,a(z * u,z * u,u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(29625(a,1),30309(a,1,3))].">
      <j1 rule="para" parents="29625 30309"/>
    </justification>
  </clause>

  <clause id="30311">
    <literal><![CDATA[
      L(x,y,(z / u) * (u / z)) = L(x,y,a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[para(29635(a,1),30310(a,1,3))].">
      <j1 rule="para" parents="29635 30310"/>
    </justification>
  </clause>

  <clause id="30312">
    <literal><![CDATA[
      L(x,y,(z / u) * (z \ u)) = L(x,y,a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(25949,a,30311,a)].">
      <j1 rule="hyper" parents="25949 30311"/>
    </justification>
  </clause>

  <clause id="30313">
    <literal><![CDATA[
      L(x,y,(z \ u) * (u \ z)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(25945,a,30312,a)].">
      <j1 rule="hyper" parents="25945 30312"/>
    </justification>
  </clause>

  <clause id="30314">
    <literal><![CDATA[
      L(T(L(x \ 1,y,z) \ 1,x \ (x \ 1)),u,w) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(25206,a,30304,a)].">
      <j1 rule="hyper" parents="25206 30304"/>
    </justification>
  </clause>

  <clause id="30315">
    <literal><![CDATA[
      L(T(L(1 / x,y,z) \ 1,1),u,w) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(28522(a,1),30314(a,1,1))].">
      <j1 rule="para" parents="28522 30314"/>
    </justification>
  </clause>

  <clause id="30316">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,u,w) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(222(a,1),30315(a,1,1))].">
      <j1 rule="para" parents="222 30315"/>
    </justification>
  </clause>

  <clause id="30317">
    <literal><![CDATA[
      L(1 / L(x,y,z),y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(30294,a,30316,a),flip(a)].">
      <j1 rule="hyper" parents="30294 30316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30318">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,z,y) = y \ (z \ (y * (T(z,y) * x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,30016,a(flip),b,30316,a),flip(a)].">
      <j1 rule="hyper" parents="370 30016 30316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30319">
    <literal><![CDATA[
      L(1 / (x * y),x,x) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2082(a,1),30317(a,1,1,2))].">
      <j1 rule="para" parents="2082 30317"/>
    </justification>
  </clause>

  <clause id="30320">
    <literal><![CDATA[
      a(x,y,((L(z,z,z) * L(u,z,z)) \ w) * v5) = a(x,y,((1 / ((z \ 1) \ u)) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(30319(a,1),27244(a,2,3,1,1))].">
      <j1 rule="para" parents="30319 27244"/>
    </justification>
  </clause>

  <clause id="30321">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = L(L(1 / a(u,T(y,x),z),x,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(29938(a,2),30318(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="29938 30318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30322">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w)) = x \ R(x,(y \ 1) \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(2757(a,1),30176(a,2,2))].">
      <j1 rule="para" parents="2757 30176"/>
    </justification>
  </clause>

  <clause id="30324">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w)) = x \ R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(27469(a,1),30322(a,2,2))].">
      <j1 rule="para" parents="27469 30322"/>
    </justification>
  </clause>

  <clause id="30325">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w)) = x \ R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[para(30180(a,1),30324(a,2,2))].">
      <j1 rule="para" parents="30180 30324"/>
    </justification>
  </clause>

  <clause id="30326">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),L(y \ z,u,w)) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,16509,a(flip),b,30325,a),flip(a)].">
      <j1 rule="hyper" parents="370 16509 30325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30327">
    <literal><![CDATA[
      a(x,L(y \ z,u,w),L(y \ z,u,w)) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,3971,a(flip),b,30326,a)].">
      <j1 rule="hyper" parents="60 3971 30326"/>
    </justification>
  </clause>

  <clause id="30328">
    <literal><![CDATA[
      a(x,y \ z,y \ z) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,30169,a(flip),b,30327,a)].">
      <j1 rule="hyper" parents="60 30169 30327"/>
    </justification>
  </clause>

  <clause id="30329">
    <literal><![CDATA[
      a(L(x,y,z),u \ w,u \ w) = a(x,u * w,L(u * w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30093,a(flip),b,30328,a),flip(a)].">
      <j1 rule="hyper" parents="370 30093 30328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30330">
    <literal><![CDATA[
      a(x,x * y,x * y) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(30328(a,1),28840(a,1,1))].">
      <j1 rule="para" parents="30328 28840"/>
    </justification>
  </clause>

  <clause id="30331">
    <literal><![CDATA[
      x * a(y,y * x,y * x) = y * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(30328(a,1),28941(a,1,2))].">
      <j1 rule="para" parents="30328 28941"/>
    </justification>
  </clause>

  <clause id="30332">
    <literal><![CDATA[
      a(L(x,y,z),(u * w) \ u,u \ (w \ u)) = a(x,(u * w) * u,L((u * w) * u,y,z))
    ]]></literal>
    <justification jstring="[hyper(27090,a,30329,a)].">
      <j1 rule="hyper" parents="27090 30329"/>
    </justification>
  </clause>

  <clause id="30333">
    <literal><![CDATA[
      a(x,(L(y,z,u) * L(w,w,R(y,z,u))) * v5,v6) = a(x,((w \ 1) \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26465,a(flip),b,30239,a),flip(a)].">
      <j1 rule="hyper" parents="370 26465 30239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30334">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),a(x,y,z) * u) = (a(x,y,z) \ u) \ ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),30288(a,2,2,1))].">
      <j1 rule="para" parents="23572 30288"/>
    </justification>
  </clause>

  <clause id="30335">
    <literal><![CDATA[
      a(x,y,((L(z,z,z) * L(u,z,z)) \ w) * v5) = a(x,y,(((z \ 1) \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,3135,a(flip),b,30320,a),flip(a)].">
      <j1 rule="hyper" parents="370 3135 30320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30336">
    <literal><![CDATA[
      a(x,y,((L(z,z,z) * L(u,z,z)) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27235,a(flip),b,30335,a),flip(a)].">
      <j1 rule="hyper" parents="370 27235 30335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30337">
    <literal><![CDATA[
      a(x,y,(L(z * u,z,z) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(1280(a,1),30336(a,1,3,1,1))].">
      <j1 rule="para" parents="1280 30336"/>
    </justification>
  </clause>

  <clause id="30338">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) * (((z * u) \ 1) \ w)) = a(x,y,(z * u) * (L(z * u,z,z) \ w))
    ]]></literal>
    <justification jstring="[para(29586(a,1),30337(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29586 30337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30339">
    <literal><![CDATA[
      a(L(x,y,z),(u * w) \ u,u \ (w \ u)) = a(x,(u * w) * u,L(L(w,u,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27169,a(flip),b,30332,a),flip(a)].">
      <j1 rule="hyper" parents="370 27169 30332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30340">
    <literal><![CDATA[
      a(L(x,y,z),(u * w) \ u,u \ (w \ u)) = a(x,L(w,u,u),L(L(w,u,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26484,a(flip),b,30339,a),flip(a)].">
      <j1 rule="hyper" parents="370 26484 30339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30341">
    <literal><![CDATA[
      a(L(x,y,z),(u * w) \ u,u \ (w \ u)) = a(x,w,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30177,a(flip),b,30340,a),flip(a)].">
      <j1 rule="hyper" parents="370 30177 30340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30343">
    <literal><![CDATA[
      a(L(x,y,z),u \ (w \ u),u \ (w \ u)) = a(x,w,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30086,a(flip),b,30341,a)].">
      <j1 rule="hyper" parents="60 30086 30341"/>
    </justification>
  </clause>

  <clause id="30344">
    <literal><![CDATA[
      a(x,y * (z \ y),L(y * (z \ y),u,w)) = a(x,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,30329,a(flip),b,30343,a)].">
      <j1 rule="hyper" parents="60 30329 30343"/>
    </justification>
  </clause>

  <clause id="30345">
    <literal><![CDATA[
      a(x,(L(y,z,u) * L(w,w,R(y,z,u))) * v5,v6) = a(x,(w \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,3045,a(flip),b,30333,a),flip(a)].">
      <j1 rule="hyper" parents="370 3045 30333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30346">
    <literal><![CDATA[
      a(x,(L(y,z,u) * L(w,w,L(y,z,u))) * v5,v6) = a(x,(w \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(27279(a,1),30345(a,1,2,1,2))].">
      <j1 rule="para" parents="27279 30345"/>
    </justification>
  </clause>

  <clause id="30347">
    <literal><![CDATA[
      a(x,(L(y,z,u) / (w \ 1)) * v5,v6) = a(x,(w \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2480(a,1),30346(a,1,2,1))].">
      <j1 rule="para" parents="2480 30346"/>
    </justification>
  </clause>

  <clause id="30348">
    <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(26570,a,30347,a)].">
      <j1 rule="hyper" parents="26570 30347"/>
    </justification>
  </clause>

  <clause id="30349">
    <literal><![CDATA[
      a(x,(y \ R(z,u,w)) * v5,v6) = a(x,(y \ L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(3064,a,30348,a),flip(a)].">
      <j1 rule="hyper" parents="3064 30348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30350">
    <literal><![CDATA[
      a(x,(y \ L(z * u,u,u)) * w,v5) = a(x,w * (y \ R(u * z,u,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27671,a(flip),b,30349,a),flip(a)].">
      <j1 rule="hyper" parents="60 27671 30349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30351">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),a(x,y,z) * u) = a(a(x,y,z),a(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,28872,a(flip),b,30334,a),flip(a)].">
      <j1 rule="hyper" parents="370 28872 30334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30352">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),a(x,y,z) * u) = a(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,28358,a(flip),b,30351,a),flip(a)].">
      <j1 rule="hyper" parents="370 28358 30351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30353">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x \ L(x,y,z),x,y) \ 1) = a(z,y,x) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(9918(a,1),29956(a,1,2,1,1))].">
      <j1 rule="para" parents="9918 29956"/>
    </justification>
  </clause>

  <clause id="30354">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,y) = a(z,y,x) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29124(a,1),30353(a,1,2))].">
      <j1 rule="para" parents="29124 30353"/>
    </justification>
  </clause>

  <clause id="30355">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(x,y,z) * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29941,a(flip),b,30354,a),flip(a)].">
      <j1 rule="hyper" parents="60 29941 30354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30356">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,x) = a(z,y,x) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(29934(a,2),30354(a,1,2))].">
      <j1 rule="para" parents="29934 30354"/>
    </justification>
  </clause>

  <clause id="30357">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,y,x)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29969,a(flip),b,30355,a),flip(a)].">
      <j1 rule="hyper" parents="60 29969 30355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30358">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,x) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29969,a(flip),b,30356,a),flip(a)].">
      <j1 rule="hyper" parents="370 29969 30356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30359">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) != u \ a(z,x,y)
    ]]></literal>
    <literal><![CDATA[
      L(y,x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(30358(a,1),45(a,1))].">
      <j1 rule="para" parents="30358 45"/>
    </justification>
  </clause>

  <clause id="30360">
    <literal><![CDATA[
      (L(x,x \ y,y) \ 1) * (x \ K(x,y * (x \ (y \ 1)))) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(9206(a,1),30024(a,1,2,2))].">
      <j1 rule="para" parents="9206 30024"/>
    </justification>
  </clause>

  <clause id="30361">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ (y \ z) = y \ (((x \ (x / y)) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(30201(a,1),30203(a,1,2,1))].">
      <j1 rule="para" parents="30201 30203"/>
    </justification>
  </clause>

  <clause id="30362">
    <literal><![CDATA[
      a(x,y,z * (((1 / u) \ w) * L((1 / u) \ w,u,u))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,28436,a(flip),b,30262,a),flip(a)].">
      <j1 rule="hyper" parents="370 28436 30262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30363">
    <literal><![CDATA[
      a(x,y,z * (((1 / u) \ w) * (T(u,u \ 1) * w))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(3710(a,1),30362(a,1,3,2,2))].">
      <j1 rule="para" parents="3710 30362"/>
    </justification>
  </clause>

  <clause id="30364">
    <literal><![CDATA[
      a(x,y,((z * u) * ((1 / z) \ u)) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27182,a(flip),b,30363,a)].">
      <j1 rule="hyper" parents="60 27182 30363"/>
    </justification>
  </clause>

  <clause id="30366">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ u)) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27726,a(flip),b,30364,a)].">
      <j1 rule="hyper" parents="60 27726 30364"/>
    </justification>
  </clause>

  <clause id="30367">
    <literal><![CDATA[
      a(x,y,z * a(u,u,u * w)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29779,a(flip),b,30366,a)].">
      <j1 rule="hyper" parents="60 29779 30366"/>
    </justification>
  </clause>

  <clause id="30368">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(26965,a,30367,a)].">
      <j1 rule="hyper" parents="26965 30367"/>
    </justification>
  </clause>

  <clause id="30369">
    <literal><![CDATA[
      (L(x,x \ y,y) \ 1) * (x \ K(x,T(x,y) \ 1)) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(25600(a,1),30360(a,1,2,2))].">
      <j1 rule="para" parents="25600 30360"/>
    </justification>
  </clause>

  <clause id="30370">
    <literal><![CDATA[
      (L(x,x \ y,y) \ 1) * (x \ K(x,x \ 1)) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(9198(a,1),30369(a,1,2,2))].">
      <j1 rule="para" parents="9198 30369"/>
    </justification>
  </clause>

  <clause id="30371">
    <literal><![CDATA[
      (L(x,x \ y,y) \ 1) * (1 / x) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1712(a,1),30370(a,1,2))].">
      <j1 rule="para" parents="1712 30370"/>
    </justification>
  </clause>

  <clause id="30373">
    <literal><![CDATA[
      x \ (L(x,x \ y,y) \ 1) = (y * ((y \ 1) / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,25346,a(flip),b,30371,a)].">
      <j1 rule="hyper" parents="60 25346 30371"/>
    </justification>
  </clause>

  <clause id="30374">
    <literal><![CDATA[
      a(x,L(y,z,u) * T(w,T(R(y,z,u),v5)),v6) = a(x,w * R(y,z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(26557,a,30237,a),flip(a)].">
      <j1 rule="hyper" parents="26557 30237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30376">
    <literal><![CDATA[
      a(x,L(y,z,u) * T(w,R(T(y,v5),z,u)),v6) = a(x,w * R(y,z,u),v6)
    ]]></literal>
    <justification jstring="[para(22(a,2),30374(a,1,2,2,2))].">
      <j1 rule="para" parents="22 30374"/>
    </justification>
  </clause>

  <clause id="30377">
    <literal><![CDATA[
      a(x,L(y,z,u) * T(w,T(y,v5)),v6) = a(x,w * R(y,z,u),v6)
    ]]></literal>
    <justification jstring="[para(23840(a,1),30376(a,1,2,2))].">
      <j1 rule="para" parents="23840 30376"/>
    </justification>
  </clause>

  <clause id="30379">
    <literal><![CDATA[
      a(x,T(y * L(z,u,w),K(z,v5)),v6) = a(x,y * R(z,u,w),v6)
    ]]></literal>
    <justification jstring="[para(25824(a,2),30377(a,1,2))].">
      <j1 rule="para" parents="25824 30377"/>
    </justification>
  </clause>

  <clause id="30380">
    <literal><![CDATA[
      a(x,y * R(z,u,w),v5) = a(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(26557,a,30379,a),flip(a)].">
      <j1 rule="hyper" parents="26557 30379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30381">
    <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(30379(a,1),26557(a,1))].">
      <j1 rule="para" parents="30379 26557"/>
    </justification>
  </clause>

  <clause id="30383">
    <literal><![CDATA[
      a(x,y * R(L(z,u,w),v5,v6),v7) = a(x,y * L(L(z,v5,v6),u,w),v7)
    ]]></literal>
    <justification jstring="[para(25(a,1),30380(a,2,2,2))].">
      <j1 rule="para" parents="25 30380"/>
    </justification>
  </clause>

  <clause id="30384">
    <literal><![CDATA[
      a(x,y * L(R(z,u,w),v5,v6),v7) = a(x,y * L(L(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(24(a,1),30383(a,1,2,2))].">
      <j1 rule="para" parents="24 30383"/>
    </justification>
  </clause>

  <clause id="30385">
    <literal><![CDATA[
      a(x,(y * z) * L(R(u,w,v5),z,y),v6) = a(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(92(a,1),30384(a,2,2))].">
      <j1 rule="para" parents="92 30384"/>
    </justification>
  </clause>

  <clause id="30386">
    <literal><![CDATA[
      a(x,y * (z * R(u,w,v5)),v6) = a(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(92(a,1),30385(a,1,2))].">
      <j1 rule="para" parents="92 30385"/>
    </justification>
  </clause>

  <clause id="30387">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * R(z \ ((1 / z) \ u),w,v5)),v6) = a(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(2107(a,1),30386(a,2,2,2))].">
      <j1 rule="para" parents="2107 30386"/>
    </justification>
  </clause>

  <clause id="30388">
    <literal><![CDATA[
      a(x,y * (z \ R(u,w,v5)),v6) = a(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(2151(a,1),30387(a,1,2,2))].">
      <j1 rule="para" parents="2151 30387"/>
    </justification>
  </clause>

  <clause id="30389">
    <literal><![CDATA[
      a(x,(y \ L(z * u,u,u)) * w,v5) = a(x,w * (y \ L(u * z,u,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,30350,a,b,30388,a)].">
      <j1 rule="hyper" parents="60 30350 30388"/>
    </justification>
  </clause>

  <clause id="30390">
    <literal><![CDATA[
      a(x,(y \ L(z * u,u,u)) * w,v5) = a(x,w * (y \ (u \ z)),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,29727,a(flip),b,30389,a),flip(a)].">
      <j1 rule="hyper" parents="370 29727 30389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30391">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (L(x,y,z) \ x)) \ x = L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,30200,a(flip),b,30242,a)].">
      <j1 rule="hyper" parents="125 30200 30242"/>
    </justification>
  </clause>

  <clause id="30392">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * w,v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(30391(a,1),3043(a,1,2,1))].">
      <j1 rule="para" parents="30391 3043"/>
    </justification>
  </clause>

  <clause id="30393">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(30391(a,1),25265(a,1,2))].">
      <j1 rule="para" parents="30391 25265"/>
    </justification>
  </clause>

  <clause id="30394">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(30391(a,1),26594(a,1,2,1))].">
      <j1 rule="para" parents="30391 26594"/>
    </justification>
  </clause>

  <clause id="30395">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(30391(a,1),26987(a,1,3))].">
      <j1 rule="para" parents="30391 26987"/>
    </justification>
  </clause>

  <clause id="30396">
    <literal><![CDATA[
      a(x,y,(L(L(z,u,w),u,w) \ v5) * v6) = a(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(30391(a,1),27234(a,1,3,1,1))].">
      <j1 rule="para" parents="30391 27234"/>
    </justification>
  </clause>

  <clause id="30397">
    <literal><![CDATA[
      L(x,y,z \ L(L(u,w,v5),w,v5)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(30391(a,1),27624(a,1,3,2))].">
      <j1 rule="para" parents="30391 27624"/>
    </justification>
  </clause>

  <clause id="30398">
    <literal><![CDATA[
      L(x,L((1 / y) * z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(586(a,1),30393(a,1,2,1))].">
      <j1 rule="para" parents="586 30393"/>
    </justification>
  </clause>

  <clause id="30399">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ (z \ w)) = v5
    ]]></literal>
    <justification jstring="[para(344(a,1),30395(a,1,3,1))].">
      <j1 rule="para" parents="344 30395"/>
    </justification>
  </clause>

  <clause id="30401">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = w
    ]]></literal>
    <justification jstring="[para(29140(a,1),30395(a,1))].">
      <j1 rule="para" parents="29140 30395"/>
    </justification>
  </clause>

  <clause id="30404">
    <literal><![CDATA[
      L((x * (L(L(x,y,z),y,z) \ u)) \ w,x * (L(L(x,y,z),y,z) \ u),x \ x) = u \ ((x \ L(L(x,y,z),y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29507,a(flip),b,30397,a),flip(a)].">
      <j1 rule="hyper" parents="60 29507 30397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30405">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3982(a,1),30398(a,1))].">
      <j1 rule="para" parents="3982 30398"/>
    </justification>
  </clause>

  <clause id="30406">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5),w,v5) \ v6)) = a(x,y,(u \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,30396,a)].">
      <j1 rule="hyper" parents="26965 30396"/>
    </justification>
  </clause>

  <clause id="30407">
    <literal><![CDATA[
      (x \ L(x,y,z)) / L((L(x,y,z) \ x) \ 1,x,y) = (L(x,y,z) \ x) * (1 / a(z,y,x))
    ]]></literal>
    <justification jstring="[para(9918(a,1),29960(a,1,1))].">
      <j1 rule="para" parents="9918 29960"/>
    </justification>
  </clause>

  <clause id="30408">
    <literal><![CDATA[
      (x \ L(x,y,z)) / L(x \ L(x,y,z),x,y) = (L(x,y,z) \ x) * (1 / a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14170(a,1),30407(a,1,2,1))].">
      <j1 rule="para" parents="14170 30407"/>
    </justification>
  </clause>

  <clause id="30409">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (a(z,y,x) \ 1) = (L(x,y,z) \ x) * (1 / a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29963(a,1),30408(a,1,2))].">
      <j1 rule="para" parents="29963 30408"/>
    </justification>
  </clause>

  <clause id="30410">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z \ L(z,y,x)) = (L(z,y,x) \ z) * (1 / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23825,a,30409,a)].">
      <j1 rule="hyper" parents="23825 30409"/>
    </justification>
  </clause>

  <clause id="30411">
    <literal><![CDATA[
      x \ ((a(y,z,x) \ 1) \ L(x,z,y)) = (L(x,z,y) \ x) * (1 / a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27574,a(flip),b,30410,a)].">
      <j1 rule="hyper" parents="60 27574 30410"/>
    </justification>
  </clause>

  <clause id="30412">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (1 / a(z,y,x)) = x \ (L(x,y,z) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29290(a,1),30411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29290 30411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30413">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (1 / a(z,y,x)) = x \ L(x * a(z,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(29965(a,2),30412(a,2,2))].">
      <j1 rule="para" parents="29965 30412"/>
    </justification>
  </clause>

  <clause id="30414">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (1 / a(z,y,x)) = x * L(x \ a(z,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3916,a(flip),b,30413,a),flip(a)].">
      <j1 rule="hyper" parents="370 3916 30413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30415">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (a(z,y,x) \ 1) = x * L(x \ a(z,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(23572(a,1),30414(a,1,2))].">
      <j1 rule="para" parents="23572 30414"/>
    </justification>
  </clause>

  <clause id="30416">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = z * L(z \ a(x,y,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28502,a(flip),b,30415,a)].">
      <j1 rule="hyper" parents="60 28502 30415"/>
    </justification>
  </clause>

  <clause id="30417">
    <literal><![CDATA[
      x * L(x \ a(y,z,x),z,y) = a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29969,a(flip),b,30416,a),flip(a)].">
      <j1 rule="hyper" parents="60 29969 30416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30418">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = x * a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,30417,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="129 30417 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30419">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,a(y,z,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30132,a(flip),b,30418,a),flip(a)].">
      <j1 rule="hyper" parents="370 30132 30418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30420">
    <literal><![CDATA[
      (x * y) * L(z,a(x,y,z),y) = x * (y * (z * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(129,a,30419,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="129 30419 13"/>
    </justification>
  </clause>

  <clause id="30421">
    <literal><![CDATA[
      L(x,L(y,a(z,u,y),u),L(y * a(z,u,y),u,z)) = L(x,y * a(z,u,y),y * a(z,u,y))
    ]]></literal>
    <justification jstring="[para(30419(a,1),29547(a,1,2))].">
      <j1 rule="para" parents="30419 29547"/>
    </justification>
  </clause>

  <clause id="30422">
    <literal><![CDATA[
      L(x,L(y,a(z,u,y),u),L(y,a(z,u,y),u)) = L(x,y * a(z,u,y),y * a(z,u,y))
    ]]></literal>
    <justification jstring="[para(30419(a,1),30421(a,1,3))].">
      <j1 rule="para" parents="30419 30421"/>
    </justification>
  </clause>

  <clause id="30423">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(z,u,y)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29547,a(flip),b,30422,a),flip(a)].">
      <j1 rule="hyper" parents="60 29547 30422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30425">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x,x) = (1 / (x \ a(z,u,x))) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29627,a(flip),b,30423,a),flip(a)].">
      <j1 rule="hyper" parents="60 29627 30423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30427">
    <literal><![CDATA[
      (1 / (x \ a(y,z,x))) * (u * a(y,z,x)) = L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,2084,a(flip),b,30425,a),flip(a)].">
      <j1 rule="hyper" parents="60 2084 30425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30428">
    <literal><![CDATA[
      ((a(x,y,z) / z) \ 1) * (u * a(x,y,z)) = L(z * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28238(a,1),30427(a,1,1))].">
      <j1 rule="para" parents="28238 30427"/>
    </justification>
  </clause>

  <clause id="30429">
    <literal><![CDATA[
      (x * (1 / y)) \ (L(x / (x * (1 / y)),x * y,z) \ x) = a(z,x * (1 / y),L(y,y,x))
    ]]></literal>
    <justification jstring="[para(3770(a,1),29990(a,1,2,1))].">
      <j1 rule="para" parents="3770 29990"/>
    </justification>
  </clause>

  <clause id="30430">
    <literal><![CDATA[
      a(x,y * (1 / z),L(z,z,y)) = L(1 / z,y * z,x) \ (1 / z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29814,a(flip),b,30429,a),flip(a)].">
      <j1 rule="hyper" parents="60 29814 30429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30432">
    <literal><![CDATA[
      a(x,y * (1 / z),L(z,z,y)) = L(z,y * z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(370,a,3985,a(flip),b,30430,a),flip(a)].">
      <j1 rule="hyper" parents="370 3985 30430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30433">
    <literal><![CDATA[
      a(x,y * (z \ 1),L(z,z,y)) = L(z,y * z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(26585,a,30432,a)].">
      <j1 rule="hyper" parents="26585 30432"/>
    </justification>
  </clause>

  <clause id="30434">
    <literal><![CDATA[
      L(x,y * x,z) \ x != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y * x,L(x,x,y)) = u
    ]]></literal>
    <justification jstring="[para(30433(a,1),26584(a,1))].">
      <j1 rule="para" parents="30433 26584"/>
    </justification>
  </clause>

  <clause id="30435">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * z,(L(y,z,u) * y) * z) = L(x,z * a(u,z,y),y * (L(y,z,u) \ z))
    ]]></literal>
    <justification jstring="[para(281(a,1),29975(a,1,2,1))].">
      <j1 rule="para" parents="281 29975"/>
    </justification>
  </clause>

  <clause id="30437">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = L(L(1 / a(u,y,z),x,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(26451(a,1),30321(a,2,1,1,1,2))].">
      <j1 rule="para" parents="26451 30321"/>
    </justification>
  </clause>

  <clause id="30438">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = L(L(a(u,y,z) \ 1,x,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(23572(a,1),30437(a,2,1,1,1))].">
      <j1 rule="para" parents="23572 30437"/>
    </justification>
  </clause>

  <clause id="30442">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * z,(y * L(y,z,u)) * z) = L(x,z * a(u,z,y),y * (L(y,z,u) \ z))
    ]]></literal>
    <justification jstring="[para(281(a,1),30435(a,1,3,1))].">
      <j1 rule="para" parents="281 30435"/>
    </justification>
  </clause>

  <clause id="30443">
    <literal><![CDATA[
      L(x,L(y,z,u) * (y \ z),L(y,z,u) * (y \ z)) = L(x,z * a(u,z,y),y * (L(y,z,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(29706,a,30442,a)].">
      <j1 rule="hyper" parents="29706 30442"/>
    </justification>
  </clause>

  <clause id="30444">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ L(x \ L(x,y,z),x,u)),x,x * L(x,y,z)) = a(u,x,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(4255(a,1),29982(a,1,1))].">
      <j1 rule="para" parents="4255 29982"/>
    </justification>
  </clause>

  <clause id="30445">
    <literal><![CDATA[
      L(1 / x,R(1 / y,z,u),L(1 / y,z,u)) \ 1 = R(1 / y,z,u) \ ((R(y \ 1,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(27279(a,1),30020(a,1,1))].">
      <j1 rule="para" parents="27279 30020"/>
    </justification>
  </clause>

  <clause id="30446">
    <literal><![CDATA[
      (1 / (x * y)) \ (y \ (x \ K(x * y,y \ (x \ 1)))) = a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(23393(a,1),30110(a,1,2,2,2))].">
      <j1 rule="para" parents="23393 30110"/>
    </justification>
  </clause>

  <clause id="30447">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),z \ v5)) = a(x,y,a(z,z,z * (L(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[para(29529(a,1),30159(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29529 30159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30448">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),z \ v5)) = a(x,y,a(z,z,L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,30158,a(flip),b,30447,a),flip(a)].">
      <j1 rule="hyper" parents="370 30158 30447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30450">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),z \ v5)) = a(x,y,a(z,z,L(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(29637(a,1),30448(a,2,3))].">
      <j1 rule="para" parents="29637 30448"/>
    </justification>
  </clause>

  <clause id="30451">
    <literal><![CDATA[
      a(x,y,a(z,z,L(z,u,w) * v5)) = a(x,y,a(z,z,z \ v5))
    ]]></literal>
    <justification jstring="[para(29529(a,1),30450(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29529 30450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30452">
    <literal><![CDATA[
      a(x,y,a(z,z,L(z,u,w) * v5)) = a(x,y,a(z,z,z * v5))
    ]]></literal>
    <justification jstring="[para(19763(a,1),30451(a,2,3))].">
      <j1 rule="para" parents="19763 30451"/>
    </justification>
  </clause>

  <clause id="30454">
    <literal><![CDATA[
      a(x,y,a(z,z,L(z,u,w) * v5)) = a(x,y,a(z,z,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,30158,a(flip),b,30452,a),flip(a)].">
      <j1 rule="hyper" parents="370 30158 30452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30455">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w * z))) = a(x,y,a(z,z,u * w))
    ]]></literal>
    <justification jstring="[para(26890(a,1),30454(a,1,3))].">
      <j1 rule="para" parents="26890 30454"/>
    </justification>
  </clause>

  <clause id="30456">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),y,y * L(y,z,u)) = a(x,y,y * L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(30269(a,1),30444(a,1,1))].">
      <j1 rule="para" parents="30269 30444"/>
    </justification>
  </clause>

  <clause id="30457">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(30456(a,1),14783(a,1))].">
      <j1 rule="para" parents="30456 14783"/>
    </justification>
  </clause>

  <clause id="30458">
    <literal><![CDATA[
      R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u) = L(1 / u,R(1 / x,y,z),L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3804(a,1),30445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3804 30445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30459">
    <literal><![CDATA[
      R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u) = L(1 / u,L(1 / x,y,z),L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(27410(a,1),30458(a,2,1))].">
      <j1 rule="para" parents="27410 30458"/>
    </justification>
  </clause>

  <clause id="30460">
    <literal><![CDATA[
      R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u) = L(1 / u,L(x,y,z),L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3805(a,1),30459(a,2,1))].">
      <j1 rule="para" parents="3805 30459"/>
    </justification>
  </clause>

  <clause id="30461">
    <literal><![CDATA[
      R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u) = L(1 / u,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(29547(a,1),30460(a,2,1))].">
      <j1 rule="para" parents="29547 30460"/>
    </justification>
  </clause>

  <clause id="30462">
    <literal><![CDATA[
      R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u) = x \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30014,a(flip),b,30461,a),flip(a)].">
      <j1 rule="hyper" parents="370 30014 30461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30464">
    <literal><![CDATA[
      (1 / (x * y)) \ (y \ (x \ K(x \ y,y \ x))) = a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y)
    ]]></literal>
    <justification jstring="[para(6901(a,1),30446(a,1,2,2,2))].">
      <j1 rule="para" parents="6901 30446"/>
    </justification>
  </clause>

  <clause id="30465">
    <literal><![CDATA[
      a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y) = (1 / (x * y)) \ (a(x,y,x * y) / (x * y))
    ]]></literal>
    <justification jstring="[para(29452(a,1),30464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29452 30464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30466">
    <literal><![CDATA[
      a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y) = L(a(x,y,x * y),x * y,x * y)
    ]]></literal>
    <justification jstring="[hyper(29293,a,30465,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29293 30465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30467">
    <literal><![CDATA[
      a(x,y,(x \ K(x * y,(x * y) \ 1)) \ y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14782,a(flip),b,30466,a),flip(a)].">
      <j1 rule="hyper" parents="370 14782 30466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30468">
    <literal><![CDATA[
      a(x,y,x \ y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(27077,a,30467,a)].">
      <j1 rule="hyper" parents="27077 30467"/>
    </justification>
  </clause>

  <clause id="30470">
    <literal><![CDATA[
      a(x,x * y,x * (x * y)) = a(x,x * y,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),30468(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4 30468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30471">
    <literal><![CDATA[
      a(x,x * y,L(y,x,x)) = a(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(3115,a,30470,a)].">
      <j1 rule="hyper" parents="3115 30470"/>
    </justification>
  </clause>

  <clause id="30472">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,u)) = L(x,y,a(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(30471(a,1),29636(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30471 29636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30473">
    <literal><![CDATA[
      L(x,y,(z \ u) * (u \ z)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(28457,a,30472,a)].">
      <j1 rule="hyper" parents="28457 30472"/>
    </justification>
  </clause>

  <clause id="30474">
    <literal><![CDATA[
      L(x,y,a(z,u \ z,u)) = L(x,y,a(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30313,a(flip),b,30473,a)].">
      <j1 rule="hyper" parents="60 30313 30473"/>
    </justification>
  </clause>

  <clause id="30475">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,x * L(x,y,z),u) \ (x * L(x,y,z))),x,L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,28561,a(flip),b,29936,a),flip(a)].">
      <j1 rule="hyper" parents="370 28561 29936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30476">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),L(x,y,z) \ x,x) = a(u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(29702(a,1),29987(a,1,1))].">
      <j1 rule="para" parents="29702 29987"/>
    </justification>
  </clause>

  <clause id="30477">
    <literal><![CDATA[
      a(x,y,L(y,z,u) \ y) \ 1 = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(28870,a,30476,a),flip(a)].">
      <j1 rule="hyper" parents="28870 30476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30479">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4030(a,1),30477(a,1,1))].">
      <j1 rule="para" parents="4030 30477"/>
    </justification>
  </clause>

  <clause id="30480">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(30457,a,30479,a),flip(a)].">
      <j1 rule="hyper" parents="30457 30479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30481">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,x * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(30479(a,1),30457(a,1))].">
      <j1 rule="para" parents="30479 30457"/>
    </justification>
  </clause>

  <clause id="30482">
    <literal><![CDATA[
      a(x,x * L(x,y,z),y) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,30275,a(flip),b,30480,a),flip(a)].">
      <j1 rule="hyper" parents="370 30275 30480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30483">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,(x * L(x,y,z)) * x) = u \ R(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(30480(a,2),29263(a,1,1))].">
      <j1 rule="para" parents="30480 29263"/>
    </justification>
  </clause>

  <clause id="30484">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L((x * x) * x,y,z)) = u \ R(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3812(a,2),30483(a,1,3))].">
      <j1 rule="para" parents="3812 30483"/>
    </justification>
  </clause>

  <clause id="30485">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(x,y,z)) = u \ R(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3810,a,30484,a)].">
      <j1 rule="hyper" parents="3810 30484"/>
    </justification>
  </clause>

  <clause id="30487">
    <literal><![CDATA[
      x \ R(x,y,y * L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28915,a(flip),b,30485,a),flip(a)].">
      <j1 rule="hyper" parents="60 28915 30485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30489">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28573(a,1),30487(a,1,2))].">
      <j1 rule="para" parents="28573 30487"/>
    </justification>
  </clause>

  <clause id="30490">
    <literal><![CDATA[
      L(x \ L(x,y,y * L(y,z,u)),w,v5) = a(y,y * L(y,z,u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(10441,a,30489,a)].">
      <j1 rule="hyper" parents="10441 30489"/>
    </justification>
  </clause>

  <clause id="30491">
    <literal><![CDATA[
      x * a(y,y * L(y,z,u),x) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(156,a,30489,a)].">
      <j1 rule="hyper" parents="156 30489"/>
    </justification>
  </clause>

  <clause id="30492">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,y * L(y,z,u),x) = w
    ]]></literal>
    <justification jstring="[para(30491(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="30491 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30493">
    <literal><![CDATA[
      a(x,x * L(x,y,z),L(u,w,v5)) = L(a(x,x * L(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(30489(a,1),30490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30489 30490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30494">
    <literal><![CDATA[
      a(x,x * L(x,y,z),L(u,w,v5)) = L(a(u,x,x * L(x,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(30480(a,1),30493(a,2,1))].">
      <j1 rule="para" parents="30480 30493"/>
    </justification>
  </clause>

  <clause id="30495">
    <literal><![CDATA[
      L(L(x,y,z) \ (x * (L(x,x * L(x,y,z),u) \ L(x,y,z))),x,L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2160(a,1),30475(a,1,1,2))].">
      <j1 rule="para" parents="2160 30475"/>
    </justification>
  </clause>

  <clause id="30496">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ (L(x,x * L(x,y,z),u) \ L(x,y,z))),x,L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2160(a,1),30495(a,1,1))].">
      <j1 rule="para" parents="2160 30495"/>
    </justification>
  </clause>

  <clause id="30497">
    <literal><![CDATA[
      L(L(x,x * L(x,y,z),u) \ x,x,L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4263(a,1),30496(a,1,1))].">
      <j1 rule="para" parents="4263 30496"/>
    </justification>
  </clause>

  <clause id="30498">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ x = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(14752,a,30497,a)].">
      <j1 rule="hyper" parents="14752 30497"/>
    </justification>
  </clause>

  <clause id="30501">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 = y \ L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(30498(a,1),14170(a,1,1))].">
      <j1 rule="para" parents="30498 14170"/>
    </justification>
  </clause>

  <clause id="30502">
    <literal><![CDATA[
      x \ L(x,x * L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(30457,a,30501,a),flip(a)].">
      <j1 rule="hyper" parents="30457 30501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30503">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) * y = L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,23634,a,b,30502,a)].">
      <j1 rule="hyper" parents="35 23634 30502"/>
    </justification>
  </clause>

  <clause id="30504">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,v5) \ L(L(x,y,z) \ x,u,w) = a(v5,x,L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),30000(a,2,3))].">
      <j1 rule="para" parents="4 30000"/>
    </justification>
  </clause>

  <clause id="30505">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,v5) \ L(L(x,y,z) \ x,u,w) = a(v5,x,L(x * L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3978,a(flip),b,30504,a),flip(a)].">
      <j1 rule="hyper" parents="370 3978 30504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30507">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,u) \ (L(x,y,z) \ x),w,v5) = a(u,x,L(x * L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(29154,a,30505,a)].">
      <j1 rule="hyper" parents="29154 30505"/>
    </justification>
  </clause>

  <clause id="30508">
    <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(29661(a,1),30068(a,1,1))].">
      <j1 rule="para" parents="29661 30068"/>
    </justification>
  </clause>

  <clause id="30510">
    <literal><![CDATA[
      L((x * (L(L(x,y,z),y,z) \ u)) \ w,x * (L(L(x,y,z),y,z) \ u),1) = u \ ((x \ L(L(x,y,z),y,z)) * w)
    ]]></literal>
    <justification jstring="[para(63(a,1),30404(a,1,3))].">
      <j1 rule="para" parents="63 30404"/>
    </justification>
  </clause>

  <clause id="30511">
    <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="[hyper(646,a,30510,a)].">
      <j1 rule="hyper" parents="646 30510"/>
    </justification>
  </clause>

  <clause id="30514">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ (u \ w) = u \ ((x \ L(L(x,y,z),y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29440,a(flip),b,30511,a)].">
      <j1 rule="hyper" parents="60 29440 30511"/>
    </justification>
  </clause>

  <clause id="30515">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ (u \ w) = u \ (L(L(x,y,z),y,z) * (x \ w))
    ]]></literal>
    <justification jstring="[para(29084(a,1),30514(a,2,2))].">
      <j1 rule="para" parents="29084 30514"/>
    </justification>
  </clause>

  <clause id="30516">
    <literal><![CDATA[
      x \ (L(L(y,z,u),z,u) * (y \ w)) = L(L(y,z,u),z,u) * (y \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,29353,a(flip),b,30515,a),flip(a)].">
      <j1 rule="hyper" parents="60 29353 30515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30517">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) \ (x \ v5) = x \ (a(L(L(x,y,z),y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(28817,a,30516,a)].">
      <j1 rule="hyper" parents="28817 30516"/>
    </justification>
  </clause>

  <clause id="30518">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) \ (x \ v5) = x \ (a(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(29020(a,1),30517(a,2,2,1))].">
      <j1 rule="para" parents="29020 30517"/>
    </justification>
  </clause>

  <clause id="30519">
    <literal><![CDATA[
      a(x,y,z) \ (x \ u) = x \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1330(a,1),30518(a,1,1,1))].">
      <j1 rule="para" parents="1330 30518"/>
    </justification>
  </clause>

  <clause id="30521">
    <literal><![CDATA[
      R(x,x,a(1 / x,y,z) \ u) * (a(1 / x,y,z) \ u) = a(1 / x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1961,a,b,30519,a)].">
      <j1 rule="hyper" parents="370 1961 30519"/>
    </justification>
  </clause>

  <clause id="30522">
    <literal><![CDATA[
      R(x,x,a(1 / x,y,z) \ u) * (a(1 / x,y,z) \ u) = a(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(2957(a,1),30521(a,2,1))].">
      <j1 rule="para" parents="2957 30521"/>
    </justification>
  </clause>

  <clause id="30523">
    <literal><![CDATA[
      R(x,x,a(x,y,z) \ u) * (a(1 / x,y,z) \ u) = a(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(2957(a,1),30522(a,1,1,3,1))].">
      <j1 rule="para" parents="2957 30522"/>
    </justification>
  </clause>

  <clause id="30524">
    <literal><![CDATA[
      R(x,x,a(x,y,z) \ u) * (a(x,y,z) \ u) = a(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(2957(a,1),30523(a,1,2,1))].">
      <j1 rule="para" parents="2957 30523"/>
    </justification>
  </clause>

  <clause id="30525">
    <literal><![CDATA[
      a(x,y,z) \ ((1 / x) \ u) = (1 / x) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(1962,a,30524,a),flip(a)].">
      <j1 rule="hyper" parents="1962 30524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30526">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = x * R(K(L(y,z,u),L(y,z,u) \ 1) * (x \ 1),y,y)
    ]]></literal>
    <justification jstring="[para(3566(a,1),30230(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3566 30230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30527">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = x * R(K(y,y \ 1) * (x \ 1),y,y)
    ]]></literal>
    <justification jstring="[para(6790(a,1),30526(a,2,2,1,1))].">
      <j1 rule="para" parents="6790 30526"/>
    </justification>
  </clause>

  <clause id="30528">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = x * R(x \ K(y,y \ 1),y,y)
    ]]></literal>
    <justification jstring="[para(4541(a,1),30527(a,2,2,1))].">
      <j1 rule="para" parents="4541 30527"/>
    </justification>
  </clause>

  <clause id="30530">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = a(x,y,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,25713,a(flip),b,30528,a),flip(a)].">
      <j1 rule="hyper" parents="370 25713 30528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30531">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = y * (a(x,y,y) / y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28110,a(flip),b,30530,a),flip(a)].">
      <j1 rule="hyper" parents="370 28110 30530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30532">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) \ R(x * (L(y,z,u) \ 1),y,y) = a(x * y,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,29424,a(flip),b,30531,a),flip(a)].">
      <j1 rule="hyper" parents="370 29424 30531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30533">
    <literal><![CDATA[
      a(x * (L(y,z,u) \ 1),y,y) = a(x * y,y,y)
    ]]></literal>
    <justification jstring="[hyper(16513,a,30532,a)].">
      <j1 rule="hyper" parents="16513 30532"/>
    </justification>
  </clause>

  <clause id="30534">
    <literal><![CDATA[
      a(x * L(y,z,u),y,y) = a(x * y,y,y)
    ]]></literal>
    <justification jstring="[hyper(26607,a,30533,a)].">
      <j1 rule="hyper" parents="26607 30533"/>
    </justification>
  </clause>

  <clause id="30535">
    <literal><![CDATA[
      a((L(x,y,z) \ u) * x,x,x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(26520,a,30534,a),flip(a)].">
      <j1 rule="hyper" parents="26520 30534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30536">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(K(w,u) * x,y,z) \ 1) \ v5)) = v5 * a(R(K(w,u) * x,y,z),L(x,y,z),v5 * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(26470(a,1),30085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26470 30085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30538">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(K(w,u) * x,y,z) \ 1) \ v5)) = v5 * a(L(K(w,u) * x,y,z),L(x,y,z),v5 * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(27318(a,1),30536(a,2,2))].">
      <j1 rule="para" parents="27318 30536"/>
    </justification>
  </clause>

  <clause id="30539">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(K(w,u) * x,y,z) \ 1) \ v5)) = v5 * a(L(x,y,z),L(x,y,z),v5 * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(26401(a,1),30538(a,2,2))].">
      <j1 rule="para" parents="26401 30538"/>
    </justification>
  </clause>

  <clause id="30541">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,y * (y * (L(y,z,u) \ y)),y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,26023,a,b,30202,a),flip(a)].">
      <j1 rule="hyper" parents="370 26023 30202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30542">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y \ 1,z,u) \ y,y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(14769(a,1),30541(a,2,2))].">
      <j1 rule="para" parents="14769 30541"/>
    </justification>
  </clause>

  <clause id="30543">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y \ 1,z,u) \ y,y * (y * L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,25719,a(flip),b,30542,a),flip(a)].">
      <j1 rule="hyper" parents="370 25719 30542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30544">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y \ 1,z,u) \ y,L(y * (y * y),z,u))
    ]]></literal>
    <justification jstring="[para(3905(a,2),30543(a,2,3))].">
      <j1 rule="para" parents="3905 30543"/>
    </justification>
  </clause>

  <clause id="30545">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y \ 1,z,u) \ y,L(L(y,y,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3980,a(flip),b,30544,a),flip(a)].">
      <j1 rule="hyper" parents="370 3980 30544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30546">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y \ 1,z,u) \ y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,14008,a(flip),b,30545,a),flip(a)].">
      <j1 rule="hyper" parents="370 14008 30545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30548">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,L(y,z,u) \ y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,4024,a(flip),b,30546,a),flip(a)].">
      <j1 rule="hyper" parents="370 4024 30546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30549">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,y * L(y,z,u),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3785,a(flip),b,30548,a),flip(a)].">
      <j1 rule="hyper" parents="370 3785 30548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30550">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * L(y * (L(y,z,u) \ y),z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,29871,a(flip),b,30549,a),flip(a)].">
      <j1 rule="hyper" parents="370 29871 30549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30551">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) * y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(30200(a,1),30550(a,1,3,2))].">
      <j1 rule="para" parents="30200 30550"/>
    </justification>
  </clause>

  <clause id="30552">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),y * (y * (L(y,z,u) \ y))) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(24037,a,30551,a)].">
      <j1 rule="hyper" parents="24037 30551"/>
    </justification>
  </clause>

  <clause id="30553">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(26002,a,30552,a)].">
      <j1 rule="hyper" parents="26002 30552"/>
    </justification>
  </clause>

  <clause id="30554">
    <literal><![CDATA[
      L(x,y * (y * L(y,z,u)),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(26288,a,30553,a)].">
      <j1 rule="hyper" parents="26288 30553"/>
    </justification>
  </clause>

  <clause id="30555">
    <literal><![CDATA[
      (x \ (((x \ L(x,y,z)) \ x) * u)) * (x \ L(x,y,z)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,28009,a,b,30553,a)].">
      <j1 rule="hyper" parents="60 28009 30553"/>
    </justification>
  </clause>

  <clause id="30556">
    <literal><![CDATA[
      L(x,L(y * (y * y),z,u),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3905(a,2),30554(a,1,2))].">
      <j1 rule="para" parents="3905 30554"/>
    </justification>
  </clause>

  <clause id="30557">
    <literal><![CDATA[
      L(x,L(L(y,y,y),z,u),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3983,a(flip),b,30556,a)].">
      <j1 rule="hyper" parents="60 3983 30556"/>
    </justification>
  </clause>

  <clause id="30558">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14838,a,30557,a)].">
      <j1 rule="hyper" parents="14838 30557"/>
    </justification>
  </clause>

  <clause id="30559">
    <literal><![CDATA[
      L(L(x,y,y * L(y,z,u)) \ x,x,L(y,z,u)) = a(y * L(y,z,u),L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(30558(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="30558 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30560">
    <literal><![CDATA[
      (x \ ((x * (L(x,y,z) \ x)) * u)) * (x \ L(x,y,z)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25381(a,1),30555(a,1,1,2,1))].">
      <j1 rule="para" parents="25381 30555"/>
    </justification>
  </clause>

  <clause id="30561">
    <literal><![CDATA[
      (x \ (x * (x * (L(x,y,z) \ u)))) * (x \ L(x,y,z)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(29656(a,1),30560(a,1,1,2))].">
      <j1 rule="para" parents="29656 30560"/>
    </justification>
  </clause>

  <clause id="30562">
    <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(4(a,1),30561(a,1,1))].">
      <j1 rule="para" parents="4 30561"/>
    </justification>
  </clause>

  <clause id="30563">
    <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(14692,a,30562,a)].">
      <j1 rule="hyper" parents="14692 30562"/>
    </justification>
  </clause>

  <clause id="30565">
    <literal><![CDATA[
      (L(x,y,z) \ u) * (x \ L(x,y,z)) = (x \ a(x,x,L(u,y,z))) * u
    ]]></literal>
    <justification jstring="[hyper(31,a,29159,a,b,30563,a),flip(a)].">
      <j1 rule="hyper" parents="31 29159 30563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30566">
    <literal><![CDATA[
      (a(x,y,z) \ a(a(x,y,z),a(x,y,z),L(u,z,y))) * u = ((L(z,y,x) \ z) \ u) * (a(x,y,z) \ L(a(x,y,z),z,y))
    ]]></literal>
    <justification jstring="[para(29953(a,1),30565(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29953 30565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30567">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(x,y,z)) = a(x * L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(30233(a,1),30559(a,1,1))].">
      <j1 rule="para" parents="30233 30559"/>
    </justification>
  </clause>

  <clause id="30568">
    <literal><![CDATA[
      a(x * L(x,y,z),L(x,y,z),u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28915,a(flip),b,30567,a),flip(a)].">
      <j1 rule="hyper" parents="60 28915 30567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30570">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,x * L(x,y,z),u) = (L(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(30568(a,1),29178(a,1,2))].">
      <j1 rule="para" parents="30568 29178"/>
    </justification>
  </clause>

  <clause id="30571">
    <literal><![CDATA[
      L(x,y,z) * (u * a(x,x * L(x,y,z),u)) = (L(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(28916,a,30570,a)].">
      <j1 rule="hyper" parents="28916 30570"/>
    </justification>
  </clause>

  <clause id="30572">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x * L(x,y,z)) = (L(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(30491(a,1),30571(a,1,2))].">
      <j1 rule="para" parents="30491 30571"/>
    </justification>
  </clause>

  <clause id="30573">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,4168,a(flip),b,30572,a),flip(a)].">
      <j1 rule="hyper" parents="60 4168 30572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30574">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(25655,a,30573,a)].">
      <j1 rule="hyper" parents="25655 30573"/>
    </justification>
  </clause>

  <clause id="30575">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(384,a,30574,a),flip(a)].">
      <j1 rule="hyper" parents="384 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30577">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,23955,a(flip),b,30574,a),flip(a)].">
      <j1 rule="hyper" parents="370 23955 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30579">
    <literal><![CDATA[
      (x \ L(x,x,y)) * z = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[para(28819(a,1),30574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28819 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30580">
    <literal><![CDATA[
      (R(x,y,z) \ L(R(x,y,z),u,w)) * v5 = L(L(x,u,w) \ x,y,z) \ v5
    ]]></literal>
    <justification jstring="[para(29126(a,1),30574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29126 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30581">
    <literal><![CDATA[
      (x \ (L(y / x,z,u) \ y)) \ w = ((y \ x) \ L(y \ x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(29808(a,1),30574(a,1,1))].">
      <j1 rule="para" parents="29808 30574"/>
    </justification>
  </clause>

  <clause id="30582">
    <literal><![CDATA[
      (x \ L(x,y,a(y,z,u))) * w = a(y,a(y,z,u),x) \ w
    ]]></literal>
    <justification jstring="[para(30088(a,1),30574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30088 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30584">
    <literal><![CDATA[
      (x \ L(x,x,L(y,z,u))) * w = a(y,x,L(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(30093(a,1),30579(a,2,1))].">
      <j1 rule="para" parents="30093 30579"/>
    </justification>
  </clause>

  <clause id="30586">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,23873,a(flip),b,30575,a),flip(a)].">
      <j1 rule="hyper" parents="370 23873 30575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30590">
    <literal><![CDATA[
      x * (y \ L(y,z,z)) = a(z,z,y) \ x
    ]]></literal>
    <justification jstring="[para(1362(a,1),30577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1362 30577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30591">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(30577(a,2),24070(a,1))].">
      <j1 rule="para" parents="30577 24070"/>
    </justification>
  </clause>

  <clause id="30592">
    <literal><![CDATA[
      x * L(x \ a(y,z,u),y,y) = a(y,y,x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29472,a(flip),b,30590,a)].">
      <j1 rule="hyper" parents="60 29472 30590"/>
    </justification>
  </clause>

  <clause id="30593">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (L(x,z,u) \ x)) = (x \ L(1 / x,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(30586(a,1),4199(a,1,2))].">
      <j1 rule="para" parents="30586 4199"/>
    </justification>
  </clause>

  <clause id="30598">
    <literal><![CDATA[
      L(x,y,z) * (u * (L(x,y,z) \ x)) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(30586(a,1),26330(a,1,2))].">
      <j1 rule="para" parents="30586 26330"/>
    </justification>
  </clause>

  <clause id="30599">
    <literal><![CDATA[
      a(x,y,y \ (y * (L(z,u,w) \ z))) = z * (L(z,u,w) \ L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[para(30586(a,1),30267(a,1,3,2))].">
      <j1 rule="para" parents="30586 30267"/>
    </justification>
  </clause>

  <clause id="30600">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ w = a(x,a(x,y,z),u) * w
    ]]></literal>
    <justification jstring="[para(30090(a,1),30582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30090 30582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30601">
    <literal><![CDATA[
      (a(x,a(x,x,y),z) * R(x,x,y)) * z = x * (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30600(a,1),28979(a,1,1))].">
      <j1 rule="para" parents="30600 28979"/>
    </justification>
  </clause>

  <clause id="30602">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) * w = a(y,x,L(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(30115(a,2),30584(a,1,1))].">
      <j1 rule="para" parents="30115 30584"/>
    </justification>
  </clause>

  <clause id="30603">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29177,a(flip),b,30592,a),flip(a)].">
      <j1 rule="hyper" parents="60 29177 30592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30604">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) \ z = L(y,y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25890,a(flip),b,30602,a),flip(a)].">
      <j1 rule="hyper" parents="60 25890 30602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30605">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(R(y,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(30602(a,1),28641(a,1))].">
      <j1 rule="para" parents="30602 28641"/>
    </justification>
  </clause>

  <clause id="30606">
    <literal><![CDATA[
      a(x,a(x,x,y),z) * (R(x,x,y) * z) = x * (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(28350,a,30601,a)].">
      <j1 rule="hyper" parents="28350 30601"/>
    </justification>
  </clause>

  <clause id="30607">
    <literal><![CDATA[
      (L(x,y,z) \ (L(L(x,y,z) \ x,u,w) \ x)) \ v5 = ((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w)) * v5
    ]]></literal>
    <justification jstring="[para(3938(a,1),30581(a,1,1,2,1,1))].">
      <j1 rule="para" parents="3938 30581"/>
    </justification>
  </clause>

  <clause id="30608">
    <literal><![CDATA[
      (x \ L(1 / x,y,z)) \ u = (L(1 / x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,27824,a(flip),b,30593,a),flip(a)].">
      <j1 rule="hyper" parents="60 27824 30593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30609">
    <literal><![CDATA[
      (L(1 / (x \ y),x \ y,y) \ (x \ y)) * z = ((x \ y) \ (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(3418(a,1),30608(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3418 30608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30610">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),x,L(x,z,u)) = L(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29882,a(flip),b,30598,a),flip(a)].">
      <j1 rule="hyper" parents="60 29882 30598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30611">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),x,L(x,z,u)) = L(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(2104(a,1),30610(a,1,1))].">
      <j1 rule="para" parents="2104 30610"/>
    </justification>
  </clause>

  <clause id="30612">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ v5 = L(x \ L(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(28638(a,1),30580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28638 30580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30613">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ v5 = L(L(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(384,a,30612,a),flip(a)].">
      <j1 rule="hyper" parents="384 30612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30614">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,u,w) \ 1) * v5 = L(L(x,y,z) \ x,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(29125(a,2),30612(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29125 30612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30615">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = v5 \ (L(L(x,y,z) \ x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(30613(a,1),29377(a,2,2))].">
      <j1 rule="para" parents="30613 29377"/>
    </justification>
  </clause>

  <clause id="30616">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,29552,a(flip),b,30614,a),flip(a)].">
      <j1 rule="hyper" parents="31 29552 30614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30617">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,30244,a(flip),b,30616,a)].">
      <j1 rule="hyper" parents="60 30244 30616"/>
    </justification>
  </clause>

  <clause id="30618">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) \ u) = u
    ]]></literal>
    <justification jstring="[hyper(30111,a,30617,a)].">
      <j1 rule="hyper" parents="30111 30617"/>
    </justification>
  </clause>

  <clause id="30619">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(29761,a,30617,a),flip(a)].">
      <j1 rule="hyper" parents="29761 30617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30620">
    <literal><![CDATA[
      x \ (a(y,z,u) \ x) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(29751,a,30617,a)].">
      <j1 rule="hyper" parents="29751 30617"/>
    </justification>
  </clause>

  <clause id="30621">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(27601,a,30617,a),flip(a)].">
      <j1 rule="hyper" parents="27601 30617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30622">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(2095,a,30617,a)].">
      <j1 rule="hyper" parents="2095 30617"/>
    </justification>
  </clause>

  <clause id="30624">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,30617,a,b,3942,a),flip(a)].">
      <j1 rule="hyper" parents="126 30617 3942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30625">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 = L(a(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(60,a,30508,a(flip),b,30617,a)].">
      <j1 rule="hyper" parents="60 30508 30617"/>
    </justification>
  </clause>

  <clause id="30626">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,29750,a(flip),b,30617,a),flip(a)].">
      <j1 rule="hyper" parents="60 29750 30617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30627">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z) \ 1,u,w) * v5) = L(a(x,y,z),u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,4072,a(flip),b,30617,a)].">
      <j1 rule="hyper" parents="60 4072 30617"/>
    </justification>
  </clause>

  <clause id="30629">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,30617,a(flip),b,27689,a)].">
      <j1 rule="hyper" parents="125 30617 27689"/>
    </justification>
  </clause>

  <clause id="30630">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(125,a,30617,a(flip),b,2074,a),flip(a)].">
      <j1 rule="hyper" parents="125 30617 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30632">
    <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(30617(a,1),2971(a,1,1))].">
      <j1 rule="para" parents="30617 2971"/>
    </justification>
  </clause>

  <clause id="30633">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) = a(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),3054(a,1,2))].">
      <j1 rule="para" parents="30617 3054"/>
    </justification>
  </clause>

  <clause id="30634">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),3101(a,1,3))].">
      <j1 rule="para" parents="30617 3101"/>
    </justification>
  </clause>

  <clause id="30635">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),3370(a,1,3))].">
      <j1 rule="para" parents="30617 3370"/>
    </justification>
  </clause>

  <clause id="30636">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),3485(a,1,2,2))].">
      <j1 rule="para" parents="30617 3485"/>
    </justification>
  </clause>

  <clause id="30638">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ v5,v6,v7)) = L(x,y,L(a(z,u,w) * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(30617(a,1),3962(a,1,3))].">
      <j1 rule="para" parents="30617 3962"/>
    </justification>
  </clause>

  <clause id="30639">
    <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(30617(a,1),4130(a,1,2))].">
      <j1 rule="para" parents="30617 4130"/>
    </justification>
  </clause>

  <clause id="30640">
    <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(30617(a,1),26593(a,1,2))].">
      <j1 rule="para" parents="30617 26593"/>
    </justification>
  </clause>

  <clause id="30642">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),29037(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30617 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30644">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(30617(a,1),29761(a,1))].">
      <j1 rule="para" parents="30617 29761"/>
    </justification>
  </clause>

  <clause id="30645">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30352,a(flip),b,30624,a)].">
      <j1 rule="hyper" parents="60 30352 30624"/>
    </justification>
  </clause>

  <clause id="30646">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,30624,a(flip),b,28440,a),flip(a)].">
      <j1 rule="hyper" parents="125 30624 28440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30648">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,30645,a)].">
      <j1 rule="hyper" parents="49 30645"/>
    </justification>
  </clause>

  <clause id="30651">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),30620(a,1,2))].">
      <j1 rule="para" parents="4 30620"/>
    </justification>
  </clause>

  <clause id="30652">
    <literal><![CDATA[
      a(x,y,z) \ 1 != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(30620(a,1),44(a,1))].">
      <j1 rule="para" parents="30620 44"/>
    </justification>
  </clause>

  <clause id="30653">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(30620(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="30620 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30654">
    <literal><![CDATA[
      (x * R(a(y,z,u) \ 1,w,v5)) * a(y,z,u) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(30620(a,1),29316(a,1,1,2,1))].">
      <j1 rule="para" parents="30620 29316"/>
    </justification>
  </clause>

  <clause id="30655">
    <literal><![CDATA[
      (x * (((y * x) \ y) * z)) * a(y,x,x) = L(z,(y * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(28841,a,30621,a),flip(a)].">
      <j1 rule="hyper" parents="28841 30621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30656">
    <literal><![CDATA[
      a((a(x,y,z) \ u) \ w,v5,v6) = a((u * a(x,y,z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(30621(a,1),26706(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30621 26706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30657">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(30621(a,1),30211(a,1,2))].">
      <j1 rule="para" parents="30621 30211"/>
    </justification>
  </clause>

  <clause id="30658">
    <literal><![CDATA[
      x * a(y,y * z,y * z) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(30330(a,1),30621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30330 30621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30660">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) * v6) = a(x,y,(a(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(30622(a,1),3084(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30622 3084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30661">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = (w * (a(x,y,z) \ 1)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(30622(a,1),3410(a,1,1))].">
      <j1 rule="para" parents="30622 3410"/>
    </justification>
  </clause>

  <clause id="30662">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) \ v5) * v6) = L(x,y,(a(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(30622(a,1),3373(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30622 3373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30663">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) \ v6)) = L(x,y,z * (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(30622(a,1),4110(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="30622 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30665">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(30622(a,2),23637(a,1))].">
      <j1 rule="para" parents="30622 23637"/>
    </justification>
  </clause>

  <clause id="30666">
    <literal><![CDATA[
      a((a(x,y,z) \ u) \ w,v5,v6) = a((a(x,y,z) * u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(30622(a,1),26706(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30622 26706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30667">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = a(a(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(29330(a,1),30622(a,1,1))].">
      <j1 rule="para" parents="29330 30622"/>
    </justification>
  </clause>

  <clause id="30668">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(29336(a,1),30622(a,1,1))].">
      <j1 rule="para" parents="29336 30622"/>
    </justification>
  </clause>

  <clause id="30669">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * u) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(30622(a,1),30211(a,1,2))].">
      <j1 rule="para" parents="30622 30211"/>
    </justification>
  </clause>

  <clause id="30670">
    <literal><![CDATA[
      (x \ K(y,z)) * (K(z,y) * (a(u,w,v5) \ 1)) = a(u,w,v5) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(25401,a,30626,a)].">
      <j1 rule="hyper" parents="25401 30626"/>
    </justification>
  </clause>

  <clause id="30671">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,4,a(flip),b,30626,a)].">
      <j1 rule="hyper" parents="128 4 30626"/>
    </justification>
  </clause>

  <clause id="30673">
    <literal><![CDATA[
      a(x,y,z) * (u * (w * (a(x,y,z) \ 1))) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27637,a(flip),b,30626,a)].">
      <j1 rule="hyper" parents="60 27637 30626"/>
    </justification>
  </clause>

  <clause id="30674">
    <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(125,a,30626,a(flip),b,27535,a(flip))].">
      <j1 rule="hyper" parents="125 30626 27535"/>
    </justification>
  </clause>

  <clause id="30675">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (w * w) = u * (a(x,y,z) \ (w * w))
    ]]></literal>
    <justification jstring="[para(30626(a,1),574(a,1,1))].">
      <j1 rule="para" parents="30626 574"/>
    </justification>
  </clause>

  <clause id="30676">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) \ ((a(x,y,z) \ (a(x,y,z) \ 1)) \ w) = (((a(x,y,z) \ 1) \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[para(30626(a,1),973(a,1,2,1))].">
      <j1 rule="para" parents="30626 973"/>
    </justification>
  </clause>

  <clause id="30677">
    <literal><![CDATA[
      (a(x,y,z) \ u) * ((a(x,y,z) \ 1) \ w) = (u * a(x,y,z)) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(30626(a,1),1289(a,1,1))].">
      <j1 rule="para" parents="30626 1289"/>
    </justification>
  </clause>

  <clause id="30678">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * (L(w,a(x,y,z) \ 1,u) * v5)) \ ((u * ((a(x,y,z) \ 1) * w)) * v5) = a(u * (a(x,y,z) \ 1),L(w,a(x,y,z) \ 1,u),v5)
    ]]></literal>
    <justification jstring="[para(30626(a,1),619(a,1,1,1))].">
      <j1 rule="para" parents="30626 619"/>
    </justification>
  </clause>

  <clause id="30679">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ v6)) = a(x,y,z * (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(30626(a,1),15784(a,1,3,2))].">
      <j1 rule="para" parents="30626 15784"/>
    </justification>
  </clause>

  <clause id="30680">
    <literal><![CDATA[
      (a(x,y,z) \ u) * K(w,v5) = u * (a(x,y,z) \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(30626(a,1),25021(a,1,1))].">
      <j1 rule="para" parents="30626 25021"/>
    </justification>
  </clause>

  <clause id="30681">
    <literal><![CDATA[
      (a(x,y,z) \ (u \ w)) \ ((u \ w) * u) = ((w / u) * (a(x,y,z) \ 1)) \ w
    ]]></literal>
    <justification jstring="[para(30626(a,1),25261(a,1,1))].">
      <j1 rule="para" parents="30626 25261"/>
    </justification>
  </clause>

  <clause id="30682">
    <literal><![CDATA[
      (x * (a(y,z,u) \ K(w,v5))) * v6 = (a(y,z,u) \ x) * (K(w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(30626(a,1),25348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30626 25348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30683">
    <literal><![CDATA[
      (x * (a(y,z,u) \ K(w,v5))) \ v6 = K(v5,w) * ((a(y,z,u) \ x) \ v6)
    ]]></literal>
    <justification jstring="[para(30626(a,1),25349(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30626 25349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30684">
    <literal><![CDATA[
      L(x,y * (a(z,u,w) \ v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (v5 * a(z,u,w)),v6) = v7
    ]]></literal>
    <justification jstring="[para(30626(a,1),26287(a,1,2,2))].">
      <j1 rule="para" parents="30626 26287"/>
    </justification>
  </clause>

  <clause id="30685">
    <literal><![CDATA[
      a((x * (a(y,z,u) \ w)) \ v5,v6,v7) = a((x * (w * a(y,z,u))) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(30626(a,1),26857(a,1,1,1,2))].">
      <j1 rule="para" parents="30626 26857"/>
    </justification>
  </clause>

  <clause id="30686">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = (1 / (a(x,y,z) \ u)) * u
    ]]></literal>
    <justification jstring="[para(30626(a,1),29325(a,2,1,2))].">
      <j1 rule="para" parents="30626 29325"/>
    </justification>
  </clause>

  <clause id="30687">
    <literal><![CDATA[
      x * (a(y,z,x) \ z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[para(30626(a,1),30103(a,1,2))].">
      <j1 rule="para" parents="30626 30103"/>
    </justification>
  </clause>

  <clause id="30688">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),30629(a,1,1))].">
      <j1 rule="para" parents="82 30629"/>
    </justification>
  </clause>

  <clause id="30691">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z) \ 1,u,w) * v5) = a(x,y,z) \ (v5 * L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27813,a(flip),b,30630,a)].">
      <j1 rule="hyper" parents="60 27813 30630"/>
    </justification>
  </clause>

  <clause id="30692">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * L(w,a(y,z,u) \ 1,x) = x * (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(129,a,30630,a(flip),b,341,a),flip(a)].">
      <j1 rule="hyper" parents="129 30630 341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30694">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ 1)) * w) / (a(y,z,u) \ w) = R(x,a(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(30630(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="30630 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30695">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ 1) \ w),x,a(y,z,u) \ 1) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(30630(a,1),344(a,2,1))].">
      <j1 rule="para" parents="30630 344"/>
    </justification>
  </clause>

  <clause id="30696">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) * (w * u) = (a(x,y,z) \ u) * T(w,u)
    ]]></literal>
    <justification jstring="[para(30630(a,1),12402(a,2,1))].">
      <j1 rule="para" parents="30630 12402"/>
    </justification>
  </clause>

  <clause id="30697">
    <literal><![CDATA[
      R(x * K(y,a(z,u,w) \ 1),y,a(z,u,w) \ 1) = ((x * y) * (a(z,u,w) \ 1)) / (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(30630(a,1),25688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30630 25688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30698">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ v5),v6) = a(x,y * (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(30630(a,1),27359(a,1,2,2))].">
      <j1 rule="para" parents="30630 27359"/>
    </justification>
  </clause>

  <clause id="30699">
    <literal><![CDATA[
      a(x,y \ (a(z,u,w) \ v5),v6) = a(x,y \ (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(30630(a,1),29230(a,1,2,2))].">
      <j1 rule="para" parents="30630 29230"/>
    </justification>
  </clause>

  <clause id="30700">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ (a(z,y,x) \ u) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(30630(a,1),30219(a,1,2))].">
      <j1 rule="para" parents="30630 30219"/>
    </justification>
  </clause>

  <clause id="30701">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(30646(a,1),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="30646 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30702">
    <literal><![CDATA[
      a((a(x,y,z) \ ((z * y) * x)) * u,w,v5) = a(((z * y) * R(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(30648(a,1),26763(a,1,1,1,1))].">
      <j1 rule="para" parents="30648 26763"/>
    </justification>
  </clause>

  <clause id="30703">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30648(a,1),30146(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30648 30146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30707">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(129,a,29336,a(flip),b,30651,a)].">
      <j1 rule="hyper" parents="129 29336 30651"/>
    </justification>
  </clause>

  <clause id="30708">
    <literal><![CDATA[
      a(x,y,z) \ 1 != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * w = u
    ]]></literal>
    <justification jstring="[para(30651(a,1),45(a,1))].">
      <j1 rule="para" parents="30651 45"/>
    </justification>
  </clause>

  <clause id="30709">
    <literal><![CDATA[
      a(x,y,z) \ (z * y) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,25338,a,b,30687,a)].">
      <j1 rule="hyper" parents="60 25338 30687"/>
    </justification>
  </clause>

  <clause id="30710">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(31,a,2157,a,b,30687,a)].">
      <j1 rule="hyper" parents="31 2157 30687"/>
    </justification>
  </clause>

  <clause id="30711">
    <literal><![CDATA[
      a(x,R(y,y,z),y) \ R(y,y,z) = L(y,R(y,y,z),x) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(28417(a,1),30710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28417 30710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30712">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,L(u,z,y) * (u \ z)) = L(x,z * a(y,z,u),u * (L(u,z,y) \ z))
    ]]></literal>
    <justification jstring="[para(30710(a,1),30443(a,1,2))].">
      <j1 rule="para" parents="30710 30443"/>
    </justification>
  </clause>

  <clause id="30713">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (R(y,z,u) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(23947,a,30619,a)].">
      <j1 rule="hyper" parents="23947 30619"/>
    </justification>
  </clause>

  <clause id="30714">
    <literal><![CDATA[
      a(x,y,y \ ((R(z,u,w) \ z) * y)) = R(z,u,w) * (z \ L(R(z,u,w) \ z,y,x))
    ]]></literal>
    <justification jstring="[para(30619(a,1),29992(a,1,3,2))].">
      <j1 rule="para" parents="30619 29992"/>
    </justification>
  </clause>

  <clause id="30715">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(484,a,30713,a)].">
      <j1 rule="hyper" parents="484 30713"/>
    </justification>
  </clause>

  <clause id="30716">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * ((R(y,z,u) \ y) \ L(R(y,z,u) \ y,w,v5)) = x * L(x \ ((R(y,z,u) \ y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(30715(a,1),25320(a,1,1))].">
      <j1 rule="para" parents="30715 25320"/>
    </justification>
  </clause>

  <clause id="30718">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(1208,a,30688,a)].">
      <j1 rule="hyper" parents="1208 30688"/>
    </justification>
  </clause>

  <clause id="30719">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28412,a(flip),b,30688,a),flip(a)].">
      <j1 rule="hyper" parents="60 28412 30688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30720">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(30688(a,1),27376(a,1,3))].">
      <j1 rule="para" parents="30688 27376"/>
    </justification>
  </clause>

  <clause id="30722">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 = v5 * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(129,a,30719,a(flip),b,30620,a),flip(a)].">
      <j1 rule="hyper" parents="129 30719 30620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30724">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 = a(w,a(y,z,u),x) * v5
    ]]></literal>
    <justification jstring="[para(30719(a,1),30622(a,1,1))].">
      <j1 rule="para" parents="30719 30622"/>
    </justification>
  </clause>

  <clause id="30725">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * a(w,a(y,z,u),x) = v6
    ]]></literal>
    <justification jstring="[para(30719(a,1),30665(a,1,1))].">
      <j1 rule="para" parents="30719 30665"/>
    </justification>
  </clause>

  <clause id="30726">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(3522,a,30720,a)].">
      <j1 rule="hyper" parents="3522 30720"/>
    </justification>
  </clause>

  <clause id="30727">
    <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(30720(a,1),3522(a,1))].">
      <j1 rule="para" parents="30720 3522"/>
    </justification>
  </clause>

  <clause id="30728">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(30104,a,30726,a),flip(a)].">
      <j1 rule="hyper" parents="30104 30726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30729">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * y) * a(w,u,z) = x * (y * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(30728(a,1),28343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30728 28343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30730">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(29131,a,30718,a),flip(a)].">
      <j1 rule="hyper" parents="29131 30718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30731">
    <literal><![CDATA[
      a(L(x * L(x,y,z),x,z * y),u,w) = a(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(30718(a,1),3976(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30718 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30732">
    <literal><![CDATA[
      L(a(x,y,z),z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(29267,a,30730,a(flip))].">
      <j1 rule="hyper" parents="29267 30730"/>
    </justification>
  </clause>

  <clause id="30733">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,u * z),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(30730(a,2),26307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30730 26307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30734">
    <literal><![CDATA[
      L(x,y,a(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(2962(a,2),30727(a,1,3))].">
      <j1 rule="para" parents="2962 30727"/>
    </justification>
  </clause>

  <clause id="30736">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (K(w,v5) / u),a(x,y,z) * u) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,29914,a(flip),b,30635,a),flip(a)].">
      <j1 rule="hyper" parents="60 29914 30635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30737">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z) * w) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,24107,a(flip),b,30635,a),flip(a)].">
      <j1 rule="hyper" parents="60 24107 30635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30738">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,w) = (w * (u / a(x,y,z))) \ (w * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,12451,a(flip),b,30636,a),flip(a)].">
      <j1 rule="hyper" parents="60 12451 30636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30739">
    <literal><![CDATA[
      x * (a(a(y,z,u),w,x) * w) = L(x,w,a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(30667(a,1),30687(a,1,2))].">
      <j1 rule="para" parents="30667 30687"/>
    </justification>
  </clause>

  <clause id="30740">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,a(z,u,w)) * v5) = v5
    ]]></literal>
    <justification jstring="[hyper(386,a,30668,a),flip(a)].">
      <j1 rule="hyper" parents="386 30668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30741">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v6 = v5
    ]]></literal>
    <justification jstring="[para(30668(a,1),156(a,1))].">
      <j1 rule="para" parents="30668 156"/>
    </justification>
  </clause>

  <clause id="30742">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(u,w,v5)) * v6 = x
    ]]></literal>
    <justification jstring="[para(30707(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="30707 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30743">
    <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(30707(a,1),23997(a,1,2))].">
      <j1 rule="para" parents="30707 23997"/>
    </justification>
  </clause>

  <clause id="30744">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(w,a(y,z,u),x) * v5 = v6
    ]]></literal>
    <justification jstring="[para(30722(a,2),23794(a,1))].">
      <j1 rule="para" parents="30722 23794"/>
    </justification>
  </clause>

  <clause id="30745">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) \ v7 = L(a(x,y,a(z,u,w)),v5,v6) * v7
    ]]></literal>
    <justification jstring="[hyper(29728,a,30740,a),flip(a)].">
      <j1 rule="hyper" parents="29728 30740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30746">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (R(z,y,x) \ z) * a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(30181(a,1),30644(a,1))].">
      <j1 rule="para" parents="30181 30644"/>
    </justification>
  </clause>

  <clause id="30748">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ y = x * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,30331,a(flip),b,30658,a),flip(a)].">
      <j1 rule="hyper" parents="60 30331 30658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30750">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * a(w,u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(156,a,30703,a)].">
      <j1 rule="hyper" parents="156 30703"/>
    </justification>
  </clause>

  <clause id="30751">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29265,a(flip),b,30703,a)].">
      <j1 rule="hyper" parents="60 29265 30703"/>
    </justification>
  </clause>

  <clause id="30752">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,30703,a(flip),b,29265,a(flip))].">
      <j1 rule="hyper" parents="129 30703 29265"/>
    </justification>
  </clause>

  <clause id="30753">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(29140(a,2),30703(a,1,1))].">
      <j1 rule="para" parents="29140 30703"/>
    </justification>
  </clause>

  <clause id="30754">
    <literal><![CDATA[
      x \ (L(a(y,y,x),z,u) \ (y \ ((1 / y) \ x))) = 1 \ a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30703(a,1),29896(a,2,2))].">
      <j1 rule="para" parents="30703 29896"/>
    </justification>
  </clause>

  <clause id="30757">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,30707,a,b,30750,a)].">
      <j1 rule="hyper" parents="32 30707 30750"/>
    </justification>
  </clause>

  <clause id="30759">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * a(u,z,a(x,x,y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(29140(a,2),30750(a,1,1))].">
      <j1 rule="para" parents="29140 30750"/>
    </justification>
  </clause>

  <clause id="30760">
    <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(125,a,30751,a(flip),b,3816,a)].">
      <j1 rule="hyper" parents="125 30751 3816"/>
    </justification>
  </clause>

  <clause id="30762">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(30092(a,2),30751(a,1,2))].">
      <j1 rule="para" parents="30092 30751"/>
    </justification>
  </clause>

  <clause id="30766">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,30603,a(flip),b,30753,a)].">
      <j1 rule="hyper" parents="60 30603 30753"/>
    </justification>
  </clause>

  <clause id="30767">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * a(u,z,a(x,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = w
    ]]></literal>
    <justification jstring="[para(30753(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="30753 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30768">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(29176,a,30766,a)].">
      <j1 rule="hyper" parents="29176 30766"/>
    </justification>
  </clause>

  <clause id="30769">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(3884,a,30766,a)].">
      <j1 rule="hyper" parents="3884 30766"/>
    </justification>
  </clause>

  <clause id="30770">
    <literal><![CDATA[
      a(x * y,z,a(u,u,z \ R(z,y,x))) = a(u,u,(z \ R(z,y,x)) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(24918(a,2),30766(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24918 30766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30771">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5))) = a(z,z,a(x,y,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(30751(a,1),30769(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30751 30769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30773">
    <literal><![CDATA[
      x \ a(y,z,L(z,u,w)) != a(w,u,a(y,z,z))
    ]]></literal>
    <literal><![CDATA[
      a(y,z,z) = x
    ]]></literal>
    <justification jstring="[para(30762(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="30762 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30774">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(384,a,30625,a)].">
      <j1 rule="hyper" parents="384 30625"/>
    </justification>
  </clause>

  <clause id="30776">
    <literal><![CDATA[
      a(x,y,y \ (L(a(z,u,w),v5,v6) * y)) = L(L(a(z,u,w) \ 1,v5,v6),y,x) \ L(a(z,u,w) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[para(30625(a,1),29989(a,1,3,2))].">
      <j1 rule="para" parents="30625 29989"/>
    </justification>
  </clause>

  <clause id="30777">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,v5) \ (v6 * v6))),v7) = a(x,y * (a(u,w,v5) \ z),v7)
    ]]></literal>
    <justification jstring="[para(30675(a,1),3098(a,1,2,2))].">
      <j1 rule="para" parents="30675 3098"/>
    </justification>
  </clause>

  <clause id="30778">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,25168,a(flip),b,30774,a)].">
      <j1 rule="hyper" parents="60 25168 30774"/>
    </justification>
  </clause>

  <clause id="30780">
    <literal><![CDATA[
      L(a(x,y,z),(a(x,y,z) \ 1) * u,(a(x,y,z) \ 1) * u) \ w = w * ((1 / (u / (a(x,y,z) \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(29610(a,1),30778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29610 30778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30782">
    <literal><![CDATA[
      L(x,L(((y \ 1) \ z) * (y * z),(y \ 1) \ z,y * y),u) = L(x,a(y,y,(y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(2082(a,1),30733(a,1,2,1,2))].">
      <j1 rule="para" parents="2082 30733"/>
    </justification>
  </clause>

  <clause id="30783">
    <literal><![CDATA[
      (x * L(a(y,z,u) \ 1,w,v5)) \ ((x * (a(y,z,u) \ 1)) * a(v5,w,a(y,z,u))) = a(x,a(y,z,u),a(v5,w,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(30760(a,1),14801(a,1,1,2))].">
      <j1 rule="para" parents="30760 14801"/>
    </justification>
  </clause>

  <clause id="30784">
    <literal><![CDATA[
      L(x,(y * z) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      z * ((((y * z) \ y) * x) * a(y,z,z)) = u
    ]]></literal>
    <justification jstring="[para(30655(a,1),14792(a,1))].">
      <j1 rule="para" parents="30655 14792"/>
    </justification>
  </clause>

  <clause id="30785">
    <literal><![CDATA[
      (a(x,y,z) * u) * ((z * (L(L(z,y,x),y,x) \ u)) \ a(x,y,z)) = a(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1
    ]]></literal>
    <justification jstring="[para(30669(a,1),28832(a,1,2,1))].">
      <j1 rule="para" parents="30669 28832"/>
    </justification>
  </clause>

  <clause id="30786">
    <literal><![CDATA[
      a(a(x,y,z) * (a(x,y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(30669(a,2),30212(a,1,1))].">
      <j1 rule="para" parents="30669 30212"/>
    </justification>
  </clause>

  <clause id="30787">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,29322,a(flip),b,30686,a),flip(a)].">
      <j1 rule="hyper" parents="370 29322 30686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30788">
    <literal><![CDATA[
      x \ L(a(y,z,u),x,a(y,z,u) * x) = (a(y,z,u) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,24013,a,b,30787,a(flip))].">
      <j1 rule="hyper" parents="125 24013 30787"/>
    </justification>
  </clause>

  <clause id="30789">
    <literal><![CDATA[
      x \ L(a(y,z,x),x,a(y,z,x)) = (a(y,z,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(30055(a,1),30788(a,1,2))].">
      <j1 rule="para" parents="30055 30788"/>
    </justification>
  </clause>

  <clause id="30790">
    <literal><![CDATA[
      (a(x,y,z) \ z) \ 1 = z \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(30043(a,1),30789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30043 30789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30791">
    <literal><![CDATA[
      (a(x,y,z) / z) \ 1 = a(x,y,z) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,28239,a,b,30790,a)].">
      <j1 rule="hyper" parents="36 28239 30790"/>
    </justification>
  </clause>

  <clause id="30793">
    <literal><![CDATA[
      (a(x,y,z) \ z) * (u * a(x,y,z)) = L(z * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30791(a,1),30428(a,1,1))].">
      <j1 rule="para" parents="30791 30428"/>
    </justification>
  </clause>

  <clause id="30794">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (w * u) = (a(x,y,z) \ u) * T(w,u)
    ]]></literal>
    <justification jstring="[hyper(29339,a,30696,a)].">
      <j1 rule="hyper" parents="29339 30696"/>
    </justification>
  </clause>

  <clause id="30795">
    <literal><![CDATA[
      a(L(x * L(x,y,z),x,z * y),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2962,a(flip),b,30731,a),flip(a)].">
      <j1 rule="hyper" parents="370 2962 30731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30796">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(30151,a,30795,a)].">
      <j1 rule="hyper" parents="30151 30795"/>
    </justification>
  </clause>

  <clause id="30797">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(z,y,x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(30795(a,1),30151(a,1))].">
      <j1 rule="para" parents="30795 30151"/>
    </justification>
  </clause>

  <clause id="30798">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(28936,a,30796,a),flip(a)].">
      <j1 rule="hyper" parents="28936 30796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30799">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w),v5,v6) = a(a(w,u,a(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[para(30796(a,1),30796(a,1,1))].">
      <j1 rule="para" parents="30796 30796"/>
    </justification>
  </clause>

  <clause id="30800">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28396,a(flip),b,30798,a)].">
      <j1 rule="hyper" parents="60 28396 30798"/>
    </justification>
  </clause>

  <clause id="30802">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (w * u) = (a(x,y,z) \ u) * T(w,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30774,a(flip),b,30794,a)].">
      <j1 rule="hyper" parents="60 30774 30794"/>
    </justification>
  </clause>

  <clause id="30803">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,28174,a(flip),b,30802,a),flip(a)].">
      <j1 rule="hyper" parents="370 28174 30802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30804">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(30803(a,1),24112(a,1,1))].">
      <j1 rule="para" parents="30803 24112"/>
    </justification>
  </clause>

  <clause id="30806">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) * u,z,w)) = L(x,y,(w * z) \ (z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(29180,a,30638,a),flip(a)].">
      <j1 rule="hyper" parents="29180 30638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30807">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ w,v5,v6),L(a(y,z,u) * w,v5,v6)) = L(x,a(y,z,u) \ w,a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29547,a(flip),b,30638,a),flip(a)].">
      <j1 rule="hyper" parents="60 29547 30638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30808">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = (a(x,y,z) \ w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(30626(a,1),30661(a,2,1))].">
      <j1 rule="para" parents="30626 30661"/>
    </justification>
  </clause>

  <clause id="30809">
    <literal><![CDATA[
      (x \ K(y,z)) * (a(u,w,v5) \ K(z,y)) = a(u,w,v5) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(19359(a,1),30670(a,1,2))].">
      <j1 rule="para" parents="19359 30670"/>
    </justification>
  </clause>

  <clause id="30810">
    <literal><![CDATA[
      a(x,y,z) * L(u \ (a(x,y,z) \ 1),w,v5) = a(x,y,z) \ L(u \ a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(30674(a,1),3877(a,1,2,1))].">
      <j1 rule="para" parents="30674 3877"/>
    </justification>
  </clause>

  <clause id="30811">
    <literal><![CDATA[
      a((a(x,y,z) \ ((y * z) * x)) * (K(u,w) * v5),v6,v7) = a(((y * z) * R(x,y,z)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(30682(a,1),26769(a,1,1))].">
      <j1 rule="para" parents="30682 26769"/>
    </justification>
  </clause>

  <clause id="30812">
    <literal><![CDATA[
      a(x,R(y,y,z),y) \ R(y,y,z) = L(y,L(y,y,z),x) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(27410(a,1),30711(a,2,1))].">
      <j1 rule="para" parents="27410 30711"/>
    </justification>
  </clause>

  <clause id="30813">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,w) = (w * (a(x,y,z) \ u)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(23572(a,1),30738(a,2,1,2))].">
      <j1 rule="para" parents="23572 30738"/>
    </justification>
  </clause>

  <clause id="30814">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) * u,z,w)) = L(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27287,a(flip),b,30806,a),flip(a)].">
      <j1 rule="hyper" parents="370 27287 30806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30815">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,30804,a(flip),b,30813,a),flip(a)].">
      <j1 rule="hyper" parents="370 30804 30813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30816">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26186,a,30815,a)].">
      <j1 rule="hyper" parents="26186 30815"/>
    </justification>
  </clause>

  <clause id="30817">
    <literal><![CDATA[
      ((x \ y) \ (y \ x)) \ z = ((y \ x) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(3418(a,1),30609(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3418 30609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30818">
    <literal><![CDATA[
      L((x \ y) \ (y \ x),x \ y,y \ x) = (x \ y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(127,a,30817,a(flip),b,4146,a),flip(a)].">
      <j1 rule="hyper" parents="127 30817 4146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30820">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) \ z,u,w) = a(((x \ y) \ (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30817(a,1),14806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30817 14806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30821">
    <literal><![CDATA[
      (x \ y) \ (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,28987,a(flip),b,30818,a),flip(a)].">
      <j1 rule="hyper" parents="60 28987 30818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30822">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4145,a,b,30821,a)].">
      <j1 rule="hyper" parents="60 4145 30821"/>
    </justification>
  </clause>

  <clause id="30823">
    <literal><![CDATA[
      a((x \ (y * (x \ y))) * z,u,w) = a(((y \ x) * (x \ y)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30821(a,1),4143(a,1,1,1))].">
      <j1 rule="para" parents="30821 4143"/>
    </justification>
  </clause>

  <clause id="30824">
    <literal><![CDATA[
      (x \ (y * (x \ y))) \ z = ((x \ y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(30821(a,1),30817(a,1,1))].">
      <j1 rule="para" parents="30821 30817"/>
    </justification>
  </clause>

  <clause id="30825">
    <literal><![CDATA[
      (x \ (y * (x \ y))) \ z = (y \ (x * (y \ x))) * z
    ]]></literal>
    <justification jstring="[para(30821(a,1),30824(a,2,1))].">
      <j1 rule="para" parents="30821 30824"/>
    </justification>
  </clause>

  <clause id="30826">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) \ z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,4143,a(flip),b,30820,a),flip(a)].">
      <j1 rule="hyper" parents="370 4143 30820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30827">
    <literal><![CDATA[
      x * ((((y * x) \ y) * z) * a(y,x,x)) = L(z,y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(30784,a,29697,a)].">
      <j1 rule="hyper" parents="30784 29697"/>
    </justification>
  </clause>

  <clause id="30828">
    <literal><![CDATA[
      x * ((((y * x) \ y) * z) * a(y,x,x)) = L(z,x,y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,30251,a(flip),b,30827,a),flip(a)].">
      <j1 rule="hyper" parents="370 30251 30827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30829">
    <literal><![CDATA[
      (a(x,y,z) \ (u \ w)) \ ((u \ w) * u) = (a(x,y,z) \ (w / u)) \ w
    ]]></literal>
    <justification jstring="[para(30626(a,1),30681(a,2,1))].">
      <j1 rule="para" parents="30626 30681"/>
    </justification>
  </clause>

  <clause id="30830">
    <literal><![CDATA[
      a((x * T(a(y,z,u) * K(w,w \ v5),v5)) \ v6,v7,v8) = a((x * (a(y,z,u) \ K(w,w \ v5))) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(28223(a,2),30685(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28223 30685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30831">
    <literal><![CDATA[
      a((((a(x,y,a(z,u,w) \ v5) \ y) * x) * (v5 * a(z,u,w))) \ v6,v7,v8) = a((x * (T(y,x) * (a(z,u,w) \ v5))) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(28876(a,1),30685(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28876 30685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30832">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z) \ 1,u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(30626(a,1),30692(a,1,1))].">
      <j1 rule="para" parents="30626 30692"/>
    </justification>
  </clause>

  <clause id="30833">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(3401(a,1),30832(a,1,2))].">
      <j1 rule="para" parents="3401 30832"/>
    </justification>
  </clause>

  <clause id="30834">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / (a(x,y,z) \ w) = R(u,a(x,y,z) \ 1,w)
    ]]></literal>
    <justification jstring="[para(30626(a,1),30694(a,1,1,1))].">
      <j1 rule="para" parents="30626 30694"/>
    </justification>
  </clause>

  <clause id="30835">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / (a(x,y,z) \ w) = R(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,2759,a(flip),b,30834,a),flip(a)].">
      <j1 rule="hyper" parents="370 2759 30834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30836">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / (a(x,y,z) \ w) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,28368,a(flip),b,30835,a),flip(a)].">
      <j1 rule="hyper" parents="370 28368 30835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30837">
    <literal><![CDATA[
      ((a(x,y,z) \ ((a(x,y,z) \ 1) \ u)) * w) / (a(x,y,z) \ w) = (w * (a(x,y,z) \ 1)) \ (w * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3410,a(flip),b,30836,a),flip(a)].">
      <j1 rule="hyper" parents="370 3410 30836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30838">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u) \ 1) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(30622(a,1),30695(a,1,1,2))].">
      <j1 rule="para" parents="30622 30695"/>
    </justification>
  </clause>

  <clause id="30839">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[hyper(3522,a,30838,a)].">
      <j1 rule="hyper" parents="3522 30838"/>
    </justification>
  </clause>

  <clause id="30840">
    <literal><![CDATA[
      x \ (L(a(y,y,x),z,u) \ (y \ ((1 / y) \ x))) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,62,a(flip),b,30754,a),flip(a)].">
      <j1 rule="hyper" parents="370 62 30754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30841">
    <literal><![CDATA[
      x \ (a(y,y,L(x,z,u)) \ (y \ ((1 / y) \ x))) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29140(a,2),30840(a,1,2,1))].">
      <j1 rule="para" parents="29140 30840"/>
    </justification>
  </clause>

  <clause id="30842">
    <literal><![CDATA[
      x \ (y \ (a(y,y,L(x,z,u)) \ ((1 / y) \ x))) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30519(a,1),30841(a,1,2))].">
      <j1 rule="para" parents="30519 30841"/>
    </justification>
  </clause>

  <clause id="30843">
    <literal><![CDATA[
      x \ (y \ ((1 / y) \ (a(y,y,L(x,z,u)) \ x))) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30525(a,1),30842(a,1,2,2))].">
      <j1 rule="para" parents="30525 30842"/>
    </justification>
  </clause>

  <clause id="30844">
    <literal><![CDATA[
      x \ (y \ ((1 / y) \ L(x,y,L(y,z,u)))) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30076(a,1),30843(a,1,2,2,2))].">
      <j1 rule="para" parents="30076 30843"/>
    </justification>
  </clause>

  <clause id="30845">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(1805(a,2),30844(a,1,2))].">
      <j1 rule="para" parents="1805 30844"/>
    </justification>
  </clause>

  <clause id="30846">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30611(a,1),30845(a,1,2))].">
      <j1 rule="para" parents="30611 30845"/>
    </justification>
  </clause>

  <clause id="30847">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(30492,a,30846,a)].">
      <j1 rule="hyper" parents="30492 30846"/>
    </justification>
  </clause>

  <clause id="30848">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(30481,a,30847,a)].">
      <j1 rule="hyper" parents="30481 30847"/>
    </justification>
  </clause>

  <clause id="30849">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30482,a(flip),b,30847,a),flip(a)].">
      <j1 rule="hyper" parents="60 30482 30847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30850">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ (L(a(x,y,z),z,y) \ u) = L(a(x,y,z),z,y) \ (a(y,z,a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(30849(a,2),30148(a,1,1))].">
      <j1 rule="para" parents="30849 30148"/>
    </justification>
  </clause>

  <clause id="30851">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(z,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4033,a(flip),b,30848,a)].">
      <j1 rule="hyper" parents="60 4033 30848"/>
    </justification>
  </clause>

  <clause id="30852">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = a(z,y,a(x,x,u)) * x
    ]]></literal>
    <justification jstring="[para(30848(a,1),30503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30848 30503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30853">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30849,a(flip),b,30851,a)].">
      <j1 rule="hyper" parents="60 30849 30851"/>
    </justification>
  </clause>

  <clause id="30854">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,u))) = a(w,w,a(x,y,a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(30851(a,2),30771(a,1,3))].">
      <j1 rule="para" parents="30851 30771"/>
    </justification>
  </clause>

  <clause id="30855">
    <literal><![CDATA[
      a(x,a(y,z,x),z) = a(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,30131,a,b,30853,a)].">
      <j1 rule="hyper" parents="60 30131 30853"/>
    </justification>
  </clause>

  <clause id="30856">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * u = u * a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,30853,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 30853 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30857">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(y,y,a(x,x,z)) = w
    ]]></literal>
    <justification jstring="[para(30853(a,2),23637(a,1,1))].">
      <j1 rule="para" parents="30853 23637"/>
    </justification>
  </clause>

  <clause id="30858">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(y,y,z)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(30853(a,1),30149(a,1,2))].">
      <j1 rule="para" parents="30853 30149"/>
    </justification>
  </clause>

  <clause id="30859">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),x,y)) = a(y,y,a(x,x,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(30796(a,1),30853(a,1,3))].">
      <j1 rule="para" parents="30796 30853"/>
    </justification>
  </clause>

  <clause id="30860">
    <literal><![CDATA[
      x \ L(x,a(y,z,x),z) = a(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,29201,a,b,30855,a)].">
      <j1 rule="hyper" parents="60 29201 30855"/>
    </justification>
  </clause>

  <clause id="30861">
    <literal><![CDATA[
      L(x,a(y,z,x),z) = L(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,28429,a,b,30860,a),flip(a)].">
      <j1 rule="hyper" parents="35 28429 30860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30862">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,30419,a,b,30861,a)].">
      <j1 rule="hyper" parents="60 30419 30861"/>
    </justification>
  </clause>

  <clause id="30863">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ L(x,y,z) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(30861(a,1),30280(a,1,1))].">
      <j1 rule="para" parents="30861 30280"/>
    </justification>
  </clause>

  <clause id="30864">
    <literal><![CDATA[
      (x * y) * L(z,z,a(y,y,x)) = x * (y * (z * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30861(a,1),30420(a,1,2))].">
      <j1 rule="para" parents="30861 30420"/>
    </justification>
  </clause>

  <clause id="30865">
    <literal><![CDATA[
      a(x,y,z) \ 1 != u \ L(z,y,x)
    ]]></literal>
    <literal><![CDATA[
      L(z,z,a(y,y,x)) = u
    ]]></literal>
    <justification jstring="[para(30863(a,1),45(a,1))].">
      <j1 rule="para" parents="30863 45"/>
    </justification>
  </clause>

  <clause id="30866">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ L(x,z,y) = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[para(30726(a,1),30863(a,1,1))].">
      <j1 rule="para" parents="30726 30863"/>
    </justification>
  </clause>

  <clause id="30867">
    <literal><![CDATA[
      a(x,y,z) \ L(z,z,a(x,y,y)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,30620,a,b,30866,a)].">
      <j1 rule="hyper" parents="35 30620 30866"/>
    </justification>
  </clause>

  <clause id="30868">
    <literal><![CDATA[
      a(x,y,z) \ 1 != u \ L(z,y,x)
    ]]></literal>
    <literal><![CDATA[
      L(z,z,a(x,y,y)) = u
    ]]></literal>
    <justification jstring="[para(30866(a,1),45(a,1))].">
      <j1 rule="para" parents="30866 45"/>
    </justification>
  </clause>

  <clause id="30869">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(z,y,y)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,25395,a,b,30867,a)].">
      <j1 rule="hyper" parents="36 25395 30867"/>
    </justification>
  </clause>

  <clause id="30870">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(30867(a,1),24094(a,1,1))].">
      <j1 rule="para" parents="30867 24094"/>
    </justification>
  </clause>

  <clause id="30871">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ L(y,z,u) = L(L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(28349(a,1),30867(a,1,2))].">
      <j1 rule="para" parents="28349 30867"/>
    </justification>
  </clause>

  <clause id="30872">
    <literal><![CDATA[
      a(x,1 / y,L(1 / y,y,z)) \ (z \ (z / y)) = L(L(1 / y,y,z),1 / y,x)
    ]]></literal>
    <justification jstring="[para(3417(a,1),30871(a,1,2))].">
      <j1 rule="para" parents="3417 30871"/>
    </justification>
  </clause>

  <clause id="30873">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) \ y),y) \ L(y * (L(y,z,u) \ y),z,u) = L(L(y * (L(y,z,u) \ y),z,u),y * (L(y,z,u) \ y),x)
    ]]></literal>
    <justification jstring="[para(30200(a,1),30871(a,1,1,3))].">
      <j1 rule="para" parents="30200 30871"/>
    </justification>
  </clause>

  <clause id="30874">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * a(x,w,a(a(u,z,y),x,w))) = w \ ((w * w) * a(x,x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(30859(a,2),28762(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="30859 28762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30875">
    <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="[para(30626(a,1),30673(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30626 30673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30876">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = a(x,y,z) * (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(23620(a,2),30875(a,1,2,2))].">
      <j1 rule="para" parents="23620 30875"/>
    </justification>
  </clause>

  <clause id="30877">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ (a(x,y,z) \ w))) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[para(23621(a,1),30875(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23621 30875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30878">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ w)) = u * (a(a(x,y,z),w,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29475,a(flip),b,30876,a),flip(a)].">
      <j1 rule="hyper" parents="60 29475 30876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30879">
    <literal><![CDATA[
      (a(x,y,z) * (u * (a(x,y,z) \ w))) / w = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,30878,a,b,30739,a(flip))].">
      <j1 rule="hyper" parents="128 30878 30739"/>
    </justification>
  </clause>

  <clause id="30880">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (w * a(x,y,z)) = (u * a(x,y,z)) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(30621(a,1),30677(a,1,2))].">
      <j1 rule="para" parents="30621 30677"/>
    </justification>
  </clause>

  <clause id="30881">
    <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(370,a,23642,a,b,30880,a),flip(a)].">
      <j1 rule="hyper" parents="370 23642 30880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30882">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * a(v5,v6,v7)) * (a(v5,v6,v7) \ a(v5,v6,v7))))) = a(x,y,z * (u * (a(v5,v6,v7) \ w)))
    ]]></literal>
    <justification jstring="[para(30880(a,1),15782(a,1,3,2,2))].">
      <j1 rule="para" parents="30880 15782"/>
    </justification>
  </clause>

  <clause id="30883">
    <literal><![CDATA[
      (a(x,y,z) * u) * (a(x,y,z) \ (a(x,y,z) \ w)) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(23621(a,1),30881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23621 30881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30884">
    <literal><![CDATA[
      L(x,L((a(y,z,u) \ w) * v5,a(y,z,u) * w,a(y,z,u) * w),v6) = L(x,(a(y,z,u) * w) \ (a(y,z,u) \ (a(y,z,u) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(30883(a,1),28903(a,1,2,1))].">
      <j1 rule="para" parents="30883 28903"/>
    </justification>
  </clause>

  <clause id="30885">
    <literal><![CDATA[
      a(((a(x,y,z) \ (z * y)) * x) * u,w,v5) = a(((z * y) * R(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(28722(a,1),30702(a,1,1,1))].">
      <j1 rule="para" parents="28722 30702"/>
    </justification>
  </clause>

  <clause id="30887">
    <literal><![CDATA[
      a(x * y,z,a(u,u,z \ R(z,y,x))) = a(u,u,a(z,y,x) * (z \ R(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,30770,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 30770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30888">
    <literal><![CDATA[
      a(x,1 / y,L(y \ 1,y,z)) \ (z \ (z / y)) = L(L(1 / y,y,z),1 / y,x)
    ]]></literal>
    <justification jstring="[para(26921(a,1),30872(a,1,1))].">
      <j1 rule="para" parents="26921 30872"/>
    </justification>
  </clause>

  <clause id="30889">
    <literal><![CDATA[
      a(((L(x,y,z) * y) * z) * u,w,v5) = a(((x * y) * R(z,y,x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(30709(a,1),30885(a,1,1,1,1))].">
      <j1 rule="para" parents="30709 30885"/>
    </justification>
  </clause>

  <clause id="30890">
    <literal><![CDATA[
      a(((L(x,y,z) * y) * z) * u,w,v5) = a(u * (x * (y * z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27345,a(flip),b,30889,a),flip(a)].">
      <j1 rule="hyper" parents="370 27345 30889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30891">
    <literal><![CDATA[
      a(((L(x,y,z) * (y \ (u * u))) * z) * w,v5,v6) = a(w * (x * ((y \ (u * u)) * z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(26087(a,1),30890(a,1,1,1,1,1))].">
      <j1 rule="para" parents="26087 30890"/>
    </justification>
  </clause>

  <clause id="30892">
    <literal><![CDATA[
      a(x,1 / y,L(y,y,z)) \ (z \ (z / y)) = L(L(1 / y,y,z),1 / y,x)
    ]]></literal>
    <justification jstring="[para(15787(a,1),30888(a,1,1))].">
      <j1 rule="para" parents="15787 30888"/>
    </justification>
  </clause>

  <clause id="30893">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) \ (z \ (z / y)) = L(L(1 / y,y,z),1 / y,x)
    ]]></literal>
    <justification jstring="[para(3041(a,1),30892(a,1,1))].">
      <j1 rule="para" parents="3041 30892"/>
    </justification>
  </clause>

  <clause id="30894">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) \ (z \ (z / y)) = L(L(1 / y,y,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3388,a(flip),b,30893,a),flip(a)].">
      <j1 rule="hyper" parents="370 3388 30893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30895">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x \ L(x,y,z),u,w)) = a(w,u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),30599(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4 30599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30896">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x \ L(x,y,z),u,w)) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,4030,a(flip),b,30895,a),flip(a)].">
      <j1 rule="hyper" parents="370 4030 30895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30899">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,x * L(x,y,z)) = x * L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(129,a,30896,a(flip),b,2160,a)].">
      <j1 rule="hyper" parents="129 30896 2160"/>
    </justification>
  </clause>

  <clause id="30900">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(30896(a,1),14871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30896 14871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30901">
    <literal><![CDATA[
      a(x,y,a(z,u,x * L(x,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(30896(a,1),14878(a,1,3))].">
      <j1 rule="para" parents="30896 14878"/>
    </justification>
  </clause>

  <clause id="30904">
    <literal><![CDATA[
      L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1) = x * a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(29124(a,2),30900(a,1,2))].">
      <j1 rule="para" parents="29124 30900"/>
    </justification>
  </clause>

  <clause id="30905">
    <literal><![CDATA[
      T(x * a(y,z,x * L(x,u,w)),L(x,u,w)) = L(x,z,y) * (L(L(x,z,y),u,w) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(30904(a,1),28055(a,1,1))].">
      <j1 rule="para" parents="30904 28055"/>
    </justification>
  </clause>

  <clause id="30906">
    <literal><![CDATA[
      R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w)) = a(w,u,R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(26949,a,30714,a),flip(a)].">
      <j1 rule="hyper" parents="26949 30714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30907">
    <literal><![CDATA[
      R(x,y,z) * (x \ L(R(x,y,z) \ x,u,w)) = a(w,u,x * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,7587,a(flip),b,30906,a),flip(a)].">
      <j1 rule="hyper" parents="370 7587 30906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30908">
    <literal><![CDATA[
      a(x,y,z * R(z,u,w)) \ (R(z,u,w) \ z) = L(R(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(30907(a,1),29861(a,1,1))].">
      <j1 rule="para" parents="30907 29861"/>
    </justification>
  </clause>

  <clause id="30909">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ (R(z,u,w) \ z) = L(R(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(28698(a,1),30908(a,1,1))].">
      <j1 rule="para" parents="28698 30908"/>
    </justification>
  </clause>

  <clause id="30910">
    <literal><![CDATA[
      (x * L(a(y,z,u) \ 1,w,v5)) * a(y,z,u) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(29338(a,1),30654(a,1,1,2))].">
      <j1 rule="para" parents="29338 30654"/>
    </justification>
  </clause>

  <clause id="30912">
    <literal><![CDATA[
      a(x,y,z) \ L((u \ w) \ a(x,y,z),u \ w,u) = a(x,y,z) * (w \ (u * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(656(a,1),30810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="656 30810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30913">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) * (1 / a(y,z,u)) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,4153,a(flip),b,30910,a)].">
      <j1 rule="hyper" parents="60 4153 30910"/>
    </justification>
  </clause>

  <clause id="30914">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) * (a(y,z,u) \ 1) = x * (a(y,z,u) \ L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23572(a,1),30913(a,1,2))].">
      <j1 rule="para" parents="23572 30913"/>
    </justification>
  </clause>

  <clause id="30915">
    <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(30653,a,30914,a)].">
      <j1 rule="hyper" parents="30653 30914"/>
    </justification>
  </clause>

  <clause id="30916">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z) \ 1,u,w) * v5) = v5 * (a(x,y,z) \ L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,30691,a,b,30915,a)].">
      <j1 rule="hyper" parents="60 30691 30915"/>
    </justification>
  </clause>

  <clause id="30917">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z) \ 1,u,w) * v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30751(a,1),30916(a,2,2))].">
      <j1 rule="para" parents="30751 30916"/>
    </justification>
  </clause>

  <clause id="30918">
    <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="[hyper(60,a,30627,a(flip),b,30917,a)].">
      <j1 rule="hyper" parents="60 30627 30917"/>
    </justification>
  </clause>

  <clause id="30920">
    <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(30774(a,1),30917(a,1,2))].">
      <j1 rule="para" parents="30774 30917"/>
    </justification>
  </clause>

  <clause id="30921">
    <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(129,a,30918,a(flip),b,2156,a)].">
      <j1 rule="hyper" parents="129 30918 2156"/>
    </justification>
  </clause>

  <clause id="30922">
    <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(2183,a,30920,a),flip(a)].">
      <j1 rule="hyper" parents="2183 30920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30923">
    <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(25581,a,30921,a)].">
      <j1 rule="hyper" parents="25581 30921"/>
    </justification>
  </clause>

  <clause id="30924">
    <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(23796,a,30921,a)].">
      <j1 rule="hyper" parents="23796 30921"/>
    </justification>
  </clause>

  <clause id="30925">
    <literal><![CDATA[
      L(a(x,y,z),z,a(x,y,z) \ u) \ u = L(a(x,y,z) \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30135,a(flip),b,30922,a),flip(a)].">
      <j1 rule="hyper" parents="60 30135 30922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30926">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x * y,z,a(x,y,z)) = (L(z,y,x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(30732(a,1),30922(a,2,1))].">
      <j1 rule="para" parents="30732 30922"/>
    </justification>
  </clause>

  <clause id="30927">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(u,u,a(z,z,y)) = L(a(y,z,u),u,z) * x
    ]]></literal>
    <justification jstring="[hyper(30857,a,30923,a)].">
      <j1 rule="hyper" parents="30857 30923"/>
    </justification>
  </clause>

  <clause id="30928">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(u,u,a(z,z,y)) = (L(u,z,y) \ u) * x
    ]]></literal>
    <justification jstring="[para(29953(a,1),30927(a,2,1))].">
      <j1 rule="para" parents="29953 30927"/>
    </justification>
  </clause>

  <clause id="30929">
    <literal><![CDATA[
      (x * a(y,z \ y,(z \ y) \ 1)) * a((z \ y) \ 1,(z \ y) \ 1,a(z \ y,z \ y,y)) = ((((y \ z) \ 1) \ 1) \ ((z \ y) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(3498(a,1),30928(a,2,1,1))].">
      <j1 rule="para" parents="3498 30928"/>
    </justification>
  </clause>

  <clause id="30930">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (z \ L(z,y,x))) = a(x * y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,30577,a(flip),b,30926,a)].">
      <j1 rule="hyper" parents="125 30577 30926"/>
    </justification>
  </clause>

  <clause id="30931">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,y,x)) = a(x * y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(8197,a,30930,a)].">
      <j1 rule="hyper" parents="8197 30930"/>
    </justification>
  </clause>

  <clause id="30932">
    <literal><![CDATA[
      a(x * y,z,a(x,y,z)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30357,a(flip),b,30931,a),flip(a)].">
      <j1 rule="hyper" parents="60 30357 30931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30933">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = a(x,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(26519,a,30932,a)].">
      <j1 rule="hyper" parents="26519 30932"/>
    </justification>
  </clause>

  <clause id="30934">
    <literal><![CDATA[
      a(x,a(y,z,x),z * y) = a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,30131,a,b,30933,a)].">
      <j1 rule="hyper" parents="60 30131 30933"/>
    </justification>
  </clause>

  <clause id="30935">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,30800,a(flip),b,30934,a)].">
      <j1 rule="hyper" parents="60 30800 30934"/>
    </justification>
  </clause>

  <clause id="30936">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(30123,a,30935,a)].">
      <j1 rule="hyper" parents="30123 30935"/>
    </justification>
  </clause>

  <clause id="30937">
    <literal><![CDATA[
      (R(x,y,z) \ x) * a(x,y,z) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(30746,a,30936,a)].">
      <j1 rule="hyper" parents="30746 30936"/>
    </justification>
  </clause>

  <clause id="30938">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * (R(y,x,z) \ y) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(30936(a,1),30185(a,1,1))].">
      <j1 rule="para" parents="30936 30185"/>
    </justification>
  </clause>

  <clause id="30939">
    <literal><![CDATA[
      L(a(x,y,z),z,a(x,y,z) \ u) \ u = (a(x,y,z) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26350,a(flip),b,30925,a),flip(a)].">
      <j1 rule="hyper" parents="370 26350 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30940">
    <literal><![CDATA[
      L(a(x,y,z),z,a(x,y,z) * u) \ u = (a(x,y,z) * z) \ (z * u)
    ]]></literal>
    <justification jstring="[para(30635(a,1),30939(a,1,1))].">
      <j1 rule="para" parents="30635 30939"/>
    </justification>
  </clause>

  <clause id="30941">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * u,w,v5) = a(u * (y * ((x \ (v6 * v6)) * z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(27905,a,30891,a)].">
      <j1 rule="hyper" parents="27905 30891"/>
    </justification>
  </clause>

  <clause id="30942">
    <literal><![CDATA[
      L(x,y * a(z,y,u),u * (L(u,y,z) \ y)) = L(x,a(z,y,u) \ y,a(z,y,u) \ y)
    ]]></literal>
    <justification jstring="[para(30710(a,1),30712(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30710 30712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30943">
    <literal><![CDATA[
      L(x,L((y * z) * ((y \ 1) \ z),(y \ 1) \ z,y * y),u) = L(x,a(y,y,(y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(15594(a,1),30782(a,1,2,1))].">
      <j1 rule="para" parents="15594 30782"/>
    </justification>
  </clause>

  <clause id="30944">
    <literal><![CDATA[
      a(((a(x,y,z) \ (y * z)) * x) * (K(u,w) * v5),v6,v7) = a(((y * z) * R(x,y,z)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(28722(a,1),30811(a,1,1,1))].">
      <j1 rule="para" parents="28722 30811"/>
    </justification>
  </clause>

  <clause id="30945">
    <literal><![CDATA[
      L(x,a(y,y,(y \ 1) \ z),u) = L(x,(y * z) * ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(615(a,1),30943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="615 30943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30946">
    <literal><![CDATA[
      L(x,a(y,y,(y \ 1) \ z),u) = L(x,(y \ z) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26092,a(flip),b,30945,a),flip(a)].">
      <j1 rule="hyper" parents="370 26092 30945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30948">
    <literal><![CDATA[
      L(x,a(y,y,1 \ (y * z)),u) = L(x,(y \ z) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(29144(a,1),30946(a,1,2))].">
      <j1 rule="para" parents="29144 30946"/>
    </justification>
  </clause>

  <clause id="30949">
    <literal><![CDATA[
      L(x,a(y,y,y * z),u) = L(x,(y \ z) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(62(a,1),30948(a,1,2,3))].">
      <j1 rule="para" parents="62 30948"/>
    </justification>
  </clause>

  <clause id="30950">
    <literal><![CDATA[
      L(x,(y \ z) * (y * z),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30042,a(flip),b,30949,a),flip(a)].">
      <j1 rule="hyper" parents="60 30042 30949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30951">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * (K(u,w) * v5),v6,v7) = a(((x * y) * R(z,x,y)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(29944(a,1),30944(a,1,1,1,1))].">
      <j1 rule="para" parents="29944 30944"/>
    </justification>
  </clause>

  <clause id="30952">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * u,w,v5) = a(((x * y) * R(z,x,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26526,a,30951,a)].">
      <j1 rule="hyper" parents="26526 30951"/>
    </justification>
  </clause>

  <clause id="30953">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * u,w,v5) = a(((x * y) * L(z,x,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27344,a(flip),b,30952,a),flip(a)].">
      <j1 rule="hyper" parents="370 27344 30952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30954">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * u,w,v5) = a((y * (T(x,y) * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(12481(a,1),30953(a,2,1,1))].">
      <j1 rule="para" parents="12481 30953"/>
    </justification>
  </clause>

  <clause id="30955">
    <literal><![CDATA[
      a(((x * L(y,x,z)) * z) * u,w,v5) = a((y * (x * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,27548,a(flip),b,30954,a),flip(a)].">
      <j1 rule="hyper" parents="370 27548 30954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30957">
    <literal><![CDATA[
      a(x * (y * ((z \ (u * u)) * w)),v5,v6) = a((y * (z * w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,30941,a(flip),b,30955,a)].">
      <j1 rule="hyper" parents="60 30941 30955"/>
    </justification>
  </clause>

  <clause id="30958">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = T(L(L(x,y,z) \ x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,17,a,b,30615,a),flip(a)].">
      <j1 rule="hyper" parents="370 17 30615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30959">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = L(T(L(x,y,z) \ x,v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,20,a,b,30958,a),flip(a)].">
      <j1 rule="hyper" parents="370 20 30958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30960">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x * L(x,y,z),u,w),v5) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(23798(a,1),30959(a,2,1))].">
      <j1 rule="para" parents="23798 30959"/>
    </justification>
  </clause>

  <clause id="30961">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) \ y = L(L(x,z,u) \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29246,a(flip),b,30960,a)].">
      <j1 rule="hyper" parents="60 29246 30960"/>
    </justification>
  </clause>

  <clause id="30964">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u \ x,u \ x) = (u \ L(x,y,z)) \ (u \ x)
    ]]></literal>
    <justification jstring="[para(74(a,1),30961(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="74 30961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30965">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * x,u * x) = (u \ L(x,y,z)) \ (u \ x)
    ]]></literal>
    <justification jstring="[hyper(29606,a,30964,a)].">
      <j1 rule="hyper" parents="29606 30964"/>
    </justification>
  </clause>

  <clause id="30966">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * a(x,w,a(a(u,z,y),x,w))) = (1 / w) \ a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,554,a(flip),b,30874,a),flip(a)].">
      <j1 rule="hyper" parents="370 554 30874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30967">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * L(w,a(a(u,z,y),x,w),x) = (1 / w) \ a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(30132(a,1),30966(a,1,2))].">
      <j1 rule="para" parents="30132 30966"/>
    </justification>
  </clause>

  <clause id="30968">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * L(w,w,a(x,x,a(u,z,y))) = (1 / w) \ a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(30861(a,1),30967(a,1,2))].">
      <j1 rule="para" parents="30861 30967"/>
    </justification>
  </clause>

  <clause id="30969">
    <literal><![CDATA[
      T(x * a(y,z,x * L(x,u,w)),x) = L(x,z,y) * (L(L(x,z,y),u,w) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(24043,a,30905,a)].">
      <j1 rule="hyper" parents="24043 30905"/>
    </justification>
  </clause>

  <clause id="30970">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),u,w) \ L(x,u,w)) = a(z,y,x * L(x,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(25238,a,30969,a),flip(a)].">
      <j1 rule="hyper" parents="25238 30969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30972">
    <literal><![CDATA[
      L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1) = a(z,y,x * L(x,u,w)) * x
    ]]></literal>
    <justification jstring="[para(10450(a,1),30970(a,1,2))].">
      <j1 rule="para" parents="10450 30970"/>
    </justification>
  </clause>

  <clause id="30973">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * z = z * a(w,u,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,30904,a(flip),b,30972,a),flip(a)].">
      <j1 rule="hyper" parents="60 30904 30972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30974">
    <literal><![CDATA[
      a(x,y,z) \ L((u \ w) \ a(x,y,z),u \ w,u) = a(x,y,z) * (w \ (a(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(30626(a,1),30912(a,2,2,2))].">
      <j1 rule="para" parents="30626 30912"/>
    </justification>
  </clause>

  <clause id="30975">
    <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="[para(656(a,1),30974(a,1,2))].">
      <j1 rule="para" parents="656 30974"/>
    </justification>
  </clause>

  <clause id="30976">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (a(x,y,z) * w)) = a(x,y,z) * (u \ (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(23620(a,2),30975(a,1,2,2))].">
      <j1 rule="para" parents="23620 30975"/>
    </justification>
  </clause>

  <clause id="30977">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((a(x,y,z) \ (a(x,y,z) \ 1)) \ w) = (((a(x,y,z) \ 1) \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[para(30622(a,1),30676(a,1,1))].">
      <j1 rule="para" parents="30622 30676"/>
    </justification>
  </clause>

  <clause id="30978">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((z \ L(L(z,y,x),y,x)) \ w) = (((a(x,y,z) \ 1) \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[para(30217(a,1),30977(a,1,2,1))].">
      <j1 rule="para" parents="30217 30977"/>
    </justification>
  </clause>

  <clause id="30979">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (z * (L(L(z,y,x),y,x) \ w)) = (((a(x,y,z) \ 1) \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[para(29085(a,1),30978(a,1,2))].">
      <j1 rule="para" parents="29085 30978"/>
    </justification>
  </clause>

  <clause id="30980">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ ((a(z,y,x) * u) \ w)) = (((a(z,y,x) \ 1) \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(60,a,29161,a(flip),b,30979,a)].">
      <j1 rule="hyper" parents="60 29161 30979"/>
    </justification>
  </clause>

  <clause id="30981">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ ((a(z,y,x) * u) \ w)) = (a(z,y,x) \ u) \ w
    ]]></literal>
    <justification jstring="[para(13579(a,1),30980(a,2,1,1))].">
      <j1 rule="para" parents="13579 30980"/>
    </justification>
  </clause>

  <clause id="30983">
    <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="[para(23620(a,1),30981(a,1,2,2,1))].">
      <j1 rule="para" parents="23620 30981"/>
    </justification>
  </clause>

  <clause id="30984">
    <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(60,a,30814,a(flip),b,30807,a)].">
      <j1 rule="hyper" parents="60 30814 30807"/>
    </justification>
  </clause>

  <clause id="30985">
    <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(60,a,28942,a(flip),b,30984,a),flip(a)].">
      <j1 rule="hyper" parents="60 28942 30984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30986">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,a(y,z,u) \ z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29547,a(flip),b,30985,a),flip(a)].">
      <j1 rule="hyper" parents="370 29547 30985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30988">
    <literal><![CDATA[
      L(x,y * a(z,y,u),u * (L(u,y,z) \ y)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,30942,a,b,30986,a)].">
      <j1 rule="hyper" parents="60 30942 30986"/>
    </justification>
  </clause>

  <clause id="30990">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y * a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(29938(a,1),30988(a,1,3))].">
      <j1 rule="para" parents="29938 30988"/>
    </justification>
  </clause>

  <clause id="30991">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),u) = L(u,x,x) \ u
    ]]></literal>
    <justification jstring="[para(30990(a,1),1362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30990 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30992">
    <literal><![CDATA[
      L(x,L(y * a(z,y,u),y,y),w) = L(x,y * a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(30990(a,1),14817(a,1,2))].">
      <j1 rule="para" parents="30990 14817"/>
    </justification>
  </clause>

  <clause id="30993">
    <literal><![CDATA[
      L(L(x,y * a(z,y,u),y * a(z,y,u)) \ x,x,y) = a(y,y,x)
    ]]></literal>
    <justification jstring="[para(30990(a,2),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="30990 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30994">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,1362,a(flip),b,30991,a),flip(a)].">
      <j1 rule="hyper" parents="370 1362 30991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30995">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,u) = w
    ]]></literal>
    <justification jstring="[para(30991(a,2),1364(a,1))].">
      <j1 rule="para" parents="30991 1364"/>
    </justification>
  </clause>

  <clause id="30996">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),w) = L(x,y * a(z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(30405,a,30992,a)].">
      <j1 rule="hyper" parents="30405 30992"/>
    </justification>
  </clause>

  <clause id="30997">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),y * a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,30990,a(flip),b,30996,a),flip(a)].">
      <j1 rule="hyper" parents="370 30990 30996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30998">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y \ a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3698,a(flip),b,30997,a)].">
      <j1 rule="hyper" parents="60 3698 30997"/>
    </justification>
  </clause>

  <clause id="30999">
    <literal><![CDATA[
      R(x,y,z \ (z \ u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(30997(a,1),28484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30997 28484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31000">
    <literal><![CDATA[
      ((x * y) * (z * a(y,y,z))) / ((1 / y) \ z) = R(x,y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,28992,a,b,30999,a)].">
      <j1 rule="hyper" parents="60 28992 30999"/>
    </justification>
  </clause>

  <clause id="31001">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,u \ T(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),30999(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="17 30999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31003">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,27432,a(flip),b,31001,a),flip(a)].">
      <j1 rule="hyper" parents="370 27432 31001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31005">
    <literal><![CDATA[
      R(x,y,L(L(z,u,w) * u,a(w,u,z) \ u,a(w,u,z) \ u)) = R(x,y,(a(w,u,z) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(30687(a,1),31003(a,1,3,1))].">
      <j1 rule="para" parents="30687 31003"/>
    </justification>
  </clause>

  <clause id="31006">
    <literal><![CDATA[
      L(x \ a(y,x,z),x,x) = a(y,x,z) / x
    ]]></literal>
    <justification jstring="[hyper(28300,a,30998,a),flip(a)].">
      <j1 rule="hyper" parents="28300 30998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31007">
    <literal><![CDATA[
      L(x,y * a(y,y,z),(y \ z) / z) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(28439(a,1),30998(a,1,3))].">
      <j1 rule="para" parents="28439 30998"/>
    </justification>
  </clause>

  <clause id="31008">
    <literal><![CDATA[
      L(a(x,y,z),y,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29319,a,31006,a)].">
      <j1 rule="hyper" parents="29319 31006"/>
    </justification>
  </clause>

  <clause id="31009">
    <literal><![CDATA[
      (1 / x) * a(y,x,z) = a(y,x,z) / x
    ]]></literal>
    <justification jstring="[hyper(790,a,31006,a)].">
      <j1 rule="hyper" parents="790 31006"/>
    </justification>
  </clause>

  <clause id="31010">
    <literal><![CDATA[
      (1 / x) \ (a(y,x,z) / x) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,31006,a(flip),b,586,a(flip))].">
      <j1 rule="hyper" parents="125 31006 586"/>
    </justification>
  </clause>

  <clause id="31011">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,31008,a,b,3942,a),flip(a)].">
      <j1 rule="hyper" parents="126 31008 3942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31012">
    <literal><![CDATA[
      (1 / x) \ a(y,x,z) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,31008,a(flip),b,29277,a),flip(a)].">
      <j1 rule="hyper" parents="129 31008 29277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31013">
    <literal><![CDATA[
      a(x,y,z) * (y \ 1) = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,31008,a(flip),b,24003,a),flip(a)].">
      <j1 rule="hyper" parents="125 31008 24003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31014">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(31008(a,1),29270(a,2,1))].">
      <j1 rule="para" parents="31008 29270"/>
    </justification>
  </clause>

  <clause id="31015">
    <literal><![CDATA[
      a(x,y,z) * (1 / y) = a(x,y,z) / y
    ]]></literal>
    <justification jstring="[hyper(23794,a,31009,a)].">
      <j1 rule="hyper" parents="23794 31009"/>
    </justification>
  </clause>

  <clause id="31016">
    <literal><![CDATA[
      (1 / x) \ (a(y,x,z) / x) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x,z) = u
    ]]></literal>
    <justification jstring="[para(31009(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31009 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31017">
    <literal><![CDATA[
      ((1 / x) * a(y,1 / x,a(z,x,u))) \ (a(z,x,u) / x) = L(a(z,x,u),1 / x,y)
    ]]></literal>
    <justification jstring="[para(31009(a,1),29945(a,2,2)),flip(a)].">
      <j1 rule="para" parents="31009 29945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31019">
    <literal><![CDATA[
      ((a(x,y,z) \ (1 / y)) * (y * a(x,y,z))) \ (a(x,y,z) \ (1 / y)) = 1 / ((1 / y) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31012(a,1),2937(a,1,1,2))].">
      <j1 rule="para" parents="31012 2937"/>
    </justification>
  </clause>

  <clause id="31020">
    <literal><![CDATA[
      L(x,y,z \ a(u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * a(u,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(31013(a,1),25241(a,1,3))].">
      <j1 rule="para" parents="31013 25241"/>
    </justification>
  </clause>

  <clause id="31021">
    <literal><![CDATA[
      T(L(x \ a(a(y,z,u),x,w),w,a(y,z,u)) \ 1,x \ (x \ v5)) = T(L(1 / x,a(y,z,u),w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(31013(a,1),29443(a,1,1,1,1))].">
      <j1 rule="para" parents="31013 29443"/>
    </justification>
  </clause>

  <clause id="31022">
    <literal><![CDATA[
      L(x,R(y,y,z),(y \ z) / z) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(28420(a,1),31007(a,1,2))].">
      <j1 rule="para" parents="28420 31007"/>
    </justification>
  </clause>

  <clause id="31023">
    <literal><![CDATA[
      L(x,R(y,y,z),z \ (y \ z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(24038,a,31022,a)].">
      <j1 rule="hyper" parents="24038 31022"/>
    </justification>
  </clause>

  <clause id="31024">
    <literal><![CDATA[
      L(x,L(y,y,z),z \ (y \ z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(27479,a,31023,a)].">
      <j1 rule="hyper" parents="27479 31023"/>
    </justification>
  </clause>

  <clause id="31025">
    <literal><![CDATA[
      L(((x \ (x / y)) \ 1) \ z,y,y) = 1 \ ((x \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,30001,a(flip),b,31024,a),flip(a)].">
      <j1 rule="hyper" parents="60 30001 31024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31027">
    <literal><![CDATA[
      L(x \ (((y \ (y / x)) \ 1) \ z),x,x) = 1 \ ((y \ (y / x)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(30361(a,1),31025(a,1,1))].">
      <j1 rule="para" parents="30361 31025"/>
    </justification>
  </clause>

  <clause id="31028">
    <literal><![CDATA[
      L(((1 / (x / a(y,x,z))) * x) \ a(y,x,z),a(y,x,z),x) = a(x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(29617(a,1),30993(a,1,1,1))].">
      <j1 rule="para" parents="29617 30993"/>
    </justification>
  </clause>

  <clause id="31029">
    <literal><![CDATA[
      L((x * ((a(y,x,z) \ x) \ 1)) \ a(y,x,z),a(y,x,z),x) = a(x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(29321(a,1),31028(a,1,1,1))].">
      <j1 rule="para" parents="29321 31028"/>
    </justification>
  </clause>

  <clause id="31030">
    <literal><![CDATA[
      ((1 / x) * a(y,x,a(z,x,u))) \ (a(z,x,u) / x) = L(a(z,x,u),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3041(a,1),31017(a,1,1,2))].">
      <j1 rule="para" parents="3041 31017"/>
    </justification>
  </clause>

  <clause id="31031">
    <literal><![CDATA[
      (a(x,y,a(z,y,u)) / y) \ (a(z,y,u) / y) = L(a(z,y,u),1 / y,x)
    ]]></literal>
    <justification jstring="[para(31009(a,1),31030(a,1,1))].">
      <j1 rule="para" parents="31009 31030"/>
    </justification>
  </clause>

  <clause id="31032">
    <literal><![CDATA[
      (a(x,y,a(z,y,u)) / y) \ (a(z,y,u) / y) = L(a(z,y,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3388,a(flip),b,31031,a),flip(a)].">
      <j1 rule="hyper" parents="370 3388 31031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31033">
    <literal><![CDATA[
      R(x,y,L(L(z,u,w) * u,u,u)) = R(x,y,(a(w,u,z) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(30986(a,1),31005(a,1,3))].">
      <j1 rule="para" parents="30986 31005"/>
    </justification>
  </clause>

  <clause id="31034">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) \ u) \ w) = R(x,y,u \ L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,31003,a(flip),b,31033,a),flip(a)].">
      <j1 rule="hyper" parents="60 31003 31033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31036">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) \ (x * w) = (w * x) / (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(30618(a,1),30837(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30618 30837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31037">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ y) = (a(z,u,w) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(30626(a,1),31036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30626 31036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31038">
    <literal><![CDATA[
      (x * (x \ y)) / (a(z,u,w) \ (x \ y)) = (a(z,u,w) \ (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,30829,a(flip),b,31037,a),flip(a)].">
      <j1 rule="hyper" parents="370 30829 31037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31039">
    <literal><![CDATA[
      x / (a(y,z,u) \ (w \ x)) = (a(y,z,u) \ (x / w)) \ x
    ]]></literal>
    <justification jstring="[hyper(382,a,31038,a)].">
      <j1 rule="hyper" parents="382 31038"/>
    </justification>
  </clause>

  <clause id="31041">
    <literal><![CDATA[
      ((a(x,y,z) \ (1 / u)) \ 1) \ K(w,v5) = (a(x,y,z) \ (u \ 1)) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(31039(a,1),15134(a,1,1))].">
      <j1 rule="para" parents="31039 15134"/>
    </justification>
  </clause>

  <clause id="31042">
    <literal><![CDATA[
      ((a(x,y,z) \ (1 / u)) \ 1) \ K(w,v5) = a(x,y,z) \ (u \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,25037,a(flip),b,31041,a),flip(a)].">
      <j1 rule="hyper" parents="370 25037 31041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31043">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ (L(a(x,y,z),z,y) \ u) = (L(z,y,x) \ z) \ (a(y,z,a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(29953(a,1),30850(a,2,1))].">
      <j1 rule="para" parents="29953 30850"/>
    </justification>
  </clause>

  <clause id="31044">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ (L(a(x,y,z),z,y) \ u) = (L(z,y,x) \ z) \ (a(y,z,a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(30668(a,1),31043(a,2,2))].">
      <j1 rule="para" parents="30668 31043"/>
    </justification>
  </clause>

  <clause id="31045">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ (L(a(x,y,z),z,y) \ u) = (z \ L(z,y,x)) * (a(y,z,a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30574,a(flip),b,31044,a),flip(a)].">
      <j1 rule="hyper" parents="370 30574 31044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31046">
    <literal><![CDATA[
      ((a(x,y,z) * (1 / y)) * (a(x,y,z) \ y)) \ (a(x,y,z) \ (1 / y)) = 1 / ((1 / y) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30881(a,1),31019(a,1,1))].">
      <j1 rule="para" parents="30881 31019"/>
    </justification>
  </clause>

  <clause id="31047">
    <literal><![CDATA[
      ((a(x,y,z) / y) * (a(x,y,z) \ y)) \ (a(x,y,z) \ (1 / y)) = 1 / ((1 / y) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31015(a,1),31046(a,1,1,1))].">
      <j1 rule="para" parents="31015 31046"/>
    </justification>
  </clause>

  <clause id="31048">
    <literal><![CDATA[
      R(x * K(y,a(z,u,w) \ 1),y,a(z,u,w) \ 1) = (a(z,u,w) \ (x * y)) / (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(30626(a,1),30697(a,2,1))].">
      <j1 rule="para" parents="30626 30697"/>
    </justification>
  </clause>

  <clause id="31049">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / (a(x,y,z) \ w) = R(u * 1,w,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23823(a,1),31048(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23823 31048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31050">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / (a(x,y,z) \ w) = R(u,w,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3(a,1),31049(a,2,1))].">
      <j1 rule="para" parents="3 31049"/>
    </justification>
  </clause>

  <clause id="31052">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / (a(x,y,z) \ w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,2711,a(flip),b,31050,a),flip(a)].">
      <j1 rule="hyper" parents="370 2711 31050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31053">
    <literal><![CDATA[
      (a(x,y,z) \ (u * w)) / (a(x,y,z) \ w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,28339,a(flip),b,31052,a),flip(a)].">
      <j1 rule="hyper" parents="370 28339 31052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31054">
    <literal><![CDATA[
      (a(x,y,z) \ (u * T(w * a(x,y,z),w))) / R(w,a(x,y,z),w) = L(u,T(w * a(x,y,z),w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(5536(a,1),31053(a,1,2))].">
      <j1 rule="para" parents="5536 31053"/>
    </justification>
  </clause>

  <clause id="31055">
    <literal><![CDATA[
      (L(x,y,z) \ (x * L(x \ L(x,y,z),u,w))) \ v5 = ((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w)) * v5
    ]]></literal>
    <justification jstring="[para(29130(a,1),30607(a,1,1,2))].">
      <j1 rule="para" parents="29130 30607"/>
    </justification>
  </clause>

  <clause id="31056">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),v5,v6) \ L(a(x,y,z) \ 1,u,w) = a(v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(26949,a,30776,a),flip(a)].">
      <j1 rule="hyper" parents="26949 30776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31057">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) \ (a(x,y,z) \ 1),v5,v6) = a(w,u,L(a(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(29154,a,31056,a)].">
      <j1 rule="hyper" parents="29154 31056"/>
    </justification>
  </clause>

  <clause id="31058">
    <literal><![CDATA[
      L(1 \ (L(a(x,y,z) / 1,u,w) \ a(x,y,z)),v5,v6) = a(w,u,L(a(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(29808(a,1),31057(a,1,1))].">
      <j1 rule="para" parents="29808 31057"/>
    </justification>
  </clause>

  <clause id="31059">
    <literal><![CDATA[
      L(1 \ (L(a(x,y,z),u,w) \ a(x,y,z)),v5,v6) = a(w,u,L(a(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(72(a,1),31058(a,1,1,2,1,1))].">
      <j1 rule="para" parents="72 31058"/>
    </justification>
  </clause>

  <clause id="31060">
    <literal><![CDATA[
      L(1 \ a(x,y,a(z,u,w)),v5,v6) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(30703(a,1),31059(a,1,1,2))].">
      <j1 rule="para" parents="30703 31059"/>
    </justification>
  </clause>

  <clause id="31061">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(62(a,1),31060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="62 31060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31062">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) \ v7 = L(a(x,y,a(z,u,w)),v5,v6) * v7
    ]]></literal>
    <justification jstring="[para(31061(a,2),30745(a,1,1))].">
      <j1 rule="para" parents="31061 30745"/>
    </justification>
  </clause>

  <clause id="31063">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) \ v7 = a(x,y,L(a(z,u,w),v5,v6)) * v7
    ]]></literal>
    <justification jstring="[para(31061(a,2),31062(a,2,1))].">
      <j1 rule="para" parents="31061 31062"/>
    </justification>
  </clause>

  <clause id="31064">
    <literal><![CDATA[
      a((x * T(a(y,z,u) * K(w,w \ v5),v5)) \ v6,v7,v8) = a(K(w \ v5,w) * ((a(y,z,u) \ x) \ v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(30683(a,1),30830(a,2,1))].">
      <j1 rule="para" parents="30683 30830"/>
    </justification>
  </clause>

  <clause id="31065">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,v6) \ v7))) = a(x,y,z * (u * (v7 * a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(195(a,1),30882(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="195 30882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31067">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) \ v5 = ((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w)) * v5
    ]]></literal>
    <justification jstring="[para(2160(a,1),31055(a,1,1))].">
      <j1 rule="para" parents="2160 31055"/>
    </justification>
  </clause>

  <clause id="31068">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w)) * v5 = a(w,u,x * L(x,y,z)) \ v5
    ]]></literal>
    <justification jstring="[para(30896(a,1),31067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30896 31067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31069">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10193,a,31068,a(flip))].">
      <j1 rule="hyper" parents="10193 31068"/>
    </justification>
  </clause>

  <clause id="31070">
    <literal><![CDATA[
      (x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w))) * v5 = a(w,u,x * L(x,y,z)) \ v5
    ]]></literal>
    <justification jstring="[para(3823(a,1),31068(a,1,1))].">
      <j1 rule="para" parents="3823 31068"/>
    </justification>
  </clause>

  <clause id="31071">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,10424,a,b,31069,a)].">
      <j1 rule="hyper" parents="60 10424 31069"/>
    </justification>
  </clause>

  <clause id="31072">
    <literal><![CDATA[
      x \ (y \ ((y * x) * (L(z,u,w) \ z))) = (L(z,u,w) \ z) * a(y,x,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,31071,a(flip),b,29968,a),flip(a)].">
      <j1 rule="hyper" parents="129 31071 29968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31073">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = L(a(x,y,y * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(31071(a,1),30507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31071 30507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31074">
    <literal><![CDATA[
      a(x,x * L(x,y,z),L(u,w,v5)) = a(u,x,L(x * L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,30494,a,b,31073,a)].">
      <j1 rule="hyper" parents="370 30494 31073"/>
    </justification>
  </clause>

  <clause id="31075">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,v5)) = a(u,z,a(y,y,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,30847,a(flip),b,31074,a),flip(a)].">
      <j1 rule="hyper" parents="60 30847 31074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31076">
    <literal><![CDATA[
      (x \ (x * a(y,z,x * L(x,u,w)))) * v5 = a(y,z,x * L(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(30900(a,1),31070(a,1,1,2))].">
      <j1 rule="para" parents="30900 31070"/>
    </justification>
  </clause>

  <clause id="31077">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ v5 = a(x,y,z * L(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(4(a,1),31076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 31076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31079">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (R(z,u,w) \ z) = L(R(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,30909,a(flip),b,31077,a),flip(a)].">
      <j1 rule="hyper" parents="60 30909 31077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31082">
    <literal><![CDATA[
      R(x,y,z) \ (x * L(x \ R(x,y,z),u,w)) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,4046,a,b,31079,a)].">
      <j1 rule="hyper" parents="32 4046 31079"/>
    </justification>
  </clause>

  <clause id="31083">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * (R(y,x,z) \ y) = L(R(y,x,z) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(30275(a,1),31079(a,1,1))].">
      <j1 rule="para" parents="30275 31079"/>
    </justification>
  </clause>

  <clause id="31084">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30938,a(flip),b,31083,a),flip(a)].">
      <j1 rule="hyper" parents="60 30938 31083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31085">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(29295,a,31084,a),flip(a)].">
      <j1 rule="hyper" parents="29295 31084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31087">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,656,a(flip),b,31085,a)].">
      <j1 rule="hyper" parents="370 656 31085"/>
    </justification>
  </clause>

  <clause id="31088">
    <literal><![CDATA[
      a(x,y,z) = (y * x) \ (y * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,94,a(flip),b,31085,a),flip(a)].">
      <j1 rule="hyper" parents="370 94 31085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31089">
    <literal><![CDATA[
      (x * y) * a(y,x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,31085,a,b,94,a(flip))].">
      <j1 rule="hyper" parents="129 31085 94"/>
    </justification>
  </clause>

  <clause id="31090">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29267,a,31085,a(flip))].">
      <j1 rule="hyper" parents="29267 31085"/>
    </justification>
  </clause>

  <clause id="31091">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(31085(a,2),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31085 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31092">
    <literal><![CDATA[
      L(x,y,z) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(31085(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="31085 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31093">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,y,u))) = L(a(z,y,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(31085(a,2),671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31085 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31094">
    <literal><![CDATA[
      L(x,L(y * R(y,z,u),y,z),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31085(a,2),4055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31085 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31095">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,y) * ((x \ R(x,y,z)) \ a(x,y,z)) = L(L(x \ R(x,y,z),u,y),x,y)
    ]]></literal>
    <justification jstring="[para(31085(a,2),29015(a,1,2,2))].">
      <j1 rule="para" parents="31085 29015"/>
    </justification>
  </clause>

  <clause id="31096">
    <literal><![CDATA[
      L(x \ R(x,y,a(z,u,w)),x,y) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(31085(a,1),30757(a,1,1))].">
      <j1 rule="para" parents="31085 30757"/>
    </justification>
  </clause>

  <clause id="31097">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * L(a(z,u,w),z,u)) = a(x,y,a(z,u,w) \ (z \ R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(31090(a,1),3861(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="31090 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31098">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,y,z) \ x) = a(y,x,a(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(31090(a,1),30710(a,1,1))].">
      <j1 rule="para" parents="31090 30710"/>
    </justification>
  </clause>

  <clause id="31099">
    <literal><![CDATA[
      (x / y) * R(y,x,z) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,31088,a,b,27869,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 31088 27869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31100">
    <literal><![CDATA[
      (x * y) * a(y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(y,x,z) = u
    ]]></literal>
    <justification jstring="[para(31088(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31088 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31101">
    <literal><![CDATA[
      (x * y) \ (x * R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x,z) = u
    ]]></literal>
    <justification jstring="[para(31089(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31089 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31103">
    <literal><![CDATA[
      R(x,y,z) * (x \ y) = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,24076,a,b,31099,a)].">
      <j1 rule="hyper" parents="60 24076 31099"/>
    </justification>
  </clause>

  <clause id="31104">
    <literal><![CDATA[
      a(L(x,y,z) * (x \ y),u,w) = a(y * a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(31103(a,1),27312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31103 27312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31105">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) * R((x \ y) \ (x \ 1),x \ y,z)) = a(x * (y \ x),x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26758,a(flip),b,31087,a),flip(a)].">
      <j1 rule="hyper" parents="370 26758 31087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31106">
    <literal><![CDATA[
      a(a(x,y,z) \ y,u,w) = a(y * a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(30710(a,1),31104(a,1,1))].">
      <j1 rule="para" parents="30710 31104"/>
    </justification>
  </clause>

  <clause id="31108">
    <literal><![CDATA[
      L(x,a(x,y,z),y * z) = a(y,x,a(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,30125,a(flip),b,31098,a)].">
      <j1 rule="hyper" parents="60 30125 31098"/>
    </justification>
  </clause>

  <clause id="31109">
    <literal><![CDATA[
      L(x,a(x,y,z),y * z) = L(x,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,29206,a(flip),b,31108,a),flip(a)].">
      <j1 rule="hyper" parents="370 29206 31108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31110">
    <literal><![CDATA[
      L(x,a(x,y,z),y) \ R(x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31109(a,1),30126(a,1,1))].">
      <j1 rule="para" parents="31109 30126"/>
    </justification>
  </clause>

  <clause id="31111">
    <literal><![CDATA[
      L(a(x,y,z),y * x,z) = a(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25843,a(flip),b,31093,a),flip(a)].">
      <j1 rule="hyper" parents="60 25843 31093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31112">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14789,a,31111,a)].">
      <j1 rule="hyper" parents="14789 31111"/>
    </justification>
  </clause>

  <clause id="31115">
    <literal><![CDATA[
      a(R(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27318,a,b,31112,a)].">
      <j1 rule="hyper" parents="60 27318 31112"/>
    </justification>
  </clause>

  <clause id="31116">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (x * z) = L(z,x,L(y,x,z))
    ]]></literal>
    <justification jstring="[para(31112(a,1),29945(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31112 29945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31117">
    <literal><![CDATA[
      L(x,y,L(z,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29945,a,b,31116,a),flip(a)].">
      <j1 rule="hyper" parents="60 29945 31116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31118">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(344(a,1),31117(a,1,3))].">
      <j1 rule="para" parents="344 31117"/>
    </justification>
  </clause>

  <clause id="31119">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(28339(a,1),31096(a,1,1,1,2))].">
      <j1 rule="para" parents="28339 31096"/>
    </justification>
  </clause>

  <clause id="31120">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(x,y,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29983(a,1),31119(a,1,1))].">
      <j1 rule="para" parents="29983 31119"/>
    </justification>
  </clause>

  <clause id="31121">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23999,a,31120,a)].">
      <j1 rule="hyper" parents="23999 31120"/>
    </justification>
  </clause>

  <clause id="31122">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23794,a,31120,a)].">
      <j1 rule="hyper" parents="23794 31120"/>
    </justification>
  </clause>

  <clause id="31123">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,30757,a,b,31120,a),flip(a)].">
      <j1 rule="hyper" parents="32 30757 31120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31124">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(30797,a,31123,a)].">
      <j1 rule="hyper" parents="30797 31123"/>
    </justification>
  </clause>

  <clause id="31125">
    <literal><![CDATA[
      x * a(a(y,z,u),w,v5) = x * a(v5,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,31123,a,b,4,a)].">
      <j1 rule="hyper" parents="129 31123 4"/>
    </justification>
  </clause>

  <clause id="31126">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29330,a,b,31123,a)].">
      <j1 rule="hyper" parents="60 29330 31123"/>
    </justification>
  </clause>

  <clause id="31127">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,31123,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 31123 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31130">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,a(y,z,u),x) = w
    ]]></literal>
    <justification jstring="[para(31123(a,1),28936(a,1))].">
      <j1 rule="para" parents="31123 28936"/>
    </justification>
  </clause>

  <clause id="31132">
    <literal><![CDATA[
      a(x,y,z) \ a(a(x,y,z),u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(31123(a,2),30760(a,1,2))].">
      <j1 rule="para" parents="31123 30760"/>
    </justification>
  </clause>

  <clause id="31133">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(w,u,z),y,x) = v5
    ]]></literal>
    <justification jstring="[para(31123(a,1),30797(a,1))].">
      <j1 rule="para" parents="31123 30797"/>
    </justification>
  </clause>

  <clause id="31134">
    <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="[para(31123(a,2),30921(a,1,2,2))].">
      <j1 rule="para" parents="31123 30921"/>
    </justification>
  </clause>

  <clause id="31135">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,31124,a,b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 31124 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31136">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,31123,a(flip),b,31124,a)].">
      <j1 rule="hyper" parents="60 31123 31124"/>
    </justification>
  </clause>

  <clause id="31137">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(z,u,w),y,x) = v5
    ]]></literal>
    <justification jstring="[para(31124(a,1),30797(a,1))].">
      <j1 rule="para" parents="31124 30797"/>
    </justification>
  </clause>

  <clause id="31138">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = L(a(a(w,u,z),y,x),v5,v6)
    ]]></literal>
    <justification jstring="[para(31124(a,2),31061(a,2,1))].">
      <j1 rule="para" parents="31124 31061"/>
    </justification>
  </clause>

  <clause id="31139">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = L(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(31124(a,1),31120(a,1,1))].">
      <j1 rule="para" parents="31124 31120"/>
    </justification>
  </clause>

  <clause id="31140">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(2973,a,31136,a),flip(a)].">
      <j1 rule="hyper" parents="2973 31136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31141">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,31136,a,b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 31136 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31143">
    <literal><![CDATA[
      (1 / x) \ a(y,y,a(z,u,w)) = (y / x) \ R(y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(31136(a,1),29770(a,1,2))].">
      <j1 rule="para" parents="31136 29770"/>
    </justification>
  </clause>

  <clause id="31144">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(z,y,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(31136(a,1),30858(a,1,2))].">
      <j1 rule="para" parents="31136 30858"/>
    </justification>
  </clause>

  <clause id="31145">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,31126,a(flip),b,30620,a),flip(a)].">
      <j1 rule="hyper" parents="129 31126 30620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31146">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(31126(a,1),30621(a,1,1))].">
      <j1 rule="para" parents="31126 30621"/>
    </justification>
  </clause>

  <clause id="31147">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(u,w,v5),z,y) \ x = v6
    ]]></literal>
    <justification jstring="[para(31126(a,1),30653(a,1,2))].">
      <j1 rule="para" parents="31126 30653"/>
    </justification>
  </clause>

  <clause id="31148">
    <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(31140(a,1),2973(a,1))].">
      <j1 rule="para" parents="31140 2973"/>
    </justification>
  </clause>

  <clause id="31149">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(a(z,u,a(v6,v5,w)),y,x) = v7
    ]]></literal>
    <justification jstring="[para(31124(a,1),31133(a,1,3))].">
      <j1 rule="para" parents="31124 31133"/>
    </justification>
  </clause>

  <clause id="31150">
    <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(26440(a,1),31148(a,1,3))].">
      <j1 rule="para" parents="26440 31148"/>
    </justification>
  </clause>

  <clause id="31151">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(31124(a,2),31148(a,1))].">
      <j1 rule="para" parents="31124 31148"/>
    </justification>
  </clause>

  <clause id="31152">
    <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(31127(a,1),23637(a,1))].">
      <j1 rule="para" parents="31127 23637"/>
    </justification>
  </clause>

  <clause id="31153">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(w,u,z),y,x) * v5 = v6
    ]]></literal>
    <justification jstring="[para(31135(a,2),23794(a,1))].">
      <j1 rule="para" parents="31135 23794"/>
    </justification>
  </clause>

  <clause id="31154">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(x,y,a(w,u,z))) = v5
    ]]></literal>
    <justification jstring="[hyper(30741,a,31141,a)].">
      <j1 rule="hyper" parents="30741 31141"/>
    </justification>
  </clause>

  <clause id="31155">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * a(u,u,L(z,y,x)) = a(u,u,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30759,a(flip),b,31141,a),flip(a)].">
      <j1 rule="hyper" parents="370 30759 31141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31156">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * a(u,u,L(z,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,u,z) = w
    ]]></literal>
    <justification jstring="[para(31141(a,2),30767(a,1))].">
      <j1 rule="para" parents="31141 30767"/>
    </justification>
  </clause>

  <clause id="31157">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v6 * a(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(31154(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="31154 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31158">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * a(y,x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31090,a(flip),b,31139,a),flip(a)].">
      <j1 rule="hyper" parents="370 31090 31139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31159">
    <literal><![CDATA[
      L(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(31139(a,1),23637(a,1))].">
      <j1 rule="para" parents="31139 23637"/>
    </justification>
  </clause>

  <clause id="31160">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) * a(z,y,x) = z \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(30849(a,2),31158(a,1,1))].">
      <j1 rule="para" parents="30849 31158"/>
    </justification>
  </clause>

  <clause id="31161">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(z,y,a(x,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31160(a,1),30707(a,1,1))].">
      <j1 rule="para" parents="31160 30707"/>
    </justification>
  </clause>

  <clause id="31162">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ R(L(x \ 1,y,z),u,w)) * a(w,u,a(L(x \ 1,y,z),L(x \ 1,y,z),u))) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(4019,a,31161,a)].">
      <j1 rule="hyper" parents="4019 31161"/>
    </justification>
  </clause>

  <clause id="31163">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),y,y)) = a(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,31008,a(flip),b,31138,a),flip(a)].">
      <j1 rule="hyper" parents="370 31008 31138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31164">
    <literal><![CDATA[
      (1 / x) \ a(y,y,a(z,u,w)) = (y / x) \ L(y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(28339(a,1),31143(a,2,2))].">
      <j1 rule="para" parents="28339 31143"/>
    </justification>
  </clause>

  <clause id="31165">
    <literal><![CDATA[
      (1 / x) \ y != (z / x) \ L(z,z,a(u,w,v5))
    ]]></literal>
    <literal><![CDATA[
      a(z,z,a(v5,w,u)) = y
    ]]></literal>
    <justification jstring="[para(31164(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="31164 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31166">
    <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(28712,a,31134,a)].">
      <j1 rule="hyper" parents="28712 31134"/>
    </justification>
  </clause>

  <clause id="31167">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * L(a(z,u,w),z,u)) = a(x,y,z \ (a(z,u,w) \ R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(30519(a,1),31097(a,2,3))].">
      <j1 rule="para" parents="30519 31097"/>
    </justification>
  </clause>

  <clause id="31168">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * L(a(z,u,w),z,u)) = a(x,y,z \ L(z,a(z,u,w),u * w))
    ]]></literal>
    <justification jstring="[para(30124(a,2),31167(a,2,3,2))].">
      <j1 rule="para" parents="30124 31167"/>
    </justification>
  </clause>

  <clause id="31169">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * L(a(z,u,w),z,u)) = a(x,y,a(z,a(z,u,w),u * w))
    ]]></literal>
    <justification jstring="[para(29200(a,1),31168(a,2,3))].">
      <j1 rule="para" parents="29200 31168"/>
    </justification>
  </clause>

  <clause id="31170">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * L(a(z,u,w),z,u)) = a(x,y,a(u,z,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(30935(a,1),31169(a,2,3))].">
      <j1 rule="para" parents="30935 31169"/>
    </justification>
  </clause>

  <clause id="31171">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (z \ R(z,u,w))) = a(x,y,a(u,z,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(31090(a,1),31170(a,1,3,2))].">
      <j1 rule="para" parents="31090 31170"/>
    </justification>
  </clause>

  <clause id="31172">
    <literal><![CDATA[
      a(x * y,z,a(u,u,z \ R(z,y,x))) = a(u,u,a(y,z,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,30887,a,b,31171,a)].">
      <j1 rule="hyper" parents="60 30887 31171"/>
    </justification>
  </clause>

  <clause id="31173">
    <literal><![CDATA[
      a(x * y,z,a(u,u,z * L(z,y,x))) = a(u,u,a(y,z,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(28674(a,1),31172(a,1,3))].">
      <j1 rule="para" parents="28674 31172"/>
    </justification>
  </clause>

  <clause id="31174">
    <literal><![CDATA[
      a(x * y,z,a(x,y,a(u,u,z))) = a(u,u,a(y,z,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30766(a,1),31173(a,1,3))].">
      <j1 rule="para" parents="30766 31173"/>
    </justification>
  </clause>

  <clause id="31175">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(u,w,x * L(x,y,z)) = L(x \ L(x,y,z),w,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30015,a(flip),b,31072,a),flip(a)].">
      <j1 rule="hyper" parents="60 30015 31072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31176">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,29124,a(flip),b,31175,a)].">
      <j1 rule="hyper" parents="125 29124 31175"/>
    </justification>
  </clause>

  <clause id="31177">
    <literal><![CDATA[
      L(L(a(x,y,z * L(z,u,w)),v5,v6),v5,v6) = (L(z,u,w) \ z) \ L(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29262,a,b,31176,a)].">
      <j1 rule="hyper" parents="370 29262 31176"/>
    </justification>
  </clause>

  <clause id="31178">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y * R(y \ 1,x \ y,z))) = a(x * (y \ x),x \ y,z)
    ]]></literal>
    <justification jstring="[para(2519(a,1),31105(a,1,2))].">
      <j1 rule="para" parents="2519 31105"/>
    </justification>
  </clause>

  <clause id="31179">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y \ R(y,x \ y,z))) = a(x * (y \ x),x \ y,z)
    ]]></literal>
    <justification jstring="[para(1987(a,1),31178(a,1,2,2))].">
      <j1 rule="para" parents="1987 31178"/>
    </justification>
  </clause>

  <clause id="31180">
    <literal><![CDATA[
      x \ ((1 / x) \ (y \ R(y,x \ y,z))) = a(x * (y \ x),x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(2105,a,31179,a)].">
      <j1 rule="hyper" parents="2105 31179"/>
    </justification>
  </clause>

  <clause id="31181">
    <literal><![CDATA[
      x \ ((y / x) \ R(y,x \ y,z)) = a(x * (y \ x),x \ y,z)
    ]]></literal>
    <justification jstring="[para(29769(a,1),31180(a,1,2))].">
      <j1 rule="para" parents="29769 31180"/>
    </justification>
  </clause>

  <clause id="31182">
    <literal><![CDATA[
      L(x \ R(x,y \ x,z),y,y) = a(y * (x \ y),y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29766,a(flip),b,31181,a)].">
      <j1 rule="hyper" parents="60 29766 31181"/>
    </justification>
  </clause>

  <clause id="31183">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,y) * ((R(x,y,z) \ x) * a(x,y,z)) = L(L(x \ R(x,y,z),u,y),x,y)
    ]]></literal>
    <justification jstring="[para(30619(a,1),31095(a,1,2))].">
      <j1 rule="para" parents="30619 31095"/>
    </justification>
  </clause>

  <clause id="31184">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,y) * a(y,x,a(z,y,x)) = L(L(x \ R(x,y,z),u,y),x,y)
    ]]></literal>
    <justification jstring="[para(30937(a,1),31183(a,1,2))].">
      <j1 rule="para" parents="30937 31183"/>
    </justification>
  </clause>

  <clause id="31185">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,y) * a(y,x,a(z,y,x)) = L(a(x,y,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,31091,a(flip),b,31184,a),flip(a)].">
      <j1 rule="hyper" parents="370 31091 31184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31186">
    <literal><![CDATA[
      L(a(x,y,z),(a(x,y,z) \ 1) * u,(a(x,y,z) \ 1) * u) \ w = w * ((1 / (a(x,y,z) * u)) * u)
    ]]></literal>
    <justification jstring="[para(30671(a,1),30780(a,2,2,1,2))].">
      <j1 rule="para" parents="30671 30780"/>
    </justification>
  </clause>

  <clause id="31187">
    <literal><![CDATA[
      L(a(x,y,z),(a(x,y,z) \ 1) * u,(a(x,y,z) \ 1) * u) \ w = w * (u * ((a(x,y,z) * u) \ 1))
    ]]></literal>
    <justification jstring="[para(28182(a,1),31186(a,2,2))].">
      <j1 rule="para" parents="28182 31186"/>
    </justification>
  </clause>

  <clause id="31188">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,(a(x,y,z) \ 1) * u) \ w = w * (u * ((a(x,y,z) * u) \ 1))
    ]]></literal>
    <justification jstring="[para(30630(a,1),31187(a,1,1,2))].">
      <j1 rule="para" parents="30630 31187"/>
    </justification>
  </clause>

  <clause id="31189">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,a(x,y,z) \ u) \ w = w * (u * ((a(x,y,z) * u) \ 1))
    ]]></literal>
    <justification jstring="[para(30630(a,1),31188(a,1,1,3))].">
      <j1 rule="para" parents="30630 31188"/>
    </justification>
  </clause>

  <clause id="31190">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ 1)) \ w = w * (x * ((a(y,z,u) * x) \ 1))
    ]]></literal>
    <justification jstring="[para(29311(a,1),31189(a,1,1))].">
      <j1 rule="para" parents="29311 31189"/>
    </justification>
  </clause>

  <clause id="31191">
    <literal><![CDATA[
      L(a(x,y,z) * (y * ((a(x,y,z) * y) \ 1)),a(x,y,z),y) = a(y,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31190(a,1),31029(a,1,1))].">
      <j1 rule="para" parents="31190 31029"/>
    </justification>
  </clause>

  <clause id="31192">
    <literal><![CDATA[
      L(a(a(x,y,z),y,a(x,y,z) * y) \ 1,a(x,y,z),y) = a(y,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14768(a,1),31191(a,1,1))].">
      <j1 rule="para" parents="14768 31191"/>
    </justification>
  </clause>

  <clause id="31193">
    <literal><![CDATA[
      L(a(a(x,y,z),y,a(x,y,z) * y),a(x,y,z),y) = a(y,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29330(a,1),31192(a,1,1))].">
      <j1 rule="para" parents="29330 31192"/>
    </justification>
  </clause>

  <clause id="31194">
    <literal><![CDATA[
      a(a(x,y,z),y,a(x,y,z) * y) = a(y,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(28782,a,31193,a),flip(a)].">
      <j1 rule="hyper" parents="28782 31193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31195">
    <literal><![CDATA[
      a(a(x,y,z),y,a(x,y,z) * y) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,31011,a(flip),b,31194,a),flip(a)].">
      <j1 rule="hyper" parents="370 31011 31194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31198">
    <literal><![CDATA[
      (a(x,y,z) * y) \ 1 = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(125,a,31195,a(flip),b,30301,a)].">
      <j1 rule="hyper" parents="125 31195 30301"/>
    </justification>
  </clause>

  <clause id="31199">
    <literal><![CDATA[
      L(x \ (a(a(y,z,u),x,w) \ 1),w,a(y,z,u)) = L(x,a(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[para(31198(a,1),30034(a,1,1))].">
      <j1 rule="para" parents="31198 30034"/>
    </justification>
  </clause>

  <clause id="31200">
    <literal><![CDATA[
      L(x \ a(a(y,z,u),x,w),w,a(y,z,u)) = L(x,a(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[para(29330(a,1),31199(a,1,1,2))].">
      <j1 rule="para" parents="29330 31199"/>
    </justification>
  </clause>

  <clause id="31201">
    <literal><![CDATA[
      T((L(x,a(y,z,u),w) \ 1) \ 1,x \ (x \ v5)) = T(L(1 / x,a(y,z,u),w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(31200(a,1),31021(a,1,1,1))].">
      <j1 rule="para" parents="31200 31021"/>
    </justification>
  </clause>

  <clause id="31202">
    <literal><![CDATA[
      T(L((x \ 1) \ 1,a(y,z,u),w),x \ (x \ v5)) = T(L(1 / x,a(y,z,u),w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(5066(a,2),31201(a,1,1))].">
      <j1 rule="para" parents="5066 31201"/>
    </justification>
  </clause>

  <clause id="31203">
    <literal><![CDATA[
      L(T((x \ 1) \ 1,x \ (x \ y)),a(z,u,w),v5) = T(L(1 / x,a(z,u,w),v5) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(25206,a,31202,a)].">
      <j1 rule="hyper" parents="25206 31202"/>
    </justification>
  </clause>

  <clause id="31204">
    <literal><![CDATA[
      T(L(1 / x,a(y,z,u),w) \ 1,v5) = L(T(x,x * (x \ v5)),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(15439(a,1),31203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15439 31203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31205">
    <literal><![CDATA[
      T(L(1 / x,a(y,z,u),w) \ 1,v5) = L(T(x,v5),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5(a,1),31204(a,2,1,2))].">
      <j1 rule="para" parents="5 31204"/>
    </justification>
  </clause>

  <clause id="31207">
    <literal><![CDATA[
      (a(x,y,z) \ (u * (w * a(x,y,z)))) / R(w,a(x,y,z),w) = L(u,T(w * a(x,y,z),w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(24120(a,1),31054(a,1,1,2,2))].">
      <j1 rule="para" parents="24120 31054"/>
    </justification>
  </clause>

  <clause id="31209">
    <literal><![CDATA[
      (a(x,y,z) * (u * (a(x,y,z) \ w))) / R(w,a(x,y,z),w) = L(u,T(w * a(x,y,z),w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30875(a,1),31207(a,1,1))].">
      <j1 rule="para" parents="30875 31207"/>
    </justification>
  </clause>

  <clause id="31211">
    <literal><![CDATA[
      (a(x,y,z) * (u * (a(x,y,z) \ w))) / w = L(u,T(w * a(x,y,z),w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15089(a,1),31209(a,1,2))].">
      <j1 rule="para" parents="15089 31209"/>
    </justification>
  </clause>

  <clause id="31213">
    <literal><![CDATA[
      L(x,T(y * a(z,u,w),y),a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,30879,a(flip),b,31211,a),flip(a)].">
      <j1 rule="hyper" parents="60 30879 31211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31214">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26171,a,31213,a)].">
      <j1 rule="hyper" parents="26171 31213"/>
    </justification>
  </clause>

  <clause id="31216">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * (R(y,z,u) \ (y * L(y \ R(y,z,u),w,v5))) = x * L(x \ ((R(y,z,u) \ y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(3823(a,1),30716(a,1,2))].">
      <j1 rule="para" parents="3823 30716"/>
    </justification>
  </clause>

  <clause id="31217">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(w,v5,y * L(y,z,u)) = x * L(x \ ((R(y,z,u) \ y) \ x),v5,w)
    ]]></literal>
    <justification jstring="[para(31082(a,1),31216(a,1,2))].">
      <j1 rule="para" parents="31082 31216"/>
    </justification>
  </clause>

  <clause id="31218">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(w,v5,y * L(y,z,u)) = x * L(x \ (x * (y \ R(y,z,u))),v5,w)
    ]]></literal>
    <justification jstring="[para(30715(a,1),31217(a,2,2,1,2))].">
      <j1 rule="para" parents="30715 31217"/>
    </justification>
  </clause>

  <clause id="31219">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(w,v5,y * L(y,z,u)) = x * L(y \ R(y,z,u),v5,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),31218(a,2,2,1))].">
      <j1 rule="para" parents="4 31218"/>
    </justification>
  </clause>

  <clause id="31220">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (z \ R(z,u,w)) = L(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,23643,a,b,31219,a),flip(a)].">
      <j1 rule="hyper" parents="32 23643 31219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31222">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = a(x,y,y * L(y,z,u)) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,94,a(flip),b,31220,a)].">
      <j1 rule="hyper" parents="370 94 31220"/>
    </justification>
  </clause>

  <clause id="31223">
    <literal><![CDATA[
      ((x \ y) * x) \ ((x \ y) * R(x,z,u)) = a(y,x,x * L(x,z,u)) * (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(30281(a,1),31222(a,2,1))].">
      <j1 rule="para" parents="30281 31222"/>
    </justification>
  </clause>

  <clause id="31224">
    <literal><![CDATA[
      ((x \ y) * x) \ ((x \ y) * R(x,z,u)) = L(x \ R(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,31220,a(flip),b,31223,a),flip(a)].">
      <j1 rule="hyper" parents="370 31220 31223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31225">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,x \ u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(822,a,31224,a)].">
      <j1 rule="hyper" parents="822 31224"/>
    </justification>
  </clause>

  <clause id="31226">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u * x) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(24975,a,31225,a),flip(a)].">
      <j1 rule="hyper" parents="24975 31225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31227">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u),x,z * y) = L(a(x,y,z),x,u * x)
    ]]></literal>
    <justification jstring="[para(31226(a,1),24922(a,1,1))].">
      <j1 rule="para" parents="31226 24922"/>
    </justification>
  </clause>

  <clause id="31228">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u * x),u * x,u) = L(x,u,u) \ L(x * (x \ R(x,y,z)),u,u)
    ]]></literal>
    <justification jstring="[para(31226(a,2),28032(a,2,1)),flip(a)].">
      <j1 rule="para" parents="31226 28032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31229">
    <literal><![CDATA[
      L(a(x,y,z),x,u * x) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,24922,a(flip),b,31227,a),flip(a)].">
      <j1 rule="hyper" parents="60 24922 31227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31230">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u) \ a(x,y,z),a(x,y,z),x) = a(u * x,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31229(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="31229 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31231">
    <literal><![CDATA[
      a(x * y,y,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(31230(a,1),30044(a,1))].">
      <j1 rule="para" parents="31230 30044"/>
    </justification>
  </clause>

  <clause id="31232">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u * x),u * x,u) = L(x,u,u) \ L(R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),31228(a,2,2,1))].">
      <j1 rule="para" parents="5 31228"/>
    </justification>
  </clause>

  <clause id="31233">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u * x),u * x,u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,7812,a(flip),b,31232,a),flip(a)].">
      <j1 rule="hyper" parents="370 7812 31232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31235">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u),u * x,u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(31226(a,1),31233(a,1,1))].">
      <j1 rule="para" parents="31226 31233"/>
    </justification>
  </clause>

  <clause id="31236">
    <literal><![CDATA[
      (a(x,y,z) \ a(a(x,y,z),a(x,y,z),L(u,z,y))) * u = ((z \ L(z,y,x)) * u) * (a(x,y,z) \ L(a(x,y,z),z,y))
    ]]></literal>
    <justification jstring="[para(30574(a,1),30566(a,2,1))].">
      <j1 rule="para" parents="30574 30566"/>
    </justification>
  </clause>

  <clause id="31237">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ ((v5 * (a(x,y,z) \ 1)) * a(w,u,a(x,y,z))) = a(v5,a(x,y,z),a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30778(a,1),30783(a,1,1))].">
      <j1 rule="para" parents="30778 30783"/>
    </justification>
  </clause>

  <clause id="31238">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ ((a(x,y,z) \ v5) * a(w,u,a(x,y,z))) = a(v5,a(x,y,z),a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30626(a,1),31237(a,1,2,1))].">
      <j1 rule="para" parents="30626 31237"/>
    </justification>
  </clause>

  <clause id="31239">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ (L(a(x,y,z),u,w) \ v5) = a(v5,a(x,y,z),a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(30922(a,1),31238(a,1,2))].">
      <j1 rule="para" parents="30922 31238"/>
    </justification>
  </clause>

  <clause id="31240">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(237,a,31239,a),flip(a)].">
      <j1 rule="hyper" parents="237 31239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31241">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,a(y,z,u))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(31239(a,1),237(a,1))].">
      <j1 rule="para" parents="31239 237"/>
    </justification>
  </clause>

  <clause id="31243">
    <literal><![CDATA[
      a(a(x,y,z),a(u,w,a(x,y,z)),v5) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30131,a,b,31240,a)].">
      <j1 rule="hyper" parents="60 30131 31240"/>
    </justification>
  </clause>

  <clause id="31244">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,a(x,y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30849,a(flip),b,31240,a)].">
      <j1 rule="hyper" parents="60 30849 31240"/>
    </justification>
  </clause>

  <clause id="31245">
    <literal><![CDATA[
      a(a(x,y,z),a(u,w,a(z,y,x)),v5) = 1
    ]]></literal>
    <justification jstring="[hyper(30797,a,31243,a)].">
      <j1 rule="hyper" parents="30797 31243"/>
    </justification>
  </clause>

  <clause id="31246">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,a(x,y,z),u)) = v5 \ v5
    ]]></literal>
    <justification jstring="[hyper(370,a,63,a,b,31244,a),flip(a)].">
      <j1 rule="hyper" parents="370 63 31244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31247">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,a(z,y,x)),v5) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[hyper(129,a,31245,a(flip),b,31121,a),flip(a)].">
      <j1 rule="hyper" parents="129 31245 31121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31248">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(30359,a,31246,a)].">
      <j1 rule="hyper" parents="30359 31246"/>
    </justification>
  </clause>

  <clause id="31249">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,v5,v6) = a(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(29154,a,31248,a)].">
      <j1 rule="hyper" parents="29154 31248"/>
    </justification>
  </clause>

  <clause id="31250">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,28948,a(flip),b,31248,a),flip(a)].">
      <j1 rule="hyper" parents="370 28948 31248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31251">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ w = L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,23619,a,b,31248,a)].">
      <j1 rule="hyper" parents="36 23619 31248"/>
    </justification>
  </clause>

  <clause id="31253">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) != w \ y
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,u,y),x) = w
    ]]></literal>
    <justification jstring="[para(31250(a,1),45(a,1))].">
      <j1 rule="para" parents="31250 45"/>
    </justification>
  </clause>

  <clause id="31254">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * x = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(30744,a,31251,a)].">
      <j1 rule="hyper" parents="30744 31251"/>
    </justification>
  </clause>

  <clause id="31255">
    <literal><![CDATA[
      x * a(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(30725,a,31251,a)].">
      <j1 rule="hyper" parents="30725 31251"/>
    </justification>
  </clause>

  <clause id="31257">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(125,a,31251,a(flip),b,30722,a(flip))].">
      <j1 rule="hyper" parents="125 31251 30722"/>
    </justification>
  </clause>

  <clause id="31258">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,a(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(31251(a,1),24094(a,1,1))].">
      <j1 rule="para" parents="31251 24094"/>
    </justification>
  </clause>

  <clause id="31259">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) \ u,a(x,y,z),w) * (a(a(x,y,z),u,w) \ u) = K(w,u * a(x,y,z)) * ((w * a(x,y,z)) \ (a(x,y,z) * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,29181,a,b,31254,a),flip(a)].">
      <j1 rule="hyper" parents="370 29181 31254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31261">
    <literal><![CDATA[
      (a(1 / x,a(y,z,u),w) * (1 / x)) \ 1 = x * (L(x,a(y,z,u),w) \ x)
    ]]></literal>
    <justification jstring="[para(31254(a,2),3864(a,1,1))].">
      <j1 rule="para" parents="31254 3864"/>
    </justification>
  </clause>

  <clause id="31262">
    <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(31254(a,1),23638(a,1,2))].">
      <j1 rule="para" parents="31254 23638"/>
    </justification>
  </clause>

  <clause id="31263">
    <literal><![CDATA[
      T((a(1 / x,a(y,z,u),w) * (1 / x)) \ 1,v5) = L(T(x,v5),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31254(a,2),31205(a,1,1,1))].">
      <j1 rule="para" parents="31254 31205"/>
    </justification>
  </clause>

  <clause id="31265">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,a(z,y,x)),v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,31247,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 31247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31266">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[para(31248(a,1),31249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31248 31249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31267">
    <literal><![CDATA[
      L(x,y,z) != a(u,a(w,v5,v6),L(v7,y,z))
    ]]></literal>
    <literal><![CDATA[
      a(u,a(w,v5,v6),v7) = x
    ]]></literal>
    <justification jstring="[para(31266(a,2),47(a,1)),flip(a)].">
      <j1 rule="para" parents="31266 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31268">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) * (1 / x)) \ 1 = x * (L(x,a(y,z,u),w) \ x)
    ]]></literal>
    <justification jstring="[para(2957(a,1),31261(a,1,1,1))].">
      <j1 rule="para" parents="2957 31261"/>
    </justification>
  </clause>

  <clause id="31269">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) / x) \ 1 = x * (L(x,a(y,z,u),w) \ x)
    ]]></literal>
    <justification jstring="[para(28721(a,1),31268(a,1,1))].">
      <j1 rule="para" parents="28721 31268"/>
    </justification>
  </clause>

  <clause id="31270">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) / x) \ 1 = x * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(31248(a,1),31269(a,2,2))].">
      <j1 rule="para" parents="31248 31269"/>
    </justification>
  </clause>

  <clause id="31271">
    <literal><![CDATA[
      T((a(x,a(y,z,u),w) * (1 / x)) \ 1,v5) = L(T(x,v5),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2957(a,1),31263(a,1,1,1,1))].">
      <j1 rule="para" parents="2957 31263"/>
    </justification>
  </clause>

  <clause id="31272">
    <literal><![CDATA[
      T((a(x,a(y,z,u),w) / x) \ 1,v5) = L(T(x,v5),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(28721(a,1),31271(a,1,1,1))].">
      <j1 rule="para" parents="28721 31271"/>
    </justification>
  </clause>

  <clause id="31273">
    <literal><![CDATA[
      T(x * a(y,a(z,u,w),x),v5) = L(T(x,v5),a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(31270(a,1),31272(a,1,1))].">
      <j1 rule="para" parents="31270 31272"/>
    </justification>
  </clause>

  <clause id="31274">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(162,a,31273,a),flip(a)].">
      <j1 rule="hyper" parents="162 31273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31275">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * w = L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(23794,a,31274,a)].">
      <j1 rule="hyper" parents="23794 31274"/>
    </justification>
  </clause>

  <clause id="31276">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(135,a,31274,a)].">
      <j1 rule="hyper" parents="135 31274"/>
    </justification>
  </clause>

  <clause id="31278">
    <literal><![CDATA[
      L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,a(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(31275(a,1),23637(a,1))].">
      <j1 rule="para" parents="31275 23637"/>
    </justification>
  </clause>

  <clause id="31279">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),a(u,w,v5),v6) = L(L(x,a(u,w,v5),v6) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31249,a,b,31276,a),flip(a)].">
      <j1 rule="hyper" parents="370 31249 31276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31280">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,29009,a(flip),b,31279,a),flip(a)].">
      <j1 rule="hyper" parents="35 29009 31279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31281">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (x \ a(y,z,u)) = a(y,z,u) * a(w,a(y,z,u),L(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(31280(a,1),29938(a,1,2,1))].">
      <j1 rule="para" parents="31280 29938"/>
    </justification>
  </clause>

  <clause id="31282">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(x,y,z),L(w,a(x,y,z),u)) = a(u,a(x,y,z),w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,30710,a(flip),b,31281,a),flip(a)].">
      <j1 rule="hyper" parents="60 30710 31281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31283">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(x,y,z),L(w,a(x,y,z),u)) = a(w,a(x,y,z),u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30724,a(flip),b,31282,a),flip(a)].">
      <j1 rule="hyper" parents="370 30724 31282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31284">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(y,z,u) = a(y,z,u) * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(29935(a,1),31283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29935 31283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31285">
    <literal><![CDATA[
      a(x,y,z) * ((u * a(x,y,z)) \ (((u * a(x,y,z)) / w) * R(w,a(x,y,z),u))) = a(x,y,z) * a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27871,a,b,31284,a)].">
      <j1 rule="hyper" parents="60 27871 31284"/>
    </justification>
  </clause>

  <clause id="31286">
    <literal><![CDATA[
      (a(x,y,z) \ a(a(x,y,z),a(x,y,z),L(u,z,y))) * u = ((z \ L(z,y,x)) * u) * a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29297(a,1),31236(a,2,2))].">
      <j1 rule="para" parents="29297 31236"/>
    </justification>
  </clause>

  <clause id="31287">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * a(y,x,a(z,y,x)) = (a(z,y,x) \ 1) * u
    ]]></literal>
    <justification jstring="[para(30624(a,1),31286(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30624 31286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31288">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * a(y,x,a(z,y,x)) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,30630,a(flip),b,31287,a),flip(a)].">
      <j1 rule="hyper" parents="370 30630 31287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31290">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,x,a(z,y,x)) * u) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(32,a,24136,a(flip),b,31288,a),flip(a)].">
      <j1 rule="hyper" parents="32 24136 31288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31291">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ (L(a(x,y,z),z,y) \ u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(60,a,31045,a,b,31290,a)].">
      <j1 rule="hyper" parents="60 31045 31290"/>
    </justification>
  </clause>

  <clause id="31292">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(x,x,a(y,y,z))) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(30856(a,1),31290(a,1,2))].">
      <j1 rule="para" parents="30856 31290"/>
    </justification>
  </clause>

  <clause id="31293">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(z,y,a(x,x,y))) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(30851(a,2),31292(a,1,2,2))].">
      <j1 rule="para" parents="30851 31292"/>
    </justification>
  </clause>

  <clause id="31294">
    <literal><![CDATA[
      a((x * L(x,y,z)) * (u * a(z,y,a(x,x,y))),w,v5) = a(a(z,y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(31293(a,1),3886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31293 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31295">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ ((L(z,y,x) \ z) \ u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(29953(a,1),31291(a,1,2,1))].">
      <j1 rule="para" parents="29953 31291"/>
    </justification>
  </clause>

  <clause id="31296">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ ((z \ L(z,y,x)) * u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(30574(a,1),31295(a,1,2))].">
      <j1 rule="para" parents="30574 31295"/>
    </justification>
  </clause>

  <clause id="31297">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) * ((z \ L(z,y,x)) * u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(30743,a,31296,a)].">
      <j1 rule="hyper" parents="30743 31296"/>
    </justification>
  </clause>

  <clause id="31298">
    <literal><![CDATA[
      a((x * L(x,y,z)) * (u * a(z,y,a(x,x,y))),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(z,y,x) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(31294(a,2),30632(a,1))].">
      <j1 rule="para" parents="31294 30632"/>
    </justification>
  </clause>

  <clause id="31299">
    <literal><![CDATA[
      (a(x,y,z) * u) * (L(L(z,y,x),y,x) * (z \ (u \ a(x,y,z)))) = a(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1
    ]]></literal>
    <justification jstring="[para(29441(a,1),30785(a,1,2))].">
      <j1 rule="para" parents="29441 30785"/>
    </justification>
  </clause>

  <clause id="31300">
    <literal><![CDATA[
      a((((a(x,y,a(z,u,w) \ v5) \ y) * x) * (v5 * a(z,u,w))) \ v6,v7,v8) = a((x * (y * (a(z,u,w) \ v5))) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,26871,a(flip),b,30831,a),flip(a)].">
      <j1 rule="hyper" parents="370 26871 30831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31302">
    <literal><![CDATA[
      a((((a(x,y,a(z,u,w) * v5) \ y) * x) * (v5 * a(z,u,w))) \ v6,v7,v8) = a((x * (y * (a(z,u,w) \ v5))) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(30634(a,1),31300(a,1,1,1,1,1,1))].">
      <j1 rule="para" parents="30634 31300"/>
    </justification>
  </clause>

  <clause id="31303">
    <literal><![CDATA[
      a((x * (y * (a(z,u,w) \ v5))) \ v6,v7,v8) = a((x * (y * (a(z,u,w) * v5))) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(29250,a,31302,a),flip(a)].">
      <j1 rule="hyper" parents="29250 31302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31304">
    <literal><![CDATA[
      a((a(x,y,z) \ (u * (a(w,v5,v6) \ v7))) \ v8,v9,v10) = a((a(x,y,z) * (u * (a(w,v5,v6) * v7))) \ v8,v9,v10)
    ]]></literal>
    <justification jstring="[hyper(60,a,30666,a,b,31303,a)].">
      <j1 rule="hyper" parents="60 30666 31303"/>
    </justification>
  </clause>

  <clause id="31305">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1 = (a(x,y,z) * u) * (u \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(30205(a,1),31299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30205 31299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31306">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1 = a(a(x,y,z),u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30301,a(flip),b,31305,a),flip(a)].">
      <j1 rule="hyper" parents="370 30301 31305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31307">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ a(x,y,z)) = a(a(x,y,z),u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30330,a(flip),b,31306,a)].">
      <j1 rule="hyper" parents="60 30330 31306"/>
    </justification>
  </clause>

  <clause id="31308">
    <literal><![CDATA[
      (a(x,y,z) / u) * (a(x,y,z) \ u) = a(a(x,y,z),u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(28330,a,31307,a)].">
      <j1 rule="hyper" parents="28330 31307"/>
    </justification>
  </clause>

  <clause id="31309">
    <literal><![CDATA[
      (a(x,y,z) / y) \ 1 = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(125,a,31195,a(flip),b,31308,a)].">
      <j1 rule="hyper" parents="125 31195 31308"/>
    </justification>
  </clause>

  <clause id="31310">
    <literal><![CDATA[
      a(a(x,y,z),y,a(x,y,z) * y) \ (a(x,y,z) \ (1 / y)) = 1 / ((1 / y) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31308(a,1),31047(a,1,1))].">
      <j1 rule="para" parents="31308 31047"/>
    </justification>
  </clause>

  <clause id="31311">
    <literal><![CDATA[
      (a(x,y,z) / y) * ((1 / (a(x,y,z) / y)) * u) = (a(x,y,z) \ y) * ((a(x,y,z) / y) * u)
    ]]></literal>
    <justification jstring="[para(31309(a,1),951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31309 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31312">
    <literal><![CDATA[
      L(K(a(x,y,z) / y,a(x,y,z) \ y) * u,a(x,y,z) / y,a(x,y,z) / y) = (a(x,y,z) / y) * ((1 / (a(x,y,z) / y)) * u)
    ]]></literal>
    <justification jstring="[para(31309(a,1),3569(a,1,1,1,2))].">
      <j1 rule="para" parents="31309 3569"/>
    </justification>
  </clause>

  <clause id="31313">
    <literal><![CDATA[
      1 / ((1 / x) \ a(y,x,z)) = 1 \ (a(y,x,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(31195(a,1),31310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31195 31310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31314">
    <literal><![CDATA[
      1 / ((1 / x) \ a(y,x,z)) = a(y,x,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(370,a,62,a(flip),b,31313,a),flip(a)].">
      <j1 rule="hyper" parents="370 62 31313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31316">
    <literal><![CDATA[
      1 / (x * a(y,x,z)) = a(y,x,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(31012(a,1),31314(a,1,2))].">
      <j1 rule="para" parents="31012 31314"/>
    </justification>
  </clause>

  <clause id="31317">
    <literal><![CDATA[
      ((x * a(y,x,z)) * u) \ ((a(y,x,z) \ (1 / x)) \ u) = a(x * a(y,x,z),x * a(y,x,z),u)
    ]]></literal>
    <justification jstring="[para(31316(a,1),28731(a,1,2,1))].">
      <j1 rule="para" parents="31316 28731"/>
    </justification>
  </clause>

  <clause id="31318">
    <literal><![CDATA[
      ((x * a(y,x,z)) * u) \ ((a(y,x,z) \ (1 / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,u) = w
    ]]></literal>
    <justification jstring="[para(31317(a,2),30995(a,1))].">
      <j1 rule="para" parents="31317 30995"/>
    </justification>
  </clause>

  <clause id="31319">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ (u \ K(w,v5)),a(x,y,z) * u) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(26273,a,30736,a)].">
      <j1 rule="hyper" parents="26273 30736"/>
    </justification>
  </clause>

  <clause id="31320">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) \ u,a(x,y,z) * u) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(26274,a,31319,a)].">
      <j1 rule="hyper" parents="26274 31319"/>
    </justification>
  </clause>

  <clause id="31321">
    <literal><![CDATA[
      L(a(x,y,z) \ (1 / u),a(x,y,z) * u,a(x,y,z) * u) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(30639,a,31320,a)].">
      <j1 rule="hyper" parents="30639 31320"/>
    </justification>
  </clause>

  <clause id="31322">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ (u \ (1 / u)) = (1 / (K(w,v5) / (a(x,y,z) \ (1 / u)))) * K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(29784,a,31321,a)].">
      <j1 rule="hyper" parents="29784 31321"/>
    </justification>
  </clause>

  <clause id="31323">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ (u \ (1 / u)) = (((a(x,y,z) \ (1 / u)) \ 1) \ K(w,v5)) * K(v5,w)
    ]]></literal>
    <justification jstring="[para(15622(a,1),31322(a,2,1))].">
      <j1 rule="para" parents="15622 31322"/>
    </justification>
  </clause>

  <clause id="31324">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ (u \ (1 / u)) = (a(x,y,z) \ (u \ K(w,v5))) * K(v5,w)
    ]]></literal>
    <justification jstring="[para(31042(a,1),31323(a,2,1))].">
      <j1 rule="para" parents="31042 31323"/>
    </justification>
  </clause>

  <clause id="31325">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ (u \ (1 / u)) = (u \ K(w,v5)) * (a(x,y,z) \ K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,30680,a(flip),b,31324,a),flip(a)].">
      <j1 rule="hyper" parents="370 30680 31324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31326">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ (u \ (1 / u)) = a(x,y,z) \ (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,30809,a(flip),b,31325,a),flip(a)].">
      <j1 rule="hyper" parents="370 30809 31325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31327">
    <literal><![CDATA[
      a(x,y * (y * L(y,z,u)),y) \ L(y * (L(y,z,u) \ y),z,u) = L(L(y * (L(y,z,u) \ y),z,u),y * (L(y,z,u) \ y),x)
    ]]></literal>
    <justification jstring="[para(27363(a,1),30873(a,1,1))].">
      <j1 rule="para" parents="27363 30873"/>
    </justification>
  </clause>

  <clause id="31328">
    <literal><![CDATA[
      a(x,L(L(y,y,y),z,u),y) \ L(y * (L(y,z,u) \ y),z,u) = L(L(y * (L(y,z,u) \ y),z,u),y * (L(y,z,u) \ y),x)
    ]]></literal>
    <justification jstring="[para(3047(a,1),31327(a,1,1))].">
      <j1 rule="para" parents="3047 31327"/>
    </justification>
  </clause>

  <clause id="31329">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),y,z),x * (L(x,y,z) \ x),u) = a(u,L(x,y,z),x) \ L(x * (L(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(15016(a,1),31328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15016 31328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31330">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),y,z),x * (L(x,y,z) \ x),u) = a(u,x,L(x,y,z)) \ L(x * (L(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),31329(a,2,1))].">
      <j1 rule="para" parents="2564 31329"/>
    </justification>
  </clause>

  <clause id="31332">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),y,z),x * (L(x,y,z) \ x),u) = a(u,x,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(30200(a,1),31330(a,2,2))].">
      <j1 rule="para" parents="30200 31330"/>
    </justification>
  </clause>

  <clause id="31333">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),y,z),x * (L(x,y,z) \ x),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30097,a(flip),b,31332,a),flip(a)].">
      <j1 rule="hyper" parents="370 30097 31332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31334">
    <literal><![CDATA[
      L(x,x * (L(x,y,z) \ x),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(30200(a,1),31333(a,1,1))].">
      <j1 rule="para" parents="30200 31333"/>
    </justification>
  </clause>

  <clause id="31335">
    <literal><![CDATA[
      L(x,x * (x * L(x,y,z)),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(26288,a,31334,a)].">
      <j1 rule="hyper" parents="26288 31334"/>
    </justification>
  </clause>

  <clause id="31336">
    <literal><![CDATA[
      L(x,L(x * (x * x),y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(3905(a,2),31335(a,1,2))].">
      <j1 rule="para" parents="3905 31335"/>
    </justification>
  </clause>

  <clause id="31337">
    <literal><![CDATA[
      L(x,L(L(x,x,x),y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,3983,a(flip),b,31336,a)].">
      <j1 rule="hyper" parents="60 3983 31336"/>
    </justification>
  </clause>

  <clause id="31338">
    <literal><![CDATA[
      L(x,L(x,y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14838,a,31337,a)].">
      <j1 rule="hyper" parents="14838 31337"/>
    </justification>
  </clause>

  <clause id="31339">
    <literal><![CDATA[
      R(L(x,x,L(y,z,u)),w,v5) = L(R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(31338(a,1),24(a,1,1))].">
      <j1 rule="para" parents="31338 24"/>
    </justification>
  </clause>

  <clause id="31340">
    <literal><![CDATA[
      L(x \ y,x \ y,L(z,x,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ y,x * y,z) = u
    ]]></literal>
    <justification jstring="[para(31338(a,1),4130(a,1))].">
      <j1 rule="para" parents="31338 4130"/>
    </justification>
  </clause>

  <clause id="31341">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(R(x,w,v5),L(x,z,u),y) = L(x \ R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(31338(a,1),7812(a,1,1))].">
      <j1 rule="para" parents="31338 7812"/>
    </justification>
  </clause>

  <clause id="31342">
    <literal><![CDATA[
      (x * (y * L(z,z,L(u,w,v5)))) / T(x * y,z) = L(L(z,y,x),L(z,w,v5),u)
    ]]></literal>
    <justification jstring="[para(31338(a,1),25837(a,1,1,2,2))].">
      <j1 rule="para" parents="31338 25837"/>
    </justification>
  </clause>

  <clause id="31343">
    <literal><![CDATA[
      L(x,x,L(y,x * z,x * z)) = L(x,(1 / (z / x)) * z,y)
    ]]></literal>
    <justification jstring="[para(29610(a,1),31338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29610 31338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31344">
    <literal><![CDATA[
      a(x,R(y,y,z),y) \ R(y,y,z) = L(y,y,L(x,y,z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(31338(a,1),30812(a,2,1))].">
      <j1 rule="para" parents="31338 30812"/>
    </justification>
  </clause>

  <clause id="31345">
    <literal><![CDATA[
      L(R(x,y,z),L(x,u,w),v5) = L(R(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,24,a(flip),b,31339,a),flip(a)].">
      <j1 rule="hyper" parents="60 24 31339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31346">
    <literal><![CDATA[
      L(x,x,L(y,x * z,x * z)) = L(x,(x \ z) * z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26268,a(flip),b,31343,a),flip(a)].">
      <j1 rule="hyper" parents="370 26268 31343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31347">
    <literal><![CDATA[
      L(x,x,L(y,z * x,z * x)) = L(x,(x \ z) * z,y)
    ]]></literal>
    <justification jstring="[para(26091(a,1),31346(a,1,3))].">
      <j1 rule="para" parents="26091 31346"/>
    </justification>
  </clause>

  <clause id="31348">
    <literal><![CDATA[
      L(x / y,x / y,L(z,u * (x / y),u * (y \ x))) = L(x / y,((x / y) \ u) * u,z)
    ]]></literal>
    <justification jstring="[para(25922(a,1),31347(a,1,3))].">
      <j1 rule="para" parents="25922 31347"/>
    </justification>
  </clause>

  <clause id="31349">
    <literal><![CDATA[
      a(x,L(y,y,z),y) \ R(y,y,z) = L(y,y,L(x,y,z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(30079(a,1),31344(a,1,1))].">
      <j1 rule="para" parents="30079 31344"/>
    </justification>
  </clause>

  <clause id="31350">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) \ R(y,y,z) = L(y,y,L(x,y,z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),31349(a,1,1))].">
      <j1 rule="para" parents="2564 31349"/>
    </justification>
  </clause>

  <clause id="31351">
    <literal><![CDATA[
      L(x,x,L(y,x,z)) * a(x,x,z) = L(R(x,x,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(30605,a,31350,a),flip(a)].">
      <j1 rule="hyper" parents="30605 31350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31352">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) = L(L(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25837,a(flip),b,31342,a),flip(a)].">
      <j1 rule="hyper" parents="60 25837 31342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31353">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x \ 1,L(u,w,v5)) = L(L(x \ 1,y,z),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(14843,a,31352,a),flip(a)].">
      <j1 rule="hyper" parents="14843 31352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31354">
    <literal><![CDATA[
      a(R(x,L(y,x,x),L(y,x,x)) \ (x \ y),z,u) = a(L(L(y,x,x),y,L(x,x,x)),z,u)
    ]]></literal>
    <justification jstring="[para(31352(a,1),29673(a,2,1))].">
      <j1 rule="para" parents="31352 29673"/>
    </justification>
  </clause>

  <clause id="31355">
    <literal><![CDATA[
      L(L(x \ 1,y,z),L(x,u,w),v5) = L(L(x \ 1,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(3530,a,31353,a),flip(a)].">
      <j1 rule="hyper" parents="3530 31353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31356">
    <literal><![CDATA[
      L(L(x \ 1,y,y),x,L(y \ x,y,y)) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30227,a(flip),b,31355,a),flip(a)].">
      <j1 rule="hyper" parents="60 30227 31355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31357">
    <literal><![CDATA[
      L(L(T(x,y) \ 1,x,y),T(x,y),L(z,u,w)) = L((x * y) \ y,L(T(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6711(a,1),31355(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6711 31355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31358">
    <literal><![CDATA[
      L(L(x \ 1,y,y),x,y * x) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(3519,a,31356,a)].">
      <j1 rule="hyper" parents="3519 31356"/>
    </justification>
  </clause>

  <clause id="31359">
    <literal><![CDATA[
      L(L(1 / x,x,y),y,y) = (((y \ x) \ (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,25214,a(flip),b,31358,a)].">
      <j1 rule="hyper" parents="60 25214 31358"/>
    </justification>
  </clause>

  <clause id="31360">
    <literal><![CDATA[
      (((x \ y) \ (x \ 1)) \ 1) \ 1 = x * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(60,a,30013,a(flip),b,31359,a),flip(a)].">
      <j1 rule="hyper" parents="60 30013 31359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31361">
    <literal><![CDATA[
      1 / (x * ((x \ 1) / y)) = ((x \ y) \ (x \ 1)) \ 1
    ]]></literal>
    <justification jstring="[hyper(221,a,31360,a)].">
      <j1 rule="hyper" parents="221 31360"/>
    </justification>
  </clause>

  <clause id="31362">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),((x \ y) \ (x \ 1)) \ 1,(x \ y) \ (x \ 1)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[para(31360(a,1),656(a,1,1))].">
      <j1 rule="para" parents="31360 656"/>
    </justification>
  </clause>

  <clause id="31363">
    <literal><![CDATA[
      a(x * ((y \ z) \ (y \ 1)),u,w) = a(x * (y * ((y \ 1) / z)),u,w)
    ]]></literal>
    <justification jstring="[para(31360(a,1),26439(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31360 26439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31364">
    <literal><![CDATA[
      a(x * (y * ((y \ 1) / z)),u,w) = a(x * ((y \ z) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,3003,a(flip),b,31363,a),flip(a)].">
      <j1 rule="hyper" parents="60 3003 31363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31365">
    <literal><![CDATA[
      a(x * (y * (z \ (y \ 1))),u,w) = a(x * ((y \ z) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26686,a,31364,a)].">
      <j1 rule="hyper" parents="26686 31364"/>
    </justification>
  </clause>

  <clause id="31366">
    <literal><![CDATA[
      a(x * ((y \ z) \ y),u,w) = a(x * (y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27515,a(flip),b,31365,a),flip(a)].">
      <j1 rule="hyper" parents="60 27515 31365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31367">
    <literal><![CDATA[
      L(L(T(x,y) \ 1,x,y),T(x,y),L(z,u,w)) = L((x * y) \ y,L(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26020,a(flip),b,31357,a),flip(a)].">
      <j1 rule="hyper" parents="370 26020 31357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31371">
    <literal><![CDATA[
      L((x * y) \ y,T(x,y),L(z,u,w)) = L((x * y) \ y,L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(6711(a,1),31367(a,1,1))].">
      <j1 rule="para" parents="6711 31367"/>
    </justification>
  </clause>

  <clause id="31372">
    <literal><![CDATA[
      L((x * y) \ y,L(x,z,u),w) = L((x * y) \ y,x,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(26171,a,31371,a),flip(a)].">
      <j1 rule="hyper" parents="26171 31371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31374">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(R(x,w,v5),x,L(y,z,u)) = L(x \ R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(31345(a,1),31341(a,1,2))].">
      <j1 rule="para" parents="31345 31341"/>
    </justification>
  </clause>

  <clause id="31375">
    <literal><![CDATA[
      a(R(x,L(y,x,x),L(y,x,x)) \ (x \ y),z,u) = a(L(L(y,x,x),y,x),z,u)
    ]]></literal>
    <justification jstring="[para(14005(a,1),31354(a,2,1))].">
      <j1 rule="para" parents="14005 31354"/>
    </justification>
  </clause>

  <clause id="31377">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) = a(R(y,x,x) \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(30172(a,1),31375(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30172 31375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31378">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) = a(L(y,x,x) \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,29687,a(flip),b,31377,a),flip(a)].">
      <j1 rule="hyper" parents="370 29687 31377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31380">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) = a(y \ (L(y,x,x) \ x),z,u)
    ]]></literal>
    <justification jstring="[para(2178(a,1),31378(a,2,1))].">
      <j1 rule="para" parents="2178 31378"/>
    </justification>
  </clause>

  <clause id="31381">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) = a(y * (L(y,x,x) * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,29683,a(flip),b,31380,a),flip(a)].">
      <j1 rule="hyper" parents="370 29683 31380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31382">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(31381(a,2),29648(a,1))].">
      <j1 rule="para" parents="31381 29648"/>
    </justification>
  </clause>

  <clause id="31383">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,u,w),v5) = L(x \ R(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(7813,a,31374,a),flip(a)].">
      <j1 rule="hyper" parents="7813 31374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31384">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,L(u,w,v5)),x,z * y) = L(a(x,y,z),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(31383(a,1),24922(a,1,1))].">
      <j1 rule="para" parents="31383 24922"/>
    </justification>
  </clause>

  <clause id="31385">
    <literal><![CDATA[
      L(a(x,y,z),L(x,u,w),v5) = L(a(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,24922,a(flip),b,31384,a),flip(a)].">
      <j1 rule="hyper" parents="60 24922 31384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31386">
    <literal><![CDATA[
      L(a(x,L(y,z,u),w),L(x,z,u),y) = x \ R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,31090,a(flip),b,31385,a),flip(a)].">
      <j1 rule="hyper" parents="370 31090 31385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31387">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),L(x,z,u),x) = x \ R(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(29139(a,1),31386(a,1,1))].">
      <j1 rule="para" parents="29139 31386"/>
    </justification>
  </clause>

  <clause id="31388">
    <literal><![CDATA[
      R(x,L(x,y,z),u) = R(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(28684,a,31387,a),flip(a)].">
      <j1 rule="hyper" parents="28684 31387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31390">
    <literal><![CDATA[
      L(R(x,x,L(y,z,u)),w,v5) \ R(x,L(x,z,u),y) = L(L(x,w,v5) \ x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(31388(a,1),29126(a,1,1,1))].">
      <j1 rule="para" parents="31388 29126"/>
    </justification>
  </clause>

  <clause id="31391">
    <literal><![CDATA[
      L(R(x,x,L(y,z,u)),w,v5) \ R(x,x,L(y,z,u)) = L(L(x,w,v5) \ x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(31388(a,1),31390(a,1,2))].">
      <j1 rule="para" parents="31388 31390"/>
    </justification>
  </clause>

  <clause id="31392">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,u,w),v5) = L(L(x,y,z) \ x,x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(29155,a,31391,a),flip(a)].">
      <j1 rule="hyper" parents="29155 31391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31393">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,L(y,u,w)),u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(31392(a,1),30063(a,1,1))].">
      <j1 rule="para" parents="31392 30063"/>
    </justification>
  </clause>

  <clause id="31395">
    <literal><![CDATA[
      L(x / y,x / y,L(z,x * (x / y),x * (y \ x))) = L(x / y,y * x,z)
    ]]></literal>
    <justification jstring="[para(77(a,1),31348(a,2,2,1))].">
      <j1 rule="para" parents="77 31348"/>
    </justification>
  </clause>

  <clause id="31396">
    <literal><![CDATA[
      L(x / y,x / y,L(z,x * (y \ x),x * (y \ x))) = L(x / y,y * x,z)
    ]]></literal>
    <justification jstring="[para(26105(a,1),31395(a,1,3))].">
      <j1 rule="para" parents="26105 31395"/>
    </justification>
  </clause>

  <clause id="31397">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),((x \ y) \ (x \ 1)) \ 1,(x \ y) \ x) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,3460,a(flip),b,31362,a)].">
      <j1 rule="hyper" parents="60 3460 31362"/>
    </justification>
  </clause>

  <clause id="31398">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),((x \ y) \ (x \ 1)) \ 1,x * (y \ x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,25615,a(flip),b,31397,a)].">
      <j1 rule="hyper" parents="60 25615 31397"/>
    </justification>
  </clause>

  <clause id="31399">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),(x \ y) \ (x \ 1),x * (y \ x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(3530,a,31398,a)].">
      <j1 rule="hyper" parents="3530 31398"/>
    </justification>
  </clause>

  <clause id="31400">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),(x \ y) \ x,x * (y \ x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(26242,a,31399,a)].">
      <j1 rule="hyper" parents="26242 31399"/>
    </justification>
  </clause>

  <clause id="31401">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),(y \ x) * x,x * (y \ x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(29629,a,31400,a)].">
      <j1 rule="hyper" parents="29629 31400"/>
    </justification>
  </clause>

  <clause id="31402">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),x * (y * x),x * (y * x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,29911,a(flip),b,31401,a)].">
      <j1 rule="hyper" parents="60 29911 31401"/>
    </justification>
  </clause>

  <clause id="31403">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),x * (y * x),L(y,x,x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(25965,a,31402,a)].">
      <j1 rule="hyper" parents="25965 31402"/>
    </justification>
  </clause>

  <clause id="31404">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),L(y,x,x),L(y,x,x)) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(26263,a,31403,a)].">
      <j1 rule="hyper" parents="26263 31403"/>
    </justification>
  </clause>

  <clause id="31405">
    <literal><![CDATA[
      L(x * ((x \ 1) / y),y,y) = 1 \ (((x \ y) \ (x \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,29547,a(flip),b,31404,a)].">
      <j1 rule="hyper" parents="60 29547 31404"/>
    </justification>
  </clause>

  <clause id="31407">
    <literal><![CDATA[
      L(x,x \ y,y) \ 1 = 1 \ (((y \ x) \ (y \ 1)) * 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,30010,a(flip),b,31405,a)].">
      <j1 rule="hyper" parents="60 30010 31405"/>
    </justification>
  </clause>

  <clause id="31408">
    <literal><![CDATA[
      L(x,x \ y,y) \ 1 = (y \ x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,187,a(flip),b,31407,a),flip(a)].">
      <j1 rule="hyper" parents="370 187 31407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31409">
    <literal><![CDATA[
      (x * ((x \ 1) / y)) * (y \ 1) = y \ ((x \ y) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(31408(a,1),30373(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31408 30373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31410">
    <literal><![CDATA[
      a((x \ ((y \ x) \ (y \ 1))) * z,u,w) = a(a(y,x \ y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(31409(a,1),28692(a,1,1,1))].">
      <j1 rule="para" parents="31409 28692"/>
    </justification>
  </clause>

  <clause id="31411">
    <literal><![CDATA[
      a((x \ ((y \ x) \ y)) * z,u,w) = a(a(y,x \ y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(27791,a,31410,a)].">
      <j1 rule="hyper" parents="27791 31410"/>
    </justification>
  </clause>

  <clause id="31412">
    <literal><![CDATA[
      a((x \ (y * (x \ y))) * z,u,w) = a(a(y,x \ y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27554,a(flip),b,31411,a)].">
      <j1 rule="hyper" parents="60 27554 31411"/>
    </justification>
  </clause>

  <clause id="31413">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ L(R(x \ 1,u,w),y,z)) * a(w,u,a(L(x \ 1,y,z),L(x \ 1,y,z),u))) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(24(a,1),31162(a,1,2,1,2))].">
      <j1 rule="para" parents="24 31162"/>
    </justification>
  </clause>

  <clause id="31414">
    <literal><![CDATA[
      L(K(a(x,y,z) / y,y) * u,a(x,y,z) / y,a(x,y,z) / y) = (a(x,y,z) / y) * ((1 / (a(x,y,z) / y)) * u)
    ]]></literal>
    <justification jstring="[para(28114(a,1),31312(a,1,1,1))].">
      <j1 rule="para" parents="28114 31312"/>
    </justification>
  </clause>

  <clause id="31416">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,a(z,x,u) / x,a(z,x,u) / x) = (a(z,x,u) / x) * ((1 / (a(z,x,u) / x)) * y)
    ]]></literal>
    <justification jstring="[para(28199(a,1),31414(a,1,1,1))].">
      <j1 rule="para" parents="28199 31414"/>
    </justification>
  </clause>

  <clause id="31417">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,a(z,x,u) / x,x \ a(z,x,u)) = (a(z,x,u) / x) * ((1 / (a(z,x,u) / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(24038,a,31416,a)].">
      <j1 rule="hyper" parents="24038 31416"/>
    </justification>
  </clause>

  <clause id="31419">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,a(z,x,u) / x,x * a(z,x,u)) = (a(z,x,u) / x) * ((1 / (a(z,x,u) / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(31020,a,31417,a)].">
      <j1 rule="hyper" parents="31020 31417"/>
    </justification>
  </clause>

  <clause id="31420">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ a(z,x,u),x * a(z,x,u)) = (a(z,x,u) / x) * ((1 / (a(z,x,u) / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(26067,a,31419,a)].">
      <j1 rule="hyper" parents="26067 31419"/>
    </justification>
  </clause>

  <clause id="31421">
    <literal><![CDATA[
      (a(x,y,z) / y) * ((1 / (a(x,y,z) / y)) * u) = L(K(y,y \ 1) * u,y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,30997,a(flip),b,31420,a),flip(a)].">
      <j1 rule="hyper" parents="60 30997 31420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31423">
    <literal><![CDATA[
      (a(x,y,z) / y) * ((1 / (a(x,y,z) / y)) * u) = y * ((1 / y) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3569,a(flip),b,31421,a),flip(a)].">
      <j1 rule="hyper" parents="370 3569 31421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31424">
    <literal><![CDATA[
      (a(x,y,z) \ y) * ((a(x,y,z) / y) * u) = y * ((1 / y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,31311,a(flip),b,31423,a)].">
      <j1 rule="hyper" parents="60 31311 31423"/>
    </justification>
  </clause>

  <clause id="31425">
    <literal><![CDATA[
      x * ((1 / x) * ((a(y,x,z) / x) \ u)) = (a(y,x,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(387,a,31424,a),flip(a)].">
      <j1 rule="hyper" parents="387 31424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31427">
    <literal><![CDATA[
      x * (x * ((a(y,x,z) / (x \ 1)) \ u)) = (a(y,x,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(7701(a,1),31425(a,1,2))].">
      <j1 rule="para" parents="7701 31425"/>
    </justification>
  </clause>

  <clause id="31428">
    <literal><![CDATA[
      x * (x * (((1 / x) \ a(y,x,z)) \ u)) = (a(y,x,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(28219(a,1),31427(a,1,2,2,1))].">
      <j1 rule="para" parents="28219 31427"/>
    </justification>
  </clause>

  <clause id="31429">
    <literal><![CDATA[
      x * (x * ((x * a(y,x,z)) \ u)) = (a(y,x,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(31012(a,1),31428(a,1,2,2,1))].">
      <j1 rule="para" parents="31012 31428"/>
    </justification>
  </clause>

  <clause id="31430">
    <literal><![CDATA[
      x * ((x * a(y,x,z)) \ (((a(y,x,z) \ x) \ x) * u)) = L(u,(a(y,x,z) \ x) \ x,a(y,x,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(31,a,530,a,b,31429,a),flip(a)].">
      <j1 rule="hyper" parents="31 530 31429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31431">
    <literal><![CDATA[
      x * ((x * a(y,x,z)) \ (((a(y,x,z) \ x) \ x) * u)) = L(u,a(y,x,z),a(y,x,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,26019,a(flip),b,31430,a),flip(a)].">
      <j1 rule="hyper" parents="370 26019 31430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31433">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ L(R(x \ 1,u,w),y,z)) * a(w,u,a(L(x \ 1,y,z),L(x,y,z),u))) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3911(a,1),31413(a,1,2,2,3))].">
      <j1 rule="para" parents="3911 31413"/>
    </justification>
  </clause>

  <clause id="31434">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ L(R(x \ 1,u,w),y,z)) * a(w,u,a(L(x,y,z),L(x,y,z),u))) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3869(a,1),31433(a,1,2,2,3))].">
      <j1 rule="para" parents="3869 31433"/>
    </justification>
  </clause>

  <clause id="31435">
    <literal><![CDATA[
      (x * x) * ((L(x,y,z) \ L(R(x \ 1,u,w),y,z)) * a(w,u,a(x,x,u))) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29529(a,1),31434(a,1,2,2,3))].">
      <j1 rule="para" parents="29529 31434"/>
    </justification>
  </clause>

  <clause id="31436">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ L(R(x \ 1,u,w),y,z)) * a(w,u,a(x,x,u)) = a(L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,4018,a(flip),b,31435,a)].">
      <j1 rule="hyper" parents="60 4018 31435"/>
    </justification>
  </clause>

  <clause id="31438">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,y,z),u,w) * a(z,y,a(x,x,y)) = a(L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(7812(a,1),31436(a,1,1))].">
      <j1 rule="para" parents="7812 31436"/>
    </justification>
  </clause>

  <clause id="31439">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(z,y,a(x,x,y)) = a(L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(1992(a,1),31438(a,1,1,1))].">
      <j1 rule="para" parents="1992 31438"/>
    </justification>
  </clause>

  <clause id="31440">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(z,y,a(x,x,y)) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3869,a(flip),b,31439,a),flip(a)].">
      <j1 rule="hyper" parents="370 3869 31439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31441">
    <literal><![CDATA[
      L((x \ R(x,y,z)) * a(z,y,a(x,x,y)),z,z) = a(L(x,z,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(28958,a,31440,a)].">
      <j1 rule="hyper" parents="28958 31440"/>
    </justification>
  </clause>

  <clause id="31442">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(y,x,a(z,y,x)) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(30849(a,1),31440(a,1,2))].">
      <j1 rule="para" parents="30849 31440"/>
    </justification>
  </clause>

  <clause id="31443">
    <literal><![CDATA[
      a(L(x,y,y),z,y) = L(a(x,z,y),y,y)
    ]]></literal>
    <justification jstring="[para(31161(a,1),31441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31161 31441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31444">
    <literal><![CDATA[
      a(L(x,y,y),z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,14782,a(flip),b,31443,a),flip(a)].">
      <j1 rule="hyper" parents="370 14782 31443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31445">
    <literal><![CDATA[
      a(x \ y,z,x) = a(y * x,z,x)
    ]]></literal>
    <justification jstring="[hyper(30215,a,31444,a)].">
      <j1 rule="hyper" parents="30215 31444"/>
    </justification>
  </clause>

  <clause id="31446">
    <literal><![CDATA[
      a(x \ y,z,x) = a(x * y,z,x)
    ]]></literal>
    <justification jstring="[hyper(2971,a,31444,a),flip(a)].">
      <j1 rule="hyper" parents="2971 31444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31448">
    <literal><![CDATA[
      L(x,y,L(z,x,x)) = (y * a(z,y,x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(31444(a,1),29945(a,2,1,2))].">
      <j1 rule="para" parents="31444 29945"/>
    </justification>
  </clause>

  <clause id="31449">
    <literal><![CDATA[
      a((L(x,y,z) \ u) * x,w,x) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (L(x,y,z) * u),w,x) = v5
    ]]></literal>
    <justification jstring="[para(31445(a,1),29684(a,1))].">
      <j1 rule="para" parents="31445 29684"/>
    </justification>
  </clause>

  <clause id="31450">
    <literal><![CDATA[
      a((x * y) \ z,u,y * x) = a((y * x) * z,u,y * x)
    ]]></literal>
    <justification jstring="[hyper(26527,a,31446,a)].">
      <j1 rule="hyper" parents="26527 31446"/>
    </justification>
  </clause>

  <clause id="31451">
    <literal><![CDATA[
      a(x \ y,z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,x) = u
    ]]></literal>
    <justification jstring="[para(31446(a,2),26519(a,1))].">
      <j1 rule="para" parents="31446 26519"/>
    </justification>
  </clause>

  <clause id="31452">
    <literal><![CDATA[
      a((x * y) \ z,u,y * x) != w
    ]]></literal>
    <literal><![CDATA[
      a(z * (x * y),u,x * y) = w
    ]]></literal>
    <justification jstring="[para(26888(a,1),31451(a,1))].">
      <j1 rule="para" parents="26888 31451"/>
    </justification>
  </clause>

  <clause id="31453">
    <literal><![CDATA[
      L(x,y,L(z,x,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29945,a,b,31448,a),flip(a)].">
      <j1 rule="hyper" parents="370 29945 31448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31454">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u)) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[para(31453(a,1),29654(a,1,3))].">
      <j1 rule="para" parents="31453 29654"/>
    </justification>
  </clause>

  <clause id="31455">
    <literal><![CDATA[
      a((x * y) * z,u,x * y) != w
    ]]></literal>
    <literal><![CDATA[
      a(z * (y * x),u,y * x) = w
    ]]></literal>
    <justification jstring="[para(31450(a,1),31452(a,1))].">
      <j1 rule="para" parents="31450 31452"/>
    </justification>
  </clause>

  <clause id="31456">
    <literal><![CDATA[
      a(L(x,y,z),z,u) = L(a(x,z,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31185,a(flip),b,31442,a),flip(a)].">
      <j1 rule="hyper" parents="60 31185 31442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31457">
    <literal><![CDATA[
      a(L(x,x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31090,a(flip),b,31456,a),flip(a)].">
      <j1 rule="hyper" parents="370 31090 31456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31458">
    <literal><![CDATA[
      a(L(x,y,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31008,a(flip),b,31456,a),flip(a)].">
      <j1 rule="hyper" parents="370 31008 31456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31459">
    <literal><![CDATA[
      a(L(x,y,z),z,y) = L(y,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(370,a,29953,a(flip),b,31456,a),flip(a)].">
      <j1 rule="hyper" parents="370 29953 31456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31460">
    <literal><![CDATA[
      a(x \ y,x,z) = a(x * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(2971,a,31458,a),flip(a)].">
      <j1 rule="hyper" parents="2971 31458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31461">
    <literal><![CDATA[
      a(x \ y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * y,x,z) = u
    ]]></literal>
    <justification jstring="[para(31458(a,1),2971(a,1))].">
      <j1 rule="para" parents="31458 2971"/>
    </justification>
  </clause>

  <clause id="31462">
    <literal><![CDATA[
      a(L(x,y,y),L(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(29547(a,1),31458(a,1,1))].">
      <j1 rule="para" parents="29547 31458"/>
    </justification>
  </clause>

  <clause id="31463">
    <literal><![CDATA[
      a(L(x,y,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31458(a,1),30207(a,1))].">
      <j1 rule="para" parents="31458 30207"/>
    </justification>
  </clause>

  <clause id="31464">
    <literal><![CDATA[
      a(L(x,x,y),y,z * L(u,w,v5)) = x \ R(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(28699,a,31457,a)].">
      <j1 rule="hyper" parents="28699 31457"/>
    </justification>
  </clause>

  <clause id="31465">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ (((1 / x) \ y) * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27320,a,b,31457,a)].">
      <j1 rule="hyper" parents="60 27320 31457"/>
    </justification>
  </clause>

  <clause id="31466">
    <literal><![CDATA[
      a(L(x,x,y),y,z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31457(a,2),44(a,1))].">
      <j1 rule="para" parents="31457 44"/>
    </justification>
  </clause>

  <clause id="31467">
    <literal><![CDATA[
      a(x \ (x / (y \ 1)),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[para(2481(a,1),31457(a,1,1))].">
      <j1 rule="para" parents="2481 31457"/>
    </justification>
  </clause>

  <clause id="31470">
    <literal><![CDATA[
      L(x,y,a(L(z,z,u),u,w)) = R(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(31457(a,1),28339(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31457 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31471">
    <literal><![CDATA[
      x \ L(x,y,a(L(z,z,u),u,w)) = L(x,y,z \ R(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(31457(a,1),30029(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="31457 30029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31472">
    <literal><![CDATA[
      a(L(x,y * R(z,u,w),v5),v5,y * L(z,u,w)) = L(y * R(z,u,w),v5,x) \ (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(28699,a,31459,a)].">
      <j1 rule="hyper" parents="28699 31459"/>
    </justification>
  </clause>

  <clause id="31473">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),z,y) = L(y,z,L(x,u,w)) \ y
    ]]></literal>
    <justification jstring="[para(25(a,1),31459(a,1,1))].">
      <j1 rule="para" parents="25 31459"/>
    </justification>
  </clause>

  <clause id="31474">
    <literal><![CDATA[
      L(x,a(y,z,u),a(a(y,z,u),w,x) * w) \ x = a(L(w,a(y,z,u),x),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(29193(a,1),31459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29193 31459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31475">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,x,a(L(z,x,y),y,y)) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(31459(a,1),30867(a,1,1))].">
      <j1 rule="para" parents="31459 30867"/>
    </justification>
  </clause>

  <clause id="31476">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(a(L(z,x,y),y,x),u,w) = L(a(L(z,x,y),y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(31459(a,1),31132(a,1,1))].">
      <j1 rule="para" parents="31459 31132"/>
    </justification>
  </clause>

  <clause id="31477">
    <literal><![CDATA[
      a(L(L(x,y,z),u,z),z,y) = L(L(y,z,x) \ y,u,z)
    ]]></literal>
    <justification jstring="[para(31459(a,1),31456(a,2,1))].">
      <j1 rule="para" parents="31459 31456"/>
    </justification>
  </clause>

  <clause id="31479">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,u,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(31124(a,2),31463(a,1))].">
      <j1 rule="para" parents="31124 31463"/>
    </justification>
  </clause>

  <clause id="31480">
    <literal><![CDATA[
      L(a(x,y,z),y,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31456(a,1),31463(a,1))].">
      <j1 rule="para" parents="31456 31463"/>
    </justification>
  </clause>

  <clause id="31481">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ x),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(26550,a,31467,a)].">
      <j1 rule="hyper" parents="26550 31467"/>
    </justification>
  </clause>

  <clause id="31482">
    <literal><![CDATA[
      a(x \ (y \ x),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26711,a(flip),b,31481,a)].">
      <j1 rule="hyper" parents="60 26711 31481"/>
    </justification>
  </clause>

  <clause id="31483">
    <literal><![CDATA[
      a(x * (y \ x),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(31461,a,31482,a)].">
      <j1 rule="hyper" parents="31461 31482"/>
    </justification>
  </clause>

  <clause id="31484">
    <literal><![CDATA[
      a((x \ y) * y,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26519,a,31483,a)].">
      <j1 rule="hyper" parents="26519 31483"/>
    </justification>
  </clause>

  <clause id="31485">
    <literal><![CDATA[
      R(x,y,z) = x * a((x \ y) * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,26381,a,b,31483,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 26381 31483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31486">
    <literal><![CDATA[
      x * a(R(y,z,u) * (x \ R(y,z,u)),L(y,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(129,a,30079,a(flip),b,31483,a(flip))].">
      <j1 rule="hyper" parents="129 30079 31483"/>
    </justification>
  </clause>

  <clause id="31487">
    <literal><![CDATA[
      x * a(y * (x \ y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31483(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31483 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31488">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,u,w)) = y \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28339(a,1),31483(a,2,2))].">
      <j1 rule="para" parents="28339 31483"/>
    </justification>
  </clause>

  <clause id="31489">
    <literal><![CDATA[
      x * (L(y,z,(x \ z) * z) \ y) = R(x,z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(129,a,29989,a(flip),b,31484,a(flip))].">
      <j1 rule="hyper" parents="129 29989 31484"/>
    </justification>
  </clause>

  <clause id="31490">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((w * u) * z)) * v5) = x * a((x \ y) * y,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(129,a,27364,a(flip),b,31484,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 27364 31484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31491">
    <literal><![CDATA[
      x * a((x \ y) * y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31484(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31484 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31492">
    <literal><![CDATA[
      (x \ (x \ y)) \ R(x \ (x \ y),x \ y,z) = a(K(x,x \ (x \ y)) * y,x \ y,z)
    ]]></literal>
    <justification jstring="[para(7886(a,1),31484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7886 31484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31493">
    <literal><![CDATA[
      L(x \ R(x,y,z),z,y) = L(z,y,(x \ y) * y) \ z
    ]]></literal>
    <justification jstring="[para(31484(a,1),29953(a,1,1))].">
      <j1 rule="para" parents="31484 29953"/>
    </justification>
  </clause>

  <clause id="31494">
    <literal><![CDATA[
      (x * a(((x \ 1) \ y) * y,y,z)) \ ((1 / x) \ u) = R(x \ 1,y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(31485(a,2),2113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31485 2113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31495">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(31485(a,2),28146(a,1,2,2))].">
      <j1 rule="para" parents="31485 28146"/>
    </justification>
  </clause>

  <clause id="31498">
    <literal><![CDATA[
      T((x * R(x,y,z)) * u,x * x) = u * (x * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29362,a(flip),b,31495,a),flip(a)].">
      <j1 rule="hyper" parents="60 29362 31495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31499">
    <literal><![CDATA[
      K(x * R(y,z,u),w) = w / T(w,x * y)
    ]]></literal>
    <justification jstring="[para(31495(a,1),5701(a,2,2))].">
      <j1 rule="para" parents="31495 5701"/>
    </justification>
  </clause>

  <clause id="31504">
    <literal><![CDATA[
      K(x * R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * y,w) = v5
    ]]></literal>
    <justification jstring="[para(31499(a,2),5734(a,1))].">
      <j1 rule="para" parents="31499 5734"/>
    </justification>
  </clause>

  <clause id="31505">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(R(y,u,w) * x,z)
    ]]></literal>
    <justification jstring="[hyper(31504,a,23985,a)].">
      <j1 rule="hyper" parents="31504 23985"/>
    </justification>
  </clause>

  <clause id="31507">
    <literal><![CDATA[
      K(R(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[hyper(12601,a,31505,a),flip(a)].">
      <j1 rule="hyper" parents="12601 31505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31510">
    <literal><![CDATA[
      K(x * (R(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),31507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 31507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31511">
    <literal><![CDATA[
      K((R(x,y,z) \ x) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27716,a,b,31510,a)].">
      <j1 rule="hyper" parents="60 27716 31510"/>
    </justification>
  </clause>

  <clause id="31512">
    <literal><![CDATA[
      K((x / y) * (y * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(676(a,1),31510(a,1,1,2))].">
      <j1 rule="para" parents="676 31510"/>
    </justification>
  </clause>

  <clause id="31514">
    <literal><![CDATA[
      (x \ (R(1 / x,y,z) \ u)) * K(u,w) = T((x \ 1) \ (R(x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(31510(a,1),15581(a,1,2))].">
      <j1 rule="para" parents="31510 15581"/>
    </justification>
  </clause>

  <clause id="31516">
    <literal><![CDATA[
      K(R(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27715,a(flip),b,31511,a)].">
      <j1 rule="hyper" parents="60 27715 31511"/>
    </justification>
  </clause>

  <clause id="31522">
    <literal><![CDATA[
      (R(x,y,z) \ u) * K(x \ u,w) = T(R(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(129,a,31516,a(flip),b,5230,a(flip))].">
      <j1 rule="hyper" parents="129 31516 5230"/>
    </justification>
  </clause>

  <clause id="31524">
    <literal><![CDATA[
      K((x / y) * z,u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),31512(a,1,1,2))].">
      <j1 rule="para" parents="5 31512"/>
    </justification>
  </clause>

  <clause id="31525">
    <literal><![CDATA[
      T(x * K(y * (z \ u),x),((y / z) * u) * x) = L(x,(z \ y) * u,x)
    ]]></literal>
    <justification jstring="[para(31524(a,1),26267(a,1,1,2))].">
      <j1 rule="para" parents="31524 26267"/>
    </justification>
  </clause>

  <clause id="31526">
    <literal><![CDATA[
      (L(x,x,y) * z) * a(y,L(x,x,y),z) = R(y,x,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(31462(a,1),29220(a,1,2))].">
      <j1 rule="para" parents="31462 29220"/>
    </justification>
  </clause>

  <clause id="31527">
    <literal><![CDATA[
      x * (L(y,z,(x \ z) * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,z,L(y,y,z)) = u
    ]]></literal>
    <justification jstring="[para(30146(a,1),31491(a,1,2))].">
      <j1 rule="para" parents="30146 31491"/>
    </justification>
  </clause>

  <clause id="31528">
    <literal><![CDATA[
      L(x,y,a(L(z,z,u),u,w)) = R(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,2780,a(flip),b,31470,a),flip(a)].">
      <j1 rule="hyper" parents="370 2780 31470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31529">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,y) = L(x,y,L(z,u,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,31473,a(flip),b,31477,a),flip(a)].">
      <j1 rule="hyper" parents="60 31473 31477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31530">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,v5,u)) = a(x,y,z * L(z,u,L(w,v5,u)))
    ]]></literal>
    <justification jstring="[para(31529(a,2),4030(a,1,3))].">
      <j1 rule="para" parents="31529 4030"/>
    </justification>
  </clause>

  <clause id="31531">
    <literal><![CDATA[
      L(x \ R(x,y * x,z),z,y * x) = L(z,y * x,T(y,x) * (y * x)) \ z
    ]]></literal>
    <justification jstring="[para(17(a,2),31493(a,2,1,3,1))].">
      <j1 rule="para" parents="17 31493"/>
    </justification>
  </clause>

  <clause id="31532">
    <literal><![CDATA[
      R(x,y,z * R(z,u,w)) = L(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(31457(a,1),31528(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31457 31528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31533">
    <literal><![CDATA[
      R(x,y,z * R(z,u,w)) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27264,a(flip),b,31532,a),flip(a)].">
      <j1 rule="hyper" parents="370 27264 31532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31534">
    <literal><![CDATA[
      R(x,y,z * R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(31533(a,2),14694(a,1))].">
      <j1 rule="para" parents="31533 14694"/>
    </justification>
  </clause>

  <clause id="31535">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,u,w)) != v5 \ L(y,x,a(z,u,w))
    ]]></literal>
    <literal><![CDATA[
      y = v5
    ]]></literal>
    <justification jstring="[para(31488(a,2),45(a,1))].">
      <j1 rule="para" parents="31488 45"/>
    </justification>
  </clause>

  <clause id="31537">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (u * (x * x)) = u * (x * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,2042,a(flip),b,31498,a)].">
      <j1 rule="hyper" parents="60 2042 31498"/>
    </justification>
  </clause>

  <clause id="31538">
    <literal><![CDATA[
      R(x,y,z) \ (x * T(x \ u,w)) = T(R(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,25034,a,b,31522,a)].">
      <j1 rule="hyper" parents="60 25034 31522"/>
    </justification>
  </clause>

  <clause id="31539">
    <literal><![CDATA[
      x * (R(x,y,z) \ T(x \ u,w)) = T(R(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,1956,a(flip),b,31538,a)].">
      <j1 rule="hyper" parents="60 1956 31538"/>
    </justification>
  </clause>

  <clause id="31540">
    <literal><![CDATA[
      T(x,y) != z * (R(z,u,w) \ T(z \ v5,y))
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) \ v5 = x
    ]]></literal>
    <justification jstring="[para(31539(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="31539 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31541">
    <literal><![CDATA[
      R(x,y,z * R(u,w,v5)) = R(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(31466,a,31464,a),flip(a)].">
      <j1 rule="hyper" parents="31466 31464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31542">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(31534,a,31541,a),flip(a)].">
      <j1 rule="hyper" parents="31534 31541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31543">
    <literal><![CDATA[
      a(x,y,R(z,z,u * L(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(31541(a,1),29243(a,1,3,1))].">
      <j1 rule="para" parents="31541 29243"/>
    </justification>
  </clause>

  <clause id="31544">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(27462,a,31542,a)].">
      <j1 rule="hyper" parents="27462 31542"/>
    </justification>
  </clause>

  <clause id="31546">
    <literal><![CDATA[
      x \ L(x,y,a(L(z,z,u),u,w)) = L(x,y,z \ L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(27264(a,1),31471(a,2,1))].">
      <j1 rule="para" parents="27264 31471"/>
    </justification>
  </clause>

  <clause id="31547">
    <literal><![CDATA[
      x \ L(x,y,a(L(z,z,u),u,w)) = L(x,y,z * L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(3862(a,1),31546(a,2,1))].">
      <j1 rule="para" parents="3862 31546"/>
    </justification>
  </clause>

  <clause id="31548">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = x \ L(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(31457(a,1),31547(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="31457 31547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31549">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = x \ L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(27264(a,1),31548(a,2,2))].">
      <j1 rule="para" parents="27264 31548"/>
    </justification>
  </clause>

  <clause id="31550">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = x \ L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3862(a,1),31549(a,2,2))].">
      <j1 rule="para" parents="3862 31549"/>
    </justification>
  </clause>

  <clause id="31551">
    <literal><![CDATA[
      x * a(y * L(y,z,u),x,x) = L(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29971,a,31550,a)].">
      <j1 rule="hyper" parents="29971 31550"/>
    </justification>
  </clause>

  <clause id="31552">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) * u = L(u,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23794,a,31551,a)].">
      <j1 rule="hyper" parents="23794 31551"/>
    </justification>
  </clause>

  <clause id="31553">
    <literal><![CDATA[
      L(x,x,y * L(y,z,u)) = a(u,z,a(x,x,y)) * x
    ]]></literal>
    <justification jstring="[para(30768(a,1),31552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30768 31552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31554">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,x,a(z,y,y)) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(16548(a,1),31475(a,1,2,3))].">
      <j1 rule="para" parents="16548 31475"/>
    </justification>
  </clause>

  <clause id="31555">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,x,a(z,y,y))) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,28594,a(flip),b,31554,a)].">
      <j1 rule="hyper" parents="60 28594 31554"/>
    </justification>
  </clause>

  <clause id="31557">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(z,y,y)) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(28429(a,1),31555(a,1,2))].">
      <j1 rule="para" parents="28429 31555"/>
    </justification>
  </clause>

  <clause id="31558">
    <literal><![CDATA[
      L(x,y,L(z,x,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,31144,a(flip),b,31557,a),flip(a)].">
      <j1 rule="hyper" parents="60 31144 31557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31559">
    <literal><![CDATA[
      L(L(x,y,z),u,L(w,x,u)) = L(a(w,u,x) \ x,y,z)
    ]]></literal>
    <justification jstring="[para(31558(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31558 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31560">
    <literal><![CDATA[
      L(L(x,y,z),u,L(w,x,u)) = L(x,y,z) * L(x \ (a(w,u,x) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(31558(a,1),10439(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31558 10439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31561">
    <literal><![CDATA[
      a(L(x,y,z),z,a(y,y,u)) * y = L(y,y * (a(x,z,y) \ y),u)
    ]]></literal>
    <justification jstring="[para(31558(a,1),30852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="31558 30852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31562">
    <literal><![CDATA[
      R(x,y,y) \ ((x * y) * z) = x \ ((x / (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28746,a(flip),b,31526,a),flip(a)].">
      <j1 rule="hyper" parents="60 28746 31526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31563">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * ((y \ 1) * z)) = L(z,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(3735,a,31562,a),flip(a)].">
      <j1 rule="hyper" parents="3735 31562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31564">
    <literal><![CDATA[
      x \ ((x / y) * (((1 / y) \ 1) * z)) = L(z,y,x * y)
    ]]></literal>
    <justification jstring="[para(2931(a,1),31563(a,1,2))].">
      <j1 rule="para" parents="2931 31563"/>
    </justification>
  </clause>

  <clause id="31565">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,x * y)
    ]]></literal>
    <justification jstring="[para(77(a,1),31564(a,1,2,2,1))].">
      <j1 rule="para" parents="77 31564"/>
    </justification>
  </clause>

  <clause id="31566">
    <literal><![CDATA[
      L(x,y,y \ z) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(12521,a,31565,a)].">
      <j1 rule="hyper" parents="12521 31565"/>
    </justification>
  </clause>

  <clause id="31568">
    <literal><![CDATA[
      x * ((x * a(y,x,z)) \ (((a(y,x,z) \ x) \ x) * u)) = L(u,a(y,x,z),x * a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,31431,a,b,31566,a)].">
      <j1 rule="hyper" parents="60 31431 31566"/>
    </justification>
  </clause>

  <clause id="31569">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31118,a,b,31566,a)].">
      <j1 rule="hyper" parents="60 31118 31566"/>
    </justification>
  </clause>

  <clause id="31570">
    <literal><![CDATA[
      L(T(x \ 1,x * y) \ z,x,y * x) = ((1 / x) * (x \ y)) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,12653,a(flip),b,31566,a),flip(a)].">
      <j1 rule="hyper" parents="60 12653 31566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31571">
    <literal><![CDATA[
      L(x,y,T(y * z,u) * y) = L(x,y,z * K(y * z,u))
    ]]></literal>
    <justification jstring="[para(15215(a,1),31566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15215 31566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31572">
    <literal><![CDATA[
      L(a(x,y,z),u,w * u) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31566(a,1),25467(a,1,1))].">
      <j1 rule="para" parents="31566 25467"/>
    </justification>
  </clause>

  <clause id="31573">
    <literal><![CDATA[
      L(a(x,y,z),u,(a(x,y,z) \ w) * u) \ w = (u \ 1) * ((a(x,y,z) * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(31569(a,1),29314(a,1,1))].">
      <j1 rule="para" parents="31569 29314"/>
    </justification>
  </clause>

  <clause id="31574">
    <literal><![CDATA[
      L(x,y,(y * z) * y) = L(x,y,z * K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(25942,a,31571,a)].">
      <j1 rule="hyper" parents="25942 31571"/>
    </justification>
  </clause>

  <clause id="31575">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) = L(x,y,z * K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(24925,a,31574,a)].">
      <j1 rule="hyper" parents="24925 31574"/>
    </justification>
  </clause>

  <clause id="31577">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,25902,a(flip),b,31575,a),flip(a)].">
      <j1 rule="hyper" parents="370 25902 31575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31578">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31575(a,2),20625(a,1))].">
      <j1 rule="para" parents="31575 20625"/>
    </justification>
  </clause>

  <clause id="31580">
    <literal><![CDATA[
      L(1 / T(x,y),T(x,y),x * z) = L(T(x,y) \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26278,a(flip),b,31577,a)].">
      <j1 rule="hyper" parents="60 26278 31577"/>
    </justification>
  </clause>

  <clause id="31581">
    <literal><![CDATA[
      a((L(x \ 1,x,y) \ L(y,x,x)) * z,u,w) = a(L(y * (1 / x),x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(31577(a,1),27979(a,1,1,1,1))].">
      <j1 rule="para" parents="31577 27979"/>
    </justification>
  </clause>

  <clause id="31582">
    <literal><![CDATA[
      L(x,L(y,z,u),L(w,y,y)) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(29547(a,1),31577(a,1,3))].">
      <j1 rule="para" parents="29547 31577"/>
    </justification>
  </clause>

  <clause id="31584">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,L(x,x,y),y) = (y * x) \ (((y * x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28053,a(flip),b,31582,a),flip(a)].">
      <j1 rule="hyper" parents="60 28053 31582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31586">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,u)) = a(x,y,z * L(z,u,L(w,v5,u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,15798,a(flip),b,31530,a)].">
      <j1 rule="hyper" parents="60 15798 31530"/>
    </justification>
  </clause>

  <clause id="31587">
    <literal><![CDATA[
      a(x,y,L(y * L(y,z,u),w,z)) = a(L(u,w,z),z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,30848,a(flip),b,31586,a),flip(a)].">
      <j1 rule="hyper" parents="370 30848 31586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31588">
    <literal><![CDATA[
      a(L(x,y,z),z,a(u,u,w)) = a(x,z,a(u,u,L(w,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,31075,a(flip),b,31587,a),flip(a)].">
      <j1 rule="hyper" parents="60 31075 31587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31589">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,z,y))) * z = L(z,z * (a(x,y,z) \ z),u)
    ]]></literal>
    <justification jstring="[para(31588(a,1),31561(a,1,1))].">
      <j1 rule="para" parents="31588 31561"/>
    </justification>
  </clause>

  <clause id="31590">
    <literal><![CDATA[
      a(x * (L(x,y,z) * u),x,x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(31449,a,30535,a)].">
      <j1 rule="hyper" parents="31449 30535"/>
    </justification>
  </clause>

  <clause id="31591">
    <literal><![CDATA[
      T(x * K(y * (z \ u),x),(y / z) * (u * x)) = L(x,(z \ y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(28200,a,31525,a)].">
      <j1 rule="hyper" parents="28200 31525"/>
    </justification>
  </clause>

  <clause id="31592">
    <literal><![CDATA[
      (x * y) \ (((x * y) * y) * z) = (x / y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4127,a(flip),b,31584,a),flip(a)].">
      <j1 rule="hyper" parents="60 4127 31584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31593">
    <literal><![CDATA[
      T(x * K(y * (z \ u),x),y * (z \ (u * x))) = L(x,(z \ y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(28247,a,31591,a)].">
      <j1 rule="hyper" parents="28247 31591"/>
    </justification>
  </clause>

  <clause id="31594">
    <literal><![CDATA[
      T(x * K(y * (z \ u),x),y * ((z \ u) * x)) = L(x,(z \ y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28864,a(flip),b,31593,a)].">
      <j1 rule="hyper" parents="60 28864 31593"/>
    </justification>
  </clause>

  <clause id="31595">
    <literal><![CDATA[
      L(x,(y \ z) * u,x) = L(x,z * (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28085,a(flip),b,31594,a),flip(a)].">
      <j1 rule="hyper" parents="60 28085 31594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31596">
    <literal><![CDATA[
      L(x,y * (z \ u),x) = L(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14614,a(flip),b,31595,a),flip(a)].">
      <j1 rule="hyper" parents="60 14614 31595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31597">
    <literal><![CDATA[
      L(x,y * (z * u),x) \ x = a(x,y \ (u / z),x)
    ]]></literal>
    <justification jstring="[para(31596(a,1),26257(a,1,1))].">
      <j1 rule="para" parents="31596 26257"/>
    </justification>
  </clause>

  <clause id="31598">
    <literal><![CDATA[
      a(x,y \ (z / u),x) = a(x,y * (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(11570,a,31597,a),flip(a)].">
      <j1 rule="hyper" parents="11570 31597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31599">
    <literal><![CDATA[
      a(x,y * (z / u),x) = a(x,y * (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(14546,a,31598,a)].">
      <j1 rule="hyper" parents="14546 31598"/>
    </justification>
  </clause>

  <clause id="31600">
    <literal><![CDATA[
      a(x,y * (z \ u),x) = a(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(26585,a,31599,a)].">
      <j1 rule="hyper" parents="26585 31599"/>
    </justification>
  </clause>

  <clause id="31601">
    <literal><![CDATA[
      a(x,(y * z) * u,x) = a(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14612,a,b,31600,a)].">
      <j1 rule="hyper" parents="60 14612 31600"/>
    </justification>
  </clause>

  <clause id="31602">
    <literal><![CDATA[
      a(x,y * (z * u),x) * x = R(x,(z * y) * u,x)
    ]]></literal>
    <justification jstring="[para(31601(a,1),11451(a,1,1))].">
      <j1 rule="para" parents="31601 11451"/>
    </justification>
  </clause>

  <clause id="31603">
    <literal><![CDATA[
      R(x,(y * z) * u,x) = R(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(11462,a,31602,a),flip(a)].">
      <j1 rule="hyper" parents="11462 31602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31604">
    <literal><![CDATA[
      R(x,y * (z \ u),x) = R(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,14613,a(flip),b,31603,a)].">
      <j1 rule="hyper" parents="60 14613 31603"/>
    </justification>
  </clause>

  <clause id="31605">
    <literal><![CDATA[
      (x / y) / R(x,x * (y * T(x,y \ x)),x) = x \ (T(x,y \ x) / y)
    ]]></literal>
    <justification jstring="[para(31604(a,1),27474(a,1,2))].">
      <j1 rule="para" parents="31604 27474"/>
    </justification>
  </clause>

  <clause id="31606">
    <literal><![CDATA[
      (x / y) / R(x,x * (y * x),x) = x \ (T(x,y \ x) / y)
    ]]></literal>
    <justification jstring="[para(27428(a,1),31605(a,1,2))].">
      <j1 rule="para" parents="27428 31605"/>
    </justification>
  </clause>

  <clause id="31607">
    <literal><![CDATA[
      (x / y) / R(x,L(y,x,x),x) = x \ (T(x,y \ x) / y)
    ]]></literal>
    <justification jstring="[para(27480(a,1),31606(a,1,2))].">
      <j1 rule="para" parents="27480 31606"/>
    </justification>
  </clause>

  <clause id="31609">
    <literal><![CDATA[
      x \ (T(x,y \ x) / y) = (x / y) / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(14592(a,1),31607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14592 31607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31611">
    <literal><![CDATA[
      x * a(R(y,z,u) * (x \ L(y,z,u)),L(y,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(27352(a,1),31486(a,1,2))].">
      <j1 rule="para" parents="27352 31486"/>
    </justification>
  </clause>

  <clause id="31612">
    <literal><![CDATA[
      T((x \ 1) \ (R(x,y,z) \ u),w) = x \ (R(1 / x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25036,a(flip),b,31514,a),flip(a)].">
      <j1 rule="hyper" parents="60 25036 31514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31614">
    <literal><![CDATA[
      T(x \ (R(1 / x,y,z) \ u),w) = x \ (R(1 / x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(7702(a,1),31612(a,1,1))].">
      <j1 rule="para" parents="7702 31612"/>
    </justification>
  </clause>

  <clause id="31615">
    <literal><![CDATA[
      x \ ((R(1 / x,y,z) \ 1) * T(R(1 / x,y,z) \ ((1 / R(1 / x,y,z)) \ u),w)) = T(x \ (R(1 / x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(2115(a,2),31614(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2115 31614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31616">
    <literal><![CDATA[
      L(L(x,y,z),u,L(w,x,u)) = L(x,y,z) * L(a(w,u,x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(30620(a,1),31560(a,2,2,1))].">
      <j1 rule="para" parents="30620 31560"/>
    </justification>
  </clause>

  <clause id="31617">
    <literal><![CDATA[
      L(x,y,z) \ L(a(u,w,x) \ x,y,z) = L(a(u,w,x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,31559,a(flip),b,31616,a(flip))].">
      <j1 rule="hyper" parents="125 31559 31616"/>
    </justification>
  </clause>

  <clause id="31619">
    <literal><![CDATA[
      L(a(x,y,z) \ z,u,w) / (L(a(x,y,z) \ 1,u,w) * (L(z,u,w) \ L(a(x,y,z) \ z,u,w))) = L(z,u,w) * ((L(z,u,w) \ L(a(x,y,z) \ z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(31617(a,1),1106(a,1,2,1))].">
      <j1 rule="para" parents="31617 1106"/>
    </justification>
  </clause>

  <clause id="31620">
    <literal><![CDATA[
      x * a(L(y,z,u) * (x \ L(y,z,u)),L(y,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(27312(a,1),31611(a,1,2))].">
      <j1 rule="para" parents="27312 31611"/>
    </justification>
  </clause>

  <clause id="31621">
    <literal><![CDATA[
      R(x,R(y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(31487,a,31620,a),flip(a)].">
      <j1 rule="hyper" parents="31487 31620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31622">
    <literal><![CDATA[
      R(x,R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(31620(a,1),31487(a,1))].">
      <j1 rule="para" parents="31620 31487"/>
    </justification>
  </clause>

  <clause id="31623">
    <literal><![CDATA[
      R(x,(y * z) * y,u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27447,a,b,31621,a)].">
      <j1 rule="hyper" parents="60 27447 31621"/>
    </justification>
  </clause>

  <clause id="31624">
    <literal><![CDATA[
      R(x,L(y,y,z),z) * (y \ z) = (x * (y \ a(y,y,z))) * z
    ]]></literal>
    <justification jstring="[para(31621(a,1),28464(a,1,1))].">
      <j1 rule="para" parents="31621 28464"/>
    </justification>
  </clause>

  <clause id="31625">
    <literal><![CDATA[
      a(x,y,R(z,L(u,w,v5),v6) * (v6 * L(u,w,v5))) = a(x,y,(z * R(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(31621(a,1),29248(a,1,3,1))].">
      <j1 rule="para" parents="31621 29248"/>
    </justification>
  </clause>

  <clause id="31626">
    <literal><![CDATA[
      R(x,L(y / z,z,z),u) = R(x,y * ((z \ y) \ y),u)
    ]]></literal>
    <justification jstring="[para(5823(a,1),31623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5823 31623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31627">
    <literal><![CDATA[
      ((x * R(y,y,z)) * z) / ((1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,L(y,y,z),z) = u
    ]]></literal>
    <justification jstring="[para(1964(a,2),31622(a,1))].">
      <j1 rule="para" parents="1964 31622"/>
    </justification>
  </clause>

  <clause id="31628">
    <literal><![CDATA[
      L(x \ R(x,y * x,z),z,y * x) = L(z,y * x,y * (y * x)) \ z
    ]]></literal>
    <justification jstring="[para(25908(a,1),31531(a,2,1))].">
      <j1 rule="para" parents="25908 31531"/>
    </justification>
  </clause>

  <clause id="31629">
    <literal><![CDATA[
      L(x \ R(x,y * x,z),z,y * x) = L(z,y * x,L(x,y,y)) \ z
    ]]></literal>
    <justification jstring="[para(3367(a,1),31628(a,2,1))].">
      <j1 rule="para" parents="3367 31628"/>
    </justification>
  </clause>

  <clause id="31631">
    <literal><![CDATA[
      L(T(x \ 1,x * y) \ z,x,y * x) = ((x * x) \ y) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(552(a,1),31570(a,2,1))].">
      <j1 rule="para" parents="552 31570"/>
    </justification>
  </clause>

  <clause id="31632">
    <literal><![CDATA[
      L(T(x \ 1,x * y) \ z,x,y * x) = y \ ((x * x) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,849,a(flip),b,31631,a),flip(a)].">
      <j1 rule="hyper" parents="370 849 31631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31633">
    <literal><![CDATA[
      L(T(x \ 1,x * y) \ z,x,y * x) = y \ (((x \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[para(946(a,1),31632(a,2,2))].">
      <j1 rule="para" parents="946 31632"/>
    </justification>
  </clause>

  <clause id="31634">
    <literal><![CDATA[
      (x * a((x \ y) * y,y,z)) \ ((1 / x) \ u) = R(x \ 1,y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(2960(a,1),31494(a,1,1,2))].">
      <j1 rule="para" parents="2960 31494"/>
    </justification>
  </clause>

  <clause id="31635">
    <literal><![CDATA[
      R(x \ 1,y,z) \ (x \ u) = R(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(31485(a,2),31634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31485 31634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31636">
    <literal><![CDATA[
      R(x \ 1,y,z) \ (x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(77(a,1),31635(a,2,2))].">
      <j1 rule="para" parents="77 31635"/>
    </justification>
  </clause>

  <clause id="31637">
    <literal><![CDATA[
      (x \ 1) \ ((x \ (R(x,y,z) \ x)) * u) = x \ ((R(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(31636(a,1),25819(a,1,2,1,2))].">
      <j1 rule="para" parents="31636 25819"/>
    </justification>
  </clause>

  <clause id="31638">
    <literal><![CDATA[
      (x \ 1) \ ((R(x,y,z) \ 1) * u) = x \ ((R(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1969(a,1),31637(a,1,2,1))].">
      <j1 rule="para" parents="1969 31637"/>
    </justification>
  </clause>

  <clause id="31639">
    <literal><![CDATA[
      x \ ((R(1 / x,y,z) \ 1) * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29664,a(flip),b,31638,a),flip(a)].">
      <j1 rule="hyper" parents="60 29664 31638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31640">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * T(v6,L(u,w,v5))) = a(x,y,(z * R(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(12402(a,1),31625(a,1,3))].">
      <j1 rule="para" parents="12402 31625"/>
    </justification>
  </clause>

  <clause id="31641">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(26968,a,31640,a),flip(a)].">
      <j1 rule="hyper" parents="26968 31640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31642">
    <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(26986,a,31641,a),flip(a)].">
      <j1 rule="hyper" parents="26986 31641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31644">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(L(x,y,z) \ x,u,w) = L(a(L(z,x,y),y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(31459(a,1),31476(a,1,2,1))].">
      <j1 rule="para" parents="31459 31476"/>
    </justification>
  </clause>

  <clause id="31645">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(x * L(x,y,z),u,w) = L(a(L(z,x,y),y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(2998(a,1),31644(a,1,2))].">
      <j1 rule="para" parents="2998 31644"/>
    </justification>
  </clause>

  <clause id="31646">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x * L(x,y,z),u,w) = L(a(L(z,x,y),y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(30591,a,31645,a)].">
      <j1 rule="hyper" parents="30591 31645"/>
    </justification>
  </clause>

  <clause id="31647">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x * L(x,y,z),u,w) = L((L(x,y,z) \ x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(31459(a,1),31646(a,2,1,1))].">
      <j1 rule="para" parents="31459 31646"/>
    </justification>
  </clause>

  <clause id="31648">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x * L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14170(a,1),31647(a,2,1))].">
      <j1 rule="para" parents="14170 31647"/>
    </justification>
  </clause>

  <clause id="31649">
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) * (x \ L(x,y,z)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23959,a,31648,a)].">
      <j1 rule="hyper" parents="23959 31648"/>
    </justification>
  </clause>

  <clause id="31650">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((w * u) * z)) * v5) = x * a((x \ y) * y,y,L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(28605(a,1),31490(a,2,2))].">
      <j1 rule="para" parents="28605 31490"/>
    </justification>
  </clause>

  <clause id="31651">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((w * u) * z)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,R(w,u,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(31490(a,2),31491(a,1))].">
      <j1 rule="para" parents="31490 31491"/>
    </justification>
  </clause>

  <clause id="31652">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a(((L(y \ 1,y,x) \ 1) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(29576(a,1),31581(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29576 31581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31653">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a((L(y \ 1,y,x) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26787,a(flip),b,31652,a),flip(a)].">
      <j1 rule="hyper" parents="370 26787 31652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31654">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a((L(y,y,x) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26821,a(flip),b,31653,a),flip(a)].">
      <j1 rule="hyper" parents="370 26821 31653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31655">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27636,a(flip),b,31654,a),flip(a)].">
      <j1 rule="hyper" parents="370 27636 31654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31656">
    <literal><![CDATA[
      a(L(x * y,y,y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27546,a(flip),b,31655,a)].">
      <j1 rule="hyper" parents="60 27546 31655"/>
    </justification>
  </clause>

  <clause id="31657">
    <literal><![CDATA[
      a(x * L(y * z,z,z),u,w) = a((z \ y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26519,a,31656,a)].">
      <j1 rule="hyper" parents="26519 31656"/>
    </justification>
  </clause>

  <clause id="31658">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((w * u) * z)) * v5) = R(x,y,L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,31485,a,b,31650,a),flip(a)].">
      <j1 rule="hyper" parents="370 31485 31650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31659">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(31651,a,31658,a)].">
      <j1 rule="hyper" parents="31651 31658"/>
    </justification>
  </clause>

  <clause id="31660">
    <literal><![CDATA[
      R(x,y,L(z \ (z \ u),w,v5) * z) = R(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,27440,a(flip),b,31659,a),flip(a)].">
      <j1 rule="hyper" parents="60 27440 31659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31661">
    <literal><![CDATA[
      a(x,y,R(z,z,L(u,w,v5) * v6) * (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(31659(a,1),29244(a,1,3,1))].">
      <j1 rule="para" parents="31659 29244"/>
    </justification>
  </clause>

  <clause id="31662">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,v5)) = R(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,27442,a(flip),b,31660,a),flip(a)].">
      <j1 rule="hyper" parents="60 27442 31660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31663">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ L(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,u * (z \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(31662(a,1),28676(a,1,3,1))].">
      <j1 rule="para" parents="31662 28676"/>
    </justification>
  </clause>

  <clause id="31664">
    <literal><![CDATA[
      L(x,a(y,z,u),a(a(y,z,u),w,x) * w) \ x = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,31112,a(flip),b,31474,a),flip(a)].">
      <j1 rule="hyper" parents="370 31112 31474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31665">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) * u,a(x,y,z),w) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(31258,a,31664,a)].">
      <j1 rule="hyper" parents="31258 31664"/>
    </justification>
  </clause>

  <clause id="31666">
    <literal><![CDATA[
      (x \ (x \ y)) \ R(x \ (x \ y),x \ y,z) = a(y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26372,a(flip),b,31492,a),flip(a)].">
      <j1 rule="hyper" parents="370 26372 31492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31667">
    <literal><![CDATA[
      L(x \ R(x,y \ x,z),y,y) = a(x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(29335,a,31666,a)].">
      <j1 rule="hyper" parents="29335 31666"/>
    </justification>
  </clause>

  <clause id="31669">
    <literal><![CDATA[
      a(x * (y \ x),x \ y,z) = a(y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31182,a(flip),b,31667,a)].">
      <j1 rule="hyper" parents="60 31182 31667"/>
    </justification>
  </clause>

  <clause id="31670">
    <literal><![CDATA[
      a((1 / x) * (L(y,x,x) \ (1 / x)),x * y,z) = a(L(y,x,x),(1 / x) \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(581(a,1),31669(a,1,2))].">
      <j1 rule="para" parents="581 31669"/>
    </justification>
  </clause>

  <clause id="31671">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (u * L(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(1961(a,1),31543(a,1,3))].">
      <j1 rule="para" parents="1961 31543"/>
    </justification>
  </clause>

  <clause id="31672">
    <literal><![CDATA[
      a(x,y,z \ (u * R(w,v5,v6))) = a(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(27014,a,31671,a),flip(a)].">
      <j1 rule="hyper" parents="27014 31671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31674">
    <literal><![CDATA[
      L(a(x,y,z),u,(a(x,y,z) * w) * u) \ w = (u \ 1) * ((a(x,y,z) * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(30662(a,1),31573(a,1,1))].">
      <j1 rule="para" parents="30662 31573"/>
    </justification>
  </clause>

  <clause id="31675">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (L(u,w,v5) * v6)) = a(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(1961(a,1),31661(a,1,3))].">
      <j1 rule="para" parents="1961 31661"/>
    </justification>
  </clause>

  <clause id="31677">
    <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(31675(a,1),27014(a,1))].">
      <j1 rule="para" parents="31675 27014"/>
    </justification>
  </clause>

  <clause id="31678">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) * w) * v5)) = a(x,y,z \ (L(u,w,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(31677,a,27227,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="31677 27227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31679">
    <literal><![CDATA[
      a(x,y,(z * u) \ (L(z,u,u) * w)) = a(x,y,(z / u) \ (z * w))
    ]]></literal>
    <justification jstring="[para(31592(a,1),31678(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31592 31678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31680">
    <literal><![CDATA[
      a(x,y,(z * u) \ (L(z,u,u) * w)) = a(x,y,(u \ z) \ (z * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,26895,a(flip),b,31679,a),flip(a)].">
      <j1 rule="hyper" parents="370 26895 31679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31681">
    <literal><![CDATA[
      a(x,y,z * (u \ R(w,v5,v6))) = a(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(673(a,1),31663(a,1,3)),flip(a)].">
      <j1 rule="para" parents="673 31663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31682">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ L(w,w,v5))) = a(x,y,(u \ a(w,w,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29773,a(flip),b,31681,a),flip(a)].">
      <j1 rule="hyper" parents="60 29773 31681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31683">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(w,w,v5)))) = a(x,y,(u \ a(w,w,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28618,a(flip),b,31682,a)].">
      <j1 rule="hyper" parents="60 28618 31682"/>
    </justification>
  </clause>

  <clause id="31684">
    <literal><![CDATA[
      a(x,y,(z \ a(u,w,w)) * v5) = a(x,y,(z \ a(w,w,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,28939,a(flip),b,31683,a)].">
      <j1 rule="hyper" parents="60 28939 31683"/>
    </justification>
  </clause>

  <clause id="31685">
    <literal><![CDATA[
      L(a(x,y,z),z,a(x,y,z) * u) \ u = (z \ 1) * ((a(x,y,z) * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(30055(a,1),31674(a,1,1))].">
      <j1 rule="para" parents="30055 31674"/>
    </justification>
  </clause>

  <clause id="31686">
    <literal><![CDATA[
      (x \ 1) * ((a(y,z,x) * (x \ 1)) \ u) = (a(y,z,x) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30940,a(flip),b,31685,a),flip(a)].">
      <j1 rule="hyper" parents="60 30940 31685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31687">
    <literal><![CDATA[
      (x \ 1) * ((x \ a(y,z,x)) \ u) = (a(y,z,x) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(24116(a,1),31686(a,1,2,1))].">
      <j1 rule="para" parents="24116 31686"/>
    </justification>
  </clause>

  <clause id="31688">
    <literal><![CDATA[
      x * (((1 / x) \ a(y,z,x)) \ u) = (a(y,z,x) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28496,a(flip),b,31687,a)].">
      <j1 rule="hyper" parents="60 28496 31687"/>
    </justification>
  </clause>

  <clause id="31689">
    <literal><![CDATA[
      (a(x,y,z) * z) \ (z * u) = z * ((z * a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(14788(a,1),31688(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14788 31688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31690">
    <literal><![CDATA[
      L(a(x \ 1,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = 1 * (x * ((x * a(z,u,x)) \ (y * a(z,u,x))))
    ]]></literal>
    <justification jstring="[para(31689(a,1),29510(a,2,2))].">
      <j1 rule="para" parents="31689 29510"/>
    </justification>
  </clause>

  <clause id="31691">
    <literal><![CDATA[
      x * ((x * a(y,x,z)) \ (a(y,x,z) * u)) = L(u,a(y,x,z),x * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(23619(a,1),31568(a,1,2,2,1))].">
      <j1 rule="para" parents="23619 31568"/>
    </justification>
  </clause>

  <clause id="31693">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = z * L(z \ x,z,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23652(a,2),31691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23652 31691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31694">
    <literal><![CDATA[
      ((x * a(y,x,z)) * (a(y,x,z) \ 1)) \ ((x * a(y,x,z)) * u) = x * L(x \ ((a(y,x,z) \ 1) \ u),x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,3410,a(flip),b,31693,a)].">
      <j1 rule="hyper" parents="60 3410 31693"/>
    </justification>
  </clause>

  <clause id="31695">
    <literal><![CDATA[
      a((1 / x) * ((x * (x * y)) \ x),x * y,z) = a(L(y,x,x),(1 / x) \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(1275(a,1),31670(a,1,1,2))].">
      <j1 rule="para" parents="1275 31670"/>
    </justification>
  </clause>

  <clause id="31696">
    <literal><![CDATA[
      a((1 / x) * (x \ ((x * y) \ x)),x * y,z) = a(L(y,x,x),(1 / x) \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(27796,a,31695,a)].">
      <j1 rule="hyper" parents="27796 31695"/>
    </justification>
  </clause>

  <clause id="31697">
    <literal><![CDATA[
      a((x * x) \ ((x * y) \ x),x * y,z) = a(L(y,x,x),(1 / x) \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(552(a,1),31696(a,1,1))].">
      <j1 rule="para" parents="552 31696"/>
    </justification>
  </clause>

  <clause id="31698">
    <literal><![CDATA[
      a((x * x) \ (x \ (y \ x)),x * y,z) = a(L(y,x,x),(1 / x) \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(27800,a,31697,a)].">
      <j1 rule="hyper" parents="27800 31697"/>
    </justification>
  </clause>

  <clause id="31699">
    <literal><![CDATA[
      a(L(x,y,y),(1 / y) \ L(x,y,y),z) = a(y \ (x \ y),y * x,z)
    ]]></literal>
    <justification jstring="[hyper(2954,a,31698,a),flip(a)].">
      <j1 rule="hyper" parents="2954 31698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31701">
    <literal><![CDATA[
      a(x \ (y \ x),x * y,z) = a(L(y,x,x),x * y,z)
    ]]></literal>
    <justification jstring="[para(581(a,1),31699(a,1,2)),flip(a)].">
      <j1 rule="para" parents="581 31699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31702">
    <literal><![CDATA[
      (a(L(x,y,y),y * x,z) \ y) * z = (y / (y * x)) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(31701(a,1),28893(a,1,1,1))].">
      <j1 rule="para" parents="31701 28893"/>
    </justification>
  </clause>

  <clause id="31703">
    <literal><![CDATA[
      a(L(x,y * L(z,u,w),v5),v5,y * L(z,u,w)) = L(y * R(z,u,w),v5,x) \ (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(27783(a,1),31472(a,1,1))].">
      <j1 rule="para" parents="27783 31472"/>
    </justification>
  </clause>

  <clause id="31704">
    <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(60,a,31459,a(flip),b,31703,a),flip(a)].">
      <j1 rule="hyper" parents="60 31459 31703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31705">
    <literal><![CDATA[
      L(a(x \ 1,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = 1 * (x * L(x \ y,x,a(z,u,x)))
    ]]></literal>
    <justification jstring="[para(25787(a,2),31690(a,2,2,2))].">
      <j1 rule="para" parents="25787 31690"/>
    </justification>
  </clause>

  <clause id="31706">
    <literal><![CDATA[
      L(a(x \ 1,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = x * L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,2,a(flip),b,31705,a),flip(a)].">
      <j1 rule="hyper" parents="370 2 31705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31707">
    <literal><![CDATA[
      L(a(x,y,a(z,u,x)) \ y,x \ 1,a(z,u,x)) = x * L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(2962(a,1),31706(a,1,1,1))].">
      <j1 rule="para" parents="2962 31706"/>
    </justification>
  </clause>

  <clause id="31708">
    <literal><![CDATA[
      L(1 \ x,y \ 1,a(z,u,y)) = y * L(y \ x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(14785(a,1),31707(a,1,1,1))].">
      <j1 rule="para" parents="14785 31707"/>
    </justification>
  </clause>

  <clause id="31709">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,x)) = L(y,x \ 1,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(62(a,1),31708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="62 31708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31711">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,x)) = L(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,3401,a(flip),b,31709,a),flip(a)].">
      <j1 rule="hyper" parents="370 3401 31709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31712">
    <literal><![CDATA[
      L(x * y,y,a(z,u,y)) = L(x,y,a(z,u,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1349,a,31711,a),flip(a)].">
      <j1 rule="hyper" parents="1349 31711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31713">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = x * L(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(129,a,31711,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="129 31711 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31714">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) = z * ((a(x,y,z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(30839(a,1),31711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30839 31711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31715">
    <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(31704(a,1),31642(a,1,3,2))].">
      <j1 rule="para" parents="31704 31642"/>
    </justification>
  </clause>

  <clause id="31716">
    <literal><![CDATA[
      a(x,y,L(z * R(u,w,v5),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * L(u,w,v5),v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(31715(a,1),26986(a,1))].">
      <j1 rule="para" parents="31715 26986"/>
    </justification>
  </clause>

  <clause id="31717">
    <literal><![CDATA[
      (a(x,y,z) \ (y * a(x,y,z))) \ ((y * a(x,y,z)) * u) = y * L(y \ ((a(x,y,z) \ 1) \ u),y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30626(a,1),31694(a,1,1))].">
      <j1 rule="para" parents="30626 31694"/>
    </justification>
  </clause>

  <clause id="31718">
    <literal><![CDATA[
      x * L(x \ ((a(y,x,z) \ 1) \ u),x,a(y,x,z)) = x \ ((x * a(y,x,z)) * u)
    ]]></literal>
    <justification jstring="[para(23622(a,1),31717(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23622 31717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31719">
    <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(30622(a,1),31718(a,1,2,1,2))].">
      <j1 rule="para" parents="30622 31718"/>
    </justification>
  </clause>

  <clause id="31720">
    <literal><![CDATA[
      x \ ((x * a(y,x,z)) * u) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(30839(a,1),31719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30839 31719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31721">
    <literal><![CDATA[
      R(x,a(y,x,z),u) * (x \ (a(y,x,z) * u)) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(2044,a,31720,a)].">
      <j1 rule="hyper" parents="2044 31720"/>
    </justification>
  </clause>

  <clause id="31722">
    <literal><![CDATA[
      x * (x * ((a(y,x,z) \ x) \ u)) = (x * a(y,x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(156,a,31720,a)].">
      <j1 rule="hyper" parents="156 31720"/>
    </justification>
  </clause>

  <clause id="31723">
    <literal><![CDATA[
      x \ ((x * y) * a(z,x,y)) = x * ((a(z,x,y) \ x) \ y)
    ]]></literal>
    <justification jstring="[para(28301(a,1),31720(a,1,2))].">
      <j1 rule="para" parents="28301 31720"/>
    </justification>
  </clause>

  <clause id="31724">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),((x * a(y,x,z)) \ x) \ u) = a(x * a(y,x,z),x * a(y,x,z),x * ((a(y,x,z) \ x) \ u))
    ]]></literal>
    <justification jstring="[para(31720(a,1),29144(a,2,3))].">
      <j1 rule="para" parents="31720 29144"/>
    </justification>
  </clause>

  <clause id="31725">
    <literal><![CDATA[
      ((x * a(y,x,z)) * u) \ ((1 / x) \ (x * ((a(y,x,z) \ x) \ u))) = a(x,x,x * ((a(y,x,z) \ x) \ u))
    ]]></literal>
    <justification jstring="[para(31722(a,1),28731(a,1,1))].">
      <j1 rule="para" parents="31722 28731"/>
    </justification>
  </clause>

  <clause id="31726">
    <literal><![CDATA[
      x * ((a(y,x,z) \ x) \ z) = L(1 / z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30017,a(flip),b,31723,a),flip(a)].">
      <j1 rule="hyper" parents="60 30017 31723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31727">
    <literal><![CDATA[
      R((a(x,y,z) \ y) / y,y,(a(x,y,z) \ y) \ z) = z / (L(1 / z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(31726(a,1),428(a,2,2))].">
      <j1 rule="para" parents="31726 428"/>
    </justification>
  </clause>

  <clause id="31728">
    <literal><![CDATA[
      L(x,a(y,x,z),u) * (x \ (a(y,x,z) * u)) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(28368(a,1),31721(a,1,1))].">
      <j1 rule="para" parents="28368 31721"/>
    </justification>
  </clause>

  <clause id="31729">
    <literal><![CDATA[
      (a(x,a(y,z,u),z) \ a(y,z,u)) * x = z * ((a(y,z,u) \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28804,a(flip),b,31728,a)].">
      <j1 rule="hyper" parents="60 28804 31728"/>
    </justification>
  </clause>

  <clause id="31730">
    <literal><![CDATA[
      (a(x,a(y,x,z),u) * a(y,x,z)) * u = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(30724(a,1),31729(a,1,1))].">
      <j1 rule="para" parents="30724 31729"/>
    </justification>
  </clause>

  <clause id="31731">
    <literal><![CDATA[
      (a(x,y,z) * a(u,a(x,y,z),y)) * u = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(31284(a,1),31730(a,1,1))].">
      <j1 rule="para" parents="31284 31730"/>
    </justification>
  </clause>

  <clause id="31732">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(u,a(x,y,z),y) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(28806,a,31731,a)].">
      <j1 rule="hyper" parents="28806 31731"/>
    </justification>
  </clause>

  <clause id="31733">
    <literal><![CDATA[
      a(x,y,z) * R(u,a(x,y,z),y) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(31100,a,31732,a)].">
      <j1 rule="hyper" parents="31100 31732"/>
    </justification>
  </clause>

  <clause id="31734">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),y) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(28368(a,1),31733(a,1,2))].">
      <j1 rule="para" parents="28368 31733"/>
    </justification>
  </clause>

  <clause id="31735">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,y,(a(x,y,z) \ y) \ z) = z / (L(1 / z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(30646(a,1),31727(a,1,1))].">
      <j1 rule="para" parents="30646 31727"/>
    </justification>
  </clause>

  <clause id="31736">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,y,y \ L(z,y,x)) = z / (L(1 / z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,31034,a(flip),b,31735,a)].">
      <j1 rule="hyper" parents="60 31034 31735"/>
    </justification>
  </clause>

  <clause id="31738">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,y \ L(z,y,x)) = z / (L(1 / z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,29338,a(flip),b,31736,a)].">
      <j1 rule="hyper" parents="60 29338 31736"/>
    </justification>
  </clause>

  <clause id="31739">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,L(z,y,x) * y) = z / (L(1 / z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,31566,a(flip),b,31738,a)].">
      <j1 rule="hyper" parents="60 31566 31738"/>
    </justification>
  </clause>

  <clause id="31740">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,L(z,y,x) * y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,28576,a(flip),b,31739,a),flip(a)].">
      <j1 rule="hyper" parents="370 28576 31739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31741">
    <literal><![CDATA[
      ((x * a(y,x,z)) * u) \ (x * ((x \ 1) \ ((a(y,x,z) \ x) \ u))) = a(x,x,x * ((a(y,x,z) \ x) \ u))
    ]]></literal>
    <justification jstring="[para(2077(a,1),31725(a,1,2))].">
      <j1 rule="para" parents="2077 31725"/>
    </justification>
  </clause>

  <clause id="31742">
    <literal><![CDATA[
      ((x * a(y,x,z)) * u) \ (x * (x \ ((a(y,x,z) \ (1 / x)) \ u))) = a(x,x,x * ((a(y,x,z) \ x) \ u))
    ]]></literal>
    <justification jstring="[para(1568(a,1),31741(a,1,2,2))].">
      <j1 rule="para" parents="1568 31741"/>
    </justification>
  </clause>

  <clause id="31743">
    <literal><![CDATA[
      a(x,x,x * ((a(y,x,z) \ x) \ u)) = ((x * a(y,x,z)) * u) \ ((a(y,x,z) \ (1 / x)) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),31742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 31742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31745">
    <literal><![CDATA[
      a(x,x,x * ((a(y,x,z) \ x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,u) = w
    ]]></literal>
    <justification jstring="[para(31743(a,2),31318(a,1))].">
      <j1 rule="para" parents="31743 31318"/>
    </justification>
  </clause>

  <clause id="31746">
    <literal><![CDATA[
      x \ ((R(1 / x,y,z) \ 1) * T(R(1 / x,y,z) \ ((R(x \ 1,y,z) \ 1) \ u),w)) = T(x \ (R(1 / x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(7106(a,1),31615(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="7106 31615"/>
    </justification>
  </clause>

  <clause id="31747">
    <literal><![CDATA[
      x \ ((R(1 / x,y,z) \ 1) * T(x \ ((1 / x) \ u),w)) = T(x \ (R(1 / x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(30462(a,1),31746(a,1,2,2,1))].">
      <j1 rule="para" parents="30462 31746"/>
    </justification>
  </clause>

  <clause id="31748">
    <literal><![CDATA[
      x * (R(x,y,z) \ T(x \ ((1 / x) \ u),w)) = T(x \ (R(1 / x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,31639,a(flip),b,31747,a)].">
      <j1 rule="hyper" parents="60 31639 31747"/>
    </justification>
  </clause>

  <clause id="31750">
    <literal><![CDATA[
      R(x,y,z) \ ((1 / x) \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(31540,a,31748,a(flip))].">
      <j1 rule="hyper" parents="31540 31748"/>
    </justification>
  </clause>

  <clause id="31751">
    <literal><![CDATA[
      R(x \ 1,y,z) \ (x \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,31635,a,b,31750,a)].">
      <j1 rule="hyper" parents="60 31635 31750"/>
    </justification>
  </clause>

  <clause id="31752">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),x * ((a(y,x,z) \ x) \ u)) = a(x * a(y,x,z),x * a(y,x,z),(a(y,x,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(30629(a,1),31724(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30629 31724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31753">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),x * ((a(y,x,z) \ x) \ u)) = a(x * a(y,x,z),x * a(y,x,z),a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[para(30622(a,1),31752(a,2,3))].">
      <j1 rule="para" parents="30622 31752"/>
    </justification>
  </clause>

  <clause id="31755">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),x * ((a(y,x,z) \ x) \ u)) = a(x,x,a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30994,a(flip),b,31753,a),flip(a)].">
      <j1 rule="hyper" parents="370 30994 31753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31756">
    <literal><![CDATA[
      a(x,x,x * ((a(y,x,z) \ x) \ u)) = a(x,x,a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(30995,a,31755,a)].">
      <j1 rule="hyper" parents="30995 31755"/>
    </justification>
  </clause>

  <clause id="31758">
    <literal><![CDATA[
      a(x,x,a(y,x,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(31745,a,31756,a),flip(a)].">
      <j1 rule="hyper" parents="31745 31756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31760">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,30002,a(flip),b,31758,a)].">
      <j1 rule="hyper" parents="60 30002 31758"/>
    </justification>
  </clause>

  <clause id="31763">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,31760,a,b,31155,a),flip(a)].">
      <j1 rule="hyper" parents="126 31760 31155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31764">
    <literal><![CDATA[
      a(x,y,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,31760,a,b,30759,a),flip(a)].">
      <j1 rule="hyper" parents="124 31760 30759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31765">
    <literal><![CDATA[
      a(x,x,L((y * x) \ z,u,w)) = a(x,x,L(x \ (y \ z),u,w))
    ]]></literal>
    <justification jstring="[para(746(a,1),31760(a,1,3))].">
      <j1 rule="para" parents="746 31760"/>
    </justification>
  </clause>

  <clause id="31766">
    <literal><![CDATA[
      a(x,x,y) \ L(y,x,z) = L(L(y,x,z),x,x)
    ]]></literal>
    <justification jstring="[para(31760(a,1),3943(a,1,1))].">
      <j1 rule="para" parents="31760 3943"/>
    </justification>
  </clause>

  <clause id="31767">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(31760(a,1),30395(a,1))].">
      <j1 rule="para" parents="31760 30395"/>
    </justification>
  </clause>

  <clause id="31768">
    <literal><![CDATA[
      L(a(x,x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(31760(a,1),30401(a,1,1))].">
      <j1 rule="para" parents="31760 30401"/>
    </justification>
  </clause>

  <clause id="31769">
    <literal><![CDATA[
      L(x,x * (a(y,z,x) \ x),u) = a(y,z,a(x,x,u)) * x
    ]]></literal>
    <justification jstring="[para(31760(a,1),31589(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="31760 31589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31770">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = u \ u
    ]]></literal>
    <justification jstring="[hyper(370,a,63,a,b,31763,a),flip(a)].">
      <j1 rule="hyper" parents="370 63 31763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31771">
    <literal><![CDATA[
      a(x,a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(31130,a,31764,a)].">
      <j1 rule="hyper" parents="31130 31764"/>
    </justification>
  </clause>

  <clause id="31772">
    <literal><![CDATA[
      1 * (R(x,x,y) * z) = x * (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(31771(a,1),30606(a,1,1))].">
      <j1 rule="para" parents="31771 30606"/>
    </justification>
  </clause>

  <clause id="31773">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(31535,a,31770,a),flip(a)].">
      <j1 rule="hyper" parents="31535 31770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31774">
    <literal><![CDATA[
      L(x,a(y,x,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(31253,a,31770,a)].">
      <j1 rule="hyper" parents="31253 31770"/>
    </justification>
  </clause>

  <clause id="31775">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(30773,a,31770,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="30773 31770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31776">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(30734,a,31773,a)].">
      <j1 rule="hyper" parents="30734 31773"/>
    </justification>
  </clause>

  <clause id="31777">
    <literal><![CDATA[
      (x * a(y,x,x)) \ z = x \ (a(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(25584,a,31773,a)].">
      <j1 rule="hyper" parents="25584 31773"/>
    </justification>
  </clause>

  <clause id="31778">
    <literal><![CDATA[
      (x * a(y,x,x)) * z = x * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(31774(a,1),28365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31774 28365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31779">
    <literal><![CDATA[
      x * (L(x,x,y) \ z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(129,a,31775,a(flip),b,30165,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 31775 30165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31780">
    <literal><![CDATA[
      L(x,x,L(y,x,z)) = a(y,x,x) \ x
    ]]></literal>
    <justification jstring="[para(31775(a,1),30097(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31775 30097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31781">
    <literal><![CDATA[
      L(x,x,y) * (x \ z) = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[para(31775(a,1),30604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31775 30604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31782">
    <literal><![CDATA[
      a(x,y,y) \ (z \ (z / y)) = L(L(1 / y,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(31775(a,1),30894(a,1,1))].">
      <j1 rule="para" parents="31775 30894"/>
    </justification>
  </clause>

  <clause id="31783">
    <literal><![CDATA[
      L(x,x,L(y,x,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28815,a(flip),b,31780,a),flip(a)].">
      <j1 rule="hyper" parents="370 28815 31780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31786">
    <literal><![CDATA[
      L(x,x,y) * a(x,x,z) = L(R(x,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(31783(a,1),31351(a,1,1))].">
      <j1 rule="para" parents="31783 31351"/>
    </justification>
  </clause>

  <clause id="31787">
    <literal><![CDATA[
      a(L(x,x,y),L(y,x,z),u) = x \ R(x,L(y,x,z),u)
    ]]></literal>
    <justification jstring="[para(31783(a,1),31457(a,1,1))].">
      <j1 rule="para" parents="31783 31457"/>
    </justification>
  </clause>

  <clause id="31788">
    <literal><![CDATA[
      (((x * y) \ x) * z) * a(x,y,y) = (y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(4068,a,31779,a),flip(a)].">
      <j1 rule="hyper" parents="4068 31779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31789">
    <literal><![CDATA[
      (x \ y) * a(z,x,x) = L(x,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(2183,a,31779,a),flip(a)].">
      <j1 rule="hyper" parents="2183 31779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31790">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ z) = z * a(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,4067,a(flip),b,31779,a)].">
      <j1 rule="hyper" parents="60 4067 31779"/>
    </justification>
  </clause>

  <clause id="31791">
    <literal><![CDATA[
      (x / y) * L(y,y,z) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(24074,a,31781,a)].">
      <j1 rule="hyper" parents="24074 31781"/>
    </justification>
  </clause>

  <clause id="31792">
    <literal><![CDATA[
      a(x,y,y) * (y \ z) = L(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(2205,a,31781,a(flip))].">
      <j1 rule="hyper" parents="2205 31781"/>
    </justification>
  </clause>

  <clause id="31793">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(1385,a,31781,a(flip))].">
      <j1 rule="hyper" parents="1385 31781"/>
    </justification>
  </clause>

  <clause id="31794">
    <literal><![CDATA[
      (a(x,y,y) \ z) * y = z * L(y,y,x)
    ]]></literal>
    <justification jstring="[para(31781(a,1),25179(a,1,1))].">
      <j1 rule="para" parents="31781 25179"/>
    </justification>
  </clause>

  <clause id="31796">
    <literal><![CDATA[
      x \ (((y / x) \ y) * a(z,y / x,y / x)) = L(y \ x,y / x,z) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(31789(a,2),29808(a,2,2)),flip(a)].">
      <j1 rule="para" parents="31789 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31798">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * L(z,z,u) = a(u,z,z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(28814(a,1),31791(a,1,1))].">
      <j1 rule="para" parents="28814 31791"/>
    </justification>
  </clause>

  <clause id="31800">
    <literal><![CDATA[
      a(x,(y \ z) * a(y,y,u),w) = a(x,L(y,y,u) \ z,w)
    ]]></literal>
    <justification jstring="[para(31792(a,1),28927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31792 28927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31801">
    <literal><![CDATA[
      L(x,x,y) * (y * (z * a(y,x,x))) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28809,a,b,31793,a)].">
      <j1 rule="hyper" parents="60 28809 31793"/>
    </justification>
  </clause>

  <clause id="31802">
    <literal><![CDATA[
      a(x,x,1 / T(x,y)) \ (y \ (T(y,x) / x)) = L(L(1 / T(x,y),x,y),x,x)
    ]]></literal>
    <justification jstring="[para(12488(a,1),31766(a,1,2))].">
      <j1 rule="para" parents="12488 31766"/>
    </justification>
  </clause>

  <clause id="31803">
    <literal><![CDATA[
      x * (y * a(x,x,z)) = R(x,x,z) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,31772,a),flip(a)].">
      <j1 rule="hyper" parents="131 31772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31806">
    <literal><![CDATA[
      (x * y) * a(y,y,z) = x * R(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,25195,a(flip),b,31803,a),flip(a)].">
      <j1 rule="hyper" parents="31 25195 31803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31807">
    <literal><![CDATA[
      x \ (R(x,x,y) * z) = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(125,a,31803,a(flip),b,23641,a)].">
      <j1 rule="hyper" parents="125 31803 23641"/>
    </justification>
  </clause>

  <clause id="31808">
    <literal><![CDATA[
      x * (y * (z * a(x,x,y))) = R(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(14786(a,1),31803(a,1,2))].">
      <j1 rule="para" parents="14786 31803"/>
    </justification>
  </clause>

  <clause id="31809">
    <literal><![CDATA[
      a(x,x,y) * (L(y,z,u) * (x * w)) = L(y,z,u) * (R(x,x,y) * w)
    ]]></literal>
    <justification jstring="[para(31803(a,1),28809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31803 28809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31810">
    <literal><![CDATA[
      R(x,x,L(y,z,u)) * a(u,z,a(y,x,x)) = x * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(31155(a,1),31803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31155 31803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31811">
    <literal><![CDATA[
      ((x * y) * z) * a(y,y,z) = (x * R(y,y,z)) * z
    ]]></literal>
    <justification jstring="[para(31806(a,1),28301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31806 28301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31812">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(1976,a,31807,a)].">
      <j1 rule="hyper" parents="1976 31807"/>
    </justification>
  </clause>

  <clause id="31813">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,3033,a(flip),b,31812,a)].">
      <j1 rule="hyper" parents="60 3033 31812"/>
    </justification>
  </clause>

  <clause id="31814">
    <literal><![CDATA[
      x \ (a(y,x,x) \ (K(z,x * a(y,x,x)) * u)) = T(x * a(y,x,x),z) \ u
    ]]></literal>
    <justification jstring="[hyper(7979,a,31777,a),flip(a)].">
      <j1 rule="hyper" parents="7979 31777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31815">
    <literal><![CDATA[
      a(x,y,(z * (u * a(w,z,z))) * v5) = a(x,y,(L(z,z,w) * u) * v5)
    ]]></literal>
    <justification jstring="[para(31778(a,1),29977(a,1,3,1))].">
      <j1 rule="para" parents="31778 29977"/>
    </justification>
  </clause>

  <clause id="31817">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(31788(a,1),30828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31788 30828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31818">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,2074,a(flip),b,31817,a),flip(a)].">
      <j1 rule="hyper" parents="370 2074 31817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31820">
    <literal><![CDATA[
      L(x \ (((y \ (y / x)) \ 1) \ z),x,x) = (y \ ((y * x) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,28994,a(flip),b,31818,a),flip(a)].">
      <j1 rule="hyper" parents="60 28994 31818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31821">
    <literal><![CDATA[
      R(x,a(y,y,z),u) * (x \ a(y,y,z)) = (z / (y * z)) * ((1 / y) \ a(x,a(y,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,31103,a,b,31813,a)].">
      <j1 rule="hyper" parents="370 31103 31813"/>
    </justification>
  </clause>

  <clause id="31822">
    <literal><![CDATA[
      x * (y * (a(x,x,y) * z)) = R(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(23620(a,2),31808(a,1,2,2))].">
      <j1 rule="para" parents="23620 31808"/>
    </justification>
  </clause>

  <clause id="31823">
    <literal><![CDATA[
      L(L(1 / T(x,y),T(x,y),x * y),T(x,y),z) = a(z,T(x,y),T(x,y)) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(214(a,1),31782(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="214 31782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31825">
    <literal><![CDATA[
      L(x,x * (a(y,z,x) \ x),u) = L(x,x * L(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30852,a,b,31769,a),flip(a)].">
      <j1 rule="hyper" parents="370 30852 31769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31827">
    <literal><![CDATA[
      L(x,x * (x * a(y,z,x)),u) = L(x,x * L(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(30684,a,31825,a)].">
      <j1 rule="hyper" parents="30684 31825"/>
    </justification>
  </clause>

  <clause id="31828">
    <literal><![CDATA[
      L(x,L(a(y,z,x),x,x),u) = L(x,x * L(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(3544,a,31827,a)].">
      <j1 rule="hyper" parents="3544 31827"/>
    </justification>
  </clause>

  <clause id="31829">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = L(x,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(14782(a,1),31828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14782 31828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31830">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * z = L(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30852,a(flip),b,31829,a)].">
      <j1 rule="hyper" parents="60 30852 31829"/>
    </justification>
  </clause>

  <clause id="31832">
    <literal><![CDATA[
      L(x,x,y * L(y,z,u)) = L(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31553,a,b,31830,a)].">
      <j1 rule="hyper" parents="60 31553 31830"/>
    </justification>
  </clause>

  <clause id="31833">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(32,a,31254,a,b,31830,a)].">
      <j1 rule="hyper" parents="32 31254 31830"/>
    </justification>
  </clause>

  <clause id="31834">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(32,a,30134,a,b,31830,a)].">
      <j1 rule="hyper" parents="32 30134 31830"/>
    </justification>
  </clause>

  <clause id="31835">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,31124,a,b,31833,a)].">
      <j1 rule="hyper" parents="370 31124 31833"/>
    </justification>
  </clause>

  <clause id="31836">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30800,a(flip),b,31833,a)].">
      <j1 rule="hyper" parents="60 30800 31833"/>
    </justification>
  </clause>

  <clause id="31837">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,u,w)) = (u / x) \ L(u,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31833(a,1),29202(a,1,2))].">
      <j1 rule="para" parents="31833 29202"/>
    </justification>
  </clause>

  <clause id="31838">
    <literal><![CDATA[
      a(x,a(y,z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(a(u,x,x),z,y) = w
    ]]></literal>
    <justification jstring="[para(31833(a,2),31133(a,1))].">
      <j1 rule="para" parents="31833 31133"/>
    </justification>
  </clause>

  <clause id="31839">
    <literal><![CDATA[
      a(x,a(y,z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(a(x,x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(31833(a,2),31137(a,1))].">
      <j1 rule="para" parents="31833 31137"/>
    </justification>
  </clause>

  <clause id="31840">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(2972,a,31834,a)].">
      <j1 rule="hyper" parents="2972 31834"/>
    </justification>
  </clause>

  <clause id="31841">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,31136,a,b,31834,a)].">
      <j1 rule="hyper" parents="370 31136 31834"/>
    </justification>
  </clause>

  <clause id="31845">
    <literal><![CDATA[
      a(a(x,a(y,z,x),u),w,v5) = a(a(y,z,a(x,x,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(31835(a,1),30799(a,1,1))].">
      <j1 rule="para" parents="31835 30799"/>
    </justification>
  </clause>

  <clause id="31846">
    <literal><![CDATA[
      x * a(y,z,a(u,u,x)) = L(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,31836,a(flip),b,30090,a)].">
      <j1 rule="hyper" parents="129 31836 30090"/>
    </justification>
  </clause>

  <clause id="31847">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(y,y,x)) = w
    ]]></literal>
    <justification jstring="[para(31841(a,1),31148(a,1))].">
      <j1 rule="para" parents="31841 31148"/>
    </justification>
  </clause>

  <clause id="31848">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,a(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(31840(a,1),2973(a,1))].">
      <j1 rule="para" parents="31840 2973"/>
    </justification>
  </clause>

  <clause id="31852">
    <literal><![CDATA[
      x * ((y * (z \ y)) / (z * ((z \ y) * (z \ y)))) = ((z \ y) \ 1) * ((y \ z) \ x)
    ]]></literal>
    <justification jstring="[para(19667(a,2),31790(a,2,2)),flip(a)].">
      <j1 rule="para" parents="19667 31790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31853">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ z) = z * a(x,x * y,x * y)
    ]]></literal>
    <justification jstring="[para(30328(a,1),31790(a,2,2))].">
      <j1 rule="para" parents="30328 31790"/>
    </justification>
  </clause>

  <clause id="31854">
    <literal><![CDATA[
      R(x,x,L(y,z,u)) * a(u,z,a(y,x,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28420,a(flip),b,31810,a),flip(a)].">
      <j1 rule="hyper" parents="370 28420 31810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31855">
    <literal><![CDATA[
      R(x,x,a(y,z,u) \ 1) * a(y * z,u,a(u \ L(u,z,y),x,x)) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(30718(a,1),31854(a,1,1,3))].">
      <j1 rule="para" parents="30718 31854"/>
    </justification>
  </clause>

  <clause id="31857">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ z) = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[hyper(370,a,30658,a(flip),b,31853,a),flip(a)].">
      <j1 rule="hyper" parents="370 30658 31853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31858">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) \ z,u,w) = a((x \ y) * ((y \ x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(31857(a,1),2968(a,1,1))].">
      <j1 rule="para" parents="31857 2968"/>
    </justification>
  </clause>

  <clause id="31859">
    <literal><![CDATA[
      a(x,x,L((y * x) \ z,u,w)) = a(x,x,L(x * (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29081,a(flip),b,31765,a),flip(a)].">
      <j1 rule="hyper" parents="370 29081 31765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31860">
    <literal><![CDATA[
      a(x,x,L((y * x) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(x * (y \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(31765(a,2),29153(a,1))].">
      <j1 rule="para" parents="31765 29153"/>
    </justification>
  </clause>

  <clause id="31861">
    <literal><![CDATA[
      a(x,x,L(x * (y \ z),u,(y * x) \ z)) = a(x,x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(26984,a,31859,a),flip(a)].">
      <j1 rule="hyper" parents="26984 31859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31863">
    <literal><![CDATA[
      1 \ ((x \ (x / y)) * (y \ z)) = (x \ ((x * y) * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(60,a,31027,a(flip),b,31820,a)].">
      <j1 rule="hyper" parents="60 31027 31820"/>
    </justification>
  </clause>

  <clause id="31864">
    <literal><![CDATA[
      (x \ ((x * y) * y)) \ z = (x \ (x / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(191,a,31863,a),flip(a)].">
      <j1 rule="hyper" parents="191 31863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31865">
    <literal><![CDATA[
      (x \ (x / ((y \ 1) \ 1))) * (((y \ 1) \ 1) \ z) = (x \ ((x * y) * y)) \ z
    ]]></literal>
    <justification jstring="[para(29255(a,1),31864(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29255 31864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31866">
    <literal><![CDATA[
      a(x,x,(y * x) \ z) = a(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(31767,a,31861,a),flip(a)].">
      <j1 rule="hyper" parents="31767 31861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31867">
    <literal><![CDATA[
      a(x,x,L(x * (y \ z),u,(y * x) \ z)) = a(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,31861,a,b,31866,a)].">
      <j1 rule="hyper" parents="60 31861 31866"/>
    </justification>
  </clause>

  <clause id="31868">
    <literal><![CDATA[
      L(x * y,L(z,x,x),a(x,x,z)) = z \ (L(z,x,x) * (R(x,x,z) * y))
    ]]></literal>
    <justification jstring="[para(31809(a,1),3944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31809 3944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31869">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) * z,u,w) = a((x \ y) * ((y \ x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,30826,a(flip),b,31858,a)].">
      <j1 rule="hyper" parents="60 30826 31858"/>
    </justification>
  </clause>

  <clause id="31870">
    <literal><![CDATA[
      a((x \ (y * (x \ y))) * z,u,w) = a((y \ x) * ((x \ y) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,30823,a,b,31869,a)].">
      <j1 rule="hyper" parents="60 30823 31869"/>
    </justification>
  </clause>

  <clause id="31871">
    <literal><![CDATA[
      a((x \ (y * (x \ y))) * y,z,u) = a((y \ x) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26439,a(flip),b,31870,a),flip(a)].">
      <j1 rule="hyper" parents="370 26439 31870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31872">
    <literal><![CDATA[
      a(a(x,y \ x,y) * x,z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,31412,a(flip),b,31871,a)].">
      <j1 rule="hyper" parents="60 31412 31871"/>
    </justification>
  </clause>

  <clause id="31873">
    <literal><![CDATA[
      a(R(x,y \ x,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(28686(a,1),31872(a,1,1))].">
      <j1 rule="para" parents="28686 31872"/>
    </justification>
  </clause>

  <clause id="31874">
    <literal><![CDATA[
      a(L(x,y \ x,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,27318,a(flip),b,31873,a)].">
      <j1 rule="hyper" parents="60 27318 31873"/>
    </justification>
  </clause>

  <clause id="31876">
    <literal><![CDATA[
      L(x * y,L(z,x,x),a(x,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x) * (z \ (R(x,x,z) * y)) = u
    ]]></literal>
    <justification jstring="[para(31868(a,2),2191(a,1))].">
      <j1 rule="para" parents="31868 2191"/>
    </justification>
  </clause>

  <clause id="31877">
    <literal><![CDATA[
      (x \ (x / (((x \ y) \ 1) \ 1))) * ((((x \ y) \ 1) \ 1) \ z) = (x \ (y * (x \ y))) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),31865(a,2,1,2,1))].">
      <j1 rule="para" parents="5 31865"/>
    </justification>
  </clause>

  <clause id="31878">
    <literal><![CDATA[
      a(x,x,T(x,y)) \ (y \ (T(y,x) / x)) = L(L(1 / T(x,y),x,y),x,x)
    ]]></literal>
    <justification jstring="[para(3078(a,1),31802(a,1,1))].">
      <j1 rule="para" parents="3078 31802"/>
    </justification>
  </clause>

  <clause id="31879">
    <literal><![CDATA[
      a(x,x,x) \ (y \ (T(y,x) / x)) = L(L(1 / T(x,y),x,y),x,x)
    ]]></literal>
    <justification jstring="[para(15514(a,1),31878(a,1,1))].">
      <j1 rule="para" parents="15514 31878"/>
    </justification>
  </clause>

  <clause id="31880">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(y,y,y) = L(L(1 / T(y,x),y,x),y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,11721,a(flip),b,31879,a)].">
      <j1 rule="hyper" parents="60 11721 31879"/>
    </justification>
  </clause>

  <clause id="31882">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(y,y,y) = L(x \ (T(x,y) / y),y,y)
    ]]></literal>
    <justification jstring="[para(12488(a,1),31880(a,2,1))].">
      <j1 rule="para" parents="12488 31880"/>
    </justification>
  </clause>

  <clause id="31883">
    <literal><![CDATA[
      x \ (a(y,x,x) \ (K(z,x) * u)) = T(x * a(y,x,x),z) \ u
    ]]></literal>
    <justification jstring="[para(21799(a,1),31814(a,1,2,2,1))].">
      <j1 rule="para" parents="21799 31814"/>
    </justification>
  </clause>

  <clause id="31884">
    <literal><![CDATA[
      T(x * a(y,x,x),z) \ 1 = x \ (a(y,x,x) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(3(a,1),31883(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 31883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31886">
    <literal><![CDATA[
      x \ (K(y,x) * (a(z,x,x) \ u)) = T(x * a(z,x,x),y) \ u
    ]]></literal>
    <justification jstring="[para(22743(a,1),31883(a,1,2))].">
      <j1 rule="para" parents="22743 31883"/>
    </justification>
  </clause>

  <clause id="31888">
    <literal><![CDATA[
      T(x * a(y,x,x),z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ (a(y,x,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(31886(a,1),7979(a,1))].">
      <j1 rule="para" parents="31886 7979"/>
    </justification>
  </clause>

  <clause id="31889">
    <literal><![CDATA[
      x \ (((y / x) \ y) * a(z,y / x,y / x)) = L(y \ x,x \ y,z) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(26018(a,1),31796(a,2,1))].">
      <j1 rule="para" parents="26018 31796"/>
    </justification>
  </clause>

  <clause id="31890">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ z) = z * (x \ (y * ((x \ y) \ 1)))
    ]]></literal>
    <justification jstring="[para(19759(a,1),31852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19759 31852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31891">
    <literal><![CDATA[
      x * (y \ (z * ((y \ z) \ 1))) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,31857,a(flip),b,31890,a),flip(a)].">
      <j1 rule="hyper" parents="60 31857 31890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31892">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ 1)) = y \ (x * (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(125,a,30748,a(flip),b,31891,a),flip(a)].">
      <j1 rule="hyper" parents="125 30748 31891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31893">
    <literal><![CDATA[
      (x \ (x / (((x \ y) \ 1) \ 1))) * ((((x \ y) \ 1) \ 1) \ z) = (y \ (x * (y \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(370,a,30825,a(flip),b,31877,a),flip(a)].">
      <j1 rule="hyper" parents="370 30825 31877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31894">
    <literal><![CDATA[
      (x \ (x * (y \ x))) * ((((x \ y) \ 1) \ 1) \ z) = (y \ (x * (y \ x))) * z
    ]]></literal>
    <justification jstring="[para(3492(a,1),31893(a,1,1,2))].">
      <j1 rule="para" parents="3492 31893"/>
    </justification>
  </clause>

  <clause id="31895">
    <literal><![CDATA[
      (x \ y) * ((((y \ x) \ 1) \ 1) \ z) = (x \ (y * (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4(a,1),31894(a,1,1))].">
      <j1 rule="para" parents="4 31894"/>
    </justification>
  </clause>

  <clause id="31896">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) * z) = (y \ (x * (y \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,4177,a(flip),b,31895,a)].">
      <j1 rule="hyper" parents="60 4177 31895"/>
    </justification>
  </clause>

  <clause id="31898">
    <literal><![CDATA[
      (x \ (y * (x \ y))) * ((x \ y) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),31896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 31896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31901">
    <literal><![CDATA[
      L(L(1 / T(x,y),T(x,y),x * y),T(x,y),z) = a(z,x,x) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(26917(a,1),31823(a,2,1))].">
      <j1 rule="para" parents="26917 31823"/>
    </justification>
  </clause>

  <clause id="31905">
    <literal><![CDATA[
      L(L(T(x,y) \ 1,x,y),T(x,y),z) = a(z,x,x) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(31580(a,1),31901(a,1,1))].">
      <j1 rule="para" parents="31580 31901"/>
    </justification>
  </clause>

  <clause id="31907">
    <literal><![CDATA[
      L((x * y) \ y,T(x,y),z) = a(z,x,x) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6711(a,1),31905(a,1,1))].">
      <j1 rule="para" parents="6711 31905"/>
    </justification>
  </clause>

  <clause id="31908">
    <literal><![CDATA[
      a(x,y,y) \ ((y * z) \ z) = L((y * z) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(26171,a,31907,a),flip(a)].">
      <j1 rule="hyper" parents="26171 31907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31912">
    <literal><![CDATA[
      R(x,x,a(y,z,u)) * a(y * z,u,a(u \ L(u,z,y),x,x)) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(2711(a,1),31855(a,1,1))].">
      <j1 rule="para" parents="2711 31855"/>
    </justification>
  </clause>

  <clause id="31913">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y * z,u,a(u \ L(u,z,y),x,x)) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(28339(a,1),31912(a,1,1))].">
      <j1 rule="para" parents="28339 31912"/>
    </justification>
  </clause>

  <clause id="31914">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y * z,u,a(u * L(u,z,y),x,x)) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(3858(a,1),31913(a,1,2,3))].">
      <j1 rule="para" parents="3858 31913"/>
    </justification>
  </clause>

  <clause id="31915">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y * z,u,a(y,z,a(x,x,u))) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(30768(a,1),31914(a,1,2,3))].">
      <j1 rule="para" parents="30768 31914"/>
    </justification>
  </clause>

  <clause id="31916">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(x,x,a(z,u,a(y,z,u))) = R(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(31174(a,1),31915(a,1,2))].">
      <j1 rule="para" parents="31174 31915"/>
    </justification>
  </clause>

  <clause id="31917">
    <literal><![CDATA[
      L(R(x,x,a(y,z,a(u,y,z))),x,a(u,y,z)) = R(x,x,z \ L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,31786,a(flip),b,31916,a)].">
      <j1 rule="hyper" parents="60 31786 31916"/>
    </justification>
  </clause>

  <clause id="31918">
    <literal><![CDATA[
      L(L(x,x,a(y,z,a(u,y,z))),x,a(u,y,z)) = R(x,x,z \ L(z,y,u))
    ]]></literal>
    <justification jstring="[para(28339(a,1),31917(a,1,1))].">
      <j1 rule="para" parents="28339 31917"/>
    </justification>
  </clause>

  <clause id="31919">
    <literal><![CDATA[
      L(L(x,x,a(y,z,a(u,y,z))),x,a(u,y,z)) = L(x,x,z * L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,31544,a(flip),b,31918,a),flip(a)].">
      <j1 rule="hyper" parents="370 31544 31918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31920">
    <literal><![CDATA[
      L(L(x,x,a(y,z,a(u,y,z))),x,a(u,y,z)) = L(x,a(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31832,a(flip),b,31919,a),flip(a)].">
      <j1 rule="hyper" parents="370 31832 31919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31921">
    <literal><![CDATA[
      (x * a(y,z \ y,z \ y)) * a((z \ y) \ 1,(z \ y) \ 1,a(z \ y,z \ y,y)) = ((((y \ z) \ 1) \ 1) \ ((z \ y) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(3091(a,1),30929(a,1,1,2))].">
      <j1 rule="para" parents="3091 30929"/>
    </justification>
  </clause>

  <clause id="31922">
    <literal><![CDATA[
      (x * a(y,z * y,z * y)) * a((z \ y) \ 1,(z \ y) \ 1,a(z \ y,z \ y,y)) = ((((y \ z) \ 1) \ 1) \ ((z \ y) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(30328(a,1),31921(a,1,1,2))].">
      <j1 rule="para" parents="30328 31921"/>
    </justification>
  </clause>

  <clause id="31923">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) * u,a(x,y,z),w) * (a(a(x,y,z),u,w) \ u) = K(w,u * a(x,y,z)) * ((w * a(x,y,z)) \ (a(x,y,z) * (u * w)))
    ]]></literal>
    <justification jstring="[para(30642(a,1),31259(a,1,1))].">
      <j1 rule="para" parents="30642 31259"/>
    </justification>
  </clause>

  <clause id="31924">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) * ((x * a(z,u,w)) \ (a(z,u,w) * (y * x))) = a(y,a(z,u,w),x) * (a(a(z,u,w),y,x) \ y)
    ]]></literal>
    <justification jstring="[para(31665(a,1),31923(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31665 31923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31925">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) * ((x * a(z,u,w)) \ (a(z,u,w) * (y * x))) = a(y,a(z,u,w),x) * (a(a(z,u,w),y,x) * y)
    ]]></literal>
    <justification jstring="[para(30667(a,1),31924(a,2,2))].">
      <j1 rule="para" parents="30667 31924"/>
    </justification>
  </clause>

  <clause id="31926">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) * ((x * a(z,u,w)) \ (a(z,u,w) * (y * x))) = y * (a(a(z,u,w),y,x) * a(y,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[hyper(28875,a,31925,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="28875 31925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31927">
    <literal><![CDATA[
      K(x,y) * ((x * a(z,u,w)) \ (a(z,u,w) * (y * x))) = y * (a(a(z,u,w),y,x) * a(y,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[para(28113(a,1),31926(a,1,1))].">
      <j1 rule="para" parents="28113 31926"/>
    </justification>
  </clause>

  <clause id="31928">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),x,a(z,u,w)) = y * (a(a(z,u,w),y,x) * a(y,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[para(24125(a,1),31927(a,1,2))].">
      <j1 rule="para" parents="24125 31927"/>
    </justification>
  </clause>

  <clause id="31930">
    <literal><![CDATA[
      L(K(x,y) * T(y,x),x,a(z,u,w)) = y * (a(a(z,u,w),y,x) * a(y,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[hyper(25751,a,31928,a)].">
      <j1 rule="hyper" parents="25751 31928"/>
    </justification>
  </clause>

  <clause id="31931">
    <literal><![CDATA[
      x * (a(a(y,z,u),x,w) * a(x,a(y,z,u),w)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5700(a,1),31930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5700 31930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31932">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * (L(w,a(x,y,z),u) * v5)) \ ((u * ((a(x,y,z) \ 1) * w)) * v5) = a(u * (a(x,y,z) \ 1),L(w,a(x,y,z) \ 1,u),v5)
    ]]></literal>
    <justification jstring="[para(3401(a,1),30678(a,1,1,2,1))].">
      <j1 rule="para" parents="3401 30678"/>
    </justification>
  </clause>

  <clause id="31933">
    <literal><![CDATA[
      L(a(x,y,z) \ z,u,w) / (L(a(x,y,z) \ 1,u,w) * L(a(x,y,z) \ 1,u,w)) = L(z,u,w) * ((L(z,u,w) \ L(a(x,y,z) \ z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(31617(a,1),31619(a,1,2,2))].">
      <j1 rule="para" parents="31617 31619"/>
    </justification>
  </clause>

  <clause id="31934">
    <literal><![CDATA[
      L(a(x,y,z) \ z,u,w) / (L(a(x,y,z),u,w) \ L(a(x,y,z) \ 1,u,w)) = L(z,u,w) * ((L(z,u,w) \ L(a(x,y,z) \ z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(30774(a,1),31933(a,1,2))].">
      <j1 rule="para" parents="30774 31933"/>
    </justification>
  </clause>

  <clause id="31935">
    <literal><![CDATA[
      L(a(x,y,z) \ z,u,w) / (a(x,y,z) \ (a(x,y,z) \ 1)) = L(z,u,w) * ((L(z,u,w) \ L(a(x,y,z) \ z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(3908(a,1),31934(a,1,2))].">
      <j1 rule="para" parents="3908 31934"/>
    </justification>
  </clause>

  <clause id="31937">
    <literal><![CDATA[
      L(a(x,y,z) \ z,u,w) / (z \ L(L(z,y,x),y,x)) = L(z,u,w) * ((L(z,u,w) \ L(a(x,y,z) \ z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(30217(a,1),31935(a,1,2))].">
      <j1 rule="para" parents="30217 31935"/>
    </justification>
  </clause>

  <clause id="31938">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ L(a(u,w,x) \ x,y,z)) \ 1) = x * (L(L(x,w,u),w,u) \ L(a(u,w,x) \ x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29165,a(flip),b,31937,a),flip(a)].">
      <j1 rule="hyper" parents="60 29165 31937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31939">
    <literal><![CDATA[
      L(x * (L(L(x,y,z),y,z) \ (a(z,y,x) \ x)),u,w) = L(x,u,w) * ((L(x,u,w) \ L(a(z,y,x) \ x,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,29210,a,b,31938,a)].">
      <j1 rule="hyper" parents="370 29210 31938"/>
    </justification>
  </clause>

  <clause id="31940">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ L(a(u,w,x) \ x,y,z)) \ 1) = L(x * ((x \ x) * a(u,w,x)),y,z)
    ]]></literal>
    <justification jstring="[para(30700(a,1),31939(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30700 31939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31941">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ L(a(u,w,x) \ x,y,z)) \ 1) = L(x * a(u,w,x),y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),31940(a,2,1,2))].">
      <j1 rule="para" parents="194 31940"/>
    </justification>
  </clause>

  <clause id="31943">
    <literal><![CDATA[
      L(x,y,z) * (L(a(u,w,x) \ 1,y,z) \ 1) = L(x * a(u,w,x),y,z)
    ]]></literal>
    <justification jstring="[para(31617(a,1),31941(a,1,2,1))].">
      <j1 rule="para" parents="31617 31941"/>
    </justification>
  </clause>

  <clause id="31944">
    <literal><![CDATA[
      L(x,y,z) * L(a(u,w,x),y,z) = L(x * a(u,w,x),y,z)
    ]]></literal>
    <justification jstring="[para(29286(a,1),31943(a,1,2))].">
      <j1 rule="para" parents="29286 31943"/>
    </justification>
  </clause>

  <clause id="31945">
    <literal><![CDATA[
      L(x * a(y,z,x),u,y) = L(x,u,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(28772(a,1),31944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28772 31944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31946">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z * a(x,u,z),y,x)) = L(a(x,u,z),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(31945(a,2),620(a,1,2,2))].">
      <j1 rule="para" parents="31945 620"/>
    </justification>
  </clause>

  <clause id="31948">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * a(x,u,z)))) = L(a(x,u,z),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(92(a,1),31946(a,1,2))].">
      <j1 rule="para" parents="92 31946"/>
    </justification>
  </clause>

  <clause id="31949">
    <literal><![CDATA[
      L(L(a(x,y,z),z,u),u * z,x) = L(a(x,y,z),L(z,u,x),x * u)
    ]]></literal>
    <justification jstring="[hyper(1199,a,31948,a)].">
      <j1 rule="hyper" parents="1199 31948"/>
    </justification>
  </clause>

  <clause id="31950">
    <literal><![CDATA[
      L(x * (y * a(z,u,w)),a(x,y,a(z,u,w)),a(a(z,u,w),x,y)) \ ((x * a(z,u,w)) * y) = a(x,y,a(z,u,w)) * a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(25840(a,1),28526(a,2,2))].">
      <j1 rule="para" parents="25840 28526"/>
    </justification>
  </clause>

  <clause id="31951">
    <literal><![CDATA[
      L(x * (y * a(z,u,w)),a(x,y,a(z,u,w)),a(a(z,u,w),x,y)) * ((x * (y * a(z,u,w))) \ (a(x,y,a(z,u,w)) * a(a(z,u,w),x,y))) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(31950(a,1),2155(a,1,2,2))].">
      <j1 rule="para" parents="31950 2155"/>
    </justification>
  </clause>

  <clause id="31952">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * L(L(T(x \ R(x,y,z),v5),u,w),x,y * z)) \ L(x \ R(x,y,z),u,w) = 1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z)
    ]]></literal>
    <justification jstring="[para(20(a,2),29097(a,1,1,2,1))].">
      <j1 rule="para" parents="20 29097"/>
    </justification>
  </clause>

  <clause id="31953">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * L(L(x \ R(x,y,z),u,w),x,y * z)) \ L(x \ R(x,y,z),u,w) = 1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z)
    ]]></literal>
    <justification jstring="[para(23944(a,1),31952(a,1,1,2,1,1))].">
      <j1 rule="para" parents="23944 31952"/>
    </justification>
  </clause>

  <clause id="31954">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * L(a(x,y,z),u,w)) \ L(x \ R(x,y,z),u,w) = 1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z)
    ]]></literal>
    <justification jstring="[para(16537(a,1),31953(a,1,1,2))].">
      <j1 rule="para" parents="16537 31953"/>
    </justification>
  </clause>

  <clause id="31956">
    <literal><![CDATA[
      (a(x,y,z) * L(L(a(x,y,z),u,w),u,w)) \ L(x \ R(x,y,z),u,w) = 1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z)
    ]]></literal>
    <justification jstring="[para(29017(a,1),31954(a,1,1))].">
      <j1 rule="para" parents="29017 31954"/>
    </justification>
  </clause>

  <clause id="31957">
    <literal><![CDATA[
      1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z) = (a(x,y,z) * a(x,y,z)) \ L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29262(a,1),31956(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29262 31956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31958">
    <literal><![CDATA[
      1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z) = L((a(x,y,z) * a(x,y,z)) \ (x \ R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3789,a,b,31957,a),flip(a)].">
      <j1 rule="hyper" parents="370 3789 31957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31960">
    <literal><![CDATA[
      1 / L(L(T(L(x \ R(x,y,z),u,w),v5),x,y * z),x,y * z) = L((x \ R(x,y,z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29329(a,1),31958(a,2,1))].">
      <j1 rule="para" parents="29329 31958"/>
    </justification>
  </clause>

  <clause id="31961">
    <literal><![CDATA[
      1 / L(L(L(x \ R(x,y,z),u,w),x,y * z),x,y * z) = L((x \ R(x,y,z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(106(a,1),31960(a,1,2,1,1))].">
      <j1 rule="para" parents="106 31960"/>
    </justification>
  </clause>

  <clause id="31962">
    <literal><![CDATA[
      1 / L(L(a(x,y,z),u,w),x,y * z) = L((x \ R(x,y,z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(16537(a,1),31961(a,1,2,1))].">
      <j1 rule="para" parents="16537 31961"/>
    </justification>
  </clause>

  <clause id="31963">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ 1,u,w) = 1 / L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29276(a,1),31962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29276 31962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31964">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ 1,u,w) \ 1 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(215,a,31963,a(flip))].">
      <j1 rule="hyper" parents="215 31963"/>
    </justification>
  </clause>

  <clause id="31965">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) \ 1 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13549(a,1),31964(a,1,1,1))].">
      <j1 rule="para" parents="13549 31964"/>
    </justification>
  </clause>

  <clause id="31966">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,28626,a,b,31965,a)].">
      <j1 rule="hyper" parents="36 28626 31965"/>
    </justification>
  </clause>

  <clause id="31967">
    <literal><![CDATA[
      L(x,L(R(y,z,u) \ y,w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(31966(a,1),27779(a,1,2))].">
      <j1 rule="para" parents="31966 27779"/>
    </justification>
  </clause>

  <clause id="31968">
    <literal><![CDATA[
      L(x,L(y * R(y,z,u),w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(26308,a,31967,a)].">
      <j1 rule="hyper" parents="26308 31967"/>
    </justification>
  </clause>

  <clause id="31969">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,z),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,31094,a(flip),b,31968,a),flip(a)].">
      <j1 rule="hyper" parents="60 31094 31968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31970">
    <literal><![CDATA[
      L(x,y * (a(z,u,y) \ y),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(30287(a,1),31969(a,1,2))].">
      <j1 rule="para" parents="30287 31969"/>
    </justification>
  </clause>

  <clause id="31971">
    <literal><![CDATA[
      L(x,y * (y * a(z,u,y)),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(30684,a,31970,a)].">
      <j1 rule="hyper" parents="30684 31970"/>
    </justification>
  </clause>

  <clause id="31972">
    <literal><![CDATA[
      L(x,L(a(y,z,u),u,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(3544,a,31971,a)].">
      <j1 rule="hyper" parents="3544 31971"/>
    </justification>
  </clause>

  <clause id="31973">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(14782(a,1),31972(a,1,2))].">
      <j1 rule="para" parents="14782 31972"/>
    </justification>
  </clause>

  <clause id="31974">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(31278,a,31973,a)].">
      <j1 rule="hyper" parents="31278 31973"/>
    </justification>
  </clause>

  <clause id="31975">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ 1) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(3522,a,31973,a),flip(a)].">
      <j1 rule="hyper" parents="3522 31973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31976">
    <literal><![CDATA[
      L(x,a(x,y,z),y) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30861,a(flip),b,31973,a),flip(a)].">
      <j1 rule="hyper" parents="370 30861 31973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31977">
    <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(129,a,31973,a,b,23622,a),flip(a)].">
      <j1 rule="hyper" parents="129 31973 23622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31979">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ R(x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31976(a,1),31110(a,1,1))].">
      <j1 rule="para" parents="31976 31110"/>
    </justification>
  </clause>

  <clause id="31980">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(31,a,31274,a,b,31974,a)].">
      <j1 rule="hyper" parents="31 31274 31974"/>
    </justification>
  </clause>

  <clause id="31981">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (((x * a(y,z,u)) / w) * R(w,a(y,z,u),x)) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,27870,a(flip),b,31980,a)].">
      <j1 rule="hyper" parents="370 27870 31980"/>
    </justification>
  </clause>

  <clause id="31982">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),y,a(v6,a(v5,w,u),z)) = x
    ]]></literal>
    <justification jstring="[para(31980(a,1),30728(a,1,1,3))].">
      <j1 rule="para" parents="31980 30728"/>
    </justification>
  </clause>

  <clause id="31983">
    <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(31975(a,1),3522(a,1))].">
      <j1 rule="para" parents="31975 3522"/>
    </justification>
  </clause>

  <clause id="31984">
    <literal><![CDATA[
      R(x,y,z) = L(x,x,a(y,y,z)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(156,a,31979,a),flip(a)].">
      <j1 rule="hyper" parents="156 31979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31985">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,23634,a,b,31979,a),flip(a)].">
      <j1 rule="hyper" parents="35 23634 31979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31986">
    <literal><![CDATA[
      x * a(y,z,u) != R(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      L(y,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[para(31979(a,1),146(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31979 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31987">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31979(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="31979 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31988">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,u))) \ (x * R(y,z,u)) = L(a(y,z,u),L(y,y,a(z,z,u)),x)
    ]]></literal>
    <justification jstring="[para(31979(a,1),94(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31979 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31989">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,a(w,w,v5)) \ L(u,w,v5))) = a(x,y,z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(31979(a,1),31681(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="31979 31681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31990">
    <literal><![CDATA[
      L(x,x,a(y,y,y \ z)) * a(x,y,y \ z) = ((x * y) * (y \ z)) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,102,a,b,31984,a),flip(a)].">
      <j1 rule="hyper" parents="60 102 31984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31991">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,a(u,x,z),x * a(z,x,u)) = w
    ]]></literal>
    <justification jstring="[para(31693(a,1),31983(a,1))].">
      <j1 rule="para" parents="31693 31983"/>
    </justification>
  </clause>

  <clause id="31992">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y * z) = u
    ]]></literal>
    <justification jstring="[para(29408(a,1),31987(a,1,1))].">
      <j1 rule="para" parents="29408 31987"/>
    </justification>
  </clause>

  <clause id="31993">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(w,v5,v6),v5 * a(v6,v5,w)) = (v5 * L(v5 \ u,v5,a(v6,v5,w))) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31693(a,1),31977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31693 31977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31994">
    <literal><![CDATA[
      L(x,x,a(y,y,y * z)) * a(x,y,y \ z) = ((x * y) * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(19763(a,1),31990(a,1,1,3))].">
      <j1 rule="para" parents="19763 31990"/>
    </justification>
  </clause>

  <clause id="31995">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,y \ z) = ((x * y) * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(29408(a,1),31994(a,1,1))].">
      <j1 rule="para" parents="29408 31994"/>
    </justification>
  </clause>

  <clause id="31996">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,y \ z) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,102,a(flip),b,31995,a),flip(a)].">
      <j1 rule="hyper" parents="370 102 31995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31997">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ 1)) = a(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(30863(a,1),31989(a,1,3,2))].">
      <j1 rule="para" parents="30863 31989"/>
    </justification>
  </clause>

  <clause id="31999">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(26991,a,31997,a)].">
      <j1 rule="hyper" parents="26991 31997"/>
    </justification>
  </clause>

  <clause id="32000">
    <literal><![CDATA[
      a(x,y,z * a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(v5,w,u) * z) = v6
    ]]></literal>
    <justification jstring="[para(31997(a,1),26991(a,1))].">
      <j1 rule="para" parents="31997 26991"/>
    </justification>
  </clause>

  <clause id="32001">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(30626(a,1),31997(a,1,3))].">
      <j1 rule="para" parents="30626 31997"/>
    </justification>
  </clause>

  <clause id="32002">
    <literal><![CDATA[
      a(x,x,y * a(z,u,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29846,a(flip),b,31999,a),flip(a)].">
      <j1 rule="hyper" parents="60 29846 31999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32003">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * ((u * z) * w)) = a(x,y,(u * z) * R(w,u,z))
    ]]></literal>
    <justification jstring="[para(16503(a,1),31999(a,2,3))].">
      <j1 rule="para" parents="16503 31999"/>
    </justification>
  </clause>

  <clause id="32004">
    <literal><![CDATA[
      a(x,y,(z \ ((z * u) * w)) / w) = a(x,y,u * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(28760(a,2),31999(a,1,3))].">
      <j1 rule="para" parents="28760 31999"/>
    </justification>
  </clause>

  <clause id="32005">
    <literal><![CDATA[
      a(x,x,(y * z) * x) = a(x,x,y * (z * x))
    ]]></literal>
    <justification jstring="[para(82(a,1),32002(a,1,3))].">
      <j1 rule="para" parents="82 32002"/>
    </justification>
  </clause>

  <clause id="32006">
    <literal><![CDATA[
      a(x,x,(y * ((z \ u) * z)) * x) = a(x,x,u * (y * x))
    ]]></literal>
    <justification jstring="[hyper(27206,a,32005,a)].">
      <j1 rule="hyper" parents="27206 32005"/>
    </justification>
  </clause>

  <clause id="32007">
    <literal><![CDATA[
      a(x,x,y * (((z \ u) * z) * x)) = a(x,x,u * (y * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,32005,a(flip),b,32006,a)].">
      <j1 rule="hyper" parents="60 32005 32006"/>
    </justification>
  </clause>

  <clause id="32008">
    <literal><![CDATA[
      a(x,x,(x * y) * z) = a(x,x,y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(27207,a,32007,a)].">
      <j1 rule="hyper" parents="27207 32007"/>
    </justification>
  </clause>

  <clause id="32009">
    <literal><![CDATA[
      a((x * y) * z,x,a(u,w,x)) = a(u,w,a(x,x,y * (z * x)))
    ]]></literal>
    <justification jstring="[para(32008(a,1),31834(a,2,3))].">
      <j1 rule="para" parents="32008 31834"/>
    </justification>
  </clause>

  <clause id="32010">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,w * a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(26970,a,32004,a)].">
      <j1 rule="hyper" parents="26970 32004"/>
    </justification>
  </clause>

  <clause id="32011">
    <literal><![CDATA[
      a((x * y) * z,x,a(u,w,x)) = a(u,w,a(x,x,y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30455,a(flip),b,32009,a),flip(a)].">
      <j1 rule="hyper" parents="370 30455 32009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32012">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * a(w,u,z))) = a(x,y,(u * w) * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(28357,a,32003,a)].">
      <j1 rule="hyper" parents="28357 32003"/>
    </justification>
  </clause>

  <clause id="32013">
    <literal><![CDATA[
      a(x,y,(z * u) * R(w,z,u)) = a(x,y,w * (z * R(u,z,w)))
    ]]></literal>
    <justification jstring="[para(31089(a,1),32012(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="31089 32012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32014">
    <literal><![CDATA[
      a(x,y,(z * u) * R(w,z,u)) = a(x,y,w * (z * L(u,z,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,28701,a(flip),b,32013,a),flip(a)].">
      <j1 rule="hyper" parents="370 28701 32013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32015">
    <literal><![CDATA[
      a(x,y,(z * u) * L(w,z,u)) = a(x,y,w * (z * L(u,z,w)))
    ]]></literal>
    <justification jstring="[hyper(28699,a,32014,a)].">
      <j1 rule="hyper" parents="28699 32014"/>
    </justification>
  </clause>

  <clause id="32016">
    <literal><![CDATA[
      a(x,y,z * (T(u,z) * w)) = a(x,y,w * (u * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12481(a,1),32015(a,1,3))].">
      <j1 rule="para" parents="12481 32015"/>
    </justification>
  </clause>

  <clause id="32017">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,u,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(32016(a,1),27092(a,1))].">
      <j1 rule="para" parents="32016 27092"/>
    </justification>
  </clause>

  <clause id="32018">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,u))) \ (x * R(y,z,u)) = L(a(y,z,u),y,L(x,y,a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,31385,a(flip),b,31988,a),flip(a)].">
      <j1 rule="hyper" parents="370 31385 31988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32019">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(z,y,x),w) = a(x,y,z) * a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(31981(a,1),31285(a,1,2))].">
      <j1 rule="para" parents="31981 31285"/>
    </justification>
  </clause>

  <clause id="32020">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(z,y,x),y * a(x,y,z)) = (y * a(x,y,z)) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30072,a(flip),b,31993,a),flip(a)].">
      <j1 rule="hyper" parents="370 30072 31993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32021">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z),u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3050(a,1),29675(a,1,1,2,1))].">
      <j1 rule="para" parents="3050 29675"/>
    </justification>
  </clause>

  <clause id="32022">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(L(x \ 1,y,z) \ 1,L(x,y,z),u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3911(a,1),32021(a,1,1,2,1))].">
      <j1 rule="para" parents="3911 32021"/>
    </justification>
  </clause>

  <clause id="32023">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(L(x \ 1,y,z),L(x,y,z),u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(2962(a,1),32022(a,1,1,2,1))].">
      <j1 rule="para" parents="2962 32022"/>
    </justification>
  </clause>

  <clause id="32024">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(L(x,y,z),L(x,y,z),u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(3869(a,1),32023(a,1,1,2,1))].">
      <j1 rule="para" parents="3869 32023"/>
    </justification>
  </clause>

  <clause id="32025">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (a(x,x,u) / (L(x \ 1,y,z) \ 1)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(29529(a,1),32024(a,1,1,2,1))].">
      <j1 rule="para" parents="29529 32024"/>
    </justification>
  </clause>

  <clause id="32026">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ ((1 / L(x \ 1,y,z)) \ a(x,x,u)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(28219(a,1),32025(a,1,1,2))].">
      <j1 rule="para" parents="28219 32025"/>
    </justification>
  </clause>

  <clause id="32028">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ (L(x \ 1,y,z) * a(x,x,u)),x,x) = a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(29774(a,1),32026(a,1,1,2))].">
      <j1 rule="para" parents="29774 32026"/>
    </justification>
  </clause>

  <clause id="32029">
    <literal><![CDATA[
      L(K(x,x \ 1) * a(x,x,y),x,x) = a(L(x \ 1,z,u) \ 1,L(x \ 1,z,u) \ 1,y * (L(x \ 1,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(25815(a,1),32028(a,1,1))].">
      <j1 rule="para" parents="25815 32028"/>
    </justification>
  </clause>

  <clause id="32031">
    <literal><![CDATA[
      L(x * (a(x,x,y) / x),x,x) = a(L(x \ 1,z,u) \ 1,L(x \ 1,z,u) \ 1,y * (L(x \ 1,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(28112(a,1),32029(a,1,1))].">
      <j1 rule="para" parents="28112 32029"/>
    </justification>
  </clause>

  <clause id="32032">
    <literal><![CDATA[
      L(a(x,x,y * x),x,x) = a(L(x \ 1,z,u) \ 1,L(x \ 1,z,u) \ 1,y * (L(x \ 1,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(29405(a,1),32031(a,1,1))].">
      <j1 rule="para" parents="29405 32031"/>
    </justification>
  </clause>

  <clause id="32033">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,u * (L(x \ 1,y,z) \ 1)) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(31768,a,32032,a),flip(a)].">
      <j1 rule="hyper" parents="31768 32032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32034">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,L(x \ 1,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(26991,a,32033,a)].">
      <j1 rule="hyper" parents="26991 32033"/>
    </justification>
  </clause>

  <clause id="32036">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z) \ 1,L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,27055,a(flip),b,32034,a)].">
      <j1 rule="hyper" parents="60 27055 32034"/>
    </justification>
  </clause>

  <clause id="32037">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,L(x \ 1,y,z),L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(3058,a,32036,a)].">
      <j1 rule="hyper" parents="3058 32036"/>
    </justification>
  </clause>

  <clause id="32038">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,L(x,y,z),L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(26747,a,32037,a)].">
      <j1 rule="hyper" parents="26747 32037"/>
    </justification>
  </clause>

  <clause id="32039">
    <literal><![CDATA[
      a(L(x \ 1,y,z),L(x,y,z),L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(2973,a,32038,a)].">
      <j1 rule="hyper" parents="2973 32038"/>
    </justification>
  </clause>

  <clause id="32040">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,3869,a(flip),b,32039,a)].">
      <j1 rule="hyper" parents="60 3869 32039"/>
    </justification>
  </clause>

  <clause id="32041">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),R(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28605,a,b,32040,a)].">
      <j1 rule="hyper" parents="60 28605 32040"/>
    </justification>
  </clause>

  <clause id="32042">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u * R(x,y,z)) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(26965,a,32041,a)].">
      <j1 rule="hyper" parents="26965 32041"/>
    </justification>
  </clause>

  <clause id="32043">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(K(w,u) * x,y,z) \ 1) \ v5)) = v5 * a(x,x,v5 * x)
    ]]></literal>
    <justification jstring="[para(32042(a,1),30539(a,2,2))].">
      <j1 rule="para" parents="32042 30539"/>
    </justification>
  </clause>

  <clause id="32044">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(K(w,u) * x,y,z) \ 1) \ v5)) = x \ ((x \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,28753,a(flip),b,32043,a),flip(a)].">
      <j1 rule="hyper" parents="370 28753 32043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32046">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(x,y,z) \ (K(u,w) * 1)) \ v5)) = x \ ((x \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(25682(a,1),32044(a,1,2,2,1))].">
      <j1 rule="para" parents="25682 32044"/>
    </justification>
  </clause>

  <clause id="32047">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,w) * ((R(x,y,z) \ K(u,w)) \ v5)) = x \ ((x \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(3(a,1),32046(a,1,2,2,1,2))].">
      <j1 rule="para" parents="3 32046"/>
    </justification>
  </clause>

  <clause id="32048">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = x \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(25116(a,1),32047(a,1,2))].">
      <j1 rule="para" parents="25116 32047"/>
    </justification>
  </clause>

  <clause id="32049">
    <literal><![CDATA[
      a(x * ((y \ ((y \ 1) \ z)) * L(y,u,w)),v5,v6) = a((R(y,u,w) \ z) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(32048(a,1),28598(a,1,1,2,1))].">
      <j1 rule="para" parents="32048 28598"/>
    </justification>
  </clause>

  <clause id="32050">
    <literal><![CDATA[
      a(x,y,z * ((u \ ((u \ 1) \ w)) * L(u,v5,v6))) = a(x,y,(R(u,v5,v6) \ w) * z)
    ]]></literal>
    <justification jstring="[para(32048(a,1),29445(a,1,3,2,1))].">
      <j1 rule="para" parents="32048 29445"/>
    </justification>
  </clause>

  <clause id="32051">
    <literal><![CDATA[
      a(x * ((L(y,z,u) \ 1) \ T(w,y)),v5,v6) = a((R(y,z,u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(29710(a,1),32049(a,1,1,2))].">
      <j1 rule="para" parents="29710 32049"/>
    </justification>
  </clause>

  <clause id="32053">
    <literal><![CDATA[
      a(x * ((L(y,z,u) \ 1) \ w),v5,v6) = a((R(y,z,u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26679,a,32051,a)].">
      <j1 rule="hyper" parents="26679 32051"/>
    </justification>
  </clause>

  <clause id="32054">
    <literal><![CDATA[
      a((R(x,y,z) \ u) * w,v5,v6) = a((L(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26430,a,32053,a),flip(a)].">
      <j1 rule="hyper" parents="26430 32053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32057">
    <literal><![CDATA[
      a(x,y,z * ((L(u,w,v5) \ 1) \ T(v6,u))) = a(x,y,(R(u,w,v5) \ v6) * z)
    ]]></literal>
    <justification jstring="[para(29710(a,1),32050(a,1,3,2))].">
      <j1 rule="para" parents="29710 32050"/>
    </justification>
  </clause>

  <clause id="32059">
    <literal><![CDATA[
      a(x,y,z * ((L(u,w,v5) \ 1) \ v6)) = a(x,y,(R(u,w,v5) \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(27091,a,32057,a)].">
      <j1 rule="hyper" parents="27091 32057"/>
    </justification>
  </clause>

  <clause id="32060">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ v5) * v6) = a(x,y,(L(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(26936,a,32059,a),flip(a)].">
      <j1 rule="hyper" parents="26936 32059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32062">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 \ a(v6,v6,R(z,u,w) \ v5))) = a(x,y,v6 \ T(R(z,u,w) \ v5,v6 \ 1))
    ]]></literal>
    <justification jstring="[para(28442(a,1),32060(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28442 32060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32063">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 \ a(v6,v6,R(z,u,w) \ v5))) = a(x,y,v6 \ (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,26886,a(flip),b,32062,a),flip(a)].">
      <j1 rule="hyper" parents="370 26886 32062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32065">
    <literal><![CDATA[
      (a(a(a(x,y,z),u,w),a(u,w,a(x,y,z)),u * (w * a(x,y,z))) \ a(u,w,a(x,y,z))) * a(a(x,y,z),u,w) = (u * (w * a(x,y,z))) \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28804,a(flip),b,31951,a)].">
      <j1 rule="hyper" parents="60 28804 31951"/>
    </justification>
  </clause>

  <clause id="32066">
    <literal><![CDATA[
      (a(x * (y * a(z,u,w)),a(x,y,a(z,u,w)),a(a(z,u,w),x,y)) * a(x,y,a(z,u,w))) * a(a(z,u,w),x,y) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(30724(a,1),32065(a,1,1))].">
      <j1 rule="para" parents="30724 32065"/>
    </justification>
  </clause>

  <clause id="32067">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * a(a(a(z,u,w),x,y),a(x,y,a(z,u,w)),x * (y * a(z,u,w)))) * a(a(z,u,w),x,y) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(31284(a,1),32066(a,1,1))].">
      <j1 rule="para" parents="31284 32066"/>
    </justification>
  </clause>

  <clause id="32068">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * a(a(z,u,w),x,y)) * a(a(a(z,u,w),x,y),a(x,y,a(z,u,w)),x * (y * a(z,u,w))) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[hyper(28806,a,32067,a)].">
      <j1 rule="hyper" parents="28806 32067"/>
    </justification>
  </clause>

  <clause id="32069">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * R(a(a(z,u,w),x,y),a(x,y,a(z,u,w)),x * (y * a(z,u,w))) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[hyper(31100,a,32068,a)].">
      <j1 rule="hyper" parents="31100 32068"/>
    </justification>
  </clause>

  <clause id="32070">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(a(a(z,u,w),x,y),a(x,y,a(z,u,w)),x * (y * a(z,u,w))) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(28368(a,1),32069(a,1,2))].">
      <j1 rule="para" parents="28368 32069"/>
    </justification>
  </clause>

  <clause id="32071">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,x,L(a(w,u,z),a(x,y,a(z,u,w)),x * (y * a(z,u,w)))) = (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(31138(a,2),32070(a,1,2))].">
      <j1 rule="para" parents="31138 32070"/>
    </justification>
  </clause>

  <clause id="32072">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y) = a(x,y,a(z,u,w)) * a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(31265(a,1),32071(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="31265 32071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32073">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,x,a(w,u,z)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(24131,a,32072,a),flip(a)].">
      <j1 rule="hyper" parents="24131 32072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32075">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,a(w,u,z),x) = a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(30742,a,32073,a)].">
      <j1 rule="hyper" parents="30742 32073"/>
    </justification>
  </clause>

  <clause id="32076">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(u,a(x,y,z),w) = a(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(31153,a,32075,a)].">
      <j1 rule="hyper" parents="31153 32075"/>
    </justification>
  </clause>

  <clause id="32077">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32076(a,1),31931(a,1,2))].">
      <j1 rule="para" parents="32076 31931"/>
    </justification>
  </clause>

  <clause id="32078">
    <literal><![CDATA[
      x * a(a(y,z,u),w,x) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(31152,a,32077,a)].">
      <j1 rule="hyper" parents="31152 32077"/>
    </justification>
  </clause>

  <clause id="32079">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(31147,a,32077,a)].">
      <j1 rule="hyper" parents="31147 32077"/>
    </justification>
  </clause>

  <clause id="32080">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * x = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(23794,a,32077,a)].">
      <j1 rule="hyper" parents="23794 32077"/>
    </justification>
  </clause>

  <clause id="32081">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,28339,a,b,32077,a),flip(a)].">
      <j1 rule="hyper" parents="370 28339 32077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32082">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(135,a,32077,a)].">
      <j1 rule="hyper" parents="135 32077"/>
    </justification>
  </clause>

  <clause id="32083">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,30726,a,b,32077,a)].">
      <j1 rule="hyper" parents="125 30726 32077"/>
    </justification>
  </clause>

  <clause id="32085">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(31,a,30032,a,b,32077,a)].">
      <j1 rule="hyper" parents="31 30032 32077"/>
    </justification>
  </clause>

  <clause id="32086">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32077(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="32077 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32087">
    <literal><![CDATA[
      L(L(a(x,y,a(z,u,w)) \ v5,a(x,y,a(z,u,w)),x),L(x,y,a(z,u,w)),v6) = (v6 * (x * a(x,y,a(z,u,w)))) \ (v6 * (x * v5))
    ]]></literal>
    <justification jstring="[para(32077(a,1),671(a,1,2))].">
      <j1 rule="para" parents="32077 671"/>
    </justification>
  </clause>

  <clause id="32089">
    <literal><![CDATA[
      a(x,x,a(y,y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,32079,a(flip),b,30858,a),flip(a)].">
      <j1 rule="hyper" parents="124 32079 30858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32090">
    <literal><![CDATA[
      a(a(a(x,y,z),u,u),w,w) = 1
    ]]></literal>
    <justification jstring="[hyper(31133,a,32089,a)].">
      <j1 rule="hyper" parents="31133 32089"/>
    </justification>
  </clause>

  <clause id="32091">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * x = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,28339,a,b,32080,a),flip(a)].">
      <j1 rule="hyper" parents="370 28339 32080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32092">
    <literal><![CDATA[
      L(x,x,a(y,y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(31986,a,32081,a)].">
      <j1 rule="hyper" parents="31986 32081"/>
    </justification>
  </clause>

  <clause id="32093">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32081(a,2),28340(a,1))].">
      <j1 rule="para" parents="32081 28340"/>
    </justification>
  </clause>

  <clause id="32094">
    <literal><![CDATA[
      L(x,x,a(y,z,a(u,y,z))) = x
    ]]></literal>
    <justification jstring="[para(30853(a,2),32092(a,1,3))].">
      <j1 rule="para" parents="30853 32092"/>
    </justification>
  </clause>

  <clause id="32095">
    <literal><![CDATA[
      (1 / x) \ a(y,y,a(z,u,w)) = a(y,y,a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(32092(a,1),30968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32092 30968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32096">
    <literal><![CDATA[
      L(x,a(y,z,x),u) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(32094(a,1),31920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32094 31920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32098">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),a(u,w,x),v5) = L(x \ L(x,x,a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(32096(a,1),10440(a,2,1,2))].">
      <j1 rule="para" parents="32096 10440"/>
    </justification>
  </clause>

  <clause id="32100">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,u,w)) = (u / x) \ L(u,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(32096(a,1),31837(a,2,2))].">
      <j1 rule="para" parents="32096 31837"/>
    </justification>
  </clause>

  <clause id="32101">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ (w \ u))) = x \ L(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,30143,a(flip),b,32082,a),flip(a)].">
      <j1 rule="hyper" parents="60 30143 32082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32104">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (x \ v5) = v5 * L(v5 \ (x \ v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32082(a,1),3831(a,1,1))].">
      <j1 rule="para" parents="32082 3831"/>
    </justification>
  </clause>

  <clause id="32108">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ L(x,v5,v6)) = L(x,v5,v6) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32085(a,1),4262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32085 4262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32111">
    <literal><![CDATA[
      (x / y) \ L(x,x,a(z,u,w)) = a(x,x,a(w,u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,31164,a(flip),b,32095,a)].">
      <j1 rule="hyper" parents="60 31164 32095"/>
    </justification>
  </clause>

  <clause id="32112">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w \ x) = w \ L(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(74(a,1),32111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="74 32111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32113">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(z,z,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(31165,a,32100,a),flip(a)].">
      <j1 rule="hyper" parents="31165 32100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32114">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(31848,a,32113,a)].">
      <j1 rule="hyper" parents="31848 32113"/>
    </justification>
  </clause>

  <clause id="32116">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * w = w * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,32113,a,b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 32113 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32119">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,u,w))) = 1
    ]]></literal>
    <justification jstring="[para(32113(a,2),32089(a,1,3))].">
      <j1 rule="para" parents="32113 32089"/>
    </justification>
  </clause>

  <clause id="32120">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * u = L(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(32113(a,1),32080(a,1,1))].">
      <j1 rule="para" parents="32113 32080"/>
    </justification>
  </clause>

  <clause id="32121">
    <literal><![CDATA[
      L(x,x,a(y,z,a(u,u,w))) = x
    ]]></literal>
    <justification jstring="[para(32113(a,2),32092(a,1,3))].">
      <j1 rule="para" parents="32113 32092"/>
    </justification>
  </clause>

  <clause id="32122">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,30854,a,b,32119,a)].">
      <j1 rule="hyper" parents="60 30854 32119"/>
    </justification>
  </clause>

  <clause id="32123">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,w))) = 1
    ]]></literal>
    <justification jstring="[para(31136(a,1),32119(a,1,3))].">
      <j1 rule="para" parents="31136 32119"/>
    </justification>
  </clause>

  <clause id="32124">
    <literal><![CDATA[
      L(x,x,a(a(y,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(30734,a,32121,a)].">
      <j1 rule="hyper" parents="30734 32121"/>
    </justification>
  </clause>

  <clause id="32127">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,u))) = x * 1
    ]]></literal>
    <justification jstring="[hyper(129,a,32122,a(flip),b,32082,a),flip(a)].">
      <j1 rule="hyper" parents="129 32122 32082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32128">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,u))) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,32127,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 32127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32129">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(32127(a,2),144(a,1))].">
      <j1 rule="para" parents="32127 144"/>
    </justification>
  </clause>

  <clause id="32130">
    <literal><![CDATA[
      (a(x,y,a(z,z,y)) * u) * w = a(x,y,a(z,z,y)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1838,a,32128,a),flip(a)].">
      <j1 rule="hyper" parents="1838 32128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32131">
    <literal><![CDATA[
      (a(x,y,a(z,z,y)) * (u * w)) \ ((a(x,y,a(z,z,y)) * u) * (w * v5)) = L(v5,L(w,u,a(x,y,a(z,z,y))),a(x,y,a(z,z,y)) * u)
    ]]></literal>
    <justification jstring="[para(32128(a,1),620(a,1,2,2,1))].">
      <j1 rule="para" parents="32128 620"/>
    </justification>
  </clause>

  <clause id="32132">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,w,u)) = x * (y * a(z,u,a(w,w,u)))
    ]]></literal>
    <justification jstring="[para(32128(a,1),28343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32128 28343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32134">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,31124,a,b,32114,a)].">
      <j1 rule="hyper" parents="370 31124 32114"/>
    </justification>
  </clause>

  <clause id="32138">
    <literal><![CDATA[
      a(a(x,y,a(z,u,y)),w,w) = 1
    ]]></literal>
    <justification jstring="[para(32134(a,1),32090(a,1,1))].">
      <j1 rule="para" parents="32134 32090"/>
    </justification>
  </clause>

  <clause id="32139">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,32134,a(flip),b,32138,a)].">
      <j1 rule="hyper" parents="60 32134 32138"/>
    </justification>
  </clause>

  <clause id="32140">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,y))) = 1
    ]]></literal>
    <justification jstring="[hyper(31847,a,32139,a)].">
      <j1 rule="hyper" parents="31847 32139"/>
    </justification>
  </clause>

  <clause id="32141">
    <literal><![CDATA[
      a(a(x,x,a(y,z,u)),y,w) = 1
    ]]></literal>
    <justification jstring="[hyper(31149,a,32140,a)].">
      <j1 rule="hyper" parents="31149 32140"/>
    </justification>
  </clause>

  <clause id="32142">
    <literal><![CDATA[
      L(x,y,a(z,z,a(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,32141,a)].">
      <j1 rule="hyper" parents="49 32141"/>
    </justification>
  </clause>

  <clause id="32143">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,y))) = x
    ]]></literal>
    <justification jstring="[para(31136(a,1),32142(a,1,3))].">
      <j1 rule="para" parents="31136 32142"/>
    </justification>
  </clause>

  <clause id="32144">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,y))) = x
    ]]></literal>
    <justification jstring="[para(32113(a,2),32142(a,1,3))].">
      <j1 rule="para" parents="32113 32142"/>
    </justification>
  </clause>

  <clause id="32145">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * u) = w * (a(x,x,a(y,z,u)) * u)
    ]]></literal>
    <justification jstring="[para(32143(a,1),28360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32143 28360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32146">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) \ w) / u = w / (u * a(x,y,a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(30106,a,32144,a)].">
      <j1 rule="hyper" parents="30106 32144"/>
    </justification>
  </clause>

  <clause id="32147">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(y,y,w)) = x \ L(y,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,32112,a(flip),b,32116,a),flip(a)].">
      <j1 rule="hyper" parents="60 32112 32116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32148">
    <literal><![CDATA[
      x \ L(x,y,z * L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29999,a,32101,a),flip(a)].">
      <j1 rule="hyper" parents="29999 32101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32149">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) \ x = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,31550,a,b,32148,a)].">
      <j1 rule="hyper" parents="60 31550 32148"/>
    </justification>
  </clause>

  <clause id="32150">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,w,u))) = (x \ y) * a(z,u,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(831,a,32132,a)].">
      <j1 rule="hyper" parents="831 32132"/>
    </justification>
  </clause>

  <clause id="32151">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * u) = w * L(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(32120(a,1),32145(a,2,2))].">
      <j1 rule="para" parents="32120 32145"/>
    </justification>
  </clause>

  <clause id="32152">
    <literal><![CDATA[
      (x * y) * a(z,z,a(u,w,y)) = x * L(y,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(23637,a,32151,a)].">
      <j1 rule="hyper" parents="23637 32151"/>
    </justification>
  </clause>

  <clause id="32153">
    <literal><![CDATA[
      (x * y) * a(z,z,a(u,w,y)) != x * v5
    ]]></literal>
    <literal><![CDATA[
      L(y,w,a(z,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(32152(a,2),40(a,1))].">
      <j1 rule="para" parents="32152 40"/>
    </justification>
  </clause>

  <clause id="32154">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) \ w) / u = w / L(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(31846(a,1),32146(a,2,2))].">
      <j1 rule="para" parents="31846 32146"/>
    </justification>
  </clause>

  <clause id="32155">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(u,w,a(v5,v5,w))) = L(z,y,x) * a(u,w,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),32150(a,2,1))].">
      <j1 rule="para" parents="13 32150"/>
    </justification>
  </clause>

  <clause id="32157">
    <literal><![CDATA[
      L(x \ L(x,x,a(y,z,u)),w,v5) = a(L(x,w,v5),a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(31262,a,32098,a),flip(a)].">
      <j1 rule="hyper" parents="31262 32098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32158">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,a(v5,v5,w)))) = L(z,y,x) * a(u,w,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[para(32132(a,1),32155(a,1,2))].">
      <j1 rule="para" parents="32132 32155"/>
    </justification>
  </clause>

  <clause id="32159">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,a(v5,v5,w))))) = L(z,y,x) * a(u,w,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[para(32132(a,1),32158(a,1,2,2))].">
      <j1 rule="para" parents="32132 32158"/>
    </justification>
  </clause>

  <clause id="32160">
    <literal><![CDATA[
      L(x * a(y,z,a(u,u,z)),w,v5) = L(x,w,v5) * a(y,z,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(629,a,32159,a)].">
      <j1 rule="hyper" parents="629 32159"/>
    </justification>
  </clause>

  <clause id="32161">
    <literal><![CDATA[
      L((x \ R(x,y,z)) * a(z,y,a(x,x,y)),u,w) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31440,a(flip),b,32160,a),flip(a)].">
      <j1 rule="hyper" parents="370 31440 32160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32162">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = L(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(31161(a,1),32161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31161 32161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32163">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,u))) \ (x * R(y,z,u)) = a(L(y,y,L(x,y,a(z,z,u))),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,32018,a,b,32162,a)].">
      <j1 rule="hyper" parents="370 32018 32162"/>
    </justification>
  </clause>

  <clause id="32164">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = a(x,a(u,w,v5),L(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,31266,a,b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 31266 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32165">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = a(v6,v5,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31138,a,b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 31138 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32166">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,L(a(w,v5,v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,31061,a,b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 31061 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32168">
    <literal><![CDATA[
      a(L(x,y * a(x,z,u),w),z,u) = L(a(x,z,u),y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,30816,a(flip),b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 30816 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32169">
    <literal><![CDATA[
      a(L(x,y,z),u,L(z,w,v5)) = a(x,u,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,29068,a(flip),b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 29068 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32170">
    <literal><![CDATA[
      a(L(x,y,z),u,z) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,14782,a(flip),b,32162,a),flip(a)].">
      <j1 rule="hyper" parents="370 14782 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32171">
    <literal><![CDATA[
      (x * y) * a(L(z,y,x),u,w) = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,32162,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 32162 13"/>
    </justification>
  </clause>

  <clause id="32176">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(28709(a,1),32162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28709 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32177">
    <literal><![CDATA[
      a(K(x,y * z) * ((x * z) \ (z * (y * x))),u,w) = L(a(a(z,y,x) \ y,u,w),z,x)
    ]]></literal>
    <justification jstring="[para(29181(a,2),32162(a,1,1))].">
      <j1 rule="para" parents="29181 32162"/>
    </justification>
  </clause>

  <clause id="32178">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = a(L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(32162(a,2),29270(a,2,1))].">
      <j1 rule="para" parents="32162 29270"/>
    </justification>
  </clause>

  <clause id="32179">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(32162(a,2),29268(a,2,2))].">
      <j1 rule="para" parents="32162 29268"/>
    </justification>
  </clause>

  <clause id="32180">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(L(z,u,w),y,x))) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(32162(a,2),30026(a,1,2,2,2))].">
      <j1 rule="para" parents="32162 30026"/>
    </justification>
  </clause>

  <clause id="32181">
    <literal><![CDATA[
      L(a(L(x,y,z),u,w * L(w,v5,v6)),y,z) = (L(w,v5,v6) \ w) \ L(L(w,v5,v6) \ w,u,x)
    ]]></literal>
    <justification jstring="[para(32162(a,2),31177(a,1,1))].">
      <j1 rule="para" parents="32162 31177"/>
    </justification>
  </clause>

  <clause id="32183">
    <literal><![CDATA[
      a((x * y) \ z,u,x) = a(y \ (x \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(30210,a,32170,a),flip(a)].">
      <j1 rule="hyper" parents="30210 32170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32190">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,w,v5)) = (a(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(32176(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="32176 617"/>
    </justification>
  </clause>

  <clause id="32193">
    <literal><![CDATA[
      a((x * y) \ z,u,L(x,w,v5)) = a(y \ (x \ z),u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30210,a,32169,a),flip(a)].">
      <j1 rule="hyper" parents="30210 32169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32196">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) = z \ L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(32178(a,2),29986(a,1,1))].">
      <j1 rule="para" parents="32178 29986"/>
    </justification>
  </clause>

  <clause id="32197">
    <literal><![CDATA[
      a(L(x,y * a(x,z,u),w),z,u) = a(L(x,y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,32162,a,b,32168,a),flip(a)].">
      <j1 rule="hyper" parents="370 32162 32168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32200">
    <literal><![CDATA[
      x \ ((x * y) * a(y \ 1,z,u)) = y * a((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(251(a,1),32179(a,2,2,1))].">
      <j1 rule="para" parents="251 32179"/>
    </justification>
  </clause>

  <clause id="32201">
    <literal><![CDATA[
      L(x \ L(x,x,a(y,z,u)),w,v5) = a(x,a(y,z,x),L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,32157,a,b,32164,a)].">
      <j1 rule="hyper" parents="60 32157 32164"/>
    </justification>
  </clause>

  <clause id="32202">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) * w = L(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(32164(a,1),31275(a,1,1))].">
      <j1 rule="para" parents="32164 31275"/>
    </justification>
  </clause>

  <clause id="32203">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,L(v6,v5,v5)) = a(v6,v5,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31458,a(flip),b,32165,a),flip(a)].">
      <j1 rule="hyper" parents="370 31458 32165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32204">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,L(v6,v6,v5)) = v6 \ R(v6,v5,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31457,a(flip),b,32165,a),flip(a)].">
      <j1 rule="hyper" parents="370 31457 32165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32205">
    <literal><![CDATA[
      L(x * (a(x,y,L(a(z,u,w),v5,v6)) * a(L(a(w,u,z),v5,v6),y,x)),y,L(a(w,u,z),v5,v6)) = x * (L(x,y,L(a(w,u,z),v5,v6)) \ x)
    ]]></literal>
    <justification jstring="[para(32165(a,1),30192(a,1,1,2,1))].">
      <j1 rule="para" parents="32165 30192"/>
    </justification>
  </clause>

  <clause id="32206">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ v7 = a(v6,v5,L(a(z,y,x),u,w)) * v7
    ]]></literal>
    <justification jstring="[para(32165(a,2),31063(a,1,1))].">
      <j1 rule="para" parents="32165 31063"/>
    </justification>
  </clause>

  <clause id="32208">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) * v6 = v6 * a(u,x,L(a(y,z,x),w,v5))
    ]]></literal>
    <justification jstring="[para(32166(a,1),30133(a,2,2))].">
      <j1 rule="para" parents="32166 30133"/>
    </justification>
  </clause>

  <clause id="32211">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) = x \ L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(30160,a,32196,a)].">
      <j1 rule="hyper" parents="30160 32196"/>
    </justification>
  </clause>

  <clause id="32212">
    <literal><![CDATA[
      x * L(x \ L(x,y,z),u,w) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,29988,a(flip),b,32196,a(flip))].">
      <j1 rule="hyper" parents="129 29988 32196"/>
    </justification>
  </clause>

  <clause id="32213">
    <literal><![CDATA[
      L(x,y,L(z,u,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14691,a,32211,a),flip(a)].">
      <j1 rule="hyper" parents="14691 32211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32214">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) != x \ v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32211(a,2),44(a,1))].">
      <j1 rule="para" parents="32211 44"/>
    </justification>
  </clause>

  <clause id="32217">
    <literal><![CDATA[
      L(x,y,z \ x) = L(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29076,a(flip),b,32213,a)].">
      <j1 rule="hyper" parents="60 29076 32213"/>
    </justification>
  </clause>

  <clause id="32219">
    <literal><![CDATA[
      L(x,y,(x \ z) \ u) = L(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(656(a,1),32213(a,1,3)),flip(a)].">
      <j1 rule="para" parents="656 32213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32222">
    <literal><![CDATA[
      L(x,y,(R(x,z,u) \ x) \ (x * w)) = L(x,y,(R(x,z,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(1969(a,1),32219(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1969 32219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32225">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,u)) = y * a((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(2962(a,1),32200(a,1,2,2))].">
      <j1 rule="para" parents="2962 32200"/>
    </justification>
  </clause>

  <clause id="32226">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,u)) = y * a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(26783(a,1),32225(a,2,2))].">
      <j1 rule="para" parents="26783 32225"/>
    </justification>
  </clause>

  <clause id="32227">
    <literal><![CDATA[
      x * a(L(x,x,y),z,u) = x * a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,32179,a(flip),b,32226,a)].">
      <j1 rule="hyper" parents="60 32179 32226"/>
    </justification>
  </clause>

  <clause id="32228">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) = L(a(x,x,a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(28429(a,1),32201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28429 32201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32229">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(31267,a,32228,a(flip))].">
      <j1 rule="hyper" parents="31267 32228"/>
    </justification>
  </clause>

  <clause id="32230">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(31839,a,32229,a)].">
      <j1 rule="hyper" parents="31839 32229"/>
    </justification>
  </clause>

  <clause id="32231">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(31838,a,32229,a)].">
      <j1 rule="hyper" parents="31838 32229"/>
    </justification>
  </clause>

  <clause id="32232">
    <literal><![CDATA[
      L(x,y,a(y,a(z,u,y),w)) = x
    ]]></literal>
    <justification jstring="[para(32229(a,2),31776(a,1,3))].">
      <j1 rule="para" parents="32229 31776"/>
    </justification>
  </clause>

  <clause id="32233">
    <literal><![CDATA[
      a(a(x,y,a(z,z,u)),w,v5) = a(a(z,z,a(x,y,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(32229(a,1),31845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32229 31845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32234">
    <literal><![CDATA[
      a(a(x,y,a(z,z,u)),w,v5) = a(z,z,a(v5,w,a(x,y,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32230,a(flip),b,32233,a),flip(a)].">
      <j1 rule="hyper" parents="370 32230 32233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32235">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) * a(z,z,a(v5,v6,a(x,y,u))) = L(a(x,y,a(z,z,u)),v6,v5) * w
    ]]></literal>
    <justification jstring="[para(32234(a,1),31166(a,1,2))].">
      <j1 rule="para" parents="32234 31166"/>
    </justification>
  </clause>

  <clause id="32236">
    <literal><![CDATA[
      a(a(L(x,y,z),u,w),v5,L(v6,v5,v5)) = a(v6,v5,L(a(w,u,x),y,z))
    ]]></literal>
    <justification jstring="[para(32162(a,2),32203(a,1,1))].">
      <j1 rule="para" parents="32162 32203"/>
    </justification>
  </clause>

  <clause id="32237">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(31479,a,32236,a)].">
      <j1 rule="hyper" parents="31479 32236"/>
    </justification>
  </clause>

  <clause id="32238">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(32236(a,1),31479(a,1))].">
      <j1 rule="para" parents="32236 31479"/>
    </justification>
  </clause>

  <clause id="32239">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,L(v6,y,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32166,a,b,32237,a)].">
      <j1 rule="hyper" parents="370 32166 32237"/>
    </justification>
  </clause>

  <clause id="32240">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,w * (u \ z),w * (u \ z)))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,29707,a(flip),b,32237,a),flip(a)].">
      <j1 rule="hyper" parents="370 29707 32237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32241">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) = a(x,y,a(z,v5,L(v6,u,w)))
    ]]></literal>
    <justification jstring="[para(32162(a,2),32237(a,2,3)),flip(a)].">
      <j1 rule="para" parents="32162 32237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32242">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26556,a,32239,a),flip(a)].">
      <j1 rule="hyper" parents="26556 32239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32244">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,L(x,u,u))) = v5
    ]]></literal>
    <justification jstring="[para(31163(a,1),32238(a,1))].">
      <j1 rule="para" parents="31163 32238"/>
    </justification>
  </clause>

  <clause id="32245">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(w,v5,L(v6,y,z))) = v7
    ]]></literal>
    <justification jstring="[para(32166(a,2),32238(a,1))].">
      <j1 rule="para" parents="32166 32238"/>
    </justification>
  </clause>

  <clause id="32246">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,z,a(x,y,L(z,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(31834(a,1),32245(a,1))].">
      <j1 rule="para" parents="31834 32245"/>
    </justification>
  </clause>

  <clause id="32247">
    <literal><![CDATA[
      x \ (L(1 / x,y,L(z,u,w)) \ 1) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(30017(a,1),32180(a,1,2))].">
      <j1 rule="para" parents="30017 32180"/>
    </justification>
  </clause>

  <clause id="32248">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = L(x,y,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(3889,a,32247,a),flip(a)].">
      <j1 rule="hyper" parents="3889 32247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32249">
    <literal><![CDATA[
      L(L(x,y * z,z) \ x,y,y) = L(z \ R(z,y * z,x),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31629,a,b,32248,a),flip(a)].">
      <j1 rule="hyper" parents="370 31629 32248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32251">
    <literal><![CDATA[
      L(L(x,y,z * R(u,w,v5)) \ x,v6,v7) = L(x,y,L(z * L(u,w,v5),v6,v7)) \ x
    ]]></literal>
    <justification jstring="[para(27272(a,2),32248(a,1,1,1))].">
      <j1 rule="para" parents="27272 32248"/>
    </justification>
  </clause>

  <clause id="32252">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) * a(L(a(w,u,z),v5,v6),y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(237,a,32206,a),flip(a)].">
      <j1 rule="hyper" parents="237 32206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32253">
    <literal><![CDATA[
      x * a(x,y,L(a(z,u,y),w,v5)) = L(x,a(z,u,y),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,32202,a(flip),b,32208,a),flip(a)].">
      <j1 rule="hyper" parents="60 32202 32208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32254">
    <literal><![CDATA[
      L(x,y,(R(x,z,u) \ x) \ (x * w)) = L(x,y,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3371,a(flip),b,32222,a),flip(a)].">
      <j1 rule="hyper" parents="370 3371 32222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32255">
    <literal><![CDATA[
      L(x,y,(R(x,z,u) \ x) \ (x * w)) = L(x,y,L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,30116,a(flip),b,32254,a),flip(a)].">
      <j1 rule="hyper" parents="370 30116 32254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32256">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6)) \ x = x \ R(x,y,L(a(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,30146,a(flip),b,32204,a)].">
      <j1 rule="hyper" parents="60 30146 32204"/>
    </justification>
  </clause>

  <clause id="32258">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,u))) \ (x * R(y,z,u)) = a(L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(31783(a,1),32163(a,2,1))].">
      <j1 rule="para" parents="31783 32163"/>
    </justification>
  </clause>

  <clause id="32260">
    <literal><![CDATA[
      a(K(x,y * z) * ((x * z) \ (z * (y * x))),u,w) = L(a(y * a(x,y,z),u,w),z,x)
    ]]></literal>
    <justification jstring="[para(31106(a,1),32177(a,2,1))].">
      <j1 rule="para" parents="31106 32177"/>
    </justification>
  </clause>

  <clause id="32261">
    <literal><![CDATA[
      a(K(x,y * z) * ((x * z) \ (z * (y * x))),u,w) = a(L(y * a(x,y,z),z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,32162,a,b,32260,a),flip(a)].">
      <j1 rule="hyper" parents="370 32162 32260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32262">
    <literal><![CDATA[
      a(L(x * a(y,x,z),z,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(32261(a,1),27334(a,1))].">
      <j1 rule="para" parents="32261 27334"/>
    </justification>
  </clause>

  <clause id="32263">
    <literal><![CDATA[
      L(a(x,y,a(z,z,y)),u,w) * v5 = (a(x,y,a(z,z,y)) * v5) * 1
    ]]></literal>
    <justification jstring="[para(32123(a,1),32235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32123 32235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32264">
    <literal><![CDATA[
      L(a(x,y,a(z,z,y)),u,w) * v5 = a(x,y,a(z,z,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(370,a,3,a(flip),b,32263,a),flip(a)].">
      <j1 rule="hyper" parents="370 3 32263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32265">
    <literal><![CDATA[
      a(x,y,L(a(z,z,y),u,w)) * v5 = a(x,y,a(z,z,y)) * v5
    ]]></literal>
    <justification jstring="[para(31061(a,2),32264(a,1,1))].">
      <j1 rule="para" parents="31061 32264"/>
    </justification>
  </clause>

  <clause id="32266">
    <literal><![CDATA[
      a(x,y,a(z,z,L(y,u,w))) * v5 = a(x,y,a(z,z,y)) * v5
    ]]></literal>
    <justification jstring="[para(15789(a,2),32265(a,1,1))].">
      <j1 rule="para" parents="15789 32265"/>
    </justification>
  </clause>

  <clause id="32267">
    <literal><![CDATA[
      a(x,y,a(z,z,L(y,u,w))) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(23996,a,32266,a)].">
      <j1 rule="hyper" parents="23996 32266"/>
    </justification>
  </clause>

  <clause id="32268">
    <literal><![CDATA[
      a(x,y,a(z,x,L(y,u,w))) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(32246,a,32267,a)].">
      <j1 rule="hyper" parents="32246 32267"/>
    </justification>
  </clause>

  <clause id="32269">
    <literal><![CDATA[
      a(x,y,a(z,u,(1 / ((u \ z) / w)) * (u \ z))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[para(29610(a,1),32240(a,1,3,3))].">
      <j1 rule="para" parents="29610 32240"/>
    </justification>
  </clause>

  <clause id="32270">
    <literal><![CDATA[
      L(L(x * a(a(y,z,u),w,v5),a(v5,w,a(y,z,u)),v5),L(v5,w,a(y,z,u)),v6) = (v6 * (v5 * a(v5,w,a(y,z,u)))) \ (v6 * (v5 * x))
    ]]></literal>
    <justification jstring="[para(31146(a,1),32087(a,1,1,1))].">
      <j1 rule="para" parents="31146 32087"/>
    </justification>
  </clause>

  <clause id="32271">
    <literal><![CDATA[
      (a(x,y,a(z,z,y)) * (u * w)) \ (a(x,y,a(z,z,y)) * (u * (w * v5))) = L(v5,L(w,u,a(x,y,a(z,z,y))),a(x,y,a(z,z,y)) * u)
    ]]></literal>
    <justification jstring="[para(32130(a,1),32131(a,1,2))].">
      <j1 rule="para" parents="32130 32131"/>
    </justification>
  </clause>

  <clause id="32272">
    <literal><![CDATA[
      x * (L(x,y,L(a(z,u,w),v5,v6)) \ x) = L(x * 1,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(32252(a,1),32205(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="32252 32205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32273">
    <literal><![CDATA[
      x * (L(x,y,L(a(z,u,w),v5,v6)) \ x) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(3(a,1),32272(a,2,1))].">
      <j1 rule="para" parents="3 32272"/>
    </justification>
  </clause>

  <clause id="32275">
    <literal><![CDATA[
      x * (x \ R(x,y,L(a(z,u,w),v5,v6))) = L(x,y,L(a(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(32256(a,1),32273(a,1,2))].">
      <j1 rule="para" parents="32256 32273"/>
    </justification>
  </clause>

  <clause id="32276">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w),v5,v6)) = L(x,y,L(a(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(298,a,32275,a)].">
      <j1 rule="hyper" parents="298 32275"/>
    </justification>
  </clause>

  <clause id="32278">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,a(v5,v5,w))) = L(x,L(y,z,a(u,w,a(v5,v5,w))),a(u,w,a(v5,v5,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(1199,a,32271,a)].">
      <j1 rule="hyper" parents="1199 32271"/>
    </justification>
  </clause>

  <clause id="32279">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,a(v5,v5,w))),a(u,w,a(v5,v5,w)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32129,a,32278,a),flip(a)].">
      <j1 rule="hyper" parents="32129 32278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32281">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,u)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(32128(a,1),32279(a,1,2))].">
      <j1 rule="para" parents="32128 32279"/>
    </justification>
  </clause>

  <clause id="32282">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) = a(a(u,w,a(v5,v5,w)) * z,y,x)
    ]]></literal>
    <justification jstring="[para(32281(a,1),29934(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="32281 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32283">
    <literal><![CDATA[
      L(x,y,z \ R(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(31160(a,1),32281(a,1,3))].">
      <j1 rule="para" parents="31160 32281"/>
    </justification>
  </clause>

  <clause id="32284">
    <literal><![CDATA[
      L(x,y,(z \ L(z,u,w)) * v5) = L(x,y,a(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(31297(a,1),32281(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31297 32281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32285">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(27266,a,32283,a)].">
      <j1 rule="hyper" parents="27266 32283"/>
    </justification>
  </clause>

  <clause id="32286">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(14694,a,32285,a)].">
      <j1 rule="hyper" parents="14694 32285"/>
    </justification>
  </clause>

  <clause id="32287">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30726,a,b,32286,a),flip(a)].">
      <j1 rule="hyper" parents="370 30726 32286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32288">
    <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(32286(a,2),30727(a,1))].">
      <j1 rule="para" parents="32286 30727"/>
    </justification>
  </clause>

  <clause id="32289">
    <literal><![CDATA[
      L(x,y,L(z * L(z,u,w),v5,v6)) = L(x,y,a(w,u,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(60,a,10451,a(flip),b,32287,a)].">
      <j1 rule="hyper" parents="60 10451 32287"/>
    </justification>
  </clause>

  <clause id="32291">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(27955(a,2),32288(a,1))].">
      <j1 rule="para" parents="27955 32288"/>
    </justification>
  </clause>

  <clause id="32292">
    <literal><![CDATA[
      L(x,y,a(z,u,u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(26888(a,1),32291(a,1,3))].">
      <j1 rule="para" parents="26888 32291"/>
    </justification>
  </clause>

  <clause id="32293">
    <literal><![CDATA[
      L(x,y,(z \ L(z,u,w)) * v5) = L(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,30635,a(flip),b,32284,a),flip(a)].">
      <j1 rule="hyper" parents="370 30635 32284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32294">
    <literal><![CDATA[
      L(x,y,z * (u \ L(u,w,v5))) = L(x,y,a(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(24037,a,32293,a)].">
      <j1 rule="hyper" parents="24037 32293"/>
    </justification>
  </clause>

  <clause id="32295">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6) * v7) = L(x,y,a(w,u,L(z,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[para(10440(a,1),32293(a,1,3,1))].">
      <j1 rule="para" parents="10440 32293"/>
    </justification>
  </clause>

  <clause id="32296">
    <literal><![CDATA[
      L(x,y,z * (u * L(u,w,v5))) = L(x,y,a(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4111,a(flip),b,32294,a)].">
      <j1 rule="hyper" parents="60 4111 32294"/>
    </justification>
  </clause>

  <clause id="32297">
    <literal><![CDATA[
      L(x,y,z * (u * (z \ R(z,w,v5)))) = L(x,y,a(v5,w,z) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(27603,a,32296,a)].">
      <j1 rule="hyper" parents="27603 32296"/>
    </justification>
  </clause>

  <clause id="32298">
    <literal><![CDATA[
      a(a(x,y,a(z,z,y)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(30044,a,32282,a),flip(a)].">
      <j1 rule="hyper" parents="30044 32282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32299">
    <literal><![CDATA[
      a(x * a(y,z,a(u,u,z)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,32298,a)].">
      <j1 rule="hyper" parents="26519 32298"/>
    </justification>
  </clause>

  <clause id="32300">
    <literal><![CDATA[
      a(x * (y * a(z,u,a(w,w,u))),v5,v6) = a(x * y,v5,v6)
    ]]></literal>
    <justification jstring="[para(32132(a,1),32299(a,1,1))].">
      <j1 rule="para" parents="32132 32299"/>
    </justification>
  </clause>

  <clause id="32301">
    <literal><![CDATA[
      a((x * L(x,y,z)) * u,w,v5) = a(a(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(31298,a,32300,a),flip(a)].">
      <j1 rule="hyper" parents="31298 32300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32302">
    <literal><![CDATA[
      a(x * (y * L(y,z,u)),w,v5) = a(a(u,z,y) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26519,a,32301,a)].">
      <j1 rule="hyper" parents="26519 32301"/>
    </justification>
  </clause>

  <clause id="32303">
    <literal><![CDATA[
      L(L(x,y,z * R(z,u,w)) \ x,v5,v6) = L(x,y,a(w,u,L(z,v5,v6))) \ x
    ]]></literal>
    <justification jstring="[para(32289(a,1),32251(a,2,1))].">
      <j1 rule="para" parents="32289 32251"/>
    </justification>
  </clause>

  <clause id="32304">
    <literal><![CDATA[
      L(x,y,z * (u * (z \ R(z,w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (a(v5,w,z) * u)) = v6
    ]]></literal>
    <justification jstring="[para(32297(a,2),28356(a,1))].">
      <j1 rule="para" parents="32297 28356"/>
    </justification>
  </clause>

  <clause id="32305">
    <literal><![CDATA[
      L(L(x,y,z * R(z,u,w)) \ x,v5,v6) = a(x,y,a(w,u,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32085,a(flip),b,32303,a),flip(a)].">
      <j1 rule="hyper" parents="370 32085 32303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32306">
    <literal><![CDATA[
      L(L(x,y,z * L(z,u,w)) \ x,v5,v6) = a(x,y,a(w,u,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(27272(a,1),32305(a,1,1,1))].">
      <j1 rule="para" parents="27272 32305"/>
    </justification>
  </clause>

  <clause id="32307">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),v5,v6) = a(x,y,a(w,u,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(32149(a,1),32306(a,1,1))].">
      <j1 rule="para" parents="32149 32306"/>
    </justification>
  </clause>

  <clause id="32308">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,L(v6,y,z))) = (L(v6,v5,w) \ v6) \ L(L(v6,v5,w) \ v6,u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,32181,a(flip),b,32307,a),flip(a)].">
      <j1 rule="hyper" parents="60 32181 32307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32309">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(u,w,a(z,y,L(x,v5,v6))) = L(L(x,y,z) \ x,w,L(u,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(129,a,29020,a(flip),b,32308,a(flip))].">
      <j1 rule="hyper" parents="129 29020 32308"/>
    </justification>
  </clause>

  <clause id="32310">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(y,u,w)) = (L(x,y,z) \ x) * a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(32268(a,1),32309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32268 32309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32311">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(y,u,w)) = L(x,y,z) \ L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,32147,a(flip),b,32310,a),flip(a)].">
      <j1 rule="hyper" parents="370 32147 32310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32312">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(y,u,w)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,30869,a(flip),b,32311,a),flip(a)].">
      <j1 rule="hyper" parents="370 30869 32311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32313">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(32312(a,1),31393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32312 31393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32314">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30395,a,32313,a),flip(a)].">
      <j1 rule="hyper" parents="30395 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32315">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32162,a,b,32313,a)].">
      <j1 rule="hyper" parents="370 32162 32313"/>
    </justification>
  </clause>

  <clause id="32316">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31091,a,b,32313,a)].">
      <j1 rule="hyper" parents="370 31091 32313"/>
    </justification>
  </clause>

  <clause id="32317">
    <literal><![CDATA[
      (a(x,y,a(z,y,u)) / y) \ (a(z,y,u) / y) = a(z,y,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,31032,a,b,32313,a)].">
      <j1 rule="hyper" parents="370 31032 32313"/>
    </justification>
  </clause>

  <clause id="32318">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,30757,a,b,32313,a)].">
      <j1 rule="hyper" parents="370 30757 32313"/>
    </justification>
  </clause>

  <clause id="32319">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,30752,a,b,32313,a)].">
      <j1 rule="hyper" parents="370 30752 32313"/>
    </justification>
  </clause>

  <clause id="32320">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,29309,a,b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 29309 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32322">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32176,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 32176 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32323">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31008,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 31008 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32324">
    <literal><![CDATA[
      a(x,y,L(z,u,u * a(x,y,z))) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,30787,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 30787 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32325">
    <literal><![CDATA[
      a(x,y,L(z,u,L(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,28915,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 28915 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32326">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,28772,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="370 28772 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32327">
    <literal><![CDATA[
      (x * y) * a(z,u,L(w,y,x)) = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,32313,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="129 32313 13"/>
    </justification>
  </clause>

  <clause id="32328">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(125,a,32313,a,b,30752,a)].">
      <j1 rule="hyper" parents="125 32313 30752"/>
    </justification>
  </clause>

  <clause id="32329">
    <literal><![CDATA[
      x \ a(y,z,L(u,x,x)) = (x \ 1) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,32313,a,b,2074,a)].">
      <j1 rule="hyper" parents="125 32313 2074"/>
    </justification>
  </clause>

  <clause id="32330">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(31159,a,32313,a(flip))].">
      <j1 rule="hyper" parents="31159 32313"/>
    </justification>
  </clause>

  <clause id="32334">
    <literal><![CDATA[
      x \ a(y,z,L(u,x,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(32313(a,2),2091(a,1,2))].">
      <j1 rule="para" parents="32313 2091"/>
    </justification>
  </clause>

  <clause id="32336">
    <literal><![CDATA[
      (L(a(x,y,z) \ (1 * a(x,y,L(z,u,w))),v5,v6) / (a(x,y,z) \ 1)) * L(a(x,y,z) \ 1,v5,v6) = (a(x,y,z) \ 1) \ L(L(a(x,y,z) \ 1,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(32313(a,2),28035(a,1,1,1,1,2,2))].">
      <j1 rule="para" parents="32313 28035"/>
    </justification>
  </clause>

  <clause id="32338">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = a(x,y,L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(32313(a,2),29270(a,2,1))].">
      <j1 rule="para" parents="32313 29270"/>
    </justification>
  </clause>

  <clause id="32339">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(32313(a,1),30395(a,1))].">
      <j1 rule="para" parents="32313 30395"/>
    </justification>
  </clause>

  <clause id="32340">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(32313(a,2),30703(a,1,1))].">
      <j1 rule="para" parents="32313 30703"/>
    </justification>
  </clause>

  <clause id="32342">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 = a(x,y,L(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(32313(a,2),30625(a,2,1))].">
      <j1 rule="para" parents="32313 30625"/>
    </justification>
  </clause>

  <clause id="32343">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) = a(y,z,L(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(32313(a,2),30778(a,2,1))].">
      <j1 rule="para" parents="32313 30778"/>
    </justification>
  </clause>

  <clause id="32344">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(32313(a,2),30803(a,1,1))].">
      <j1 rule="para" parents="32313 30803"/>
    </justification>
  </clause>

  <clause id="32345">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (a(x,y,z) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(32313(a,2),30918(a,1,1))].">
      <j1 rule="para" parents="32313 30918"/>
    </justification>
  </clause>

  <clause id="32346">
    <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(32313(a,2),30921(a,2,1))].">
      <j1 rule="para" parents="32313 30921"/>
    </justification>
  </clause>

  <clause id="32347">
    <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(32313(a,2),30922(a,2,1))].">
      <j1 rule="para" parents="32313 30922"/>
    </justification>
  </clause>

  <clause id="32348">
    <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(32313(a,2),30923(a,2,1))].">
      <j1 rule="para" parents="32313 30923"/>
    </justification>
  </clause>

  <clause id="32349">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,a(x,y,z)) * v5) = a(x,y,L(z,w,u)) * v5
    ]]></literal>
    <justification jstring="[para(32313(a,2),30924(a,2,1))].">
      <j1 rule="para" parents="32313 30924"/>
    </justification>
  </clause>

  <clause id="32351">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32313(a,2),31480(a,1))].">
      <j1 rule="para" parents="32313 31480"/>
    </justification>
  </clause>

  <clause id="32352">
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(32313(a,2),31572(a,1,1))].">
      <j1 rule="para" parents="32313 31572"/>
    </justification>
  </clause>

  <clause id="32353">
    <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(32313(a,2),31944(a,1,2))].">
      <j1 rule="para" parents="32313 31944"/>
    </justification>
  </clause>

  <clause id="32354">
    <literal><![CDATA[
      L(a(x,y,L(z,z,u)),u * z,x) = L(a(x,y,z),L(z,u,x),x * u)
    ]]></literal>
    <justification jstring="[para(32313(a,2),31949(a,1,1))].">
      <j1 rule="para" parents="32313 31949"/>
    </justification>
  </clause>

  <clause id="32358">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(27010,a,32323,a),flip(a)].">
      <j1 rule="hyper" parents="27010 32323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32359">
    <literal><![CDATA[
      a(x,y,L(y,z,u) \ w) = a(x,y,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29559,a(flip),b,32323,a)].">
      <j1 rule="hyper" parents="60 29559 32323"/>
    </justification>
  </clause>

  <clause id="32360">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29054,a(flip),b,32323,a)].">
      <j1 rule="hyper" parents="60 29054 32323"/>
    </justification>
  </clause>

  <clause id="32361">
    <literal><![CDATA[
      x * a((x \ y) * y,y,z) = R(x,y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,32323,a(flip),b,31484,a(flip))].">
      <j1 rule="hyper" parents="129 32323 31484"/>
    </justification>
  </clause>

  <clause id="32362">
    <literal><![CDATA[
      a(x,y,L((1 / y) * z,y,u)) = a(x,y,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(1359(a,1),32323(a,1,3))].">
      <j1 rule="para" parents="1359 32323"/>
    </justification>
  </clause>

  <clause id="32364">
    <literal><![CDATA[
      a(x,y,(x * z) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(30399,a,32326,a),flip(a)].">
      <j1 rule="hyper" parents="30399 32326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32366">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(29238,a,32326,a),flip(a)].">
      <j1 rule="hyper" parents="29238 32326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32372">
    <literal><![CDATA[
      a(x,y,L(x,z,u) \ w) = a(x,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29559,a(flip),b,32326,a)].">
      <j1 rule="hyper" parents="60 29559 32326"/>
    </justification>
  </clause>

  <clause id="32374">
    <literal><![CDATA[
      a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,1),32326(a,1,3))].">
      <j1 rule="para" parents="25 32326"/>
    </justification>
  </clause>

  <clause id="32376">
    <literal><![CDATA[
      a(x,y,(x \ z) \ u) = a(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(656(a,1),32326(a,1,3)),flip(a)].">
      <j1 rule="para" parents="656 32326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32377">
    <literal><![CDATA[
      a(x,y,L((x * z) \ u,w,v5)) = a(x,y,L(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(746(a,1),32326(a,1,3))].">
      <j1 rule="para" parents="746 32326"/>
    </justification>
  </clause>

  <clause id="32378">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ u,w,v5)) = a(x,y,L(z \ (x * u),w,v5))
    ]]></literal>
    <justification jstring="[para(1078(a,1),32326(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1078 32326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32385">
    <literal><![CDATA[
      a(x,y,(x * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(32326(a,1),30399(a,1))].">
      <j1 rule="para" parents="32326 30399"/>
    </justification>
  </clause>

  <clause id="32387">
    <literal><![CDATA[
      L(x * y,x,z) \ (x * y) = a(z,x,x * L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(30266,a,32358,a)].">
      <j1 rule="hyper" parents="30266 32358"/>
    </justification>
  </clause>

  <clause id="32390">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,y * z) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(32358(a,1),31996(a,1,2))].">
      <j1 rule="para" parents="32358 31996"/>
    </justification>
  </clause>

  <clause id="32391">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w,y,z)) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,32162,a,b,32314,a)].">
      <j1 rule="hyper" parents="60 32162 32314"/>
    </justification>
  </clause>

  <clause id="32392">
    <literal><![CDATA[
      R(x,y,L(z,x,y)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,32314,a(flip),b,31090,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 32314 31090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32393">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) * (u \ 1) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,32314,a(flip),b,24003,a),flip(a)].">
      <j1 rule="hyper" parents="125 32314 24003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32396">
    <literal><![CDATA[
      L(x,L(y,z,L(u,y,z)) \ w,v5) = L(x,(y * a(y,z,u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(32392(a,1),27771(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="32392 27771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32397">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,z,y)) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(32262,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="32262 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32398">
    <literal><![CDATA[
      a(L(x,y,y),z,L(u,x,y)) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(31382,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="31382 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32399">
    <literal><![CDATA[
      a(x * y,z,L(u,y,y)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(30215,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="30215 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32400">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,x)) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(30210,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="30210 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32402">
    <literal><![CDATA[
      a(x * y,z,L(u,x,y)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30047,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="30047 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32403">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(27321,a,32315,a)].">
      <j1 rule="hyper" parents="27321 32315"/>
    </justification>
  </clause>

  <clause id="32404">
    <literal><![CDATA[
      a((x * y) \ (y * z),u,w) = a(x \ z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(26682,a,32315,a)].">
      <j1 rule="hyper" parents="26682 32315"/>
    </justification>
  </clause>

  <clause id="32405">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(26538,a,32315,a)].">
      <j1 rule="hyper" parents="26538 32315"/>
    </justification>
  </clause>

  <clause id="32406">
    <literal><![CDATA[
      a(x \ y,z,L(u,x,x)) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2971,a,32315,a),flip(a)].">
      <j1 rule="hyper" parents="2971 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32408">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,u))) \ (x * R(y,z,u)) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,32258,a,b,32315,a)].">
      <j1 rule="hyper" parents="60 32258 32315"/>
    </justification>
  </clause>

  <clause id="32409">
    <literal><![CDATA[
      a(x,y,L(z,u * a(x,y,z),w)) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32197,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 32197 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32410">
    <literal><![CDATA[
      a(x,L(y,x,z),L(u,x,y)) = x \ R(x,L(y,x,z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,31787,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 31787 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32411">
    <literal><![CDATA[
      a(L(x,y,y),z,L(u,y,w)) = a((y * w) \ (w * (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,30225,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 30225 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32412">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w,v5,v6) \ v7) = a(x,u,L(R(w,v5,v6) \ v7,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29716,a(flip),b,32315,a)].">
      <j1 rule="hyper" parents="60 29716 32315"/>
    </justification>
  </clause>

  <clause id="32413">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29047,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 29047 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32414">
    <literal><![CDATA[
      a((x * y) \ (z * y),u,w) = a(x \ z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,27327,a(flip),b,32315,a)].">
      <j1 rule="hyper" parents="60 27327 32315"/>
    </justification>
  </clause>

  <clause id="32415">
    <literal><![CDATA[
      a(x,y,L(z,x,u * x)) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25552,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 25552 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32416">
    <literal><![CDATA[
      a((x \ y) * y,z,L(u,w,x)) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,24935,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 24935 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32417">
    <literal><![CDATA[
      a(x \ y,z,L(u,x \ y,y)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3870,a(flip),b,32315,a),flip(a)].">
      <j1 rule="hyper" parents="60 3870 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32418">
    <literal><![CDATA[
      a(x \ y,z,L(u,x,x)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(32315(a,1),2971(a,1))].">
      <j1 rule="para" parents="32315 2971"/>
    </justification>
  </clause>

  <clause id="32419">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a((x * u) * u,y,z) = w
    ]]></literal>
    <justification jstring="[para(32315(a,1),26612(a,1))].">
      <j1 rule="para" parents="32315 26612"/>
    </justification>
  </clause>

  <clause id="32420">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u * (x * u),y,z) = w
    ]]></literal>
    <justification jstring="[para(32315(a,1),26614(a,1))].">
      <j1 rule="para" parents="32315 26614"/>
    </justification>
  </clause>

  <clause id="32421">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = a((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(29610(a,1),32315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29610 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32422">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ (x \ z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(32315(a,1),30210(a,1))].">
      <j1 rule="para" parents="32315 30210"/>
    </justification>
  </clause>

  <clause id="32423">
    <literal><![CDATA[
      (a(x,y * x,L(z,y,y)) \ y) * z = (y / (y * x)) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(32315(a,1),31702(a,1,1,1))].">
      <j1 rule="para" parents="32315 31702"/>
    </justification>
  </clause>

  <clause id="32424">
    <literal><![CDATA[
      a(L(x,y,x * z),u,w) = a(x,u,L(w,y,z \ x))
    ]]></literal>
    <justification jstring="[para(32217(a,1),32315(a,1,1))].">
      <j1 rule="para" parents="32217 32315"/>
    </justification>
  </clause>

  <clause id="32425">
    <literal><![CDATA[
      x * a(y \ (x \ y),z,u) = x * a(x,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[para(32315(a,1),32227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32315 32227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32426">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) \ w,v5,v6)) = a(x,y,L(L(x,z,u) * w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(29468,a,32325,a)].">
      <j1 rule="hyper" parents="29468 32325"/>
    </justification>
  </clause>

  <clause id="32429">
    <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(32391(a,1),30207(a,1))].">
      <j1 rule="para" parents="32391 30207"/>
    </justification>
  </clause>

  <clause id="32431">
    <literal><![CDATA[
      a(x \ y,z,x \ u) = a(y * x,z,x * u)
    ]]></literal>
    <justification jstring="[hyper(27010,a,32399,a),flip(a)].">
      <j1 rule="hyper" parents="27010 32399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32432">
    <literal><![CDATA[
      a(x \ y,z,u * x) = a(y * x,z,x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29054,a(flip),b,32399,a),flip(a)].">
      <j1 rule="hyper" parents="60 29054 32399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32433">
    <literal><![CDATA[
      a(x \ y,z,x * u) = a(y * x,z,x \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29051,a(flip),b,32399,a),flip(a)].">
      <j1 rule="hyper" parents="60 29051 32399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32434">
    <literal><![CDATA[
      a(x * (y * z),u,(1 / (y * z)) * (y * (z * w))) = a((y * z) \ x,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[para(590(a,1),32399(a,1,3))].">
      <j1 rule="para" parents="590 32399"/>
    </justification>
  </clause>

  <clause id="32435">
    <literal><![CDATA[
      a(x \ y,z,x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,x * u) = w
    ]]></literal>
    <justification jstring="[para(32399(a,1),27010(a,1))].">
      <j1 rule="para" parents="32399 27010"/>
    </justification>
  </clause>

  <clause id="32436">
    <literal><![CDATA[
      a(x * ((y * z) * u),w,L(v5,x,u * (z * y))) = a(x \ (u * (z * y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26744,a,32402,a)].">
      <j1 rule="hyper" parents="26744 32402"/>
    </justification>
  </clause>

  <clause id="32437">
    <literal><![CDATA[
      a(x * (y * z),u,L(w,x,z * y)) = a(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26548,a,32402,a)].">
      <j1 rule="hyper" parents="26548 32402"/>
    </justification>
  </clause>

  <clause id="32438">
    <literal><![CDATA[
      a(x \ y,z,(y * x) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,x \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(32402(a,1),30399(a,1))].">
      <j1 rule="para" parents="32402 30399"/>
    </justification>
  </clause>

  <clause id="32439">
    <literal><![CDATA[
      a((x \ y) \ x,z,(x \ (y \ 1)) \ u) = a(x * (x \ y),z,(y \ 1) \ (x * u))
    ]]></literal>
    <justification jstring="[para(3725(a,1),32413(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3725 32413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32440">
    <literal><![CDATA[
      a(x,y,(x * z) \ (x \ u)) = a(x,y,L(z,x,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,3160,a(flip),b,32364,a),flip(a)].">
      <j1 rule="hyper" parents="60 3160 32364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32441">
    <literal><![CDATA[
      a(x \ y,z,y \ ((x \ y) * u)) = a(x \ y,z,x \ u)
    ]]></literal>
    <justification jstring="[hyper(26997,a,32376,a),flip(a)].">
      <j1 rule="hyper" parents="26997 32376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32442">
    <literal><![CDATA[
      a(x,y,L((x \ z) * u,x * z,x * z)) = a(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,29614,a,b,32376,a)].">
      <j1 rule="hyper" parents="60 29614 32376"/>
    </justification>
  </clause>

  <clause id="32444">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x \ y) \ x) = a(z * (x \ y),u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26889,a(flip),b,32431,a),flip(a)].">
      <j1 rule="hyper" parents="370 26889 32431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32445">
    <literal><![CDATA[
      a(L(x,y,y) * L(x * y,y,y),z,L(x * y,y,y) \ u) = a(L(1 / y,y,x),z,L(x * y,y,y) * u)
    ]]></literal>
    <justification jstring="[para(28999(a,1),32433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28999 32433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32447">
    <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(29022(a,1),32339(a,1,1))].">
      <j1 rule="para" parents="29022 32339"/>
    </justification>
  </clause>

  <clause id="32450">
    <literal><![CDATA[
      L(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(32391(a,1),32339(a,1,1))].">
      <j1 rule="para" parents="32391 32339"/>
    </justification>
  </clause>

  <clause id="32455">
    <literal><![CDATA[
      R(x,y,L(z,y,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31491,a,32361,a),flip(a)].">
      <j1 rule="hyper" parents="31491 32361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32456">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * (z * a(y,y,z))) / ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31000,a,b,32455,a),flip(a)].">
      <j1 rule="hyper" parents="60 31000 32455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32457">
    <literal><![CDATA[
      a(x,y,L(z,u,L(z,w,x) * u)) = a(x,y,L(L(z,w,x),u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27117,a(flip),b,32374,a),flip(a)].">
      <j1 rule="hyper" parents="60 27117 32374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32458">
    <literal><![CDATA[
      a(x * (x * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,L(u,x,x)) = w
    ]]></literal>
    <justification jstring="[para(2956(a,2),32429(a,1))].">
      <j1 rule="para" parents="2956 32429"/>
    </justification>
  </clause>

  <clause id="32460">
    <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(27318(a,2),32429(a,1))].">
      <j1 rule="para" parents="27318 32429"/>
    </justification>
  </clause>

  <clause id="32462">
    <literal><![CDATA[
      a((x \ y) * L(y,x,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,L(u,y,y)) = w
    ]]></literal>
    <justification jstring="[para(27978(a,2),32429(a,1))].">
      <j1 rule="para" parents="27978 32429"/>
    </justification>
  </clause>

  <clause id="32465">
    <literal><![CDATA[
      a(x,y,L(z,x,u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = w
    ]]></literal>
    <justification jstring="[para(32415(a,2),32429(a,1))].">
      <j1 rule="para" parents="32415 32429"/>
    </justification>
  </clause>

  <clause id="32469">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(30752(a,2),32447(a,1))].">
      <j1 rule="para" parents="30752 32447"/>
    </justification>
  </clause>

  <clause id="32470">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,L(w,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(30757(a,2),32447(a,1))].">
      <j1 rule="para" parents="30757 32447"/>
    </justification>
  </clause>

  <clause id="32474">
    <literal><![CDATA[
      a(x,y \ z,(((1 / z) * y) \ 1) \ u) = a(x,y \ z,L(y \ z,y,z) * u)
    ]]></literal>
    <justification jstring="[para(1491(a,1),32359(a,1,3,1))].">
      <j1 rule="para" parents="1491 32359"/>
    </justification>
  </clause>

  <clause id="32475">
    <literal><![CDATA[
      a(L(x,y,z),u,L(L(x,y,z),y,z) \ w) = a(L(x,y,z),u,w * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29079,a(flip),b,32372,a),flip(a)].">
      <j1 rule="hyper" parents="370 29079 32372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32476">
    <literal><![CDATA[
      a(x \ y,z,(((1 / y) * x) \ 1) \ u) = a(x \ y,z,L(x \ y,x,y) * u)
    ]]></literal>
    <justification jstring="[para(1491(a,1),32372(a,1,3,1))].">
      <j1 rule="para" parents="1491 32372"/>
    </justification>
  </clause>

  <clause id="32477">
    <literal><![CDATA[
      a((x \ y) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,L(L(u,x,y),y,y)) = w
    ]]></literal>
    <justification jstring="[para(32398(a,1),32429(a,1))].">
      <j1 rule="para" parents="32398 32429"/>
    </justification>
  </clause>

  <clause id="32479">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ x)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,x * w)) = v5
    ]]></literal>
    <justification jstring="[para(32424(a,1),32429(a,1))].">
      <j1 rule="para" parents="32424 32429"/>
    </justification>
  </clause>

  <clause id="32480">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = x \ R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(31092,a,32316,a),flip(a)].">
      <j1 rule="hyper" parents="31092 32316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32481">
    <literal><![CDATA[
      R(x,y,L(z,u,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(28681,a,32480,a),flip(a)].">
      <j1 rule="hyper" parents="28681 32480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32482">
    <literal><![CDATA[
      R(x,y,(x \ z) \ u) = R(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(656(a,1),32481(a,1,3)),flip(a)].">
      <j1 rule="para" parents="656 32481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32488">
    <literal><![CDATA[
      L(x * y,x,z) \ (x * y) = a(z,x,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(2480(a,1),32387(a,2,3))].">
      <j1 rule="para" parents="2480 32387"/>
    </justification>
  </clause>

  <clause id="32489">
    <literal><![CDATA[
      L(x * y,x,z) \ (x * y) = a(z,x,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,26882,a(flip),b,32488,a),flip(a)].">
      <j1 rule="hyper" parents="370 26882 32488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32490">
    <literal><![CDATA[
      L(x * y,x,z) \ (x * y) = a(z,x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3082,a(flip),b,32489,a),flip(a)].">
      <j1 rule="hyper" parents="370 3082 32489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32492">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,z,y)) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32315,a(flip),b,32397,a),flip(a)].">
      <j1 rule="hyper" parents="370 32315 32397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32493">
    <literal><![CDATA[
      a((x * y) \ ((z \ u) * w),v5,L(v6,y,x)) = a(y \ (x \ ((u / z) * w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26684,a,32400,a)].">
      <j1 rule="hyper" parents="26684 32400"/>
    </justification>
  </clause>

  <clause id="32494">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,L(x,y,y)) = a(y \ ((x * y) \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,27117,a(flip),b,32400,a)].">
      <j1 rule="hyper" parents="60 27117 32400"/>
    </justification>
  </clause>

  <clause id="32495">
    <literal><![CDATA[
      a((x * y) \ z,u,(x * y) \ w) = a(y \ (x \ z),u,y \ (x \ w))
    ]]></literal>
    <justification jstring="[para(344(a,1),32400(a,1,3))].">
      <j1 rule="para" parents="344 32400"/>
    </justification>
  </clause>

  <clause id="32497">
    <literal><![CDATA[
      a(x,y,a((x * z) \ u,w,v5)) = a(x,y,a(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(32400(a,1),32242(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32400 32242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32498">
    <literal><![CDATA[
      a((x * y) \ (y * z),u,(x * y) \ w) = a(x \ z,u,x \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29236,a(flip),b,32404,a),flip(a)].">
      <j1 rule="hyper" parents="370 29236 32404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32499">
    <literal><![CDATA[
      a(x,y,L(z,u * a(x,y,z),w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32315,a(flip),b,32409,a),flip(a)].">
      <j1 rule="hyper" parents="370 32315 32409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32500">
    <literal><![CDATA[
      a(x,y,L(z,u * a(x,y,z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32409(a,2),32429(a,1))].">
      <j1 rule="para" parents="32409 32429"/>
    </justification>
  </clause>

  <clause id="32501">
    <literal><![CDATA[
      a(((a(x,y,z) * u) * w) \ (((u * v5) * a(x,y,z)) * w),v6,v7) = a(L(v5,u,a(x,y,z)),v6,L(v7,a(x,y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(24122(a,1),32414(a,2,1))].">
      <j1 rule="para" parents="24122 32414"/>
    </justification>
  </clause>

  <clause id="32502">
    <literal><![CDATA[
      a((x \ y) * y,z,(u * x) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * y,z,u \ (x \ w)) = v5
    ]]></literal>
    <justification jstring="[para(32416(a,1),29238(a,1))].">
      <j1 rule="para" parents="32416 29238"/>
    </justification>
  </clause>

  <clause id="32503">
    <literal><![CDATA[
      a(x \ (y \ x),z,u) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(451,a,32425,a),flip(a)].">
      <j1 rule="hyper" parents="451 32425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32505">
    <literal><![CDATA[
      a(x \ (y \ x),z,y \ u) = a(y,z,(x * y) \ (x * u))
    ]]></literal>
    <justification jstring="[para(94(a,1),32503(a,2,3))].">
      <j1 rule="para" parents="94 32503"/>
    </justification>
  </clause>

  <clause id="32506">
    <literal><![CDATA[
      a((x * y) \ (y \ (x * y)),z,T(y \ 1,y * x) \ u) = a(y,z,x \ (((y \ 1) \ x) * u))
    ]]></literal>
    <justification jstring="[para(31633(a,1),32503(a,2,3))].">
      <j1 rule="para" parents="31633 32503"/>
    </justification>
  </clause>

  <clause id="32507">
    <literal><![CDATA[
      a(x,y,z \ (x \ (x \ u))) = a(x,y,L(z,x,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(32385,a,32440,a)].">
      <j1 rule="hyper" parents="32385 32440"/>
    </justification>
  </clause>

  <clause id="32508">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = w
    ]]></literal>
    <justification jstring="[para(24013(a,1),32465(a,1,3))].">
      <j1 rule="para" parents="24013 32465"/>
    </justification>
  </clause>

  <clause id="32509">
    <literal><![CDATA[
      a(x * a(y,x,z),u,y) = a(x,u,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(26984,a,32492,a)].">
      <j1 rule="hyper" parents="26984 32492"/>
    </justification>
  </clause>

  <clause id="32510">
    <literal><![CDATA[
      a(x,y,L(z,u * a(x,y,z),u * a(x,y,z))) = a(x,y,L(z,u,z * (u * a(x,y,z))))
    ]]></literal>
    <justification jstring="[hyper(60,a,27117,a(flip),b,32499,a)].">
      <j1 rule="hyper" parents="60 27117 32499"/>
    </justification>
  </clause>

  <clause id="32511">
    <literal><![CDATA[
      a(x,y,L(z,x,x) \ u) = a(x,y,z \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29668,a(flip),b,32507,a),flip(a)].">
      <j1 rule="hyper" parents="60 29668 32507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32512">
    <literal><![CDATA[
      a(x,y,z \ L(L(u,L(z,x,x),L(z,x,x)),x,x)) = a(x,y,(L(z,x,x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2072(a,1),32511(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2072 32511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32513">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = L(a(u,y,L(z,x,y)) * 1,y,x)
    ]]></literal>
    <justification jstring="[para(32342(a,1),30438(a,2,1))].">
      <j1 rule="para" parents="32342 30438"/>
    </justification>
  </clause>

  <clause id="32515">
    <literal><![CDATA[
      R(x,y,y \ z) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(31992,a,32390,a),flip(a)].">
      <j1 rule="hyper" parents="31992 32390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32516">
    <literal><![CDATA[
      R(x,y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y * z) = u
    ]]></literal>
    <justification jstring="[para(32390(a,1),31992(a,1))].">
      <j1 rule="para" parents="32390 31992"/>
    </justification>
  </clause>

  <clause id="32517">
    <literal><![CDATA[
      x * (L(y,z,(x \ z) * z) \ y) = R(x,z,z * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,31489,a,b,32515,a)].">
      <j1 rule="hyper" parents="60 31489 32515"/>
    </justification>
  </clause>

  <clause id="32518">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,102,a,b,32515,a)].">
      <j1 rule="hyper" parents="60 102 32515"/>
    </justification>
  </clause>

  <clause id="32519">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) * z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,1037,a(flip),b,32515,a),flip(a)].">
      <j1 rule="hyper" parents="60 1037 32515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32520">
    <literal><![CDATA[
      R(x,y,y * z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(32515(a,1),430(a,1,1))].">
      <j1 rule="para" parents="32515 430"/>
    </justification>
  </clause>

  <clause id="32522">
    <literal><![CDATA[
      R(x,x \ y,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,x \ y,(x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(32482(a,1),32516(a,1))].">
      <j1 rule="para" parents="32482 32516"/>
    </justification>
  </clause>

  <clause id="32523">
    <literal><![CDATA[
      R(x,y,z * y) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(27433(a,1),32520(a,1,1))].">
      <j1 rule="para" parents="27433 32520"/>
    </justification>
  </clause>

  <clause id="32524">
    <literal><![CDATA[
      R(a(x,y,z),u * a(x,y,z),(u * a(x,y,z)) * w) * w = (z * (L(L(z,y,x),y,x) \ u)) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(30657(a,1),32520(a,2,1))].">
      <j1 rule="para" parents="30657 32520"/>
    </justification>
  </clause>

  <clause id="32525">
    <literal><![CDATA[
      a(x,y,L(z,u,u * w)) * w = (a(x,y,z) * u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(32320(a,2),32520(a,1,1))].">
      <j1 rule="para" parents="32320 32520"/>
    </justification>
  </clause>

  <clause id="32526">
    <literal><![CDATA[
      R(x,y * z,u * (z * y)) * u = (x * (z * y)) * ((z * y) \ u)
    ]]></literal>
    <justification jstring="[para(27390(a,1),32523(a,1,1))].">
      <j1 rule="para" parents="27390 32523"/>
    </justification>
  </clause>

  <clause id="32527">
    <literal><![CDATA[
      a(x \ y,z,y \ ((x \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,x * u) = w
    ]]></literal>
    <justification jstring="[para(32441(a,2),32435(a,1))].">
      <j1 rule="para" parents="32441 32435"/>
    </justification>
  </clause>

  <clause id="32528">
    <literal><![CDATA[
      a((x \ y) \ z,u,(y \ x) * x) = a(z * (x \ y),u,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29633,a(flip),b,32444,a)].">
      <j1 rule="hyper" parents="60 29633 32444"/>
    </justification>
  </clause>

  <clause id="32529">
    <literal><![CDATA[
      a(x \ (y \ x),z,y \ u) = a(y,z,x \ (y \ (x * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32366,a(flip),b,32505,a),flip(a)].">
      <j1 rule="hyper" parents="370 32366 32505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32531">
    <literal><![CDATA[
      R(x,y,y * (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,z,y)) = u
    ]]></literal>
    <justification jstring="[para(32517(a,1),31527(a,1))].">
      <j1 rule="para" parents="32517 31527"/>
    </justification>
  </clause>

  <clause id="32532">
    <literal><![CDATA[
      a(x,y,(z * y) \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(y * u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(32362(a,1),27171(a,1))].">
      <j1 rule="para" parents="32362 27171"/>
    </justification>
  </clause>

  <clause id="32533">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = a((u / x) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,2958,a(flip),b,32421,a),flip(a)].">
      <j1 rule="hyper" parents="370 2958 32421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32534">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26388,a(flip),b,32533,a),flip(a)].">
      <j1 rule="hyper" parents="370 26388 32533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32535">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ u) * u,y,z) = w
    ]]></literal>
    <justification jstring="[para(32533(a,2),26524(a,1))].">
      <j1 rule="para" parents="32533 26524"/>
    </justification>
  </clause>

  <clause id="32536">
    <literal><![CDATA[
      a(x,y,L(T(z * x,K(x,u)) \ w,v5,v6)) = a(x,y,L(T(z,T(x,u)) \ (x \ w),v5,v6))
    ]]></literal>
    <justification jstring="[para(8487(a,2),32377(a,1,3,1,1))].">
      <j1 rule="para" parents="8487 32377"/>
    </justification>
  </clause>

  <clause id="32537">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x * z,x * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(x * z) * u) = w
    ]]></literal>
    <justification jstring="[para(32377(a,1),27010(a,1))].">
      <j1 rule="para" parents="32377 27010"/>
    </justification>
  </clause>

  <clause id="32538">
    <literal><![CDATA[
      a(x,y,L(1 \ (x * (z \ u)),x,z)) = a(x,y,(z * (x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3409(a,1),32378(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3409 32378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32539">
    <literal><![CDATA[
      a((x * y) \ (y * (x \ z)),u,w) = a(z,u,L(L(w,x,y),x,x))
    ]]></literal>
    <justification jstring="[hyper(32429,a,32411,a),flip(a)].">
      <j1 rule="hyper" parents="32429 32411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32540">
    <literal><![CDATA[
      a(x,y,L(z,u,L(z,w,x) * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32374,a(flip),b,32457,a),flip(a)].">
      <j1 rule="hyper" parents="370 32374 32457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32542">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,L(z,w,x) * u) = a(x,y,L(z,u,u)) \ 1
    ]]></literal>
    <justification jstring="[para(32540(a,1),32338(a,2,1))].">
      <j1 rule="para" parents="32540 32338"/>
    </justification>
  </clause>

  <clause id="32543">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(31136(a,1),32469(a,1,2))].">
      <j1 rule="para" parents="31136 32469"/>
    </justification>
  </clause>

  <clause id="32545">
    <literal><![CDATA[
      a(x,y,L(z,u * x,u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ u) * u,y,z) = w
    ]]></literal>
    <justification jstring="[para(26091(a,1),32535(a,1,3))].">
      <j1 rule="para" parents="26091 32535"/>
    </justification>
  </clause>

  <clause id="32546">
    <literal><![CDATA[
      a((x * (y \ z)) * (y * x),u,(y * x) * w) = a(z,u,L(L((y * x) \ w,y,x),y,y))
    ]]></literal>
    <justification jstring="[hyper(32435,a,32539,a)].">
      <j1 rule="hyper" parents="32435 32539"/>
    </justification>
  </clause>

  <clause id="32548">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(u,w,a(z,y,x)) = a(x,y,z) * a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(32073(a,1),32346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32073 32346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32549">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6)) = a(v6,v5,a(x,y,z)) * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(32328(a,1),32347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32328 32347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32550">
    <literal><![CDATA[
      a((x \ y) * y,z,(x \ y) * u) = a(x,z,y \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(32535,a,32442,a)].">
      <j1 rule="hyper" parents="32535 32442"/>
    </justification>
  </clause>

  <clause id="32551">
    <literal><![CDATA[
      a(x,x * y,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x * y,(x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(32442(a,1),32351(a,1))].">
      <j1 rule="para" parents="32442 32351"/>
    </justification>
  </clause>

  <clause id="32552">
    <literal><![CDATA[
      a(x * (y \ x),z,(y \ x) * u) = a(y,z,x \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(26519,a,32550,a)].">
      <j1 rule="hyper" parents="26519 32550"/>
    </justification>
  </clause>

  <clause id="32553">
    <literal><![CDATA[
      a(x * (y \ x),z,u * (y \ x)) = a(y,z,x \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(26965,a,32552,a)].">
      <j1 rule="hyper" parents="26965 32552"/>
    </justification>
  </clause>

  <clause id="32554">
    <literal><![CDATA[
      a(x * (x * (y \ x)),z,u * ((x \ y) \ x)) = a(x \ y,z,x \ ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,31366,a(flip),b,32553,a)].">
      <j1 rule="hyper" parents="60 31366 32553"/>
    </justification>
  </clause>

  <clause id="32555">
    <literal><![CDATA[
      a(L(x,y,y) \ z,u,L(x,y,y)) = a(y \ ((x * y) \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(29689,a,32494,a)].">
      <j1 rule="hyper" parents="29689 32494"/>
    </justification>
  </clause>

  <clause id="32556">
    <literal><![CDATA[
      a(x * L(y,z,z),u,L(y,z,z)) = a(z \ ((y * z) \ x),u,y)
    ]]></literal>
    <justification jstring="[hyper(31451,a,32555,a)].">
      <j1 rule="hyper" parents="31451 32555"/>
    </justification>
  </clause>

  <clause id="32557">
    <literal><![CDATA[
      a(x \ y,y,((x \ y) * z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y * x,y,x * z) = u
    ]]></literal>
    <justification jstring="[para(32360(a,1),32527(a,1))].">
      <j1 rule="para" parents="32360 32527"/>
    </justification>
  </clause>

  <clause id="32558">
    <literal><![CDATA[
      a(x,y,L(1 \ (x * (z \ u)),x,z)) = a(x,y,(z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3086,a(flip),b,32538,a),flip(a)].">
      <j1 rule="hyper" parents="370 3086 32538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32559">
    <literal><![CDATA[
      a(x,y,L(1 \ (x * (z \ u)),x,z)) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32366,a(flip),b,32558,a),flip(a)].">
      <j1 rule="hyper" parents="370 32366 32558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32560">
    <literal><![CDATA[
      a(x,y,L(x * (z \ u),x,z)) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[para(62(a,1),32559(a,1,3,1))].">
      <j1 rule="para" parents="62 32559"/>
    </justification>
  </clause>

  <clause id="32561">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,(1 / x) * z)) = a(x,y,(x * z) \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1274(a,1),32560(a,2,3))].">
      <j1 rule="para" parents="1274 32560"/>
    </justification>
  </clause>

  <clause id="32562">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,L(z,w,x) * u) = L(a(x,y,z) \ 1,u,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,32338,a,b,32542,a),flip(a)].">
      <j1 rule="hyper" parents="370 32338 32542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32563">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,31740,a(flip),b,32562,a),flip(a)].">
      <j1 rule="hyper" parents="60 31740 32562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32565">
    <literal><![CDATA[
      a(x,y,z) \ 1 = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,31014,a(flip),b,32563,a)].">
      <j1 rule="hyper" parents="60 31014 32563"/>
    </justification>
  </clause>

  <clause id="32566">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(30868,a,32565,a)].">
      <j1 rule="hyper" parents="30868 32565"/>
    </justification>
  </clause>

  <clause id="32567">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(30865,a,32565,a)].">
      <j1 rule="hyper" parents="30865 32565"/>
    </justification>
  </clause>

  <clause id="32568">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(30708,a,32565,a)].">
      <j1 rule="hyper" parents="30708 32565"/>
    </justification>
  </clause>

  <clause id="32569">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(30652,a,32565,a),flip(a)].">
      <j1 rule="hyper" parents="30652 32565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32572">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(36,a,14170,a,b,32565,a),flip(a)].">
      <j1 rule="hyper" parents="36 14170 32565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32573">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(129,a,32565,a(flip),b,30620,a)].">
      <j1 rule="hyper" parents="129 32565 30620"/>
    </justification>
  </clause>

  <clause id="32581">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(32565(a,1),30621(a,1,1))].">
      <j1 rule="para" parents="32565 30621"/>
    </justification>
  </clause>

  <clause id="32587">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,32566,a(flip),b,32080,a),flip(a)].">
      <j1 rule="hyper" parents="126 32566 32080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32588">
    <literal><![CDATA[
      a(x \ a(y,z,z),u,w) = a(a(y,z,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(32566(a,1),27324(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="32566 27324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32589">
    <literal><![CDATA[
      L(x,y,z) \ x != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(32566(a,1),30870(a,1,2))].">
      <j1 rule="para" parents="32566 30870"/>
    </justification>
  </clause>

  <clause id="32590">
    <literal><![CDATA[
      a(x,y,L(z,x,a(u,w,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(32566(a,1),32315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32566 32315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32591">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,30862,a,b,32567,a)].">
      <j1 rule="hyper" parents="60 30862 32567"/>
    </justification>
  </clause>

  <clause id="32593">
    <literal><![CDATA[
      a(x,y,(z \ a(u,u,w)) * v5) = a(x,y,(z * a(u,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(32567(a,1),27179(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="32567 27179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32594">
    <literal><![CDATA[
      x * (y * (z * a(x,y,z))) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(32567(a,1),30864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32567 30864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32595">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(32567(a,1),31979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32567 31979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32596">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(32567(a,1),31984(a,2,1))].">
      <j1 rule="para" parents="32567 31984"/>
    </justification>
  </clause>

  <clause id="32597">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(32567(a,1),31985(a,2,2))].">
      <j1 rule="para" parents="32567 31985"/>
    </justification>
  </clause>

  <clause id="32600">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[para(32567(a,1),32408(a,1,1,2))].">
      <j1 rule="para" parents="32567 32408"/>
    </justification>
  </clause>

  <clause id="32601">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * u = u
    ]]></literal>
    <justification jstring="[para(32587(a,2),2(a,1,1))].">
      <j1 rule="para" parents="32587 2"/>
    </justification>
  </clause>

  <clause id="32602">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(32587(a,2),131(a,1,1))].">
      <j1 rule="para" parents="32587 131"/>
    </justification>
  </clause>

  <clause id="32603">
    <literal><![CDATA[
      a(x,y,z) \ L(z,z,a(u,u,w)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(125,a,32567,a,b,32568,a)].">
      <j1 rule="hyper" parents="125 32567 32568"/>
    </justification>
  </clause>

  <clause id="32624">
    <literal><![CDATA[
      a(L(x,y,z) * a(z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(32569(a,2),26520(a,1,1,1))].">
      <j1 rule="para" parents="32569 26520"/>
    </justification>
  </clause>

  <clause id="32625">
    <literal><![CDATA[
      a(x,y,z \ (u \ z)) \ ((u * z) \ z) = L((u * z) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(27058(a,1),32569(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27058 32569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32630">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = L(x,u,z) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(32569(a,2),30793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32569 30793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32631">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(32569(a,2),31714(a,2,2,1))].">
      <j1 rule="para" parents="32569 31714"/>
    </justification>
  </clause>

  <clause id="32633">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,a(x,w,v5)) = L(L(z,u,a(x,w,v5)),y,x)
    ]]></literal>
    <justification jstring="[para(32322(a,1),32569(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32322 32569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32636">
    <literal><![CDATA[
      x \ (((y / x) \ y) * a(z,y / x,y / x)) = a(z,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,31889,a,b,32572,a)].">
      <j1 rule="hyper" parents="370 31889 32572"/>
    </justification>
  </clause>

  <clause id="32637">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30146,a,b,32572,a)].">
      <j1 rule="hyper" parents="370 30146 32572"/>
    </justification>
  </clause>

  <clause id="32641">
    <literal><![CDATA[
      a(x,y,z \ y) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32490,a(flip),b,32572,a)].">
      <j1 rule="hyper" parents="370 32490 32572"/>
    </justification>
  </clause>

  <clause id="32652">
    <literal><![CDATA[
      a(x,y * z,L(z,z,y)) = a(x,y * z,z)
    ]]></literal>
    <justification jstring="[hyper(30434,a,32572,a(flip))].">
      <j1 rule="hyper" parents="30434 32572"/>
    </justification>
  </clause>

  <clause id="32655">
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(32572(a,2),2998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32572 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32657">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(32572(a,2),4030(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32572 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32664">
    <literal><![CDATA[
      L(x,a(y,z,u) * L(u,z,y),w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(32572(a,2),26024(a,1,2,1))].">
      <j1 rule="para" parents="32572 26024"/>
    </justification>
  </clause>

  <clause id="32665">
    <literal><![CDATA[
      L(x,a(y,z,u) * L(u,z,y),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(32572(a,2),26191(a,1,2,1))].">
      <j1 rule="para" parents="32572 26191"/>
    </justification>
  </clause>

  <clause id="32670">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ u)) = (x * a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(32572(a,2),29656(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="32572 29656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32671">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(32572(a,2),29738(a,2,2,2))].">
      <j1 rule="para" parents="32572 29738"/>
    </justification>
  </clause>

  <clause id="32672">
    <literal><![CDATA[
      a(x,y,z) * (y * z) = y * (z * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(32572(a,2),29972(a,1,1))].">
      <j1 rule="para" parents="32572 29972"/>
    </justification>
  </clause>

  <clause id="32673">
    <literal><![CDATA[
      L(a(x,y,z),z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32572(a,2),30044(a,1,1))].">
      <j1 rule="para" parents="32572 30044"/>
    </justification>
  </clause>

  <clause id="32674">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * L(z,z,y) = x * (y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(32572(a,2),30147(a,1,1,2,1))].">
      <j1 rule="para" parents="32572 30147"/>
    </justification>
  </clause>

  <clause id="32675">
    <literal><![CDATA[
      L(a(x,y,z),u * z,u * z) = (u \ L(z,y,x)) \ (u \ z)
    ]]></literal>
    <justification jstring="[para(32572(a,2),30965(a,1,1))].">
      <j1 rule="para" parents="32572 30965"/>
    </justification>
  </clause>

  <clause id="32676">
    <literal><![CDATA[
      L(a(x,y * x,z),y,y) = L(x \ R(x,y * x,z),z,y * x)
    ]]></literal>
    <justification jstring="[para(32572(a,2),32249(a,1,1))].">
      <j1 rule="para" parents="32572 32249"/>
    </justification>
  </clause>

  <clause id="32679">
    <literal><![CDATA[
      x * a((x \ y) * y,y,z) = R(x,y,y * (z \ y))
    ]]></literal>
    <justification jstring="[para(32572(a,2),32517(a,1,2))].">
      <j1 rule="para" parents="32572 32517"/>
    </justification>
  </clause>

  <clause id="32683">
    <literal><![CDATA[
      L(x,y,L(z * a(u,w,z),v5,v6)) = L(x,y,L(L(z,w,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(32591(a,1),29071(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="32591 29071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32689">
    <literal><![CDATA[
      a(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(370,a,2014,a,b,32595,a),flip(a)].">
      <j1 rule="hyper" parents="370 2014 32595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32690">
    <literal><![CDATA[
      a(x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1987,a,b,32595,a),flip(a)].">
      <j1 rule="hyper" parents="370 1987 32595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32691">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,z,u)) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,28537,a(flip),b,32595,a)].">
      <j1 rule="hyper" parents="370 28537 32595"/>
    </justification>
  </clause>

  <clause id="32705">
    <literal><![CDATA[
      R(x,y,z) = x * (L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(129,a,32572,a(flip),b,32595,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 32572 32595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32710">
    <literal><![CDATA[
      a(x,y,z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32595(a,2),44(a,1))].">
      <j1 rule="para" parents="32595 44"/>
    </justification>
  </clause>

  <clause id="32728">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u),u * x,u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(32595(a,2),31235(a,1,1,1))].">
      <j1 rule="para" parents="32595 31235"/>
    </justification>
  </clause>

  <clause id="32729">
    <literal><![CDATA[
      a(x,y,z) * (u * (x * x)) = u * (x * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(32595(a,2),31537(a,1,1))].">
      <j1 rule="para" parents="32595 31537"/>
    </justification>
  </clause>

  <clause id="32731">
    <literal><![CDATA[
      R(x,y,L(a(z,u,y),w,v5)) = L(x,a(z,u,y),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,32253,a(flip),b,32596,a),flip(a)].">
      <j1 rule="hyper" parents="370 32253 32596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32734">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32596(a,2),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="32596 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32747">
    <literal><![CDATA[
      a(x,y,z) * T(x,u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(26375(a,1),32597(a,2,1)),flip(a)].">
      <j1 rule="para" parents="26375 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32749">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(32470,a,32601,a)].">
      <j1 rule="hyper" parents="32470 32601"/>
    </justification>
  </clause>

  <clause id="32750">
    <literal><![CDATA[
      x * a(y,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(31157,a,32601,a)].">
      <j1 rule="hyper" parents="31157 32601"/>
    </justification>
  </clause>

  <clause id="32751">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(31156,a,32601,a),flip(a)].">
      <j1 rule="hyper" parents="31156 32601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32752">
    <literal><![CDATA[
      L(a(x,x,y),z,z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31139,a(flip),b,32601,a)].">
      <j1 rule="hyper" parents="60 31139 32601"/>
    </justification>
  </clause>

  <clause id="32754">
    <literal><![CDATA[
      a(x,y,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32689(a,2),290(a,1,1)),flip(b)].">
      <j1 rule="para" parents="32689 290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32757">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(32153,a,32750,a)].">
      <j1 rule="hyper" parents="32153 32750"/>
    </justification>
  </clause>

  <clause id="32759">
    <literal><![CDATA[
      ((((x \ y) \ 1) \ 1) \ ((y \ x) \ 1)) * z = z * a(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,31922,a(flip),b,32750,a)].">
      <j1 rule="hyper" parents="60 31922 32750"/>
    </justification>
  </clause>

  <clause id="32760">
    <literal><![CDATA[
      (x \ 1) * a(y,y,z) = x \ a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,28750,a(flip),b,32750,a),flip(a)].">
      <j1 rule="hyper" parents="60 28750 32750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32762">
    <literal><![CDATA[
      L(x,y,y) * (x \ z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(29878,a,32757,a)].">
      <j1 rule="hyper" parents="29878 32757"/>
    </justification>
  </clause>

  <clause id="32763">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,29406,a(flip),b,32757,a)].">
      <j1 rule="hyper" parents="60 29406 32757"/>
    </justification>
  </clause>

  <clause id="32764">
    <literal><![CDATA[
      (x * y) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(32757(a,1),28343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32757 28343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32765">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(32763(a,1),47(a,2))].">
      <j1 rule="para" parents="32763 47"/>
    </justification>
  </clause>

  <clause id="32766">
    <literal><![CDATA[
      a(x,y * (z \ y),y * (z \ y)) = a(x,z,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30344,a(flip),b,32749,a),flip(a)].">
      <j1 rule="hyper" parents="60 30344 32749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32767">
    <literal><![CDATA[
      a(x,y,y) * (z \ 1) = z \ a(x,y,y)
    ]]></literal>
    <justification jstring="[para(32749(a,1),32393(a,1,1))].">
      <j1 rule="para" parents="32749 32393"/>
    </justification>
  </clause>

  <clause id="32768">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,w))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(32238,a,32751,a)].">
      <j1 rule="hyper" parents="32238 32751"/>
    </justification>
  </clause>

  <clause id="32770">
    <literal><![CDATA[
      a(x,x,L(y * T(z,u),w,v5)) = a(x,x,L(z \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(29467,a,32751,a),flip(a)].">
      <j1 rule="hyper" parents="29467 32751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32771">
    <literal><![CDATA[
      a(x,x,y \ z) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(27010,a,32751,a),flip(a)].">
      <j1 rule="hyper" parents="27010 32751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32774">
    <literal><![CDATA[
      a(x,x,L(L(y,z,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),32751(a,1,3))].">
      <j1 rule="para" parents="25 32751"/>
    </justification>
  </clause>

  <clause id="32775">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,z) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(32751(a,1),14184(a,2,1))].">
      <j1 rule="para" parents="32751 14184"/>
    </justification>
  </clause>

  <clause id="32776">
    <literal><![CDATA[
      a(x,x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y * z) = u
    ]]></literal>
    <justification jstring="[para(32751(a,1),27010(a,1))].">
      <j1 rule="para" parents="32751 27010"/>
    </justification>
  </clause>

  <clause id="32777">
    <literal><![CDATA[
      a(x,x,y) * (z \ 1) = z \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(32751(a,1),32393(a,1,1))].">
      <j1 rule="para" parents="32751 32393"/>
    </justification>
  </clause>

  <clause id="32778">
    <literal><![CDATA[
      a(x,x,y) \ (z * z) = z * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(32751(a,1),32344(a,1,1))].">
      <j1 rule="para" parents="32751 32344"/>
    </justification>
  </clause>

  <clause id="32780">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,w)) = a(y * x,z,a(u,u,w))
    ]]></literal>
    <justification jstring="[para(32752(a,1),32399(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32752 32399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32782">
    <literal><![CDATA[
      a(x,y,z \ (x * y)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32376,a(flip),b,32641,a)].">
      <j1 rule="hyper" parents="60 32376 32641"/>
    </justification>
  </clause>

  <clause id="32784">
    <literal><![CDATA[
      R(x,y,z) = z * (L(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29791,a(flip),b,32705,a),flip(a)].">
      <j1 rule="hyper" parents="370 29791 32705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32785">
    <literal><![CDATA[
      a(x,x,(y \ z) * z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(26951,a,32771,a),flip(a)].">
      <j1 rule="hyper" parents="26951 32771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32786">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,z * (u \ ((u * y) * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,32010,a(flip),b,32771,a)].">
      <j1 rule="hyper" parents="60 32010 32771"/>
    </justification>
  </clause>

  <clause id="32787">
    <literal><![CDATA[
      a(x,x,y * L(z * u,u,u)) = a(x,x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29669,a(flip),b,32771,a),flip(a)].">
      <j1 rule="hyper" parents="60 29669 32771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32788">
    <literal><![CDATA[
      a(x,x,(y * z) * (y * (z * u))) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),32771(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13 32771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32789">
    <literal><![CDATA[
      a(x,x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,(y \ z) * (w * w)) = u
    ]]></literal>
    <justification jstring="[para(32771(a,1),26989(a,1))].">
      <j1 rule="para" parents="32771 26989"/>
    </justification>
  </clause>

  <clause id="32790">
    <literal><![CDATA[
      (x \ y) * (z \ a(z,z,x * y)) = z \ T(x \ y,z \ 1)
    ]]></literal>
    <justification jstring="[para(32771(a,1),28442(a,1,2,2))].">
      <j1 rule="para" parents="32771 28442"/>
    </justification>
  </clause>

  <clause id="32791">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 \ a(v6,v6,R(z,u,w) * v5))) = a(x,y,v6 \ (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(32771(a,1),32063(a,1,3,2,2))].">
      <j1 rule="para" parents="32771 32063"/>
    </justification>
  </clause>

  <clause id="32794">
    <literal><![CDATA[
      L(x,y,z) * R(z,y,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(129,a,32784,a,b,2160,a)].">
      <j1 rule="hyper" parents="129 32784 2160"/>
    </justification>
  </clause>

  <clause id="32795">
    <literal><![CDATA[
      a(x,x,y * (z \ y)) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,32785,a)].">
      <j1 rule="hyper" parents="26965 32785"/>
    </justification>
  </clause>

  <clause id="32796">
    <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(32794(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="32794 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32797">
    <literal><![CDATA[
      (x * y) \ (L(x,z,y) * (R(y,z,x) * u)) = L(u,R(y,z,x),L(x,z,y))
    ]]></literal>
    <justification jstring="[para(32794(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32794 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32798">
    <literal><![CDATA[
      ((L(x,y,z) * (R(z,y,x) * u)) / u) \ (x * z) = a(L(x,y,z),R(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(32794(a,1),25781(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32794 25781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32801">
    <literal><![CDATA[
      a(x,y,z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * z) = u
    ]]></literal>
    <justification jstring="[para(32490(a,1),32589(a,1))].">
      <j1 rule="para" parents="32490 32589"/>
    </justification>
  </clause>

  <clause id="32807">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * (y \ x),z,u) = w
    ]]></literal>
    <justification jstring="[para(28537(a,1),32734(a,1))].">
      <j1 rule="para" parents="28537 32734"/>
    </justification>
  </clause>

  <clause id="32808">
    <literal><![CDATA[
      a(x * (y \ x),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x,z) = u
    ]]></literal>
    <justification jstring="[para(31483(a,2),32734(a,1))].">
      <j1 rule="para" parents="31483 32734"/>
    </justification>
  </clause>

  <clause id="32809">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ (((1 / x) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(31465(a,2),32734(a,1))].">
      <j1 rule="para" parents="31465 32734"/>
    </justification>
  </clause>

  <clause id="32810">
    <literal><![CDATA[
      a(x,L(y,x,z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,x,z),u) = w
    ]]></literal>
    <justification jstring="[para(32410(a,2),32734(a,1))].">
      <j1 rule="para" parents="32410 32734"/>
    </justification>
  </clause>

  <clause id="32822">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ L(x,v5,v6)) = a(v6,v5,x) \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,30036,a(flip),b,32573,a)].">
      <j1 rule="hyper" parents="60 30036 32573"/>
    </justification>
  </clause>

  <clause id="32823">
    <literal><![CDATA[
      x \ (a(y,z,x) \ u) = u * L(u \ (x \ u),z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,32573,a(flip),b,25319,a)].">
      <j1 rule="hyper" parents="125 32573 25319"/>
    </justification>
  </clause>

  <clause id="32824">
    <literal><![CDATA[
      x \ (a(y,z,x) \ K(u,w)) = L(x \ K(u,w),z,y)
    ]]></literal>
    <justification jstring="[hyper(125,a,32573,a(flip),b,25743,a(flip))].">
      <j1 rule="hyper" parents="125 32573 25743"/>
    </justification>
  </clause>

  <clause id="32825">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,u)) = (x * L(y,z,u)) * a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(27967,a,32581,a)].">
      <j1 rule="hyper" parents="27967 32581"/>
    </justification>
  </clause>

  <clause id="32827">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),x,a(v5,v6,v6))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,31136,a,b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="370 31136 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32829">
    <literal><![CDATA[
      (1 / L(x,a(x,y,z),z)) \ u = u * (a(x,x,u) * T(x,u))
    ]]></literal>
    <justification jstring="[para(32747(a,2),29541(a,2,2))].">
      <j1 rule="para" parents="32747 29541"/>
    </justification>
  </clause>

  <clause id="32831">
    <literal><![CDATA[
      a(x,x,y) \ (z \ a(x,x,y)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(23999,a,32760,a)].">
      <j1 rule="hyper" parents="23999 32760"/>
    </justification>
  </clause>

  <clause id="32832">
    <literal><![CDATA[
      a(x * (y \ a(z,z,u)),w,v5) = a(x * (a(z,z,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(32760(a,1),26668(a,1,1,2))].">
      <j1 rule="para" parents="32760 26668"/>
    </justification>
  </clause>

  <clause id="32833">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,w,v5))) = a(x,y,z * (u * a(w,w,v5)))
    ]]></literal>
    <justification jstring="[para(32760(a,1),27079(a,1,3,2))].">
      <j1 rule="para" parents="32760 27079"/>
    </justification>
  </clause>

  <clause id="32836">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(1385,a,32762,a(flip))].">
      <j1 rule="hyper" parents="1385 32762"/>
    </justification>
  </clause>

  <clause id="32837">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(781,a,32762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="781 32762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32838">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,L(x,z,z)) = (a(z,z,x) \ y) \ L(x,z,z)
    ]]></literal>
    <justification jstring="[para(32762(a,1),251(a,2,1))].">
      <j1 rule="para" parents="32762 251"/>
    </justification>
  </clause>

  <clause id="32839">
    <literal><![CDATA[
      L(x,y,y) * L(1 / z,z,x) = a(y,y,x) \ (x / z)
    ]]></literal>
    <justification jstring="[para(3417(a,2),32762(a,1,2))].">
      <j1 rule="para" parents="3417 32762"/>
    </justification>
  </clause>

  <clause id="32840">
    <literal><![CDATA[
      (a(x,x,y) \ z) * y = z * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(32762(a,1),25179(a,1,1))].">
      <j1 rule="para" parents="32762 25179"/>
    </justification>
  </clause>

  <clause id="32841">
    <literal><![CDATA[
      a(x,x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (z / y) * L(y,x,x) = u
    ]]></literal>
    <justification jstring="[para(32762(a,1),24074(a,1))].">
      <j1 rule="para" parents="32762 24074"/>
    </justification>
  </clause>

  <clause id="32842">
    <literal><![CDATA[
      L((x \ y) \ (x \ 1),z,z) * (1 / (x * ((x \ 1) / y))) = a(z,z,(x \ y) \ (x \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(31361(a,2),32762(a,1,2))].">
      <j1 rule="para" parents="31361 32762"/>
    </justification>
  </clause>

  <clause id="32843">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,v5,v5))) = a(x,y,z * (a(w,v5,v5) * u))
    ]]></literal>
    <justification jstring="[para(32767(a,1),15784(a,1,3,2))].">
      <j1 rule="para" parents="32767 15784"/>
    </justification>
  </clause>

  <clause id="32845">
    <literal><![CDATA[
      a(x,x,y) \ ((z \ 1) \ 1) = (z \ a(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,28243,a(flip),b,32777,a)].">
      <j1 rule="hyper" parents="125 28243 32777"/>
    </justification>
  </clause>

  <clause id="32846">
    <literal><![CDATA[
      L(x,y,y) * (z * a(y,y,x)) = x * z
    ]]></literal>
    <justification jstring="[hyper(25235,a,32836,a),flip(a)].">
      <j1 rule="hyper" parents="25235 32836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32847">
    <literal><![CDATA[
      L(x,y,y) * (R(y,y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31809,a(flip),b,32836,a)].">
      <j1 rule="hyper" parents="60 31809 32836"/>
    </justification>
  </clause>

  <clause id="32849">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(29798,a,32837,a)].">
      <j1 rule="hyper" parents="29798 32837"/>
    </justification>
  </clause>

  <clause id="32853">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u) * w) = a(x,y,((z \ u) \ 1) * (((z * u) \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(32837(a,1),30338(a,2,3)),flip(a)].">
      <j1 rule="para" parents="32837 30338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32855">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,32849,a,b,31155,a),flip(a)].">
      <j1 rule="hyper" parents="126 32849 31155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32857">
    <literal><![CDATA[
      1 * (R(x,y,y) * z) = x * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(32855(a,1),28886(a,1,1))].">
      <j1 rule="para" parents="32855 28886"/>
    </justification>
  </clause>

  <clause id="32859">
    <literal><![CDATA[
      L(L(x,y,z) * (a(u,u,w) \ 1),x,x) = L((x \ 1) \ 1,y,z) * (a(u,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(32775(a,1),3267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32775 3267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32860">
    <literal><![CDATA[
      a(x,y,z \ (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (x * z)) = u
    ]]></literal>
    <justification jstring="[para(32364(a,1),32801(a,1))].">
      <j1 rule="para" parents="32364 32801"/>
    </justification>
  </clause>

  <clause id="32862">
    <literal><![CDATA[
      a(x \ y,y,z) = a(y * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32808,a,26439,a)].">
      <j1 rule="hyper" parents="32808 26439"/>
    </justification>
  </clause>

  <clause id="32863">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = a(u,y,x) \ L(x,x,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,24030,a,b,32603,a)].">
      <j1 rule="hyper" parents="370 24030 32603"/>
    </justification>
  </clause>

  <clause id="32866">
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(32655(a,2),31151(a,1))].">
      <j1 rule="para" parents="32655 31151"/>
    </justification>
  </clause>

  <clause id="32867">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (z \ L(z,y,x)) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(32655(a,1),31649(a,1,1))].">
      <j1 rule="para" parents="32655 31649"/>
    </justification>
  </clause>

  <clause id="32870">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,x))) = 1
    ]]></literal>
    <justification jstring="[para(32657(a,1),30901(a,1,3))].">
      <j1 rule="para" parents="32657 30901"/>
    </justification>
  </clause>

  <clause id="32871">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) = x * L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(32657(a,1),30899(a,1,2))].">
      <j1 rule="para" parents="32657 30899"/>
    </justification>
  </clause>

  <clause id="32872">
    <literal><![CDATA[
      x * a(y,z,x * L(x,u,w)) = a(w,u,a(y,z,x)) * x
    ]]></literal>
    <justification jstring="[para(32657(a,1),30973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32657 30973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32877">
    <literal><![CDATA[
      (x * y) * (z * a(y,y,z)) = (x * R(y,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(60,a,31811,a(flip),b,32764,a),flip(a)].">
      <j1 rule="hyper" parents="60 31811 32764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32878">
    <literal><![CDATA[
      a(x,(T(y * z,u) * a(w,w,z)) * v5,v6) = a(x,(y * (z * a(w,w,z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(32764(a,1),26467(a,2,2,1))].">
      <j1 rule="para" parents="32764 26467"/>
    </justification>
  </clause>

  <clause id="32880">
    <literal><![CDATA[
      a(x,y * (z * (u * (a(w,w,v5) \ u))),v6) = a(x,y * (a(w,w,v5) \ z),v6)
    ]]></literal>
    <justification jstring="[para(32778(a,1),30777(a,1,2,2,2))].">
      <j1 rule="para" parents="32778 30777"/>
    </justification>
  </clause>

  <clause id="32881">
    <literal><![CDATA[
      a(x,y,y * (x \ (z \ (x * y)))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26951,a,32782,a),flip(a)].">
      <j1 rule="hyper" parents="26951 32782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32883">
    <literal><![CDATA[
      x * (y * a(x,z,z)) = R(x,z,z) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,32857,a),flip(a)].">
      <j1 rule="hyper" parents="131 32857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32885">
    <literal><![CDATA[
      L(x,x,y) * (R(y,x,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(32883(a,1),31801(a,1,2))].">
      <j1 rule="para" parents="32883 31801"/>
    </justification>
  </clause>

  <clause id="32886">
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = a(x,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(25306,a,32600,a)].">
      <j1 rule="hyper" parents="25306 32600"/>
    </justification>
  </clause>

  <clause id="32887">
    <literal><![CDATA[
      a(x,y,L(z,x,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32600(a,1),25473(a,1))].">
      <j1 rule="para" parents="32600 25473"/>
    </justification>
  </clause>

  <clause id="32888">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(32600(a,1),31101(a,1))].">
      <j1 rule="para" parents="32600 31101"/>
    </justification>
  </clause>

  <clause id="32889">
    <literal><![CDATA[
      a(x,x,a(y,z,u \ w)) = a(x,x,a(y,z,u * w))
    ]]></literal>
    <justification jstring="[para(3101(a,1),32768(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3101 32768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32891">
    <literal><![CDATA[
      a(x \ a(y,y,z),u,w) = a(a(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27743,a(flip),b,32588,a)].">
      <j1 rule="hyper" parents="60 27743 32588"/>
    </justification>
  </clause>

  <clause id="32892">
    <literal><![CDATA[
      L(1 / x,y,z) \ L(u,x,x) = (x * a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,4104,a,b,32670,a)].">
      <j1 rule="hyper" parents="60 4104 32670"/>
    </justification>
  </clause>

  <clause id="32893">
    <literal><![CDATA[
      R(x,y,y * (z \ y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31491,a,32679,a),flip(a)].">
      <j1 rule="hyper" parents="31491 32679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32894">
    <literal><![CDATA[
      R(x,y,L(z,z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32531,a,32893,a)].">
      <j1 rule="hyper" parents="32531 32893"/>
    </justification>
  </clause>

  <clause id="32895">
    <literal><![CDATA[
      (x * y) * L(1 / z,z,y) = R(x,y,z) * (y / z)
    ]]></literal>
    <justification jstring="[para(32894(a,1),4126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32894 4126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32896">
    <literal><![CDATA[
      a(x * y,z,a(u,u,w)) = a(w,u,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(31848,a,32780,a),flip(a)].">
      <j1 rule="hyper" parents="31848 32780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32897">
    <literal><![CDATA[
      ((a(x,y,a(z,z,u)) \ w) / u) * L(u,z,z) = w * L(w \ (a(z,z,u) \ w),y,x)
    ]]></literal>
    <justification jstring="[hyper(32841,a,32823,a)].">
      <j1 rule="hyper" parents="32841 32823"/>
    </justification>
  </clause>

  <clause id="32898">
    <literal><![CDATA[
      T(x * a(y,x,x),z) \ 1 = L(x \ K(z,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31884,a,b,32824,a)].">
      <j1 rule="hyper" parents="60 31884 32824"/>
    </justification>
  </clause>

  <clause id="32899">
    <literal><![CDATA[
      a(x,x,y) \ L((z \ 1) \ 1,u,w) = (L(z,u,w) \ a(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(5066(a,2),32845(a,1,2))].">
      <j1 rule="para" parents="5066 32845"/>
    </justification>
  </clause>

  <clause id="32900">
    <literal><![CDATA[
      ((x * R(y,y,z)) * z) / ((1 / y) \ z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(32877(a,1),32456(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32877 32456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32901">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,w,x)) = a(x,w,a((x * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32497,a,b,32896,a),flip(a)].">
      <j1 rule="hyper" parents="370 32497 32896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32902">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,w,y)) = a(y,w,a(z \ (y \ x),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32497,a(flip),b,32896,a),flip(a)].">
      <j1 rule="hyper" parents="370 32497 32896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32903">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u * z,w,y)) = v5
    ]]></literal>
    <justification jstring="[para(32896(a,1),31848(a,1))].">
      <j1 rule="para" parents="32896 31848"/>
    </justification>
  </clause>

  <clause id="32904">
    <literal><![CDATA[
      T(x,y) \ (a(z,x,x) \ 1) = L(x \ K(y,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(31888,a,32898,a)].">
      <j1 rule="hyper" parents="31888 32898"/>
    </justification>
  </clause>

  <clause id="32905">
    <literal><![CDATA[
      R(x,L(y,y,z),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31627,a,32900,a)].">
      <j1 rule="hyper" parents="31627 32900"/>
    </justification>
  </clause>

  <clause id="32906">
    <literal><![CDATA[
      (x * (y \ a(y,y,z))) * z = R(x,y,z) * (y \ z)
    ]]></literal>
    <justification jstring="[para(32905(a,1),31624(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32905 31624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32907">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (T(x,y) / y)) = L(y \ K(x,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,28889,a,b,32904,a)].">
      <j1 rule="hyper" parents="60 28889 32904"/>
    </justification>
  </clause>

  <clause id="32908">
    <literal><![CDATA[
      (x * (y \ z)) \ (R(x,y,z) * (y \ z)) = a(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(32906(a,1),30083(a,1,2))].">
      <j1 rule="para" parents="32906 30083"/>
    </justification>
  </clause>

  <clause id="32909">
    <literal><![CDATA[
      a(x,y * (z \ y),y * (z \ y)) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32749,a(flip),b,32766,a),flip(a)].">
      <j1 rule="hyper" parents="370 32749 32766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32910">
    <literal><![CDATA[
      a(x,x,(y * (z * u)) * (z * y)) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(27033,a,32788,a)].">
      <j1 rule="hyper" parents="27033 32788"/>
    </justification>
  </clause>

  <clause id="32911">
    <literal><![CDATA[
      a(x,x,(y * (z * u)) * (y * z)) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(26965,a,32788,a)].">
      <j1 rule="hyper" parents="26965 32788"/>
    </justification>
  </clause>

  <clause id="32912">
    <literal><![CDATA[
      a(x,x,L((y * z) * (y * (z * u)),w,v5)) = a(x,x,L(L(u,w,v5),z,y))
    ]]></literal>
    <justification jstring="[para(4231(a,2),32788(a,1,3))].">
      <j1 rule="para" parents="4231 32788"/>
    </justification>
  </clause>

  <clause id="32916">
    <literal><![CDATA[
      T(x,y) \ ((x * a(z,u,x)) * w) = x * (L(T(x,y),u,z) \ w)
    ]]></literal>
    <justification jstring="[para(32892(a,1),25895(a,1,2))].">
      <j1 rule="para" parents="32892 25895"/>
    </justification>
  </clause>

  <clause id="32917">
    <literal><![CDATA[
      a(x,x,((y * (z * u)) \ (y * z)) * (w * w)) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(32789,a,32911,a)].">
      <j1 rule="hyper" parents="32789 32911"/>
    </justification>
  </clause>

  <clause id="32918">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = L(x,u,z) * (a(z,u,x) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,23641,a,b,32630,a),flip(a)].">
      <j1 rule="hyper" parents="370 23641 32630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32919">
    <literal><![CDATA[
      a(x,y,y) \ (z * (x * y)) = z * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(60,a,31798,a(flip),b,32674,a)].">
      <j1 rule="hyper" parents="60 31798 32674"/>
    </justification>
  </clause>

  <clause id="32920">
    <literal><![CDATA[
      (x * (y * z)) * L(z,z,y) = (x * (y / (z \ 1))) * z
    ]]></literal>
    <justification jstring="[para(32919(a,1),31794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32919 31794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32921">
    <literal><![CDATA[
      (x * (y * (z * z))) \ ((x * (y / (z \ 1))) * z) = a(x,y * z,L(z,z,y))
    ]]></literal>
    <justification jstring="[para(32920(a,1),618(a,1,2))].">
      <j1 rule="para" parents="32920 618"/>
    </justification>
  </clause>

  <clause id="32922">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,v5)) = L(x,u,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,32276,a(flip),b,32731,a),flip(a)].">
      <j1 rule="hyper" parents="60 32276 32731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32923">
    <literal><![CDATA[
      a(x,x,L(y \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(z * y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32770(a,1),27164(a,1))].">
      <j1 rule="para" parents="32770 27164"/>
    </justification>
  </clause>

  <clause id="32924">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,a(v5,v6,v6)))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(32238,a,32827,a)].">
      <j1 rule="hyper" parents="32238 32827"/>
    </justification>
  </clause>

  <clause id="32925">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = a(u,y,x) \ L(x,x,(w / v5) * (v5 / w))
    ]]></literal>
    <justification jstring="[para(28432(a,1),32863(a,2,2,3))].">
      <j1 rule="para" parents="28432 32863"/>
    </justification>
  </clause>

  <clause id="32928">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = w * a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(32657(a,1),32872(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32657 32872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32929">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,31141,a,b,32928,a)].">
      <j1 rule="hyper" parents="32 31141 32928"/>
    </justification>
  </clause>

  <clause id="32930">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,31127,a,b,32928,a)].">
      <j1 rule="hyper" parents="32 31127 32928"/>
    </justification>
  </clause>

  <clause id="32931">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(32,a,23620,a,b,32928,a)].">
      <j1 rule="hyper" parents="32 23620 32928"/>
    </justification>
  </clause>

  <clause id="32935">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,31136,a,b,32929,a)].">
      <j1 rule="hyper" parents="370 31136 32929"/>
    </justification>
  </clause>

  <clause id="32936">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,32929,a)].">
      <j1 rule="hyper" parents="370 26381 32929"/>
    </justification>
  </clause>

  <clause id="32938">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a(flip),b,32929,a)].">
      <j1 rule="hyper" parents="370 32929 32929"/>
    </justification>
  </clause>

  <clause id="32939">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(129,a,32929,a,b,32340,a)].">
      <j1 rule="hyper" parents="129 32929 32340"/>
    </justification>
  </clause>

  <clause id="32940">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,32929,a,b,32083,a)].">
      <j1 rule="hyper" parents="129 32929 32083"/>
    </justification>
  </clause>

  <clause id="32941">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(129,a,32929,a,b,32082,a)].">
      <j1 rule="hyper" parents="129 32929 32082"/>
    </justification>
  </clause>

  <clause id="32942">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(v5,w,a(x,y,u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,27827,a,b,32929,a)].">
      <j1 rule="hyper" parents="60 27827 32929"/>
    </justification>
  </clause>

  <clause id="32943">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(129,a,32929,a(flip),b,32083,a)].">
      <j1 rule="hyper" parents="129 32929 32083"/>
    </justification>
  </clause>

  <clause id="32944">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,32929,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 32929 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32946">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * z,w,a(v5,y,x)) = v6
    ]]></literal>
    <justification jstring="[para(32929(a,1),26519(a,1))].">
      <j1 rule="para" parents="32929 26519"/>
    </justification>
  </clause>

  <clause id="32947">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)) * v5,v6) = a(z,u,a(w,y,x)) * T(v5,v6)
    ]]></literal>
    <justification jstring="[para(32929(a,1),28197(a,1,1,1))].">
      <j1 rule="para" parents="32929 28197"/>
    </justification>
  </clause>

  <clause id="32950">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(x,y,w),u,z) = v5
    ]]></literal>
    <justification jstring="[para(32929(a,1),31133(a,1))].">
      <j1 rule="para" parents="32929 31133"/>
    </justification>
  </clause>

  <clause id="32951">
    <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(32929(a,1),31148(a,1))].">
      <j1 rule="para" parents="32929 31148"/>
    </justification>
  </clause>

  <clause id="32952">
    <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(32929(a,2),31148(a,1))].">
      <j1 rule="para" parents="32929 31148"/>
    </justification>
  </clause>

  <clause id="32957">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,x) = a(w,y,L(x,u,z))
    ]]></literal>
    <justification jstring="[para(32929(a,1),32318(a,1,1))].">
      <j1 rule="para" parents="32929 32318"/>
    </justification>
  </clause>

  <clause id="32958">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,x) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,L(x,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(32929(a,1),32470(a,1,1))].">
      <j1 rule="para" parents="32929 32470"/>
    </justification>
  </clause>

  <clause id="32959">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,y))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32244,a,32930,a)].">
      <j1 rule="hyper" parents="32244 32930"/>
    </justification>
  </clause>

  <clause id="32962">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(129,a,32930,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="129 32930 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32966">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a(flip),b,32931,a)].">
      <j1 rule="hyper" parents="370 32929 32931"/>
    </justification>
  </clause>

  <clause id="32967">
    <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(32931(a,1),23637(a,1,1))].">
      <j1 rule="para" parents="32931 23637"/>
    </justification>
  </clause>

  <clause id="32968">
    <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(32931(a,1),31148(a,1))].">
      <j1 rule="para" parents="32931 31148"/>
    </justification>
  </clause>

  <clause id="32970">
    <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(32931(a,1),32093(a,1,2))].">
      <j1 rule="para" parents="32931 32093"/>
    </justification>
  </clause>

  <clause id="32971">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,w) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(32931(a,1),32318(a,1,1))].">
      <j1 rule="para" parents="32931 32318"/>
    </justification>
  </clause>

  <clause id="32972">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w \ u))) = a(z,z,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(32795(a,2),32931(a,1,3))].">
      <j1 rule="para" parents="32795 32931"/>
    </justification>
  </clause>

  <clause id="32975">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a,b,32935,a)].">
      <j1 rule="hyper" parents="370 32929 32935"/>
    </justification>
  </clause>

  <clause id="32976">
    <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(32935(a,1),31148(a,1))].">
      <j1 rule="para" parents="32935 31148"/>
    </justification>
  </clause>

  <clause id="32977">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,a(w,x,y)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(32935(a,1),32073(a,1,2))].">
      <j1 rule="para" parents="32935 32073"/>
    </justification>
  </clause>

  <clause id="32979">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32931,a,b,32938,a)].">
      <j1 rule="hyper" parents="370 32931 32938"/>
    </justification>
  </clause>

  <clause id="32980">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a,b,32938,a)].">
      <j1 rule="hyper" parents="370 32929 32938"/>
    </justification>
  </clause>

  <clause id="32981">
    <literal><![CDATA[
      a(x,y,a(y,z,a(u,w,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(370,a,32139,a(flip),b,32938,a),flip(a)].">
      <j1 rule="hyper" parents="370 32139 32938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32982">
    <literal><![CDATA[
      a(x,y,a(y,z,(y * u) * w)) = a(x,z,a(y,y,u * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32011,a(flip),b,32938,a),flip(a)].">
      <j1 rule="hyper" parents="370 32011 32938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32983">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(129,a,32938,a,b,32083,a)].">
      <j1 rule="hyper" parents="129 32938 32083"/>
    </justification>
  </clause>

  <clause id="32986">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) = a(v5,y,a(x,w * u,z))
    ]]></literal>
    <justification jstring="[para(26459(a,1),32938(a,1,3))].">
      <j1 rule="para" parents="26459 32938"/>
    </justification>
  </clause>

  <clause id="32988">
    <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(32938(a,1),31148(a,1))].">
      <j1 rule="para" parents="32938 31148"/>
    </justification>
  </clause>

  <clause id="32989">
    <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(32938(a,2),31148(a,1))].">
      <j1 rule="para" parents="32938 31148"/>
    </justification>
  </clause>

  <clause id="32991">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,u,z) = a(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[para(32938(a,2),32318(a,1,1))].">
      <j1 rule="para" parents="32938 32318"/>
    </justification>
  </clause>

  <clause id="32993">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(w,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32938(a,1),32543(a,1,2))].">
      <j1 rule="para" parents="32938 32543"/>
    </justification>
  </clause>

  <clause id="32995">
    <literal><![CDATA[
      a(x,y,z) \ a(z,u,a(x,y,w)) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(32966(a,1),30760(a,1,2))].">
      <j1 rule="para" parents="32966 30760"/>
    </justification>
  </clause>

  <clause id="32996">
    <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(32966(a,1),31148(a,1))].">
      <j1 rule="para" parents="32966 31148"/>
    </justification>
  </clause>

  <clause id="32997">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z,a(u,w,y)) = v5
    ]]></literal>
    <justification jstring="[para(32966(a,1),32093(a,1,2))].">
      <j1 rule="para" parents="32966 32093"/>
    </justification>
  </clause>

  <clause id="32998">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(z,u,x)) = a(z,u,L(x,y,w)) * v5
    ]]></literal>
    <justification jstring="[para(32966(a,1),32348(a,1,1))].">
      <j1 rule="para" parents="32966 32348"/>
    </justification>
  </clause>

  <clause id="32999">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,z)) = a(y * x,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32896,a,b,32975,a),flip(a)].">
      <j1 rule="hyper" parents="370 32896 32975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33000">
    <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(32975(a,1),31148(a,1))].">
      <j1 rule="para" parents="32975 31148"/>
    </justification>
  </clause>

  <clause id="33001">
    <literal><![CDATA[
      a(x,y * a(z,u,w),a(w,v5,z)) = a(x,v5,a(z,y,w))
    ]]></literal>
    <justification jstring="[para(30045(a,1),32979(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30045 32979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33002">
    <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(32979(a,1),31148(a,1))].">
      <j1 rule="para" parents="32979 31148"/>
    </justification>
  </clause>

  <clause id="33003">
    <literal><![CDATA[
      a(x,y,a(z,x,u \ w)) = a(x,x,a(z,y,u * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32889,a(flip),b,32980,a),flip(a)].">
      <j1 rule="hyper" parents="370 32889 32980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33004">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(w,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(32980(a,1),31148(a,1))].">
      <j1 rule="para" parents="32980 31148"/>
    </justification>
  </clause>

  <clause id="33005">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,w) = a(z,y,L(w,u,x))
    ]]></literal>
    <justification jstring="[para(32980(a,1),32318(a,1,1))].">
      <j1 rule="para" parents="32980 32318"/>
    </justification>
  </clause>

  <clause id="33006">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,v5,a(v6,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(32929(a,2),32980(a,1,3))].">
      <j1 rule="para" parents="32929 32980"/>
    </justification>
  </clause>

  <clause id="33008">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32941,a(flip),b,32983,a)].">
      <j1 rule="hyper" parents="60 32941 32983"/>
    </justification>
  </clause>

  <clause id="33009">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,32940,a(flip),b,32983,a)].">
      <j1 rule="hyper" parents="60 32940 32983"/>
    </justification>
  </clause>

  <clause id="33010">
    <literal><![CDATA[
      L(x,y,a(z,z * y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(32765,a,33008,a),flip(a)].">
      <j1 rule="hyper" parents="32765 33008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33011">
    <literal><![CDATA[
      L(x,y,a(y * z,u,z)) = L(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(32292,a,33008,a),flip(a)].">
      <j1 rule="hyper" parents="32292 33008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33012">
    <literal><![CDATA[
      L(x,a(y,z,z),z * y) = L(x,z,a(y,z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30141,a,b,33008,a)].">
      <j1 rule="hyper" parents="370 30141 33008"/>
    </justification>
  </clause>

  <clause id="33013">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),v5,v6) = L(L(x,v5,v6),u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,25,a,b,33008,a)].">
      <j1 rule="hyper" parents="370 25 33008"/>
    </justification>
  </clause>

  <clause id="33014">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),a(v5,w,u),a(z,y,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,31982,a(flip),b,33008,a),flip(a)].">
      <j1 rule="hyper" parents="370 31982 33008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33015">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(w,y,z) * u) = a(w,y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(33008(a,1),28360(a,1,1))].">
      <j1 rule="para" parents="33008 28360"/>
    </justification>
  </clause>

  <clause id="33016">
    <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(33008(a,1),30727(a,1))].">
      <j1 rule="para" parents="33008 30727"/>
    </justification>
  </clause>

  <clause id="33017">
    <literal><![CDATA[
      L(x * y,y,a(z,u,y)) = L(x,u,a(y,y,z)) * y
    ]]></literal>
    <justification jstring="[para(33008(a,1),31712(a,2,1))].">
      <j1 rule="para" parents="33008 31712"/>
    </justification>
  </clause>

  <clause id="33018">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = x * L(y,u,a(x,x,z))
    ]]></literal>
    <justification jstring="[para(33008(a,1),31713(a,2,2))].">
      <j1 rule="para" parents="33008 31713"/>
    </justification>
  </clause>

  <clause id="33020">
    <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(33009(a,1),30727(a,1))].">
      <j1 rule="para" parents="33009 30727"/>
    </justification>
  </clause>

  <clause id="33021">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = x * L(y,u,a(z,x,x))
    ]]></literal>
    <justification jstring="[para(33009(a,1),31713(a,2,2))].">
      <j1 rule="para" parents="33009 31713"/>
    </justification>
  </clause>

  <clause id="33022">
    <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(31123(a,2),32951(a,1))].">
      <j1 rule="para" parents="31123 32951"/>
    </justification>
  </clause>

  <clause id="33023">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v6,v5,a(x,y,a(z,u,w))) = v7
    ]]></literal>
    <justification jstring="[para(32929(a,2),32951(a,1,3))].">
      <j1 rule="para" parents="32929 32951"/>
    </justification>
  </clause>

  <clause id="33024">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,a(v6,v5,z))) = v7
    ]]></literal>
    <justification jstring="[para(32938(a,1),32951(a,1,3))].">
      <j1 rule="para" parents="32938 32951"/>
    </justification>
  </clause>

  <clause id="33025">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,a(v5,z,y * x)) = v6
    ]]></literal>
    <justification jstring="[para(26381(a,1),32968(a,1))].">
      <j1 rule="para" parents="26381 32968"/>
    </justification>
  </clause>

  <clause id="33027">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,a(y * x,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(26381(a,1),32976(a,1))].">
      <j1 rule="para" parents="26381 32976"/>
    </justification>
  </clause>

  <clause id="33029">
    <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(26459(a,1),32996(a,1,3))].">
      <j1 rule="para" parents="26459 32996"/>
    </justification>
  </clause>

  <clause id="33032">
    <literal><![CDATA[
      a(x,y,a(z,x,x * u)) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(31231,a,32936,a),flip(a)].">
      <j1 rule="hyper" parents="31231 32936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33033">
    <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(32942(a,2),32968(a,1))].">
      <j1 rule="para" parents="32942 32968"/>
    </justification>
  </clause>

  <clause id="33034">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,a(x,y,z)) * a(v5,v6,a(v7,v8,v9))) = a(v7,v8,a(v9,v6,v5)) * a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32349,a,b,32944,a)].">
      <j1 rule="hyper" parents="370 32349 32944"/>
    </justification>
  </clause>

  <clause id="33036">
    <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(32962(a,1),29193(a,1,1))].">
      <j1 rule="para" parents="32962 29193"/>
    </justification>
  </clause>

  <clause id="33037">
    <literal><![CDATA[
      a(x,x,a(y,z,u * (w \ u))) = a(x,x,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(32951,a,32972,a)].">
      <j1 rule="hyper" parents="32951 32972"/>
    </justification>
  </clause>

  <clause id="33038">
    <literal><![CDATA[
      L(x,a(y,z,z),z * y) = L(x,z,a(y,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30474,a(flip),b,33012,a),flip(a)].">
      <j1 rule="hyper" parents="370 30474 33012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33039">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(1 / ((x * y) / x),1 / ((x * y) / x),u)) = L(L(x,y,y),1 / ((x * y) / x),a(u,z,1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(12651(a,1),33018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12651 33018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33040">
    <literal><![CDATA[
      a(x,y,a(z,x,u \ (w \ u))) = a(x,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,33003,a,b,33037,a)].">
      <j1 rule="hyper" parents="60 33003 33037"/>
    </justification>
  </clause>

  <clause id="33041">
    <literal><![CDATA[
      L(x,a(y,z,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,33010,a(flip),b,33038,a),flip(a)].">
      <j1 rule="hyper" parents="370 33010 33038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33043">
    <literal><![CDATA[
      a(x,y,a(z \ (u \ z),x,w)) = a(x,x,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(31148,a,33040,a)].">
      <j1 rule="hyper" parents="31148 33040"/>
    </justification>
  </clause>

  <clause id="33044">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23794,a,32939,a)].">
      <j1 rule="hyper" parents="23794 32939"/>
    </justification>
  </clause>

  <clause id="33045">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(32971(a,1),32602(a,1))].">
      <j1 rule="para" parents="32971 32602"/>
    </justification>
  </clause>

  <clause id="33046">
    <literal><![CDATA[
      a(x * a(y,x,z),u,a(y,x,z)) = a(x,x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(30995,a,33001,a),flip(a)].">
      <j1 rule="hyper" parents="30995 33001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33047">
    <literal><![CDATA[
      a(x,y,a(z,z,z * (x \ u))) * a(z,y,z * (x \ u)) = a(z,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32560,a(flip),b,33005,a),flip(a)].">
      <j1 rule="hyper" parents="370 32560 33005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33048">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) \ u,z,w)) * a(x,y,K(w,u * z) * ((w * z) \ (z * (u * w)))) = a(x,y,a(z,u,w) \ u)
    ]]></literal>
    <justification jstring="[para(29181(a,2),33044(a,1,2,3))].">
      <j1 rule="para" parents="29181 33044"/>
    </justification>
  </clause>

  <clause id="33049">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,L(x,u,w)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[para(32975(a,1),33044(a,1,1))].">
      <j1 rule="para" parents="32975 33044"/>
    </justification>
  </clause>

  <clause id="33050">
    <literal><![CDATA[
      a(x,y,a(y * a(z,y,x),u,z)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(32976,a,33046,a)].">
      <j1 rule="hyper" parents="32976 33046"/>
    </justification>
  </clause>

  <clause id="33051">
    <literal><![CDATA[
      a(x,y,a(z,x,x * u)) * a(z,y,u \ (u / (1 / x))) = a(z,y,x)
    ]]></literal>
    <justification jstring="[para(12657(a,1),33049(a,1,2,3))].">
      <j1 rule="para" parents="12657 33049"/>
    </justification>
  </clause>

  <clause id="33052">
    <literal><![CDATA[
      1 * a(x,x,L(y,z,a(u,w,z))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(32981(a,1),33049(a,1,1))].">
      <j1 rule="para" parents="32981 33049"/>
    </justification>
  </clause>

  <clause id="33053">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,w,z))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,33052,a)].">
      <j1 rule="hyper" parents="131 33052"/>
    </justification>
  </clause>

  <clause id="33054">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(33008(a,1),33053(a,1,3))].">
      <j1 rule="para" parents="33008 33053"/>
    </justification>
  </clause>

  <clause id="33055">
    <literal><![CDATA[
      a(x,x,(y * a(z,z,u)) \ w) = a(x,x,y \ (a(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(29238,a,33054,a),flip(a)].">
      <j1 rule="hyper" parents="29238 33054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33056">
    <literal><![CDATA[
      a(x,x,y) \ (a(z,z,u) * w) = a(z,z,u) * (a(x,x,y) \ w)
    ]]></literal>
    <justification jstring="[para(33054(a,1),32344(a,1,1))].">
      <j1 rule="para" parents="33054 32344"/>
    </justification>
  </clause>

  <clause id="33057">
    <literal><![CDATA[
      L(x * (y * a(z,u,x)),x,a(z,u,x)) = L(x,u,z) * (x * (L(L(x,u,z),u,z) \ y))
    ]]></literal>
    <justification jstring="[para(30657(a,1),32918(a,2,2))].">
      <j1 rule="para" parents="30657 32918"/>
    </justification>
  </clause>

  <clause id="33058">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,y,L(a(y,v5,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(28485,a,32922,a)].">
      <j1 rule="hyper" parents="28485 32922"/>
    </justification>
  </clause>

  <clause id="33059">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(w,u,a(x,v5,a(v6,y,z)))
    ]]></literal>
    <justification jstring="[hyper(32988,a,33006,a),flip(a)].">
      <j1 rule="hyper" parents="32988 33006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33060">
    <literal><![CDATA[
      a(x,y,a(z,u * w,a(v5,v6,v7))) = a(x,v6,a(v5,y,a(v7,w * u,z)))
    ]]></literal>
    <justification jstring="[para(32986(a,1),33006(a,2,3))].">
      <j1 rule="para" parents="32986 33006"/>
    </justification>
  </clause>

  <clause id="33061">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,y,w)) = x
    ]]></literal>
    <justification jstring="[para(32232(a,1),33014(a,1,1))].">
      <j1 rule="para" parents="32232 33014"/>
    </justification>
  </clause>

  <clause id="33063">
    <literal><![CDATA[
      L(x * y,z,L(a(z,x,x),x,x)) = L(z,x,x) * (z \ (R(x,x,z) * y))
    ]]></literal>
    <justification jstring="[hyper(31876,a,33058,a),flip(a)].">
      <j1 rule="hyper" parents="31876 33058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33064">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = (u \ L(z,y,x)) \ (u \ z)
    ]]></literal>
    <justification jstring="[hyper(32447,a,32675,a)].">
      <j1 rule="hyper" parents="32447 32675"/>
    </justification>
  </clause>

  <clause id="33065">
    <literal><![CDATA[
      L(a(x,y,L(z,x,u)),u * x,u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(32313(a,2),32728(a,1,1))].">
      <j1 rule="para" parents="32313 32728"/>
    </justification>
  </clause>

  <clause id="33066">
    <literal><![CDATA[
      a(x,x,R(y,z,y) * a(u,R(y,z,y),z)) = a(x,x,u * (z \ (T(y * z,y) * u)))
    ]]></literal>
    <justification jstring="[para(5537(a,1),32786(a,2,3,2,2,1))].">
      <j1 rule="para" parents="5537 32786"/>
    </justification>
  </clause>

  <clause id="33067">
    <literal><![CDATA[
      L(x,y,(1 / L(z,a(z,u,w),w)) \ v5) = L(x,y,v5 * (a(z,z,v5) * z))
    ]]></literal>
    <justification jstring="[para(32829(a,2),25924(a,1,3))].">
      <j1 rule="para" parents="32829 25924"/>
    </justification>
  </clause>

  <clause id="33068">
    <literal><![CDATA[
      a(x,y,L(z,x,y \ z)) = a(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32886,a(flip),b,32908,a)].">
      <j1 rule="hyper" parents="60 32886 32908"/>
    </justification>
  </clause>

  <clause id="33069">
    <literal><![CDATA[
      a(x,y,L(z,x,z * y)) = a(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(32217(a,1),33068(a,1,3))].">
      <j1 rule="para" parents="32217 33068"/>
    </justification>
  </clause>

  <clause id="33070">
    <literal><![CDATA[
      a(x,L(y,y,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32887,a,33069,a),flip(a)].">
      <j1 rule="hyper" parents="32887 33069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33071">
    <literal><![CDATA[
      a(x,y \ z,z) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4094,a(flip),b,33070,a),flip(a)].">
      <j1 rule="hyper" parents="60 4094 33070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33072">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,z,a(u,w,y)) = v6
    ]]></literal>
    <justification jstring="[para(32944(a,1),32967(a,1))].">
      <j1 rule="para" parents="32944 32967"/>
    </justification>
  </clause>

  <clause id="33073">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,v6,a(v7,v8,v9)) != v10
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) * a(v7,v8,a(v5,v6,v9)) = v10
    ]]></literal>
    <justification jstring="[para(32944(a,2),32967(a,1))].">
      <j1 rule="para" parents="32944 32967"/>
    </justification>
  </clause>

  <clause id="33074">
    <literal><![CDATA[
      a(x,y,(1 / (z / u)) * z) = (z \ L(u,y,x)) \ (z \ u)
    ]]></literal>
    <justification jstring="[para(29617(a,1),33064(a,1,3))].">
      <j1 rule="para" parents="29617 33064"/>
    </justification>
  </clause>

  <clause id="33075">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ (x \ y) = a(u,z,(x / y) * x)
    ]]></literal>
    <justification jstring="[hyper(27009,a,33074,a),flip(a)].">
      <j1 rule="hyper" parents="27009 33074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33076">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ (x \ y) = a(u,z,(y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,26896,a(flip),b,33075,a),flip(a)].">
      <j1 rule="hyper" parents="370 26896 33075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33077">
    <literal><![CDATA[
      (a(x,x,y) \ L((z \ 1) \ 1,u,w)) \ ((z \ a(x,x,y)) \ 1) = a(w,u,(((z \ 1) \ 1) \ a(x,x,y)) * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(32845(a,1),33076(a,1,2))].">
      <j1 rule="para" parents="32845 33076"/>
    </justification>
  </clause>

  <clause id="33078">
    <literal><![CDATA[
      a(x,y,L(L(z,x,u),u * x,u)) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(32447,a,33065,a)].">
      <j1 rule="hyper" parents="32447 33065"/>
    </justification>
  </clause>

  <clause id="33079">
    <literal><![CDATA[
      a(x,y,(z \ a(u,w,w)) * v5) = a(x,y,(z * a(w,w,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,31684,a,b,32593,a)].">
      <j1 rule="hyper" parents="60 31684 32593"/>
    </justification>
  </clause>

  <clause id="33080">
    <literal><![CDATA[
      a(x,y,z \ (y \ z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,31908,a,b,32625,a),flip(a)].">
      <j1 rule="hyper" parents="36 31908 32625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33081">
    <literal><![CDATA[
      a(x,y * (z \ y),y * (z \ y)) \ ((z * y) \ y) = L((z * y) \ y,y \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(30328(a,1),32625(a,1,1))].">
      <j1 rule="para" parents="30328 32625"/>
    </justification>
  </clause>

  <clause id="33082">
    <literal><![CDATA[
      L(x \ R(x,y * x,z),z,y * x) = a(x,y * x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(32447,a,32676,a),flip(a)].">
      <j1 rule="hyper" parents="32447 32676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33084">
    <literal><![CDATA[
      a(L(x,x,L(L(y,z,u),w,v5)) * L(y * a(u,z,y),w,v5),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x \ L(y * a(u,z,y),w,v5),v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(32683(a,1),27323(a,1,1,1))].">
      <j1 rule="para" parents="32683 27323"/>
    </justification>
  </clause>

  <clause id="33085">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,u)) = a(u,z,y) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,32825,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 32825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33086">
    <literal><![CDATA[
      a(x,y,a(z \ (x \ u),w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x * z) * u,w,a(y,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(32902(a,1),26519(a,1))].">
      <j1 rule="para" parents="32902 26519"/>
    </justification>
  </clause>

  <clause id="33087">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)) * v5,v6) = T(a(w,u,a(x,y,z)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,28197,a,b,32947,a)].">
      <j1 rule="hyper" parents="370 28197 32947"/>
    </justification>
  </clause>

  <clause id="33088">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,a(z,x,u)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[para(32979(a,1),32977(a,1,1))].">
      <j1 rule="para" parents="32979 32977"/>
    </justification>
  </clause>

  <clause id="33089">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (y * w) = y * (a(x,y,a(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(32124(a,1),33015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32124 33015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33090">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(z,u,a(y,x,w))
    ]]></literal>
    <justification jstring="[hyper(30073,a,33036,a)].">
      <j1 rule="hyper" parents="30073 33036"/>
    </justification>
  </clause>

  <clause id="33091">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) * L((x * a(y,z,a(u,x,w))) \ 1,u,a(y,z,w)) = (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(33036(a,1),3816(a,2,2))].">
      <j1 rule="para" parents="33036 3816"/>
    </justification>
  </clause>

  <clause id="33092">
    <literal><![CDATA[
      ((x * a(y,z,a(u,x,w))) \ v5) \ (v5 * L(v5 \ ((x * a(y,z,a(u,x,w))) \ v5),u,a(y,z,w))) = (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(33036(a,1),25314(a,2,2))].">
      <j1 rule="para" parents="33036 25314"/>
    </justification>
  </clause>

  <clause id="33093">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),y,a(w,z,u)) = L(x,a(w,z,u),y)
    ]]></literal>
    <justification jstring="[para(32938(a,2),33036(a,1,1,2))].">
      <j1 rule="para" parents="32938 33036"/>
    </justification>
  </clause>

  <clause id="33094">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(w,z,y)) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[para(32966(a,1),33036(a,1,1,2))].">
      <j1 rule="para" parents="32966 33036"/>
    </justification>
  </clause>

  <clause id="33095">
    <literal><![CDATA[
      a(x,x,(y * a(z,z,u)) \ w) = a(x,x,y * (a(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32771,a(flip),b,33055,a),flip(a)].">
      <j1 rule="hyper" parents="370 32771 33055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33096">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w)) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(26965,a,33079,a),flip(a)].">
      <j1 rule="hyper" parents="26965 33079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33097">
    <literal><![CDATA[
      L(a(x,y * x,z),z,y * x) = a(x,y * x,L(z,y,y))
    ]]></literal>
    <justification jstring="[para(32595(a,2),33082(a,1,1))].">
      <j1 rule="para" parents="32595 33082"/>
    </justification>
  </clause>

  <clause id="33098">
    <literal><![CDATA[
      a(x,y * x,L(z,y,y)) = a(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(32673,a,33097,a),flip(a)].">
      <j1 rule="hyper" parents="32673 33097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33099">
    <literal><![CDATA[
      a(x,y * x,L(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y * x,z) = u
    ]]></literal>
    <justification jstring="[para(33097(a,1),32673(a,1))].">
      <j1 rule="para" parents="33097 32673"/>
    </justification>
  </clause>

  <clause id="33100">
    <literal><![CDATA[
      a(x,y * x,y \ z) = a(x,y * x,y * z)
    ]]></literal>
    <justification jstring="[hyper(27010,a,33098,a),flip(a)].">
      <j1 rule="hyper" parents="27010 33098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33102">
    <literal><![CDATA[
      a(x \ a(y,z,y),u * (x \ a(y,z,y)),u * w) = a(x,u * (x \ a(y,z,y)),u \ w)
    ]]></literal>
    <justification jstring="[hyper(27326,a,33100,a),flip(a)].">
      <j1 rule="hyper" parents="27326 33100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33103">
    <literal><![CDATA[
      a(x,y * x,y * z) * x = R(x,y * x,y \ z)
    ]]></literal>
    <justification jstring="[para(33100(a,1),32597(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33100 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33104">
    <literal><![CDATA[
      R(x,y * x,y \ z) = R(x,y * x,y * z)
    ]]></literal>
    <justification jstring="[hyper(32754,a,33103,a),flip(a)].">
      <j1 rule="hyper" parents="32754 33103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33106">
    <literal><![CDATA[
      L(x,y,a(z,L(z,y,u),u)) * (a(u,y,z) * L(z,y,u)) = R(x / (1 / z),z,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,33015,a,b,33085,a)].">
      <j1 rule="hyper" parents="370 33015 33085"/>
    </justification>
  </clause>

  <clause id="33107">
    <literal><![CDATA[
      a(x,L(y * L(z,u,w),a(w,u,z),a(w,u,z)) * v5,v6) = a(x,(a(w,u,z) * R(y / (1 / z),z,L(z,u,w))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(33085(a,2),3046(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="33085 3046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33108">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)) * v5,v6) = T(v5 * a(z,y,a(w,u,x)),v6)
    ]]></literal>
    <justification jstring="[para(32944(a,1),33087(a,2,1))].">
      <j1 rule="para" parents="32944 33087"/>
    </justification>
  </clause>

  <clause id="33109">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,y,a(z,x,w)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(33072,a,33088,a)].">
      <j1 rule="hyper" parents="33072 33088"/>
    </justification>
  </clause>

  <clause id="33110">
    <literal><![CDATA[
      (x * (a(y,x,a(z,z,u)) * w)) / T(a(y,x,a(z,z,u)) * x,w) = L(w,x,a(y,x,a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(128,a,33089,a(flip),b,15634,a)].">
      <j1 rule="hyper" parents="128 33089 15634"/>
    </justification>
  </clause>

  <clause id="33111">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),z,a(u,w,y)) = x * a(y,z,a(w,x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33013,a(flip),b,33090,a)].">
      <j1 rule="hyper" parents="60 33013 33090"/>
    </justification>
  </clause>

  <clause id="33112">
    <literal><![CDATA[
      L(x * a(a(y,y,z),u,a(w,x,y)),a(y,y,z),a(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,33061,a(flip),b,33093,a),flip(a)].">
      <j1 rule="hyper" parents="370 33061 33093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33113">
    <literal><![CDATA[
      L(x * a(y,z,a(z * a(u,z,y),x,u)),z * a(u,z,y),a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,31693,a(flip),b,33094,a),flip(a)].">
      <j1 rule="hyper" parents="370 31693 33094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33114">
    <literal><![CDATA[
      a(x,x,(y * a(z,z,u)) \ w) = a(x,x,y * (w * a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,30679,a(flip),b,33095,a),flip(a)].">
      <j1 rule="hyper" parents="370 30679 33095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33115">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w)) * v5) = a(x,y,v5 * (a(w,u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32843,a(flip),b,33096,a),flip(a)].">
      <j1 rule="hyper" parents="370 32843 33096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33116">
    <literal><![CDATA[
      a(x,y,a(L(z,y,y),u,w)) * a(u,y,a(L(z,y,y),x,w)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[para(32323(a,1),33109(a,2,2))].">
      <j1 rule="para" parents="32323 33109"/>
    </justification>
  </clause>

  <clause id="33117">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),z,a(y,w,u)) = x * a(u,z,a(w,x,y))
    ]]></literal>
    <justification jstring="[para(31973(a,1),33111(a,1,1))].">
      <j1 rule="para" parents="31973 33111"/>
    </justification>
  </clause>

  <clause id="33118">
    <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="[para(32935(a,1),33111(a,2,2))].">
      <j1 rule="para" parents="32935 33111"/>
    </justification>
  </clause>

  <clause id="33119">
    <literal><![CDATA[
      L(x * a(y,y,a(a(z,x,y),u,w)),a(y,y,w),a(y,u,z)) = x
    ]]></literal>
    <justification jstring="[para(32230(a,1),33112(a,1,1,2))].">
      <j1 rule="para" parents="32230 33112"/>
    </justification>
  </clause>

  <clause id="33120">
    <literal><![CDATA[
      a(x,x,(y * a(z,z,u)) * w) = a(x,x,y * (w * a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(32776,a,33114,a)].">
      <j1 rule="hyper" parents="32776 33114"/>
    </justification>
  </clause>

  <clause id="33121">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),z,a(y,w,u)) = x * a(u,x,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(32979(a,1),33117(a,2,2))].">
      <j1 rule="para" parents="32979 33117"/>
    </justification>
  </clause>

  <clause id="33122">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,a(u,w,y))),a(y,y,u),a(y,w,z)) = x
    ]]></literal>
    <justification jstring="[para(32930(a,1),33119(a,1,1,2,3))].">
      <j1 rule="para" parents="32930 33119"/>
    </justification>
  </clause>

  <clause id="33123">
    <literal><![CDATA[
      a(x,x,(a(y,y,z) * u) * w) = a(x,x,u * (w * a(y,y,z)))
    ]]></literal>
    <justification jstring="[hyper(27002,a,33120,a)].">
      <j1 rule="hyper" parents="27002 33120"/>
    </justification>
  </clause>

  <clause id="33124">
    <literal><![CDATA[
      a(x,x,y * (a(z,u,u) * w)) = a(x,x,w * (y * a(u,u,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33115,a(flip),b,33120,a)].">
      <j1 rule="hyper" parents="60 33115 33120"/>
    </justification>
  </clause>

  <clause id="33125">
    <literal><![CDATA[
      L(x * 1,a(y,y,z),a(y,u,w)) = x
    ]]></literal>
    <justification jstring="[para(32870(a,1),33122(a,1,1,2))].">
      <j1 rule="para" parents="32870 33122"/>
    </justification>
  </clause>

  <clause id="33126">
    <literal><![CDATA[
      L(x,a(y,y,z),a(y,u,w)) = x
    ]]></literal>
    <justification jstring="[para(3(a,1),33125(a,1,1))].">
      <j1 rule="para" parents="3 33125"/>
    </justification>
  </clause>

  <clause id="33128">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,y,w)) * (a(y,z,u) / a(y,y,w)) = (x * a(y,z,u)) * (1 / a(y,y,w))
    ]]></literal>
    <justification jstring="[para(33126(a,1),32895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33126 32895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33129">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32212,a(flip),b,32871,a),flip(a)].">
      <j1 rule="hyper" parents="370 32212 32871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33131">
    <literal><![CDATA[
      L(x,y,z) * a(x,y,a(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(32935(a,1),33129(a,1,2))].">
      <j1 rule="para" parents="32935 33129"/>
    </justification>
  </clause>

  <clause id="33132">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),z * y,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1867(a,1),32917(a,1,3))].">
      <j1 rule="para" parents="1867 32917"/>
    </justification>
  </clause>

  <clause id="33133">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = a(u,y,x) \ L(x,x,(w / v5) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(25922(a,1),32925(a,2,2))].">
      <j1 rule="para" parents="25922 32925"/>
    </justification>
  </clause>

  <clause id="33134">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = a(u,y,x) \ L(x,x,(w \ v5) * (v5 \ w))
    ]]></literal>
    <justification jstring="[para(25911(a,1),33133(a,2,2))].">
      <j1 rule="para" parents="25911 33133"/>
    </justification>
  </clause>

  <clause id="33135">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = a(u,y,x) \ L(x,x,a(w,w * v5,v5))
    ]]></literal>
    <justification jstring="[para(30473(a,1),33134(a,2,2))].">
      <j1 rule="para" parents="30473 33134"/>
    </justification>
  </clause>

  <clause id="33136">
    <literal><![CDATA[
      a(x,y,z) \ L(z,z,a(u,u * w,w)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(24975,a,33135,a),flip(a)].">
      <j1 rule="hyper" parents="24975 33135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33137">
    <literal><![CDATA[
      a(x,y,z) \ L(z,z,a(u,u * w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = v5
    ]]></literal>
    <justification jstring="[para(33135(a,1),3532(a,1))].">
      <j1 rule="para" parents="33135 3532"/>
    </justification>
  </clause>

  <clause id="33138">
    <literal><![CDATA[
      L(a(x,y,z),L(z,u,x),x * u) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(28870,a,32354,a),flip(a)].">
      <j1 rule="hyper" parents="28870 32354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33139">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,x),x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(32447,a,33138,a)].">
      <j1 rule="hyper" parents="32447 33138"/>
    </justification>
  </clause>

  <clause id="33141">
    <literal><![CDATA[
      a(x,y,L(z,z,L(x * u,u,x))) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(31338(a,1),33139(a,1,3))].">
      <j1 rule="para" parents="31338 33139"/>
    </justification>
  </clause>

  <clause id="33142">
    <literal><![CDATA[
      a(x,y,L(z,z,u \ x)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(29076(a,1),33141(a,1,3))].">
      <j1 rule="para" parents="29076 33141"/>
    </justification>
  </clause>

  <clause id="33143">
    <literal><![CDATA[
      a(x,y,L(z,z,x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(32479,a,33142,a)].">
      <j1 rule="hyper" parents="32479 33142"/>
    </justification>
  </clause>

  <clause id="33144">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) * (a(x,y,z) \ w) = w * a(x * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(33143(a,1),32345(a,1,1))].">
      <j1 rule="para" parents="33143 32345"/>
    </justification>
  </clause>

  <clause id="33145">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) \ v5,v6,v7)) = a(x,y,L(L(z,u,w) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(32429,a,32412,a),flip(a)].">
      <j1 rule="hyper" parents="32429 32412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33147">
    <literal><![CDATA[
      (a(x,y * x,z) \ y) * z = (y / (y * x)) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(33098(a,1),32423(a,1,1,1))].">
      <j1 rule="para" parents="33098 32423"/>
    </justification>
  </clause>

  <clause id="33148">
    <literal><![CDATA[
      a(L(x,y,z),u,x \ w) = a(L(x,y,z),u,w * x)
    ]]></literal>
    <justification jstring="[hyper(30216,a,32475,a)].">
      <j1 rule="hyper" parents="30216 32475"/>
    </justification>
  </clause>

  <clause id="33149">
    <literal><![CDATA[
      a(L(x,y,z),u,w * x) = a(x,u,L(x \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(32429,a,33148,a),flip(a)].">
      <j1 rule="hyper" parents="32429 33148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33150">
    <literal><![CDATA[
      a(x,y,L(x \ z,u,w)) = a(x,y,L(z * x,u,w))
    ]]></literal>
    <justification jstring="[hyper(32429,a,33149,a),flip(a)].">
      <j1 rule="hyper" parents="32429 33149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33153">
    <literal><![CDATA[
      a(x \ (y \ z),u,x \ (y \ w)) = a(z * (y * x),u,(y * x) * w)
    ]]></literal>
    <justification jstring="[hyper(32435,a,32495,a),flip(a)].">
      <j1 rule="hyper" parents="32435 32495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33154">
    <literal><![CDATA[
      a((x * y) * (z * x),u,(z * x) * w) = a(z \ y,u,z \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(32435,a,32498,a)].">
      <j1 rule="hyper" parents="32435 32498"/>
    </justification>
  </clause>

  <clause id="33155">
    <literal><![CDATA[
      x \ (x * a(y,z / x,z / x)) = a(y,x \ z,z \ x)
    ]]></literal>
    <justification jstring="[para(77(a,1),32636(a,1,2,1))].">
      <j1 rule="para" parents="77 32636"/>
    </justification>
  </clause>

  <clause id="33157">
    <literal><![CDATA[
      x \ (x * a(y,z / x,x \ z)) = a(y,x \ z,z \ x)
    ]]></literal>
    <justification jstring="[para(26882(a,1),33155(a,1,2,2))].">
      <j1 rule="para" parents="26882 33155"/>
    </justification>
  </clause>

  <clause id="33158">
    <literal><![CDATA[
      x \ (x * a(y,x \ z,x \ z)) = a(y,x \ z,z \ x)
    ]]></literal>
    <justification jstring="[para(26454(a,1),33157(a,1,2,2))].">
      <j1 rule="para" parents="26454 33157"/>
    </justification>
  </clause>

  <clause id="33159">
    <literal><![CDATA[
      x \ (x * a(y,x * z,x * z)) = a(y,x \ z,z \ x)
    ]]></literal>
    <justification jstring="[para(30328(a,1),33158(a,1,2,2))].">
      <j1 rule="para" parents="30328 33158"/>
    </justification>
  </clause>

  <clause id="33160">
    <literal><![CDATA[
      a(x,y \ z,z \ y) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(386,a,33159,a),flip(a)].">
      <j1 rule="hyper" parents="386 33159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33162">
    <literal><![CDATA[
      a(x,y * z,y * z) * x = R(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(33160(a,1),28516(a,1,1))].">
      <j1 rule="para" parents="33160 28516"/>
    </justification>
  </clause>

  <clause id="33163">
    <literal><![CDATA[
      R(x,y \ z,z \ y) = R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(32754,a,33162,a),flip(a)].">
      <j1 rule="hyper" parents="32754 33162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33165">
    <literal><![CDATA[
      R(x,y \ z,z \ y) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30180,a,b,33163,a),flip(a)].">
      <j1 rule="hyper" parents="370 30180 33163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33166">
    <literal><![CDATA[
      R(x,x \ y,y \ x) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,1110,a(flip),b,33165,a),flip(a)].">
      <j1 rule="hyper" parents="370 1110 33165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33167">
    <literal><![CDATA[
      R(x,y \ x,x \ y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,12701,a,b,33166,a)].">
      <j1 rule="hyper" parents="60 12701 33166"/>
    </justification>
  </clause>

  <clause id="33168">
    <literal><![CDATA[
      R(x,y * x,y * x) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,33163,a(flip),b,33167,a)].">
      <j1 rule="hyper" parents="60 33163 33167"/>
    </justification>
  </clause>

  <clause id="33169">
    <literal><![CDATA[
      x * a(y,z * y,z * y) = x * (y \ (z * ((y \ z) \ 1)))
    ]]></literal>
    <justification jstring="[para(33168(a,1),16512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33168 16512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33170">
    <literal><![CDATA[
      x * a(y,z * y,z * y) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,31891,a(flip),b,33169,a),flip(a)].">
      <j1 rule="hyper" parents="370 31891 33169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33172">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * a(u,z,x \ (x / (1 / y))) = a(u,z,y)
    ]]></literal>
    <justification jstring="[para(33032(a,1),33051(a,1,1))].">
      <j1 rule="para" parents="33032 33051"/>
    </justification>
  </clause>

  <clause id="33173">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * a(u,z,x \ (y \ x)) = a(u,z,y)
    ]]></literal>
    <justification jstring="[para(27043(a,1),33172(a,1,2))].">
      <j1 rule="para" parents="27043 33172"/>
    </justification>
  </clause>

  <clause id="33174">
    <literal><![CDATA[
      a((x \ y) * z,u,z * (x \ w)) = a(y * (x * z),u,(x * z) * w)
    ]]></literal>
    <justification jstring="[hyper(32435,a,33153,a)].">
      <j1 rule="hyper" parents="32435 33153"/>
    </justification>
  </clause>

  <clause id="33176">
    <literal><![CDATA[
      a((x * y) * (z * x),u,(z * x) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * z,u,z * (x \ w)) = v5
    ]]></literal>
    <justification jstring="[para(33154(a,2),32435(a,1))].">
      <j1 rule="para" parents="33154 32435"/>
    </justification>
  </clause>

  <clause id="33177">
    <literal><![CDATA[
      a(x * (x * y),z,(x * y) * u) = a(y,z,y * (x \ u))
    ]]></literal>
    <justification jstring="[para(194(a,1),33174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 33174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33178">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,(R(1 / y,z,y) * u) * 1) = a((R(1 / y,z,y) \ x) * u,w,u * L(y,z,y))
    ]]></literal>
    <justification jstring="[para(11718(a,1),33174(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11718 33174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33179">
    <literal><![CDATA[
      a(x,y,L((z * x) * u,z,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(32458,a,33177,a)].">
      <j1 rule="hyper" parents="32458 33177"/>
    </justification>
  </clause>

  <clause id="33180">
    <literal><![CDATA[
      a(x,y * x,(y * x) * z) = a(x,y * x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(33099,a,33179,a)].">
      <j1 rule="hyper" parents="33099 33179"/>
    </justification>
  </clause>

  <clause id="33181">
    <literal><![CDATA[
      a(x,y,L((x * z) * u,z,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(27170,a,33179,a)].">
      <j1 rule="hyper" parents="27170 33179"/>
    </justification>
  </clause>

  <clause id="33182">
    <literal><![CDATA[
      a(x,y,L((z * x) * R(u,x,z),u,u)) = a(x,y,x * (u \ (x \ T(z * x,u))))
    ]]></literal>
    <justification jstring="[para(29192(a,2),33179(a,1,3,1))].">
      <j1 rule="para" parents="29192 33179"/>
    </justification>
  </clause>

  <clause id="33183">
    <literal><![CDATA[
      a(x * (y * x),z,(y * x) * u) = a(y,z,y * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(32420,a,33181,a)].">
      <j1 rule="hyper" parents="32420 33181"/>
    </justification>
  </clause>

  <clause id="33184">
    <literal><![CDATA[
      a(x,y * x,x * (y \ (z \ 1))) = a(x,y * x,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(26991,a,33180,a),flip(a)].">
      <j1 rule="hyper" parents="26991 33180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33185">
    <literal><![CDATA[
      x \ R(x,y * x,x * (y \ z)) = a(x,y * x,(y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32595,a(flip),b,33180,a)].">
      <j1 rule="hyper" parents="370 32595 33180"/>
    </justification>
  </clause>

  <clause id="33186">
    <literal><![CDATA[
      a((x \ y) * y,z,y * (x \ u)) = a(x,z,x * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33174,a,b,33183,a)].">
      <j1 rule="hyper" parents="60 33174 33183"/>
    </justification>
  </clause>

  <clause id="33187">
    <literal><![CDATA[
      a(x,y,L(L(z * (x \ u),x,z),z,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(32477,a,33186,a)].">
      <j1 rule="hyper" parents="32477 33186"/>
    </justification>
  </clause>

  <clause id="33188">
    <literal><![CDATA[
      a(x,y * x,(y \ z) * x) = a(x,y * x,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27084,a(flip),b,33184,a)].">
      <j1 rule="hyper" parents="60 27084 33184"/>
    </justification>
  </clause>

  <clause id="33189">
    <literal><![CDATA[
      R(x,y * x,(y * x) * z) = R(x,y * x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(35,a,32595,a(flip),b,33185,a)].">
      <j1 rule="hyper" parents="35 32595 33185"/>
    </justification>
  </clause>

  <clause id="33190">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(29468,a,33187,a)].">
      <j1 rule="hyper" parents="29468 33187"/>
    </justification>
  </clause>

  <clause id="33191">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ (x \ u)),x,x * z)) = a(x,y,x * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,32377,a(flip),b,33190,a)].">
      <j1 rule="hyper" parents="60 32377 33190"/>
    </justification>
  </clause>

  <clause id="33192">
    <literal><![CDATA[
      a(x \ (y \ 1),z,L((y \ 1) \ ((x \ (y \ 1)) \ u),x \ (y \ 1),y \ 1)) = a(x \ (y \ 1),z,(x \ y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(1473(a,1),33190(a,2,3))].">
      <j1 rule="para" parents="1473 33190"/>
    </justification>
  </clause>

  <clause id="33194">
    <literal><![CDATA[
      ((x \ y) \ ((y \ x) \ 1)) * z = z * a(y,x * y,x * y)
    ]]></literal>
    <justification jstring="[para(4190(a,1),32759(a,1,1))].">
      <j1 rule="para" parents="4190 32759"/>
    </justification>
  </clause>

  <clause id="33195">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) * z = z * a(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[para(29106(a,1),33194(a,1,1))].">
      <j1 rule="para" parents="29106 33194"/>
    </justification>
  </clause>

  <clause id="33196">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) * z = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[hyper(370,a,33170,a(flip),b,33195,a),flip(a)].">
      <j1 rule="hyper" parents="370 33170 33195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33197">
    <literal><![CDATA[
      (x \ (y * (1 / (x \ y)))) * z = ((y \ x) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(31892(a,1),33196(a,1,1))].">
      <j1 rule="para" parents="31892 33196"/>
    </justification>
  </clause>

  <clause id="33198">
    <literal><![CDATA[
      (x * y) \ (L(x,z,y) * (R(y,z,x) * u)) = L(u,L(y,z,x),L(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,27410,a(flip),b,32797,a),flip(a)].">
      <j1 rule="hyper" parents="370 27410 32797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33199">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),y,w)) = a(x,x,L((w * y) * w,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,15786,a(flip),b,32912,a),flip(a)].">
      <j1 rule="hyper" parents="60 15786 32912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33200">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),y,w)) = a(x,x,L(L(y,w,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,27169,a(flip),b,33199,a),flip(a)].">
      <j1 rule="hyper" parents="370 27169 33199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33201">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),y,w)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32774,a(flip),b,33200,a),flip(a)].">
      <j1 rule="hyper" parents="370 32774 33200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33203">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),33201(a,1,3))].">
      <j1 rule="para" parents="25 33201"/>
    </justification>
  </clause>

  <clause id="33204">
    <literal><![CDATA[
      a(x,x,L(y,z * y,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33132,a(flip),b,33203,a),flip(a)].">
      <j1 rule="hyper" parents="60 33132 33203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33206">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z * y,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(33204(a,1),14184(a,2,1))].">
      <j1 rule="para" parents="33204 14184"/>
    </justification>
  </clause>

  <clause id="33207">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z * y,u) = L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,32338,a,b,33206,a),flip(a)].">
      <j1 rule="hyper" parents="370 32338 33206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33208">
    <literal><![CDATA[
      L((a(x,x,y) \ 1) \ L(a(x,x,y) \ 1,z,u),a(x,x,y) \ 1,z * y) = a(u,z * y,a(x,x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(33207(a,1),29963(a,1,1,2))].">
      <j1 rule="para" parents="33207 29963"/>
    </justification>
  </clause>

  <clause id="33209">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (L(a(x,x,y) \ 1,z,u) \ u) = R(u,z * y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(33207(a,1),32784(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="33207 32784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33210">
    <literal><![CDATA[
      L(x,y,y) * (x \ (R(y,y,x) * z)) = L(y * z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(14782(a,1),33063(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14782 33063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33212">
    <literal><![CDATA[
      L(x,y,z * (a(u,u,z) * u)) = L(x,y,(1 / u) \ z)
    ]]></literal>
    <justification jstring="[para(615(a,1),33067(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="615 33067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33213">
    <literal><![CDATA[
      L(x,y,z * (a(u,u,z) * u)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3376,a(flip),b,33212,a),flip(a)].">
      <j1 rule="hyper" parents="370 3376 33212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33214">
    <literal><![CDATA[
      L(x,y,z * R(u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(28421(a,1),33213(a,1,3,2))].">
      <j1 rule="para" parents="28421 33213"/>
    </justification>
  </clause>

  <clause id="33215">
    <literal><![CDATA[
      L(x,y,z * L(u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(27274,a,33214,a)].">
      <j1 rule="hyper" parents="27274 33214"/>
    </justification>
  </clause>

  <clause id="33216">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,L(u,u,w) * w) = L(x,z / (y \ 1),u \ w)
    ]]></literal>
    <justification jstring="[hyper(26261,a,33215,a)].">
      <j1 rule="hyper" parents="26261 33215"/>
    </justification>
  </clause>

  <clause id="33217">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,L(u,u,w) * w) = L(x,(y \ 1) \ z,u \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26018,a(flip),b,33216,a),flip(a)].">
      <j1 rule="hyper" parents="370 26018 33216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33218">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,L(u,u,w) * w) = L(x,y \ z,u \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,3392,a(flip),b,33217,a),flip(a)].">
      <j1 rule="hyper" parents="370 3392 33217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33219">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,L(y,y,z) * z) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29605,a(flip),b,33218,a),flip(a)].">
      <j1 rule="hyper" parents="370 29605 33218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33220">
    <literal><![CDATA[
      L(L(x,x,y),x * y,x * y) = (1 / (y * (1 / x))) * y
    ]]></literal>
    <justification jstring="[hyper(60,a,29618,a(flip),b,33219,a),flip(a)].">
      <j1 rule="hyper" parents="60 29618 33219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33221">
    <literal><![CDATA[
      L((1 / (x / y)) * x,y,x) = (1 / (x * (1 / y))) * x
    ]]></literal>
    <justification jstring="[hyper(60,a,29608,a(flip),b,33220,a)].">
      <j1 rule="hyper" parents="60 29608 33220"/>
    </justification>
  </clause>

  <clause id="33222">
    <literal><![CDATA[
      (1 / (x * y)) * (x * (y * y)) = (1 / (x * (1 / y))) * x
    ]]></literal>
    <justification jstring="[hyper(29646,a,33221,a)].">
      <j1 rule="hyper" parents="29646 33221"/>
    </justification>
  </clause>

  <clause id="33223">
    <literal><![CDATA[
      x * a(y * z,u,a(y,w,u)) = x * a(z,u,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,32345,a(flip),b,33144,a),flip(a)].">
      <j1 rule="hyper" parents="60 32345 33144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33226">
    <literal><![CDATA[
      a(x,y,a(z,z,x * u)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32,a,32944,a(flip),b,33223,a),flip(a)].">
      <j1 rule="hyper" parents="32 32944 33223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33228">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ (x \ u)),x,z)) = a(x,y,x * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(32508,a,33191,a)].">
      <j1 rule="hyper" parents="32508 33191"/>
    </justification>
  </clause>

  <clause id="33229">
    <literal><![CDATA[
      a(x,y,x * ((x * z) \ u)) = a(x,y,x * (z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33190,a(flip),b,33228,a),flip(a)].">
      <j1 rule="hyper" parents="60 33190 33228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33230">
    <literal><![CDATA[
      (x * y) \ (L(x,y,y) * (R(y,y,x) * z)) = L(z,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(370,a,31582,a(flip),b,33198,a),flip(a)].">
      <j1 rule="hyper" parents="370 31582 33198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33231">
    <literal><![CDATA[
      L(x \ (y \ (L(y,x,x) * (R(x,x,y) * z))),x,y) = L(z,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(1198,a,33230,a)].">
      <j1 rule="hyper" parents="1198 33230"/>
    </justification>
  </clause>

  <clause id="33232">
    <literal><![CDATA[
      L(R(x,x,y) \ z,L(x,x,y),y) = (y * x) \ (L(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),33230(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 33230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33233">
    <literal><![CDATA[
      L(x \ (L(y,x,x) * (y \ (R(x,x,y) * z))),x,y) = L(z,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(2156(a,1),33231(a,1,1,2))].">
      <j1 rule="para" parents="2156 33231"/>
    </justification>
  </clause>

  <clause id="33234">
    <literal><![CDATA[
      L(x \ L(x * y,z,a(z,x,x)),x,z) = L(y,L(x,x,z),z)
    ]]></literal>
    <justification jstring="[para(33210(a,1),33233(a,1,1,2))].">
      <j1 rule="para" parents="33210 33233"/>
    </justification>
  </clause>

  <clause id="33235">
    <literal><![CDATA[
      L(x * L(x \ y,z,a(z,x,x)),x,z) = L(y,L(x,x,z),z)
    ]]></literal>
    <justification jstring="[para(3916(a,1),33234(a,1,1))].">
      <j1 rule="para" parents="3916 33234"/>
    </justification>
  </clause>

  <clause id="33236">
    <literal><![CDATA[
      L(L(x * (x \ y),x,a(z,z,x)),x,z) = L(y,L(x,x,z),z)
    ]]></literal>
    <justification jstring="[para(33021(a,2),33235(a,1,1))].">
      <j1 rule="para" parents="33021 33235"/>
    </justification>
  </clause>

  <clause id="33237">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),y,z) = L(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),33236(a,1,1,1))].">
      <j1 rule="para" parents="5 33236"/>
    </justification>
  </clause>

  <clause id="33238">
    <literal><![CDATA[
      L(x,L(y,y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(32757(a,1),33237(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32757 33237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33239">
    <literal><![CDATA[
      (x * y) \ (L(x,y,y) * z) = L(R(y,y,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,33232,a(flip),b,33238,a)].">
      <j1 rule="hyper" parents="60 33232 33238"/>
    </justification>
  </clause>

  <clause id="33240">
    <literal><![CDATA[
      a(x,y,L(R(z,z,u) \ w,z,u)) = a(x,y,(z \ u) \ (u * w))
    ]]></literal>
    <justification jstring="[para(33239(a,1),31680(a,1,3))].">
      <j1 rule="para" parents="33239 31680"/>
    </justification>
  </clause>

  <clause id="33241">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u) \ w,z,u)) = a(x,y,(z \ u) \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,33145,a(flip),b,33240,a)].">
      <j1 rule="hyper" parents="60 33145 33240"/>
    </justification>
  </clause>

  <clause id="33242">
    <literal><![CDATA[
      a(x,y,L(L(x,x,z) \ u,x,z)) = a(x,y,z \ (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32376,a(flip),b,33241,a),flip(a)].">
      <j1 rule="hyper" parents="370 32376 33241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33243">
    <literal><![CDATA[
      a(x,y,L(L(x,x,z) * u,x,z)) = a(x,y,z \ (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,32426,a(flip),b,33242,a)].">
      <j1 rule="hyper" parents="60 32426 33242"/>
    </justification>
  </clause>

  <clause id="33244">
    <literal><![CDATA[
      a(x \ y,z,L(L(x \ y,x \ y,y) * u,x \ y,y)) = a(x \ y,z,((x \ y) * (y * u)) / T(y,x \ (y * u)))
    ]]></literal>
    <justification jstring="[para(25809(a,2),33243(a,2,3))].">
      <j1 rule="para" parents="25809 33243"/>
    </justification>
  </clause>

  <clause id="33245">
    <literal><![CDATA[
      a((x \ y) * y,z,y \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,(x * y) * u) = w
    ]]></literal>
    <justification jstring="[para(32534(a,1),32537(a,1))].">
      <j1 rule="para" parents="32534 32537"/>
    </justification>
  </clause>

  <clause id="33246">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,a(w,v5,v6)) = L(z,y,x) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,32108,a(flip),b,32822,a),flip(a)].">
      <j1 rule="hyper" parents="60 32108 32822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33247">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,a(z,w,v5)) = L(L(x,u,a(z,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32633,a(flip),b,33246,a),flip(a)].">
      <j1 rule="hyper" parents="60 32633 33246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33250">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,z) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,33131,a(flip),b,33247,a),flip(a)].">
      <j1 rule="hyper" parents="60 33131 33247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33251">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,L(z,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(30067(a,1),33250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30067 33250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33252">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,w) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(30726(a,1),33250(a,1,1))].">
      <j1 rule="para" parents="30726 33250"/>
    </justification>
  </clause>

  <clause id="33253">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(32566(a,1),33250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32566 33250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33254">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(32757(a,1),33250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32757 33250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33255">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,z) = L(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[para(33009(a,1),33250(a,1,1))].">
      <j1 rule="para" parents="33009 33250"/>
    </justification>
  </clause>

  <clause id="33256">
    <literal><![CDATA[
      L(x \ y,x \ y,z) = L(x \ y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(31340,a,33253,a),flip(a)].">
      <j1 rule="hyper" parents="31340 33253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33257">
    <literal><![CDATA[
      L(x / y,y \ x,L(z,u,u)) = L(x / y,x / y,z)
    ]]></literal>
    <justification jstring="[hyper(26067,a,33253,a)].">
      <j1 rule="hyper" parents="26067 33253"/>
    </justification>
  </clause>

  <clause id="33258">
    <literal><![CDATA[
      L(x \ 1,x,L(y,z,z)) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3530,a,33253,a)].">
      <j1 rule="hyper" parents="3530 33253"/>
    </justification>
  </clause>

  <clause id="33260">
    <literal><![CDATA[
      L(1 / x,x,L(y,z,z)) = ((1 / x) * u) / (x * (L(x,x,y) \ u))
    ]]></literal>
    <justification jstring="[para(33253(a,1),4167(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="33253 4167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33262">
    <literal><![CDATA[
      L(L(x \ (y \ z),x * (y \ z),u),x,y) = L((y * x) \ z,x \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(33256(a,1),746(a,1,1))].">
      <j1 rule="para" parents="33256 746"/>
    </justification>
  </clause>

  <clause id="33263">
    <literal><![CDATA[
      a(x,y,L(z \ u,z * u,u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(33256(a,1),27248(a,1,3,1))].">
      <j1 rule="para" parents="33256 27248"/>
    </justification>
  </clause>

  <clause id="33264">
    <literal><![CDATA[
      ((x / L(y,z,a(u,w,v5))) * L(y,z,u)) \ (x * L(L(y,z,a(u,w,v5)),z,L(u,w,v5))) = L(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(33251(a,1),2477(a,1,1,2))].">
      <j1 rule="para" parents="33251 2477"/>
    </justification>
  </clause>

  <clause id="33265">
    <literal><![CDATA[
      x \ L(L(x,y,a(z,u,w)),y,w) = L(x \ L(x,y,w),u,z)
    ]]></literal>
    <justification jstring="[hyper(125,a,33252,a,b,32212,a)].">
      <j1 rule="hyper" parents="125 33252 32212"/>
    </justification>
  </clause>

  <clause id="33266">
    <literal><![CDATA[
      L(L(x,y,z),y,a(u,w,z)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,25,a,b,33252,a)].">
      <j1 rule="hyper" parents="60 25 33252"/>
    </justification>
  </clause>

  <clause id="33267">
    <literal><![CDATA[
      L(L(x,y,a(y * z,u,z)),u,y * z) = L(x,u,y \ z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29077,a(flip),b,33255,a),flip(a)].">
      <j1 rule="hyper" parents="370 29077 33255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33268">
    <literal><![CDATA[
      L(x \ 1,x,L(y,z,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,3401,a(flip),b,33258,a),flip(a)].">
      <j1 rule="hyper" parents="370 3401 33258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33269">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = (a(z,z,x) \ y) \ L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32838,a(flip),b,33268,a),flip(a)].">
      <j1 rule="hyper" parents="60 32838 33268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33271">
    <literal><![CDATA[
      L(x / y,y \ x,L(z,u,u)) = L(x / y,x / y,L(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,33253,a,b,33257,a),flip(a)].">
      <j1 rule="hyper" parents="370 33253 33257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33272">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(33011(a,1),33267(a,1,1))].">
      <j1 rule="para" parents="33011 33267"/>
    </justification>
  </clause>

  <clause id="33273">
    <literal><![CDATA[
      L(x,y,L(x,z,u) \ w) = L(x,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(28718(a,1),33272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28718 33272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33274">
    <literal><![CDATA[
      L(x,y,(R(x,z,u) \ x) \ (x * w)) = L(x,y,L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,32255,a,b,33273,a)].">
      <j1 rule="hyper" parents="60 32255 33273"/>
    </justification>
  </clause>

  <clause id="33275">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(y,x,x) = z \ y
    ]]></literal>
    <justification jstring="[hyper(797,a,33269,a),flip(a)].">
      <j1 rule="hyper" parents="797 33269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33277">
    <literal><![CDATA[
      (x * a(y,y,z)) \ z = x \ L(z,y,y)
    ]]></literal>
    <justification jstring="[para(23622(a,1),33275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23622 33275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33278">
    <literal><![CDATA[
      (x * a(y,y,z)) \ L(z,y,u) = x \ L(L(z,y,u),y,y)
    ]]></literal>
    <justification jstring="[para(31760(a,1),33277(a,1,1,2))].">
      <j1 rule="para" parents="31760 33277"/>
    </justification>
  </clause>

  <clause id="33279">
    <literal><![CDATA[
      L(x / y,y \ x,L(z,u,u)) = L(x / y,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31396,a(flip),b,33271,a),flip(a)].">
      <j1 rule="hyper" parents="370 31396 33271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33280">
    <literal><![CDATA[
      L(x / y,y \ x,z) = L(x / y,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(31578,a,33279,a)].">
      <j1 rule="hyper" parents="31578 33279"/>
    </justification>
  </clause>

  <clause id="33282">
    <literal><![CDATA[
      L(x / (y * x),x \ (y \ x),z) = L(x / (y * x),(y * x) * x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29726,a(flip),b,33280,a)].">
      <j1 rule="hyper" parents="60 29726 33280"/>
    </justification>
  </clause>

  <clause id="33283">
    <literal><![CDATA[
      L(x,y,(x * z) * (x \ R(x,u,w))) = L(x,y,L(x,u,w) * z)
    ]]></literal>
    <justification jstring="[para(30715(a,1),33274(a,1,3))].">
      <j1 rule="para" parents="30715 33274"/>
    </justification>
  </clause>

  <clause id="33284">
    <literal><![CDATA[
      L(x,y,x * (z * (x \ R(x,u,w)))) = L(x,y,L(x,u,w) * z)
    ]]></literal>
    <justification jstring="[para(28680(a,1),33283(a,1,3))].">
      <j1 rule="para" parents="28680 33283"/>
    </justification>
  </clause>

  <clause id="33285">
    <literal><![CDATA[
      L(x,y,x * (a(z,u,x) * w)) = L(x,y,L(x,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(32304,a,33284,a)].">
      <j1 rule="hyper" parents="32304 33284"/>
    </justification>
  </clause>

  <clause id="33286">
    <literal><![CDATA[
      L(x,y,x * (z * a(u,w,x))) = L(x,y,L(x,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(25950,a,33285,a)].">
      <j1 rule="hyper" parents="25950 33285"/>
    </justification>
  </clause>

  <clause id="33287">
    <literal><![CDATA[
      L(1 / x,x,L(y,z,z)) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4167,a(flip),b,33260,a),flip(a)].">
      <j1 rule="hyper" parents="370 4167 33260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33289">
    <literal><![CDATA[
      L(x,y,y) * L(1 / z,z,x) = L(x,y,y) / z
    ]]></literal>
    <justification jstring="[hyper(129,a,33287,a(flip),b,3417,a(flip))].">
      <j1 rule="hyper" parents="129 33287 3417"/>
    </justification>
  </clause>

  <clause id="33290">
    <literal><![CDATA[
      a(x,x,y) \ (y / z) = L(y,x,x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,32839,a(flip),b,33289,a)].">
      <j1 rule="hyper" parents="60 32839 33289"/>
    </justification>
  </clause>

  <clause id="33291">
    <literal><![CDATA[
      (L(x,y,y) / z) * a(y,y,x) = x / z
    ]]></literal>
    <justification jstring="[hyper(23635,a,33290,a)].">
      <j1 rule="hyper" parents="23635 33290"/>
    </justification>
  </clause>

  <clause id="33292">
    <literal><![CDATA[
      L(x,y,y) \ (L(x,y,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(125,a,33290,a(flip),b,32762,a)].">
      <j1 rule="hyper" parents="125 33290 32762"/>
    </justification>
  </clause>

  <clause id="33293">
    <literal><![CDATA[
      (L(x,y,y) * z) \ L(x,y,y) = ((x \ (x / z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(33292(a,1),3501(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33292 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33294">
    <literal><![CDATA[
      (L(x,y,y) * z) \ L(x,y,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,3501,a(flip),b,33293,a),flip(a)].">
      <j1 rule="hyper" parents="370 3501 33293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33295">
    <literal><![CDATA[
      (((1 / x) * y) * z) \ L(x \ y,x,x) = ((x \ y) * z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(586(a,1),33294(a,1,1,1))].">
      <j1 rule="para" parents="586 33294"/>
    </justification>
  </clause>

  <clause id="33296">
    <literal><![CDATA[
      (((1 / x) * y) * z) \ ((1 / x) * y) = ((x \ y) * z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(586(a,1),33295(a,1,2))].">
      <j1 rule="para" parents="586 33295"/>
    </justification>
  </clause>

  <clause id="33297">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ y) = ((x * y) * z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(4290,a,33296,a),flip(a)].">
      <j1 rule="hyper" parents="4290 33296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33298">
    <literal><![CDATA[
      L(x / (y * x),x \ (y \ x),z) = L(x / (y * x),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26264,a(flip),b,33282,a),flip(a)].">
      <j1 rule="hyper" parents="370 26264 33282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33299">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ ((y * (z / (x \ 1))) * x)) = a(y,z * x,L(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(1382,a,32921,a)].">
      <j1 rule="hyper" parents="1382 32921"/>
    </justification>
  </clause>

  <clause id="33300">
    <literal><![CDATA[
      a(x,y * z,L(z,z,y)) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(26832,a,33299,a),flip(a)].">
      <j1 rule="hyper" parents="26832 33299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33301">
    <literal><![CDATA[
      a(x,y \ z,y) = a(x,z * y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,32652,a(flip),b,33300,a),flip(a)].">
      <j1 rule="hyper" parents="60 32652 33300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33302">
    <literal><![CDATA[
      a(x,y \ z,z) = a(x,y * z,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33071,a,b,33301,a)].">
      <j1 rule="hyper" parents="60 33071 33301"/>
    </justification>
  </clause>

  <clause id="33303">
    <literal><![CDATA[
      a(x,y \ z,L(y \ z,y,z) * u) = a(x,y \ z,((1 / z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(3116,a,32474,a),flip(a)].">
      <j1 rule="hyper" parents="3116 32474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33304">
    <literal><![CDATA[
      a(x,y \ z,L(y \ z,y,z) * u) = a(x,y \ z,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3153,a(flip),b,33303,a),flip(a)].">
      <j1 rule="hyper" parents="370 3153 33303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33305">
    <literal><![CDATA[
      a(x,y \ z,(z * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(33304(a,1),27175(a,1))].">
      <j1 rule="para" parents="33304 27175"/>
    </justification>
  </clause>

  <clause id="33306">
    <literal><![CDATA[
      a(x \ y,z,L(x \ y,x,y) * u) = a(x \ y,z,((1 / y) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(3116,a,32476,a),flip(a)].">
      <j1 rule="hyper" parents="3116 32476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33307">
    <literal><![CDATA[
      a(x \ y,z,L(x \ y,x,y) * u) = a(x \ y,z,(y * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3153,a(flip),b,33306,a),flip(a)].">
      <j1 rule="hyper" parents="370 3153 33306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33308">
    <literal><![CDATA[
      a(x \ y,z,(y * x) \ u) = a(x \ y,z,(y * x) * u)
    ]]></literal>
    <justification jstring="[hyper(27175,a,33307,a),flip(a)].">
      <j1 rule="hyper" parents="27175 33307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33309">
    <literal><![CDATA[
      a(x \ y,z,(y * x) * u) = a(x * y,z,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(32438,a,33308,a),flip(a)].">
      <j1 rule="hyper" parents="32438 33308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33310">
    <literal><![CDATA[
      a(R(x \ 1,y,z) \ x,u,(x * R(x \ 1,y,z)) * w) = a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w))
    ]]></literal>
    <justification jstring="[para(959(a,1),33309(a,2,1))].">
      <j1 rule="para" parents="959 33309"/>
    </justification>
  </clause>

  <clause id="33311">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a((x \ T(y,x \ 1)) \ (x \ 1),z,(x \ (y * (1 / x))) * u)
    ]]></literal>
    <justification jstring="[para(4453(a,1),33309(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4453 33309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33312">
    <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(32493(a,1),32422(a,1))].">
      <j1 rule="para" parents="32493 32422"/>
    </justification>
  </clause>

  <clause id="33313">
    <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(370,a,30079,a(flip),b,32796,a),flip(a)].">
      <j1 rule="hyper" parents="370 30079 32796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33314">
    <literal><![CDATA[
      ((L(x,y,z) * (R(z,y,x) * u)) / u) \ (x * z) = a(L(x,y,z),L(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(370,a,30079,a(flip),b,32798,a),flip(a)].">
      <j1 rule="hyper" parents="370 30079 32798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33315">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) * (((z * u) \ 1) \ w)) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,30368,a(flip),b,32853,a),flip(a)].">
      <j1 rule="hyper" parents="60 30368 32853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33316">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * ((z \ u) \ 1)) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(26936,a,33315,a)].">
      <j1 rule="hyper" parents="26936 33315"/>
    </justification>
  </clause>

  <clause id="33317">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (z \ u)) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(26994,a,33316,a)].">
      <j1 rule="hyper" parents="26994 33316"/>
    </justification>
  </clause>

  <clause id="33318">
    <literal><![CDATA[
      L((x * y) \ z,y \ (x \ z),u) = L((x * y) \ z,y * (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(60,a,746,a(flip),b,33262,a),flip(a)].">
      <j1 rule="hyper" parents="60 746 33262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33319">
    <literal><![CDATA[
      (L(x,x,y) * (R(y,x,x) * z)) \ ((x * y) * z) = a(x,L(y,x,x),L(z,x,y * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32415,a,b,33313,a),flip(a)].">
      <j1 rule="hyper" parents="370 32415 33313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33320">
    <literal><![CDATA[
      ((L(x,y,y) * (R(y,y,x) * z)) / z) \ (x * y) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31462,a(flip),b,33314,a),flip(a)].">
      <j1 rule="hyper" parents="370 31462 33314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33321">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (x * y) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(32847(a,1),33320(a,1,1,1))].">
      <j1 rule="para" parents="32847 33320"/>
    </justification>
  </clause>

  <clause id="33322">
    <literal><![CDATA[
      a(x,L(y,y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(25782,a,33321,a),flip(a)].">
      <j1 rule="hyper" parents="25782 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33323">
    <literal><![CDATA[
      a(x * y,L(y,y,x),z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26752,a(flip),b,33322,a)].">
      <j1 rule="hyper" parents="60 26752 33322"/>
    </justification>
  </clause>

  <clause id="33324">
    <literal><![CDATA[
      a(x,y \ x,z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,4094,a(flip),b,33322,a),flip(a)].">
      <j1 rule="hyper" parents="60 4094 33322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33325">
    <literal><![CDATA[
      a((x \ y) \ x,z,(x \ (y \ 1)) \ u) = a(y,z,(y \ 1) \ (x * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),32439(a,2,1))].">
      <j1 rule="para" parents="5 32439"/>
    </justification>
  </clause>

  <clause id="33326">
    <literal><![CDATA[
      a((x \ y) \ x,z,(x \ (y \ 1)) \ u) = a(y,z,1 \ (y * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32376,a(flip),b,33325,a),flip(a)].">
      <j1 rule="hyper" parents="370 32376 33325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33327">
    <literal><![CDATA[
      a((x \ y) \ x,z,(x \ (y \ 1)) \ u) = a(y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[para(62(a,1),33326(a,2,3))].">
      <j1 rule="para" parents="62 33326"/>
    </justification>
  </clause>

  <clause id="33328">
    <literal><![CDATA[
      a((x \ y) \ x,z,(x \ y) \ u) = a(y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(3122,a,33327,a)].">
      <j1 rule="hyper" parents="3122 33327"/>
    </justification>
  </clause>

  <clause id="33329">
    <literal><![CDATA[
      a(x * (x \ y),z,(x \ y) * u) = a(y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(32435,a,33328,a)].">
      <j1 rule="hyper" parents="32435 33328"/>
    </justification>
  </clause>

  <clause id="33330">
    <literal><![CDATA[
      a(x,y,(z \ x) * u) = a(x,y,x * (z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),33329(a,1,1))].">
      <j1 rule="para" parents="5 33329"/>
    </justification>
  </clause>

  <clause id="33331">
    <literal><![CDATA[
      a(x,y,z * (u \ x)) = a(x,y,x * (u * z))
    ]]></literal>
    <justification jstring="[hyper(26965,a,33330,a)].">
      <j1 rule="hyper" parents="26965 33330"/>
    </justification>
  </clause>

  <clause id="33332">
    <literal><![CDATA[
      a(x,y,(x \ (z \ x)) * u) = a(x,y,x * ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27238,a(flip),b,33330,a)].">
      <j1 rule="hyper" parents="60 27238 33330"/>
    </justification>
  </clause>

  <clause id="33333">
    <literal><![CDATA[
      a(x,y,x * (z * u)) * x = R(x,y,(z \ x) * u)
    ]]></literal>
    <justification jstring="[para(33330(a,1),32597(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33330 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33334">
    <literal><![CDATA[
      a(x,y,(z * u) * x) = a(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,33331,a)].">
      <j1 rule="hyper" parents="370 26888 33331"/>
    </justification>
  </clause>

  <clause id="33335">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,z)) = a(x,y,a(z,v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(33331(a,2),31136(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33331 31136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33336">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) = a(v5,y,a(x,w,x * (u * z)))
    ]]></literal>
    <justification jstring="[para(33331(a,1),32938(a,2,3))].">
      <j1 rule="para" parents="33331 32938"/>
    </justification>
  </clause>

  <clause id="33337">
    <literal><![CDATA[
      a(a((x * y) * z,u,z),w,v5) = a(a(z,u,y * (x \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(33334(a,1),30796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33334 30796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33338">
    <literal><![CDATA[
      a(x,y,z * (u \ x)) * x = R(x,y,(u * z) * x)
    ]]></literal>
    <justification jstring="[para(33334(a,1),32597(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33334 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33339">
    <literal><![CDATA[
      R(x,y,(z \ x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(33333(a,1),32754(a,1))].">
      <j1 rule="para" parents="33333 32754"/>
    </justification>
  </clause>

  <clause id="33340">
    <literal><![CDATA[
      R(x,y,(z * u) * x) = R(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(32754,a,33338,a),flip(a)].">
      <j1 rule="hyper" parents="32754 33338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33341">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,z,u * (w \ y))) = a(x * (y \ x),z,(w * u) * y)
    ]]></literal>
    <justification jstring="[para(33340(a,1),32691(a,1,2,2))].">
      <j1 rule="para" parents="33340 32691"/>
    </justification>
  </clause>

  <clause id="33342">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ z))) = a(x,y,a(z,u,z * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(31150,a,33335,a),flip(a)].">
      <j1 rule="hyper" parents="31150 33335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33343">
    <literal><![CDATA[
      a(a(x,y,z * (u \ x)),w,v5) = a((u * z) * x,y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(33022,a,33337,a),flip(a)].">
      <j1 rule="hyper" parents="33022 33337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33344">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,z)) = a(z,u,a(w,v5,y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(33022,a,33343,a),flip(a)].">
      <j1 rule="hyper" parents="33022 33343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33345">
    <literal><![CDATA[
      a(x,y,a(x * (z * u),w,v5)) = a(x,w,a(v5,y,u * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(33027,a,33344,a)].">
      <j1 rule="hyper" parents="33027 33344"/>
    </justification>
  </clause>

  <clause id="33346">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ x))) = a(x,u,a(z,y,x * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(31148,a,33345,a),flip(a)].">
      <j1 rule="hyper" parents="31148 33345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33347">
    <literal><![CDATA[
      a(x * (y \ x),z,(u * w) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (y \ x),z,w * (u \ y)) = v5
    ]]></literal>
    <justification jstring="[para(33341(a,1),32807(a,1))].">
      <j1 rule="para" parents="33341 32807"/>
    </justification>
  </clause>

  <clause id="33348">
    <literal><![CDATA[
      a(x,T(a(y,y,z) * (u * z),w) * v5,v6) = a(x,(u * (z * a(y,y,z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28210(a,2),32878(a,1,2,1))].">
      <j1 rule="para" parents="28210 32878"/>
    </justification>
  </clause>

  <clause id="33349">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,y))) * a(u,y,a(L(z,y,y),x,w)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[para(32241(a,1),33116(a,1,1))].">
      <j1 rule="para" parents="32241 33116"/>
    </justification>
  </clause>

  <clause id="33350">
    <literal><![CDATA[
      a(x,y,L((z * x) * L(u,x,z),u,u)) = a(x,y,x * (u \ (x \ T(z * x,u))))
    ]]></literal>
    <justification jstring="[hyper(31716,a,33182,a)].">
      <j1 rule="hyper" parents="31716 33182"/>
    </justification>
  </clause>

  <clause id="33351">
    <literal><![CDATA[
      a(x,(y * (z * a(u,u,z))) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,(a(u,u,z) * (y * z)) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(33348(a,1),26567(a,1))].">
      <j1 rule="para" parents="33348 26567"/>
    </justification>
  </clause>

  <clause id="33352">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,u,a(L(w,u,u),z,x)) = a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(32959(a,1),33349(a,1,1))].">
      <j1 rule="para" parents="32959 33349"/>
    </justification>
  </clause>

  <clause id="33353">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,u,a(w,z,L(x,u,u))) = a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(32241(a,1),33352(a,1,2))].">
      <j1 rule="para" parents="32241 33352"/>
    </justification>
  </clause>

  <clause id="33354">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,z,a(y,u,w)) = a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(32959(a,1),33353(a,1,2))].">
      <j1 rule="para" parents="32959 33353"/>
    </justification>
  </clause>

  <clause id="33355">
    <literal><![CDATA[
      (a(x,x,a(x,y,a(z,u,w))) / x) \ a(y,a(x,u,w),z) = x * (a(x,z,a(y,u,w)) * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(33354(a,1),29849(a,1,2))].">
      <j1 rule="para" parents="33354 29849"/>
    </justification>
  </clause>

  <clause id="33356">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,a(v5,v6,v6)))) * a(x,z,a(y,u,L(w,x,a(v5,v6,v6)))) = a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(32590(a,1),33354(a,2,2))].">
      <j1 rule="para" parents="32590 33354"/>
    </justification>
  </clause>

  <clause id="33357">
    <literal><![CDATA[
      a(x,y,L(z * (x * u),u,u)) = a(x,y,x * (u \ (x \ T(z * x,u))))
    ]]></literal>
    <justification jstring="[para(92(a,1),33350(a,1,3,1))].">
      <j1 rule="para" parents="92 33350"/>
    </justification>
  </clause>

  <clause id="33358">
    <literal><![CDATA[
      a(x,y,L(z * (x * u),u,u)) = a(x,y,(u \ (x \ (z * x))) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,27262,a(flip),b,33357,a),flip(a)].">
      <j1 rule="hyper" parents="370 27262 33357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33360">
    <literal><![CDATA[
      a(x,y,L(z * (x * u),u,u)) = a(x,y,(u \ T(z,x)) * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),33358(a,2,3,1,2))].">
      <j1 rule="para" parents="17 33358"/>
    </justification>
  </clause>

  <clause id="33361">
    <literal><![CDATA[
      a(x,y,L(z * (x * u),u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ z) * x) = w
    ]]></literal>
    <justification jstring="[para(33360(a,2),27007(a,1))].">
      <j1 rule="para" parents="33360 27007"/>
    </justification>
  </clause>

  <clause id="33362">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,y,x)) = a(z * (x * y),u,(1 / (x * (1 / y))) * x)
    ]]></literal>
    <justification jstring="[para(33222(a,1),32434(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33222 32434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33363">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,y,x)) = a(z * (x * y),u,(x * (1 / y)) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3079,a(flip),b,33362,a),flip(a)].">
      <j1 rule="hyper" parents="370 3079 33362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33364">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,y,x)) = a(z * (x * y),u,L(1 / y,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26929,a(flip),b,33363,a),flip(a)].">
      <j1 rule="hyper" parents="370 26929 33363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33365">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,y,x)) = a(z * (x * y),u,L(y \ 1,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26921,a(flip),b,33364,a),flip(a)].">
      <j1 rule="hyper" parents="370 26921 33364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33366">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,y,x)) = a(z * (x * y),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,15787,a(flip),b,33365,a),flip(a)].">
      <j1 rule="hyper" parents="370 15787 33365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33367">
    <literal><![CDATA[
      a(x * (y * z),u,L(z,y,y)) = a(z \ (y \ x),u,z)
    ]]></literal>
    <justification jstring="[hyper(32422,a,33366,a),flip(a)].">
      <j1 rule="hyper" parents="32422 33366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33368">
    <literal><![CDATA[
      a(x * (y * z),u,L(z,y,y)) = a((y \ x) * z,u,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31445,a(flip),b,33367,a),flip(a)].">
      <j1 rule="hyper" parents="370 31445 33367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33370">
    <literal><![CDATA[
      a(x,y,z \ L(L(u,L(z,x,x),L(z,x,x)),x,x)) = a(x,y,L(z,x,x) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,3109,a(flip),b,32512,a),flip(a)].">
      <j1 rule="hyper" parents="370 3109 32512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33371">
    <literal><![CDATA[
      a(x,y,z \ L(L(u,z,z),x,x)) = a(x,y,L(z,x,x) * u)
    ]]></literal>
    <justification jstring="[para(29547(a,1),33370(a,1,3,2,1))].">
      <j1 rule="para" parents="29547 33370"/>
    </justification>
  </clause>

  <clause id="33372">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(u,x,x)) = a(x,y,L(z,x,x) * u)
    ]]></literal>
    <justification jstring="[para(2085(a,1),33371(a,1,3))].">
      <j1 rule="para" parents="2085 33371"/>
    </justification>
  </clause>

  <clause id="33374">
    <literal><![CDATA[
      a(x,y,L(z,x,x) * u) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(27068,a,33372,a),flip(a)].">
      <j1 rule="hyper" parents="27068 33372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33375">
    <literal><![CDATA[
      a(x * (y \ x),z,u * L(y \ x,x * (y \ x),x * (y \ x))) = a(y,z,x \ (y * L(u,x * (y \ x),x * (y \ x))))
    ]]></literal>
    <justification jstring="[hyper(60,a,32553,a(flip),b,33374,a),flip(a)].">
      <j1 rule="hyper" parents="60 32553 33374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33376">
    <literal><![CDATA[
      L(L(x,y,z) * (a(u,u,w) \ 1),x,x) = a(u,u,w) \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,30626,a(flip),b,32859,a),flip(a)].">
      <j1 rule="hyper" parents="370 30626 32859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33377">
    <literal><![CDATA[
      L(L(x,y,z) * (a(u,u,w) \ 1),x,x) = (L(x,y,z) \ a(u,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(370,a,32899,a(flip),b,33376,a),flip(a)].">
      <j1 rule="hyper" parents="370 32899 33376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33378">
    <literal><![CDATA[
      L(a(x,x,y) \ L(z,u,w),z,z) = (L(z,u,w) \ a(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(30626(a,1),33377(a,1,1))].">
      <j1 rule="para" parents="30626 33377"/>
    </justification>
  </clause>

  <clause id="33379">
    <literal><![CDATA[
      (x / L(y,z,a(z,u,w))) * L(y,z,z) = x * L(x \ (a(z,z,y) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(32154(a,1),32897(a,1,1))].">
      <j1 rule="para" parents="32154 32897"/>
    </justification>
  </clause>

  <clause id="33380">
    <literal><![CDATA[
      (x / L(y,z,a(z,u,w))) * L(y,z,z) = x * L(a(z,z,y) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(30620(a,1),33379(a,2,2,1))].">
      <j1 rule="para" parents="30620 33379"/>
    </justification>
  </clause>

  <clause id="33381">
    <literal><![CDATA[
      (x / L(y,z,a(z,u,w))) * L(y,z,z) = a(z,z,L(y,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,32343,a(flip),b,33380,a),flip(a)].">
      <j1 rule="hyper" parents="370 32343 33380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33383">
    <literal><![CDATA[
      a(x,x,R(y,z,y) * a(u,y,z)) = a(x,x,u * (z \ (T(y * z,y) * u)))
    ]]></literal>
    <justification jstring="[para(15012(a,1),33066(a,1,3,2))].">
      <j1 rule="para" parents="15012 33066"/>
    </justification>
  </clause>

  <clause id="33384">
    <literal><![CDATA[
      a(x,x,L(y,z,y) * a(u,y,z)) = a(x,x,u * (z \ (T(y * z,y) * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,28605,a(flip),b,33383,a)].">
      <j1 rule="hyper" parents="60 28605 33383"/>
    </justification>
  </clause>

  <clause id="33386">
    <literal><![CDATA[
      a(x,x,y * (z \ (T(u * z,u) * y))) = a(x,x,u * a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(27108,a,33384,a),flip(a)].">
      <j1 rule="hyper" parents="27108 33384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33388">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,z * (u \ ((y * u) * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27135,a(flip),b,33386,a),flip(a)].">
      <j1 rule="hyper" parents="60 27135 33386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33390">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (a(x,x,L(y,z,u)) * u) = R(u,z * y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(32342(a,1),33209(a,1,2))].">
      <j1 rule="para" parents="32342 33209"/>
    </justification>
  </clause>

  <clause id="33391">
    <literal><![CDATA[
      a(x,x,y) \ (a(x,x,L(y,z,u)) * u) = R(u,z * y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(30701,a,33390,a)].">
      <j1 rule="hyper" parents="30701 33390"/>
    </justification>
  </clause>

  <clause id="33392">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (a(x,x,y) \ u) = R(u,z * y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(60,a,33056,a(flip),b,33391,a)].">
      <j1 rule="hyper" parents="60 33056 33391"/>
    </justification>
  </clause>

  <clause id="33393">
    <literal><![CDATA[
      R(x,y * z,a(u,u,z) \ 1) = x * a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32345,a(flip),b,33392,a),flip(a)].">
      <j1 rule="hyper" parents="60 32345 33392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33394">
    <literal><![CDATA[
      R(x,y * z,a(u,u,z) \ 1) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32077,a(flip),b,33393,a),flip(a)].">
      <j1 rule="hyper" parents="370 32077 33393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33395">
    <literal><![CDATA[
      R(x,y * z,a(u,u,z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(2741,a,33394,a)].">
      <j1 rule="hyper" parents="2741 33394"/>
    </justification>
  </clause>

  <clause id="33396">
    <literal><![CDATA[
      L(x,y * z,a(u,u,z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(28340,a,33395,a)].">
      <j1 rule="hyper" parents="28340 33395"/>
    </justification>
  </clause>

  <clause id="33397">
    <literal><![CDATA[
      L(x,y,a(z,u * z,y)) = L(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(33020,a,33396,a)].">
      <j1 rule="hyper" parents="33020 33396"/>
    </justification>
  </clause>

  <clause id="33398">
    <literal><![CDATA[
      a(x,L(y,x,x),L(z,x,y * x)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(32885(a,1),33319(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32885 33319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33399">
    <literal><![CDATA[
      a(x,L(y,x,x),L(z,x,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,9,a,b,33398,a),flip(a)].">
      <j1 rule="hyper" parents="370 9 33398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33400">
    <literal><![CDATA[
      a(x,L(y,x,x),L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32465,a,33399,a)].">
      <j1 rule="hyper" parents="32465 33399"/>
    </justification>
  </clause>

  <clause id="33401">
    <literal><![CDATA[
      a(x,L(y,x,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32810,a,33400,a)].">
      <j1 rule="hyper" parents="32810 33400"/>
    </justification>
  </clause>

  <clause id="33402">
    <literal><![CDATA[
      a(x,x \ y,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(26593,a,33401,a),flip(a)].">
      <j1 rule="hyper" parents="26593 33401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33403">
    <literal><![CDATA[
      a(x,x \ y,z) = a(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,29042,a(flip),b,33401,a)].">
      <j1 rule="hyper" parents="60 29042 33401"/>
    </justification>
  </clause>

  <clause id="33404">
    <literal><![CDATA[
      a(x * y,(1 / (x * y)) * (x * (y * z)),u) = a(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(590(a,1),33401(a,1,2))].">
      <j1 rule="para" parents="590 33401"/>
    </justification>
  </clause>

  <clause id="33405">
    <literal><![CDATA[
      R(x,L(y,x,x),z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(33401(a,1),32597(a,2,1))].">
      <j1 rule="para" parents="33401 32597"/>
    </justification>
  </clause>

  <clause id="33406">
    <literal><![CDATA[
      a(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y * x,z) = u
    ]]></literal>
    <justification jstring="[para(33402(a,2),26564(a,1))].">
      <j1 rule="para" parents="33402 26564"/>
    </justification>
  </clause>

  <clause id="33407">
    <literal><![CDATA[
      a(x,x * y,z) \ L(z,z,a(u,u * w,w)) = L(z,x \ y,x)
    ]]></literal>
    <justification jstring="[para(33402(a,1),33136(a,1,1))].">
      <j1 rule="para" parents="33402 33136"/>
    </justification>
  </clause>

  <clause id="33408">
    <literal><![CDATA[
      a(x,y \ x,z) = a(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33324,a,b,33403,a)].">
      <j1 rule="hyper" parents="60 33324 33403"/>
    </justification>
  </clause>

  <clause id="33409">
    <literal><![CDATA[
      (a(x,y * x,z) \ y) * z = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(33403(a,1),25783(a,1,1,1))].">
      <j1 rule="para" parents="33403 25783"/>
    </justification>
  </clause>

  <clause id="33410">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) \ (u \ (w * z))) = a(x,y,a(u,w * u,z))
    ]]></literal>
    <justification jstring="[para(33403(a,1),28865(a,2,3))].">
      <j1 rule="para" parents="33403 28865"/>
    </justification>
  </clause>

  <clause id="33411">
    <literal><![CDATA[
      a(x,(y \ x) * x,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26560,a,33408,a),flip(a)].">
      <j1 rule="hyper" parents="26560 33408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33412">
    <literal><![CDATA[
      L(x,(y * (z \ y)) * z,u) = L(x,a(y,z * y,z),u)
    ]]></literal>
    <justification jstring="[para(33408(a,1),26695(a,2,2))].">
      <j1 rule="para" parents="33408 26695"/>
    </justification>
  </clause>

  <clause id="33413">
    <literal><![CDATA[
      a(x,y * x,z) * x = R(x,y \ x,z)
    ]]></literal>
    <justification jstring="[para(33408(a,1),32597(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33408 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33414">
    <literal><![CDATA[
      a(x,x * (y \ x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26564,a,33411,a)].">
      <j1 rule="hyper" parents="26564 33411"/>
    </justification>
  </clause>

  <clause id="33415">
    <literal><![CDATA[
      R(x,L(y,x,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32597,a,b,33405,a),flip(a)].">
      <j1 rule="hyper" parents="370 32597 33405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33416">
    <literal><![CDATA[
      R(x,y * ((x \ y) \ y),z) = R(x,y / x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31626,a(flip),b,33415,a)].">
      <j1 rule="hyper" parents="60 31626 33415"/>
    </justification>
  </clause>

  <clause id="33417">
    <literal><![CDATA[
      R(x,y \ x,z) = R(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(32754,a,33413,a),flip(a)].">
      <j1 rule="hyper" parents="32754 33413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33418">
    <literal><![CDATA[
      R(x,y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y * x,z) = u
    ]]></literal>
    <justification jstring="[para(33413(a,1),32754(a,1))].">
      <j1 rule="para" parents="33413 32754"/>
    </justification>
  </clause>

  <clause id="33420">
    <literal><![CDATA[
      R(x,(y \ x) * x,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27387,a(flip),b,33417,a),flip(a)].">
      <j1 rule="hyper" parents="60 27387 33417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33421">
    <literal><![CDATA[
      R(x,y * x,z * (y \ x)) * z = (x * (y \ x)) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(33417(a,1),32523(a,1,1))].">
      <j1 rule="para" parents="33417 32523"/>
    </justification>
  </clause>

  <clause id="33422">
    <literal><![CDATA[
      R(x,y * ((x \ y) \ y),z) = R(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,27386,a(flip),b,33416,a),flip(a)].">
      <j1 rule="hyper" parents="370 27386 33416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33423">
    <literal><![CDATA[
      R(x,x \ y,z) = R(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27427,a(flip),b,33422,a),flip(a)].">
      <j1 rule="hyper" parents="60 27427 33422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33424">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) * z) = R(x,y * x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(32522,a,33423,a)].">
      <j1 rule="hyper" parents="32522 33423"/>
    </justification>
  </clause>

  <clause id="33426">
    <literal><![CDATA[
      (x / (x * y)) * ((x * y) * z) = y * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33147,a(flip),b,33409,a)].">
      <j1 rule="hyper" parents="60 33147 33409"/>
    </justification>
  </clause>

  <clause id="33427">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = (y / (y * T(x,u))) * ((y * T(x,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,25573,a(flip),b,33426,a)].">
      <j1 rule="hyper" parents="370 25573 33426"/>
    </justification>
  </clause>

  <clause id="33428">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) * z) = R(x,y * x,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33104,a(flip),b,33424,a),flip(a)].">
      <j1 rule="hyper" parents="370 33104 33424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33429">
    <literal><![CDATA[
      R(x,y * x,y * (x * z)) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,32519,a(flip),b,33428,a),flip(a)].">
      <j1 rule="hyper" parents="60 32519 33428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33430">
    <literal><![CDATA[
      R(x,(y \ x) * x,x * (y * (x * z))) = ((y \ x) * ((x \ (y \ x)) \ z)) / z
    ]]></literal>
    <justification jstring="[hyper(33339,a,33429,a)].">
      <j1 rule="hyper" parents="33339 33429"/>
    </justification>
  </clause>

  <clause id="33431">
    <literal><![CDATA[
      L(x,y \ z,y) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(33137,a,33407,a),flip(a)].">
      <j1 rule="hyper" parents="33137 33407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33433">
    <literal><![CDATA[
      L(x,y \ z,y) = L(x,z * y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26023,a,b,33431,a),flip(a)].">
      <j1 rule="hyper" parents="370 26023 33431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33435">
    <literal><![CDATA[
      a(L((x \ L(y,z,y)) \ u,x * y,x),w,v5) = a(y \ (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(33431(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="33431 14833"/>
    </justification>
  </clause>

  <clause id="33436">
    <literal><![CDATA[
      a(x,y,L(z \ u,w * z,w)) = a(x,y,(w \ z) \ (w \ u))
    ]]></literal>
    <justification jstring="[para(33431(a,1),29049(a,1,3))].">
      <j1 rule="para" parents="33431 29049"/>
    </justification>
  </clause>

  <clause id="33437">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,w),x * y,x) = x \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(33431(a,1),29269(a,1,2))].">
      <j1 rule="para" parents="33431 29269"/>
    </justification>
  </clause>

  <clause id="33438">
    <literal><![CDATA[
      a(L(x,y * x,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33431(a,1),31874(a,1,1))].">
      <j1 rule="para" parents="33431 31874"/>
    </justification>
  </clause>

  <clause id="33439">
    <literal><![CDATA[
      x * L(y,x * z,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(129,a,33433,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="129 33433 93"/>
    </justification>
  </clause>

  <clause id="33440">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,((1 / x) \ y) * (x * y),x * y) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(28731(a,1),33439(a,2,2,1))].">
      <j1 rule="para" parents="28731 33439"/>
    </justification>
  </clause>

  <clause id="33441">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * L(z,(x * ((y \ x) \ 1)) * y,y) = y * ((x \ (y * (1 / (x \ y)))) * z)
    ]]></literal>
    <justification jstring="[para(31892(a,1),33439(a,2,2,1))].">
      <j1 rule="para" parents="31892 33439"/>
    </justification>
  </clause>

  <clause id="33442">
    <literal><![CDATA[
      a(x,y,L(z,u * x,u)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(32429,a,33438,a)].">
      <j1 rule="hyper" parents="32429 33438"/>
    </justification>
  </clause>

  <clause id="33443">
    <literal><![CDATA[
      a((x \ y) * y,z,L(u,x,y)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,33078,a(flip),b,33442,a),flip(a)].">
      <j1 rule="hyper" parents="60 33078 33442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33444">
    <literal><![CDATA[
      a((x \ y) * y,z,L(u,x,y)) = L(a(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(32595(a,2),33443(a,2,1))].">
      <j1 rule="para" parents="32595 33443"/>
    </justification>
  </clause>

  <clause id="33445">
    <literal><![CDATA[
      a((x \ y) * y,z,L(u,x,y)) = a(x,z,L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,32313,a,b,33444,a),flip(a)].">
      <j1 rule="hyper" parents="370 32313 33444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33446">
    <literal><![CDATA[
      a((x \ y) * y,z,(y * x) \ (y * u)) = a(x,z,L(x \ u,y,y))
    ]]></literal>
    <justification jstring="[para(94(a,1),33445(a,1,3))].">
      <j1 rule="para" parents="94 33445"/>
    </justification>
  </clause>

  <clause id="33447">
    <literal><![CDATA[
      a((x \ (y * x)) * (y * x),z,y \ (((x \ 1) \ y) * u)) = a(x,z,L(T(x \ 1,x * y) \ u,y * x,y * x))
    ]]></literal>
    <justification jstring="[para(31633(a,1),33445(a,1,3))].">
      <j1 rule="para" parents="31633 33445"/>
    </justification>
  </clause>

  <clause id="33448">
    <literal><![CDATA[
      a((x \ y) * y,z,x \ u) = a(x,z,(y \ x) \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33442,a(flip),b,33436,a)].">
      <j1 rule="hyper" parents="60 33442 33436"/>
    </justification>
  </clause>

  <clause id="33449">
    <literal><![CDATA[
      (x \ y) * a(z,u,L(w,x * y,x)) = x \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32313(a,2),33437(a,1,2))].">
      <j1 rule="para" parents="32313 33437"/>
    </justification>
  </clause>

  <clause id="33450">
    <literal><![CDATA[
      a((x \ y) * y,z,y \ (x \ (y * u))) = a(x,z,L(x \ u,y,y))
    ]]></literal>
    <justification jstring="[hyper(32502,a,33446,a)].">
      <j1 rule="hyper" parents="32502 33446"/>
    </justification>
  </clause>

  <clause id="33451">
    <literal><![CDATA[
      a(x,y,(x * z) * (z * u)) = a(x,y,L(x \ u,z,z))
    ]]></literal>
    <justification jstring="[hyper(33245,a,33450,a)].">
      <j1 rule="hyper" parents="33245 33450"/>
    </justification>
  </clause>

  <clause id="33452">
    <literal><![CDATA[
      a(x,y,(x * z) * (z * u)) = a(x,y,L(u * x,z,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33150,a(flip),b,33451,a),flip(a)].">
      <j1 rule="hyper" parents="370 33150 33451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33453">
    <literal><![CDATA[
      a(x,y,L(z * x,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * (x * u)) = w
    ]]></literal>
    <justification jstring="[para(33452(a,1),27041(a,1))].">
      <j1 rule="para" parents="33452 27041"/>
    </justification>
  </clause>

  <clause id="33454">
    <literal><![CDATA[
      a((x \ L(y,z,y)) \ u,w,L(v5,x * y,x)) = a(y \ (x * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32429,a,33435,a)].">
      <j1 rule="hyper" parents="32429 33435"/>
    </justification>
  </clause>

  <clause id="33455">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(w,x * y,x)) = a(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(614(a,1),33454(a,1,1,1,2))].">
      <j1 rule="para" parents="614 33454"/>
    </justification>
  </clause>

  <clause id="33456">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(y,x * y,x)) = a((x * z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,31445,a(flip),b,33455,a),flip(a)].">
      <j1 rule="hyper" parents="370 31445 33455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33457">
    <literal><![CDATA[
      a((x \ y) \ z,u,(y \ x) * x) = a((x * z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31454,a(flip),b,33456,a)].">
      <j1 rule="hyper" parents="60 31454 33456"/>
    </justification>
  </clause>

  <clause id="33458">
    <literal><![CDATA[
      a((x * y) * z,u,z) = a(y * (x \ z),u,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32528,a(flip),b,33457,a),flip(a)].">
      <j1 rule="hyper" parents="60 32528 33457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33459">
    <literal><![CDATA[
      a(x * (y \ (z * (L(L(z,u,w),u,w) \ v5))),v6,z * (L(L(z,u,w),u,w) \ v5)) = a(v5 * (y * x),v6,z * (L(L(z,u,w),u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(30208,a,33458,a),flip(a)].">
      <j1 rule="hyper" parents="30208 33458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33460">
    <literal><![CDATA[
      a(((1 / x) * y) * L(z,x,x),u,L(z,x,x)) = a(y * (x * z),u,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(581(a,1),33458(a,2,1,2))].">
      <j1 rule="para" parents="581 33458"/>
    </justification>
  </clause>

  <clause id="33461">
    <literal><![CDATA[
      a((((x \ 1) \ 1) * y) * R(z,x,x),u,R(z,x,x)) = a(y * T(z * (x \ 1),x),u,R(z,x,x))
    ]]></literal>
    <justification jstring="[para(4476(a,1),33458(a,2,1,2))].">
      <j1 rule="para" parents="4476 33458"/>
    </justification>
  </clause>

  <clause id="33462">
    <literal><![CDATA[
      a(x * y,L(y,y,x),z) = a(x * y,(1 / (x * (1 / y))) * x,z)
    ]]></literal>
    <justification jstring="[para(33222(a,1),33404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33222 33404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33463">
    <literal><![CDATA[
      a(x * y,L(y,y,x),z) = a(x * y,(x * (1 / y)) * x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,3042,a(flip),b,33462,a),flip(a)].">
      <j1 rule="hyper" parents="370 3042 33462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33464">
    <literal><![CDATA[
      a(x * y,L(1 / y,x,x),z) = a(x * y,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(370,a,26484,a(flip),b,33463,a)].">
      <j1 rule="hyper" parents="370 26484 33463"/>
    </justification>
  </clause>

  <clause id="33465">
    <literal><![CDATA[
      a(x * y,L(y \ 1,x,x),z) = a(x * y,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(26577,a,33464,a)].">
      <j1 rule="hyper" parents="26577 33464"/>
    </justification>
  </clause>

  <clause id="33466">
    <literal><![CDATA[
      a(x * y,L(y,y,x),z) = a(x * y,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(26747,a,33465,a),flip(a)].">
      <j1 rule="hyper" parents="26747 33465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33467">
    <literal><![CDATA[
      a(x * y,L(y,x,x),z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33323,a(flip),b,33466,a),flip(a)].">
      <j1 rule="hyper" parents="60 33323 33466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33468">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = (y / (x * y)) * ((y * T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),33427(a,2,1,2))].">
      <j1 rule="para" parents="107 33427"/>
    </justification>
  </clause>

  <clause id="33469">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = (y / (x * y)) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),33468(a,2,2,1))].">
      <j1 rule="para" parents="107 33468"/>
    </justification>
  </clause>

  <clause id="33470">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * z) = y * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25562,a(flip),b,33469,a),flip(a)].">
      <j1 rule="hyper" parents="60 25562 33469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33471">
    <literal><![CDATA[
      ((x \ y) * ((y \ (x \ y)) \ z)) / z = R(y,x,y * (x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33420,a(flip),b,33430,a),flip(a)].">
      <j1 rule="hyper" parents="60 33420 33430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33472">
    <literal><![CDATA[
      a(x \ ((y * x) \ ((1 / x) * z)),u,y) = a(z * (x * y),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,32556,a(flip),b,33460,a)].">
      <j1 rule="hyper" parents="60 32556 33460"/>
    </justification>
  </clause>

  <clause id="33473">
    <literal><![CDATA[
      a(x \ ((y * x) \ ((x \ 1) * z)),u,y) = a(z * (x * y),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(33312,a,33472,a)].">
      <j1 rule="hyper" parents="33312 33472"/>
    </justification>
  </clause>

  <clause id="33474">
    <literal><![CDATA[
      a(x \ ((y * x) \ (x * z)),u,y) = a(z * (x * y),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27542,a(flip),b,33473,a)].">
      <j1 rule="hyper" parents="60 27542 33473"/>
    </justification>
  </clause>

  <clause id="33475">
    <literal><![CDATA[
      a(x \ ((y * x) \ (x * z)),u,y) = a((x \ z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,33368,a(flip),b,33474,a),flip(a)].">
      <j1 rule="hyper" parents="370 33368 33474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33477">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = L(a(u,y,L(z,x,y)),y,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),32513(a,2,1))].">
      <j1 rule="para" parents="3 32513"/>
    </justification>
  </clause>

  <clause id="33479">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,T(y,x),u) \ T(y,x))))) = a(u,y,L(L(z,x,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32313,a,b,33477,a),flip(a)].">
      <j1 rule="hyper" parents="370 32313 33477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33481">
    <literal><![CDATA[
      x \ (y \ (x * (z * (L(z,y,u) \ T(y,x))))) = a(u,y,L(L(z,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(26015(a,1),33479(a,1,2,2,2,2,1))].">
      <j1 rule="para" parents="26015 33479"/>
    </justification>
  </clause>

  <clause id="33483">
    <literal><![CDATA[
      x \ (y \ (x * T(z * (L(z,y,u) \ y),x))) = a(u,y,L(L(z,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(28327(a,2),33481(a,1,2,2,2))].">
      <j1 rule="para" parents="28327 33481"/>
    </justification>
  </clause>

  <clause id="33484">
    <literal><![CDATA[
      x \ (y \ (x * T(y * a(z,y,u),x))) = a(z,y,L(L(u,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(29938(a,1),33483(a,1,2,2,2,1))].">
      <j1 rule="para" parents="29938 33483"/>
    </justification>
  </clause>

  <clause id="33485">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,y,u)) * x)) = a(z,y,L(L(u,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(107(a,1),33484(a,1,2,2))].">
      <j1 rule="para" parents="107 33484"/>
    </justification>
  </clause>

  <clause id="33486">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = a(z,y,L(L(u,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(31720(a,1),33485(a,1,2))].">
      <j1 rule="para" parents="31720 33485"/>
    </justification>
  </clause>

  <clause id="33487">
    <literal><![CDATA[
      a(x,y,L(T(z,T(x,u)) \ (x \ w),v5,v6)) = a(x,y,L((z * x) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(27165,a,32536,a),flip(a)].">
      <j1 rule="hyper" parents="27165 32536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33488">
    <literal><![CDATA[
      a(x,y,L((z * x) \ u,w,v5)) = a(x,y,L(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(27165,a,33487,a),flip(a)].">
      <j1 rule="hyper" parents="27165 33487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33490">
    <literal><![CDATA[
      a(x,x,L(y \ (x \ z),u,w)) = a(x,x,L(x * (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(31860,a,33488,a),flip(a)].">
      <j1 rule="hyper" parents="31860 33488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33492">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ (x \ u)),x,z * x)) = a(x,y,x * ((z * x) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33190,a(flip),b,33488,a),flip(a)].">
      <j1 rule="hyper" parents="60 33190 33488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33493">
    <literal><![CDATA[
      a(x,x,L((x \ y) * z,u,w)) = a(x,x,L(x * (z \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(32923,a,33490,a)].">
      <j1 rule="hyper" parents="32923 33490"/>
    </justification>
  </clause>

  <clause id="33494">
    <literal><![CDATA[
      a(x,x,L(x * (y \ z),u,w)) = a(x,x,L(x * (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(29852,a,33493,a),flip(a)].">
      <j1 rule="hyper" parents="29852 33493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33495">
    <literal><![CDATA[
      a(x,x,L(x * (y * z),u,(z * x) \ y)) = a(x,x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,31867,a(flip),b,33494,a),flip(a)].">
      <j1 rule="hyper" parents="60 31867 33494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33496">
    <literal><![CDATA[
      a(x,x,x * (y \ z)) = a(x,x,x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(33045,a,33495,a),flip(a)].">
      <j1 rule="hyper" parents="33045 33495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33497">
    <literal><![CDATA[
      a(x,y,a(z,z,z * (u * x))) * a(z,y,z * (x \ u)) = a(z,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(33496(a,1),33047(a,1,1,3))].">
      <j1 rule="para" parents="33496 33047"/>
    </justification>
  </clause>

  <clause id="33498">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ (x \ u)),x,z)) = a(x,y,x * ((z * x) \ u))
    ]]></literal>
    <justification jstring="[hyper(32465,a,33492,a)].">
      <j1 rule="hyper" parents="32465 33492"/>
    </justification>
  </clause>

  <clause id="33499">
    <literal><![CDATA[
      a(x,y,x * ((z * x) \ u)) = a(x,y,x * (z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33190,a(flip),b,33498,a),flip(a)].">
      <j1 rule="hyper" parents="60 33190 33498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33500">
    <literal><![CDATA[
      a(x,y,a(z,z,u * x)) * a(z,y,z * (x \ u)) = a(z,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(30158(a,1),33497(a,1,1))].">
      <j1 rule="para" parents="30158 33497"/>
    </justification>
  </clause>

  <clause id="33501">
    <literal><![CDATA[
      a(x * y,z,a(u,u,y)) * a(u,z,u * (y \ x)) = a(u,z,y \ (u \ x))
    ]]></literal>
    <justification jstring="[para(32966(a,1),33500(a,1,1))].">
      <j1 rule="para" parents="32966 33500"/>
    </justification>
  </clause>

  <clause id="33502">
    <literal><![CDATA[
      a((x * y) * x,z,a(u,u,x)) * a(u,z,u * y) = a(u,z,x \ (u \ (x * y)))
    ]]></literal>
    <justification jstring="[para(4(a,1),33501(a,1,2,3,2))].">
      <j1 rule="para" parents="4 33501"/>
    </justification>
  </clause>

  <clause id="33503">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),u,u)) * a(z,y,z * x) = a(z,y,u \ (z \ (u * x)))
    ]]></literal>
    <justification jstring="[para(32405(a,1),33502(a,1,1))].">
      <j1 rule="para" parents="32405 33502"/>
    </justification>
  </clause>

  <clause id="33504">
    <literal><![CDATA[
      a(x,y,z \ (x \ (z * u))) = a(u,y,a(x,x,z)) * a(x,y,x * u)
    ]]></literal>
    <justification jstring="[para(14782(a,1),33503(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="14782 33503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33511">
    <literal><![CDATA[
      a(x,y,L(L((z * u) \ w,z,u),z,z)) = a((z \ x) * z,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(33176,a,32546,a),flip(a)].">
      <j1 rule="hyper" parents="33176 32546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33512">
    <literal><![CDATA[
      a(x,y,L(L((z * u) \ w,z,u),z,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(33511(a,2),26520(a,1))].">
      <j1 rule="para" parents="33511 26520"/>
    </justification>
  </clause>

  <clause id="33513">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (T(x,y) / y)) = (x * y) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,5266,a(flip),b,32907,a),flip(a)].">
      <j1 rule="hyper" parents="370 5266 32907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33514">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (T(x,y) / y)) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,6712,a(flip),b,33513,a),flip(a)].">
      <j1 rule="hyper" parents="370 6712 33513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33515">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (y \ T(x,y))) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(26944(a,1),33514(a,1,2))].">
      <j1 rule="para" parents="26944 33514"/>
    </justification>
  </clause>

  <clause id="33516">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),T(y,x),x \ (y \ x)) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(26945(a,1),33515(a,1,2))].">
      <j1 rule="para" parents="26945 33515"/>
    </justification>
  </clause>

  <clause id="33517">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),y,x \ (y \ x)) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(26451(a,1),33516(a,1,2))].">
      <j1 rule="para" parents="26451 33516"/>
    </justification>
  </clause>

  <clause id="33520">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(T(y,x),y,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(33080(a,1),33517(a,1,2))].">
      <j1 rule="para" parents="33080 33517"/>
    </justification>
  </clause>

  <clause id="33521">
    <literal><![CDATA[
      (x \ (T(x,y) / y)) * a(y,y,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(26375(a,1),33520(a,1,2))].">
      <j1 rule="para" parents="26375 33520"/>
    </justification>
  </clause>

  <clause id="33523">
    <literal><![CDATA[
      L(x \ (T(x,y) / y),y,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,31882,a(flip),b,33521,a)].">
      <j1 rule="hyper" parents="60 31882 33521"/>
    </justification>
  </clause>

  <clause id="33525">
    <literal><![CDATA[
      L(x \ (T(x,x / y) / (x / y)),x / y,x / y) = ((y \ x) * x) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,25261,a,b,33523,a),flip(a)].">
      <j1 rule="hyper" parents="370 25261 33523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33526">
    <literal><![CDATA[
      L((x \ y) \ (T(x \ y,1 / x) / (1 / x)),1 / x,1 / x) = ((x * x) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(552(a,1),33523(a,2,1))].">
      <j1 rule="para" parents="552 33523"/>
    </justification>
  </clause>

  <clause id="33527">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),x / y,x / y) = ((y \ x) * x) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(5747(a,1),33525(a,1,1,2))].">
      <j1 rule="para" parents="5747 33525"/>
    </justification>
  </clause>

  <clause id="33528">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),x / y,y \ x) = ((y \ x) * x) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(24038,a,33527,a)].">
      <j1 rule="hyper" parents="24038 33527"/>
    </justification>
  </clause>

  <clause id="33529">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y \ x,y \ x) = ((y \ x) * x) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(26067,a,33528,a)].">
      <j1 rule="hyper" parents="26067 33528"/>
    </justification>
  </clause>

  <clause id="33530">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y * x,y * x) = ((y \ x) * x) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(29606,a,33529,a)].">
      <j1 rule="hyper" parents="29606 33529"/>
    </justification>
  </clause>

  <clause id="33531">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y * x,y * x) = L(x \ y,x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(370,a,94,a,b,33530,a),flip(a)].">
      <j1 rule="hyper" parents="370 94 33530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33532">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y * x,y * x) = ((x / y) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(370,a,25261,a(flip),b,33530,a),flip(a)].">
      <j1 rule="hyper" parents="370 25261 33530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33533">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y * x,y * x) = L(x \ y,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,13896,a(flip),b,33531,a),flip(a)].">
      <j1 rule="hyper" parents="370 13896 33531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33534">
    <literal><![CDATA[
      L(x \ (x / T(x / y,x)),y * x,y * x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,24919,a(flip),b,33533,a),flip(a)].">
      <j1 rule="hyper" parents="370 24919 33533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33535">
    <literal><![CDATA[
      T(x / y,x) = ((y / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(60,a,33532,a(flip),b,33534,a),flip(a)].">
      <j1 rule="hyper" parents="60 33532 33534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33536">
    <literal><![CDATA[
      a(x,y,z * (T(u / w,u) \ w)) = a(x,y,z * ((w / u) * w))
    ]]></literal>
    <justification jstring="[para(33535(a,2),26940(a,1,3,2,1))].">
      <j1 rule="para" parents="33535 26940"/>
    </justification>
  </clause>

  <clause id="33537">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ w)) = a(x,y,z * ((w / u) * w))
    ]]></literal>
    <justification jstring="[hyper(27093,a,33536,a)].">
      <j1 rule="hyper" parents="27093 33536"/>
    </justification>
  </clause>

  <clause id="33538">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ u)) = a(x,y,z * ((u / w) * u))
    ]]></literal>
    <justification jstring="[hyper(27094,a,33537,a)].">
      <j1 rule="hyper" parents="27094 33537"/>
    </justification>
  </clause>

  <clause id="33539">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ u)) = a(x,y,z * ((w \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,27024,a(flip),b,33538,a),flip(a)].">
      <j1 rule="hyper" parents="370 27024 33538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33540">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * ((w \ u) * u)) = v5
    ]]></literal>
    <justification jstring="[para(33538(a,2),27095(a,1))].">
      <j1 rule="para" parents="33538 27095"/>
    </justification>
  </clause>

  <clause id="33541">
    <literal><![CDATA[
      a(x * (x * (y \ x)),z,u * ((y \ x) * x)) = a(x \ y,z,x \ ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,32554,a(flip),b,33539,a),flip(a)].">
      <j1 rule="hyper" parents="60 32554 33539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33542">
    <literal><![CDATA[
      a(x \ y,z,L(u * ((x \ y) * y),y,y)) = a(y \ x,z,y \ ((y \ x) * u))
    ]]></literal>
    <justification jstring="[hyper(32458,a,33541,a)].">
      <j1 rule="hyper" parents="32458 33541"/>
    </justification>
  </clause>

  <clause id="33543">
    <literal><![CDATA[
      a(x \ y,z,x \ ((x \ y) * u)) = a(y \ x,z,(x \ u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(33361,a,33542,a),flip(a)].">
      <j1 rule="hyper" parents="33361 33542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33544">
    <literal><![CDATA[
      L(x * (y * a(z,u,x)),x,a(z,u,x)) = x * (L(x,u,z) * (L(L(x,u,z),u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,2153,a(flip),b,33057,a),flip(a)].">
      <j1 rule="hyper" parents="370 2153 33057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33545">
    <literal><![CDATA[
      L((x * y) \ y,y \ (x \ y),z) = a(z,x,x) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(32909(a,1),33081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32909 33081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33546">
    <literal><![CDATA[
      L((x * y) \ y,y * (x \ y),z) = a(z,x,x) \ ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(60,a,33318,a(flip),b,33545,a)].">
      <j1 rule="hyper" parents="60 33318 33545"/>
    </justification>
  </clause>

  <clause id="33548">
    <literal><![CDATA[
      L((x * y) \ y,y * (x \ y),z) = L((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31908,a(flip),b,33546,a),flip(a)].">
      <j1 rule="hyper" parents="370 31908 33546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33549">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,((x \ 1) \ y) * (x * y),x * y) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(26254(a,1),33440(a,1,2))].">
      <j1 rule="para" parents="26254 33440"/>
    </justification>
  </clause>

  <clause id="33550">
    <literal><![CDATA[
      L(x * (y * a(z,u,x)),x,a(z,u,x)) = x * (x * (L(x,u,z) \ y))
    ]]></literal>
    <justification jstring="[para(29929(a,1),33544(a,2,2))].">
      <j1 rule="para" parents="29929 33544"/>
    </justification>
  </clause>

  <clause id="33551">
    <literal><![CDATA[
      L(x * (y * a(z,u,x)),x,a(z,u,x)) = (x * a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,32670,a(flip),b,33550,a),flip(a)].">
      <j1 rule="hyper" parents="370 32670 33550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33552">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,(x \ y) * (x * y),x * y) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(3393(a,1),33549(a,1,2))].">
      <j1 rule="para" parents="3393 33549"/>
    </justification>
  </clause>

  <clause id="33553">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,a(y,x,x),x * y) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(30950(a,1),33552(a,1,2))].">
      <j1 rule="para" parents="30950 33552"/>
    </justification>
  </clause>

  <clause id="33554">
    <literal><![CDATA[
      (x * y) * (a(x,x,y) * z) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(33041(a,1),33553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33041 33553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33555">
    <literal><![CDATA[
      (x * (y * (a(x,x,y) * z))) \ (((1 / x) \ y) * z) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(125,a,33554,a(flip),b,82,a)].">
      <j1 rule="hyper" parents="125 33554 82"/>
    </justification>
  </clause>

  <clause id="33557">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ (((1 / x) \ y) * z) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(31822(a,1),33555(a,1,1))].">
      <j1 rule="para" parents="31822 33555"/>
    </justification>
  </clause>

  <clause id="33558">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32809,a,33557,a),flip(a)].">
      <j1 rule="hyper" parents="32809 33557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33560">
    <literal><![CDATA[
      a(x,y,L(z,u,z * (u * a(x,y,z)))) = a(x,y,L(z,u,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(32500,a,32510,a),flip(a)].">
      <j1 rule="hyper" parents="32500 32510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33561">
    <literal><![CDATA[
      a(x,y,L(z,u,z * (u * a(x,y,z)))) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(370,a,32324,a(flip),b,33560,a),flip(a)].">
      <j1 rule="hyper" parents="370 32324 33560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33562">
    <literal><![CDATA[
      a(x,y,L(z,u,L(z,y,x) * u)) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(33286(a,1),33561(a,1,3))].">
      <j1 rule="para" parents="33286 33561"/>
    </justification>
  </clause>

  <clause id="33563">
    <literal><![CDATA[
      x \ a(y,z,L(u,x,x)) = (a(y,z,u) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(125,a,32540,a(flip),b,33562,a(flip))].">
      <j1 rule="hyper" parents="125 32540 33562"/>
    </justification>
  </clause>

  <clause id="33564">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ 1 = (u \ 1) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32334,a,33563,a),flip(a)].">
      <j1 rule="hyper" parents="32334 33563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33565">
    <literal><![CDATA[
      ((x \ 1) * a(y,z,u)) \ (x \ (1 / x)) = a(y,z,u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(33564(a,1),31326(a,1,1))].">
      <j1 rule="para" parents="33564 31326"/>
    </justification>
  </clause>

  <clause id="33566">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((1 / x) \ (1 / x)) = a(y,z,u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2148,a,33565,a)].">
      <j1 rule="hyper" parents="2148 33565"/>
    </justification>
  </clause>

  <clause id="33567">
    <literal><![CDATA[
      (x * a(y,z,u)) \ 1 = a(y,z,u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(63(a,1),33566(a,1,2))].">
      <j1 rule="para" parents="63 33566"/>
    </justification>
  </clause>

  <clause id="33569">
    <literal><![CDATA[
      T(a(x,y,z) \ (L(u,u,u) \ 1),u \ 1) = 1 / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(33567(a,1),28533(a,1,1))].">
      <j1 rule="para" parents="33567 28533"/>
    </justification>
  </clause>

  <clause id="33570">
    <literal><![CDATA[
      T(a(x,y,z) \ (1 / u),u \ 1) = 1 / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(1327(a,1),33569(a,1,1,2))].">
      <j1 rule="para" parents="1327 33569"/>
    </justification>
  </clause>

  <clause id="33571">
    <literal><![CDATA[
      1 / (a(x,y,z) * u) = a(x,y,z) \ (1 / u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28225,a(flip),b,33570,a),flip(a)].">
      <j1 rule="hyper" parents="60 28225 33570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33572">
    <literal><![CDATA[
      1 / (x * a(y,z,u)) = a(y,z,u) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(23620(a,1),33571(a,1,2))].">
      <j1 rule="para" parents="23620 33571"/>
    </justification>
  </clause>

  <clause id="33573">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),u,u) = L((a(x,y,z) \ (1 / (a(x,y,z) / u))) * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(33571(a,1),29917(a,2,1,1))].">
      <j1 rule="para" parents="33571 29917"/>
    </justification>
  </clause>

  <clause id="33575">
    <literal><![CDATA[
      a(x,x,y) \ (1 / (L(y,x,x) / z)) = 1 / (y / z)
    ]]></literal>
    <justification jstring="[para(33291(a,1),33572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33291 33572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33576">
    <literal><![CDATA[
      (1 / (L(x,y,y) / z)) * L(x,y,y) = (1 / (x / z)) * x
    ]]></literal>
    <justification jstring="[para(33575(a,1),32840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33575 32840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33577">
    <literal><![CDATA[
      L(x,(y \ z) * x,x * L(z * y,y,y)) = (1 / ((z * y) / x)) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29701,a,b,33576,a)].">
      <j1 rule="hyper" parents="60 29701 33576"/>
    </justification>
  </clause>

  <clause id="33578">
    <literal><![CDATA[
      L(x,(y \ z) * x,x * (y \ z)) = (1 / ((z * y) / x)) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(29890,a,33577,a)].">
      <j1 rule="hyper" parents="29890 33577"/>
    </justification>
  </clause>

  <clause id="33580">
    <literal><![CDATA[
      (1 / ((x \ y) / z)) * (x \ y) = (1 / ((y * x) / z)) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,29616,a(flip),b,33578,a)].">
      <j1 rule="hyper" parents="60 29616 33578"/>
    </justification>
  </clause>

  <clause id="33581">
    <literal><![CDATA[
      a(x,y,a(z,u,(1 / ((z * u) / w)) * (z * u))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[para(33580(a,1),32269(a,1,3,3))].">
      <j1 rule="para" parents="33580 32269"/>
    </justification>
  </clause>

  <clause id="33582">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,x * z)) = a(x,y,(x * z) \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3369(a,1),32561(a,1,3))].">
      <j1 rule="para" parents="3369 32561"/>
    </justification>
  </clause>

  <clause id="33583">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,z)) = a(x,y,(x * z) \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(32508,a,33582,a)].">
      <j1 rule="hyper" parents="32508 33582"/>
    </justification>
  </clause>

  <clause id="33584">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,z)) = a(x,y,(x * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3151,a(flip),b,33583,a),flip(a)].">
      <j1 rule="hyper" parents="370 3151 33583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33585">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,z)) = a(x,y,z \ (x \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32364,a(flip),b,33584,a),flip(a)].">
      <j1 rule="hyper" parents="370 32364 33584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33586">
    <literal><![CDATA[
      a(x,y,L(x * (((1 / x) * z) \ u),x,z)) = a(x,y,z \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29668,a(flip),b,33585,a),flip(a)].">
      <j1 rule="hyper" parents="370 29668 33585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33587">
    <literal><![CDATA[
      a(x \ a(y,z,y),u * (x \ a(y,z,y)),u * w) = a(x,x * u,u \ w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26485,a(flip),b,33102,a),flip(a)].">
      <j1 rule="hyper" parents="370 26485 33102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33589">
    <literal><![CDATA[
      a(x \ a(y,z,y),x * u,u * w) = a(x,x * u,u \ w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26485,a(flip),b,33587,a)].">
      <j1 rule="hyper" parents="60 26485 33587"/>
    </justification>
  </clause>

  <clause id="33590">
    <literal><![CDATA[
      a(x,x * y,y \ z) = a(x,x * y,y * z)
    ]]></literal>
    <justification jstring="[hyper(27326,a,33589,a),flip(a)].">
      <j1 rule="hyper" parents="27326 33589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33592">
    <literal><![CDATA[
      a(x,x * y,(x \ y) * z) = a(x,x * y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(32551,a,33590,a)].">
      <j1 rule="hyper" parents="32551 33590"/>
    </justification>
  </clause>

  <clause id="33593">
    <literal><![CDATA[
      a(x,x * (y \ x),(y \ x) * (x * z)) = a(x,x * (y \ x),x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33332,a(flip),b,33592,a),flip(a)].">
      <j1 rule="hyper" parents="60 33332 33592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33594">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),(x \ (a(y,z,y) \ u)) * w) = a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w)))
    ]]></literal>
    <justification jstring="[para(14311(a,1),33592(a,2,3))].">
      <j1 rule="para" parents="14311 33592"/>
    </justification>
  </clause>

  <clause id="33595">
    <literal><![CDATA[
      a(x,x * (y \ x),(y \ x) * (x * z)) = a(x,y,x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33414,a(flip),b,33593,a),flip(a)].">
      <j1 rule="hyper" parents="370 33414 33593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33596">
    <literal><![CDATA[
      a(x,x * (y \ x),x * (y * (x * z))) = a(x,y,x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33330,a(flip),b,33595,a)].">
      <j1 rule="hyper" parents="60 33330 33595"/>
    </justification>
  </clause>

  <clause id="33597">
    <literal><![CDATA[
      a(x,y,x * ((y * x) * z)) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33414,a(flip),b,33596,a),flip(a)].">
      <j1 rule="hyper" parents="60 33414 33596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33598">
    <literal><![CDATA[
      L(x,y,a(z,z,L(u,y,u))) * (a(u,y,z) * L(z,y,u)) = R(x / (1 / z),z,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(29139(a,1),33106(a,1,1,3))].">
      <j1 rule="para" parents="29139 33106"/>
    </justification>
  </clause>

  <clause id="33599">
    <literal><![CDATA[
      L((x \ y) \ (T(x \ y,x \ 1) / (1 / x)),1 / x,1 / x) = ((x * x) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4443(a,1),33526(a,1,1,2,1))].">
      <j1 rule="para" parents="4443 33526"/>
    </justification>
  </clause>

  <clause id="33600">
    <literal><![CDATA[
      a(x,y,a(z,u,((z * u) / w) * (z * u))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[para(3079(a,1),33581(a,1,3))].">
      <j1 rule="para" parents="3079 33581"/>
    </justification>
  </clause>

  <clause id="33601">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ (z * u)) * (z * u))) = a(x,y,((u * z) * w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[para(26896(a,1),33600(a,1,3))].">
      <j1 rule="para" parents="26896 33600"/>
    </justification>
  </clause>

  <clause id="33602">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) * (a(u,y,z) * L(z,y,u)) = R(x / (1 / z),z,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(26960(a,1),33598(a,1,1,3))].">
      <j1 rule="para" parents="26960 33598"/>
    </justification>
  </clause>

  <clause id="33604">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,u)) = L(x,z,a(y,y,u)) * y
    ]]></literal>
    <justification jstring="[para(32568(a,1),33602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32568 33602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33605">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,u)) = L(x * y,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33017,a,b,33604,a),flip(a)].">
      <j1 rule="hyper" parents="370 33017 33604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33606">
    <literal><![CDATA[
      L(((x \ 1) * (x \ y)) \ (x \ y),1 / x,1 / x) = ((x * x) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(12699(a,1),33599(a,1,1))].">
      <j1 rule="para" parents="12699 33599"/>
    </justification>
  </clause>

  <clause id="33607">
    <literal><![CDATA[
      L((x * (x \ y)) \ ((1 / x) \ y),1 / x,1 / x) = ((x * x) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(2113(a,1),33606(a,1,1))].">
      <j1 rule="para" parents="2113 33606"/>
    </justification>
  </clause>

  <clause id="33608">
    <literal><![CDATA[
      L(x \ ((1 / y) \ x),1 / y,1 / y) = ((y * y) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),33607(a,1,1,1))].">
      <j1 rule="para" parents="5 33607"/>
    </justification>
  </clause>

  <clause id="33609">
    <literal><![CDATA[
      L(x \ ((1 / y) \ x),y,y) = ((y * y) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(3523,a,33608,a)].">
      <j1 rule="hyper" parents="3523 33608"/>
    </justification>
  </clause>

  <clause id="33611">
    <literal><![CDATA[
      L(x \ ((1 / y) \ x),y,y) = x \ ((y * y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,849,a(flip),b,33609,a),flip(a)].">
      <j1 rule="hyper" parents="370 849 33609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33612">
    <literal><![CDATA[
      L(x \ ((1 / y) \ x),y,y) = x \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(936(a,1),33611(a,2,2))].">
      <j1 rule="para" parents="936 33611"/>
    </justification>
  </clause>

  <clause id="33613">
    <literal><![CDATA[
      L(T(x,(1 / y) \ 1) \ (x * ((1 / y) \ a(1 / y,1 / y,x))),y,y) = T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(28442(a,2),33612(a,1,1,2))].">
      <j1 rule="para" parents="28442 33612"/>
    </justification>
  </clause>

  <clause id="33614">
    <literal><![CDATA[
      a((x * y) \ T(x,y),z,T(y \ 1,y * x) \ u) = a(y,z,x \ (((y \ 1) \ x) * u))
    ]]></literal>
    <justification jstring="[para(17(a,2),32506(a,1,1,2))].">
      <j1 rule="para" parents="17 32506"/>
    </justification>
  </clause>

  <clause id="33615">
    <literal><![CDATA[
      a((x * y) \ y,z,T(x \ 1,x * y) \ u) = a(x,z,y \ (((x \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[para(6712(a,1),33614(a,1,1))].">
      <j1 rule="para" parents="6712 33614"/>
    </justification>
  </clause>

  <clause id="33616">
    <literal><![CDATA[
      a((x * y) \ y,z,(x \ 1) \ u) = a(x,z,y \ (((x \ 1) \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(26979,a,33615,a)].">
      <j1 rule="hyper" parents="26979 33615"/>
    </justification>
  </clause>

  <clause id="33617">
    <literal><![CDATA[
      a(x,y,z \ (((x \ 1) \ z) * u)) = a((x * z) \ z,y,x \ u)
    ]]></literal>
    <justification jstring="[hyper(3116,a,33616,a),flip(a)].">
      <j1 rule="hyper" parents="3116 33616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33619">
    <literal><![CDATA[
      a(x,y,z \ (((x \ 1) \ z) * u)) = a(z \ (x \ z),y,x \ u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26784,a(flip),b,33617,a),flip(a)].">
      <j1 rule="hyper" parents="370 26784 33617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33620">
    <literal><![CDATA[
      a(x,y,z \ (((x \ 1) \ z) * u)) = a(x,y,z \ (x \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32529,a(flip),b,33619,a),flip(a)].">
      <j1 rule="hyper" parents="370 32529 33619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33621">
    <literal><![CDATA[
      a(x,y,z \ (x \ (z * u))) = a(x,y,z \ ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3152,a(flip),b,33620,a),flip(a)].">
      <j1 rule="hyper" parents="60 3152 33620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33622">
    <literal><![CDATA[
      a(x,y,z \ ((x \ z) * u)) = a(u,y,a(x,x,z)) * a(x,y,x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,33504,a(flip),b,33621,a),flip(a)].">
      <j1 rule="hyper" parents="60 33504 33621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33623">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 \ a(v6,v6,L(z,u,w) * v5))) = a(x,y,v6 \ (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(28605(a,1),32791(a,1,3,2,2))].">
      <j1 rule="para" parents="28605 32791"/>
    </justification>
  </clause>

  <clause id="33624">
    <literal><![CDATA[
      L((x \ y) \ (x \ 1),z,z) * (1 / (x * ((x \ 1) / y))) = a(z,z,(x \ y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3155(a,1),32842(a,2,1))].">
      <j1 rule="para" parents="3155 32842"/>
    </justification>
  </clause>

  <clause id="33625">
    <literal><![CDATA[
      L((x \ y) \ (x \ 1),z,z) * (1 / (x * ((x \ 1) / y))) = a(z,z,(y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(29633(a,1),33624(a,2,1))].">
      <j1 rule="para" parents="29633 33624"/>
    </justification>
  </clause>

  <clause id="33626">
    <literal><![CDATA[
      L((x \ y) \ (x \ 1),z,z) * (((x \ y) \ (x \ 1)) \ 1) = a(z,z,(y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(31361(a,1),33625(a,1,2))].">
      <j1 rule="para" parents="31361 33625"/>
    </justification>
  </clause>

  <clause id="33627">
    <literal><![CDATA[
      ((x \ y) \ (x \ 1)) \ L((x \ y) \ (x \ 1),z,z) = a(z,z,(y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(1776,a,33626,a)].">
      <j1 rule="hyper" parents="1776 33626"/>
    </justification>
  </clause>

  <clause id="33628">
    <literal><![CDATA[
      (x \ y) \ ((x \ 1) * L((x \ 1) \ (x \ y),z,z)) = a(z,z,(y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(4048,a,33627,a)].">
      <j1 rule="hyper" parents="4048 33627"/>
    </justification>
  </clause>

  <clause id="33629">
    <literal><![CDATA[
      (x \ y) \ ((x \ 1) * L(x \ ((1 / x) \ y),z,z)) = a(z,z,(y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(2104(a,1),33628(a,1,2,2,1))].">
      <j1 rule="para" parents="2104 33628"/>
    </justification>
  </clause>

  <clause id="33630">
    <literal><![CDATA[
      a(x,x,(y \ z) * z) \ 1 = (z \ y) \ (z \ L(y,x,x))
    ]]></literal>
    <justification jstring="[para(2107(a,1),33629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2107 33629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33631">
    <literal><![CDATA[
      (x \ y) \ (x \ L(y,z,z)) = a(z,z,y) \ 1
    ]]></literal>
    <justification jstring="[para(32785(a,1),33630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32785 33630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33632">
    <literal><![CDATA[
      a(x,x,y) * (z \ L(y,x,x)) = z \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,30651,a,b,33631,a)].">
      <j1 rule="hyper" parents="36 30651 33631"/>
    </justification>
  </clause>

  <clause id="33633">
    <literal><![CDATA[
      a(x,x,y) \ (z \ y) = z \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,30620,a,b,33631,a)].">
      <j1 rule="hyper" parents="35 30620 33631"/>
    </justification>
  </clause>

  <clause id="33635">
    <literal><![CDATA[
      a(a(x,x,y) * ((z \ L(y,x,x)) \ 1),u,w) = a(z \ y,u,w)
    ]]></literal>
    <justification jstring="[para(33632(a,1),2995(a,2,1))].">
      <j1 rule="para" parents="33632 2995"/>
    </justification>
  </clause>

  <clause id="33636">
    <literal><![CDATA[
      a(x \ L(y \ L(z,u,u),a(u,u,z),a(u,u,z)),w,v5) = a(x \ (a(u,u,z) * (y \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(33632(a,1),26710(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33632 26710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33637">
    <literal><![CDATA[
      a(x * (a(y,y,z) \ ((u \ L(z,y,y)) \ a(y,y,z))),w,v5) = a(x * ((u \ z) \ a(y,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(33632(a,1),27794(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="33632 27794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33638">
    <literal><![CDATA[
      a(x,a(y,y,z) * (u \ z),w) = a(x,u \ L(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(33633(a,1),30633(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33633 30633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33639">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ u)) = a(x,y,w \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(33633(a,1),30634(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33633 30634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33640">
    <literal><![CDATA[
      L(x,y,a(z,z,u) * (w \ u)) = L(x,y,w \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(33633(a,1),30635(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33633 30635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33641">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * (w \ u)) * v5) = a(x,y,(w \ L(u,z,z)) * v5)
    ]]></literal>
    <justification jstring="[para(33633(a,1),30660(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="33633 30660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33642">
    <literal><![CDATA[
      a(x,y \ (a(z,z,u) * (w \ u)),v5) = a(x,y \ (w \ L(u,z,z)),v5)
    ]]></literal>
    <justification jstring="[para(33633(a,1),30699(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33633 30699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33643">
    <literal><![CDATA[
      a(x,a(y,y,z * y) * (u \ (y \ z)),w) = a(x,u \ L(y \ z,y,y),w)
    ]]></literal>
    <justification jstring="[para(26930(a,1),33638(a,1,2,1))].">
      <j1 rule="para" parents="26930 33638"/>
    </justification>
  </clause>

  <clause id="33644">
    <literal><![CDATA[
      a(x,x,a(y,y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,u * L(z,y,y)) = w
    ]]></literal>
    <justification jstring="[para(33639(a,2),32776(a,1))].">
      <j1 rule="para" parents="33639 32776"/>
    </justification>
  </clause>

  <clause id="33645">
    <literal><![CDATA[
      a((x \ L(y,z,z)) \ a(z,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(32777(a,1),33635(a,1,1))].">
      <j1 rule="para" parents="32777 33635"/>
    </justification>
  </clause>

  <clause id="33646">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ L(x,y,y)),u,w) = a(z \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,32891,a(flip),b,33645,a)].">
      <j1 rule="hyper" parents="60 32891 33645"/>
    </justification>
  </clause>

  <clause id="33647">
    <literal><![CDATA[
      a(a(x * y,y,y) * (z \ L(y \ x,y,y)),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[para(31445(a,1),33646(a,1,1,1))].">
      <j1 rule="para" parents="31445 33646"/>
    </justification>
  </clause>

  <clause id="33648">
    <literal><![CDATA[
      a(x,x,(y \ z) * (u * a(w,w,z))) = a(x,x,(y \ L(z,w,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,33123,a(flip),b,33641,a)].">
      <j1 rule="hyper" parents="60 33123 33641"/>
    </justification>
  </clause>

  <clause id="33649">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) * a(y,y,u),w) = a(x,y \ (z \ L(u,y,y)),w)
    ]]></literal>
    <justification jstring="[para(28798(a,1),33642(a,1,2))].">
      <j1 rule="para" parents="28798 33642"/>
    </justification>
  </clause>

  <clause id="33650">
    <literal><![CDATA[
      a(x,L(y,y,z) \ (u \ z),w) = a(x,y \ (u \ L(z,y,y)),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,31800,a(flip),b,33649,a)].">
      <j1 rule="hyper" parents="60 31800 33649"/>
    </justification>
  </clause>

  <clause id="33651">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) * a(z,z,u),w) = a(x,y \ L(z \ u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29413,a(flip),b,33643,a)].">
      <j1 rule="hyper" parents="60 29413 33643"/>
    </justification>
  </clause>

  <clause id="33652">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) * a(z,z,u),w) = a(x,y \ ((1 / z) * u),w)
    ]]></literal>
    <justification jstring="[para(586(a,1),33651(a,2,2,2))].">
      <j1 rule="para" parents="586 33651"/>
    </justification>
  </clause>

  <clause id="33653">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) * a(z,z,u),w) = a(x,y \ ((z \ 1) * u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26619,a(flip),b,33652,a),flip(a)].">
      <j1 rule="hyper" parents="370 26619 33652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33654">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) * a(z,z,u),w) = a(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,29230,a(flip),b,33653,a),flip(a)].">
      <j1 rule="hyper" parents="370 29230 33653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33655">
    <literal><![CDATA[
      a(x,(y \ (R(z \ 1,z,u) \ u)) * a(R(z \ 1,z,u),R(z \ 1,z,u),u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(2784(a,1),33654(a,2,2,2))].">
      <j1 rule="para" parents="2784 33654"/>
    </justification>
  </clause>

  <clause id="33656">
    <literal><![CDATA[
      a(a(x * y,y,y) * (z \ ((1 / y) * x)),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[para(586(a,1),33647(a,1,1,2,2))].">
      <j1 rule="para" parents="586 33647"/>
    </justification>
  </clause>

  <clause id="33657">
    <literal><![CDATA[
      a(a(x * y,y,y) * (z \ (y * x)),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,26797,a(flip),b,33656,a)].">
      <j1 rule="hyper" parents="60 26797 33656"/>
    </justification>
  </clause>

  <clause id="33658">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (y * x)),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,29486,a(flip),b,33657,a)].">
      <j1 rule="hyper" parents="60 29486 33657"/>
    </justification>
  </clause>

  <clause id="33659">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (x * y)),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26687,a,33658,a)].">
      <j1 rule="hyper" parents="26687 33658"/>
    </justification>
  </clause>

  <clause id="33660">
    <literal><![CDATA[
      a(a((x \ 1) \ 1,y * (x * x),y * (x * x)) * (z \ ((x * x) * (x * T(y,x * x)))),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(1255(a,1),33659(a,1,1,2,2))].">
      <j1 rule="para" parents="1255 33659"/>
    </justification>
  </clause>

  <clause id="33661">
    <literal><![CDATA[
      a(x,y,z \ T(L(u,w,v5) \ v6,z \ 1)) = a(x,y,z \ (R(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[para(32790(a,1),33623(a,1,3))].">
      <j1 rule="para" parents="32790 33623"/>
    </justification>
  </clause>

  <clause id="33662">
    <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(33661(a,1),26969(a,1))].">
      <j1 rule="para" parents="33661 26969"/>
    </justification>
  </clause>

  <clause id="33663">
    <literal><![CDATA[
      (x * (a(y,x,a(z,z,u)) * w)) / T(x * a(z,x,a(u,z,y)),w) = L(w,x,a(y,x,a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(33108(a,1),33110(a,1,2))].">
      <j1 rule="para" parents="33108 33110"/>
    </justification>
  </clause>

  <clause id="33664">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,y,w)) * (a(y,z,u) / a(y,y,w)) = (x * a(y,z,u)) * (a(y,y,w) \ 1)
    ]]></literal>
    <justification jstring="[para(23572(a,1),33128(a,2,2))].">
      <j1 rule="para" parents="23572 33128"/>
    </justification>
  </clause>

  <clause id="33665">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * L(z,(x * (y \ x)) * y,y) = y * ((x \ (y * (1 / (x \ y)))) * z)
    ]]></literal>
    <justification jstring="[para(3786(a,1),33441(a,1,2))].">
      <j1 rule="para" parents="3786 33441"/>
    </justification>
  </clause>

  <clause id="33666">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * L(z,a(x,y * x,y),y) = y * ((x \ (y * (1 / (x \ y)))) * z)
    ]]></literal>
    <justification jstring="[para(33412(a,1),33665(a,1,2))].">
      <j1 rule="para" parents="33412 33665"/>
    </justification>
  </clause>

  <clause id="33667">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * L(z,y,a(x,y * x,y)) = y * ((x \ (y * (1 / (x \ y)))) * z)
    ]]></literal>
    <justification jstring="[para(26346(a,1),33666(a,1,2))].">
      <j1 rule="para" parents="26346 33666"/>
    </justification>
  </clause>

  <clause id="33668">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * L(z,y,a(y,y,x)) = y * ((x \ (y * (1 / (x \ y)))) * z)
    ]]></literal>
    <justification jstring="[para(33397(a,1),33667(a,1,2))].">
      <j1 rule="para" parents="33397 33667"/>
    </justification>
  </clause>

  <clause id="33669">
    <literal><![CDATA[
      x * ((y \ (x * (1 / (y \ x)))) * z) = (y * ((x \ y) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(31776(a,1),33668(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31776 33668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33670">
    <literal><![CDATA[
      x * (((x \ y) * (y \ x)) \ z) = (y * ((x \ y) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(33197(a,1),33669(a,1,2))].">
      <j1 rule="para" parents="33197 33669"/>
    </justification>
  </clause>

  <clause id="33671">
    <literal><![CDATA[
      x * (((1 / (x \ y)) * (y \ x)) \ ((x \ y) \ z)) = (y * ((x \ y) \ 1)) * (((x \ y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1274(a,2),33670(a,1,2))].">
      <j1 rule="para" parents="1274 33670"/>
    </justification>
  </clause>

  <clause id="33672">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * (((y \ x) \ 1) \ z) = y * ((x \ (y * (x \ y))) \ ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(30822(a,1),33671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30822 33671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33673">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * (((y \ x) \ 1) \ z) = y * ((y \ (x * (y \ x))) * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(30825(a,1),33672(a,2,2))].">
      <j1 rule="para" parents="30825 33672"/>
    </justification>
  </clause>

  <clause id="33674">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) * (((y \ x) \ 1) \ z) = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(31898(a,1),33673(a,2,2))].">
      <j1 rule="para" parents="31898 33673"/>
    </justification>
  </clause>

  <clause id="33675">
    <literal><![CDATA[
      (x * (y \ x)) * ((y \ x) \ z) = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,1289,a(flip),b,33674,a)].">
      <j1 rule="hyper" parents="60 1289 33674"/>
    </justification>
  </clause>

  <clause id="33676">
    <literal><![CDATA[
      (x * T(y,y \ x)) * (((y \ x) \ x) \ z) = (y \ x) * ((x \ (y \ x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(1007,a,33675,a)].">
      <j1 rule="hyper" parents="1007 33675"/>
    </justification>
  </clause>

  <clause id="33677">
    <literal><![CDATA[
      R(x,y * x,z * (y \ x)) * z = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33421,a,b,33675,a)].">
      <j1 rule="hyper" parents="60 33421 33675"/>
    </justification>
  </clause>

  <clause id="33678">
    <literal><![CDATA[
      (x \ y) * ((y \ (x \ y)) \ z) = (y * x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,25357,a(flip),b,33676,a),flip(a)].">
      <j1 rule="hyper" parents="60 25357 33676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33680">
    <literal><![CDATA[
      R(x,y,x * (y * (x * z))) = ((x * y) * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(33678(a,1),33471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33678 33471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33681">
    <literal><![CDATA[
      R(x,y,x * (y * (x * z))) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32518,a(flip),b,33680,a),flip(a)].">
      <j1 rule="hyper" parents="370 32518 33680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33682">
    <literal><![CDATA[
      a((((x \ 1) \ 1) * y) * R(z,x,x),u,L(z,x,x)) = a(y * T(z * (x \ 1),x),u,R(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(27195,a,33461,a)].">
      <j1 rule="hyper" parents="27195 33461"/>
    </justification>
  </clause>

  <clause id="33683">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),u,u) = L((a(x,y,z) \ ((u \ a(x,y,z)) \ 1)) * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(28236(a,1),33573(a,2,1,1,2))].">
      <j1 rule="para" parents="28236 33573"/>
    </justification>
  </clause>

  <clause id="33684">
    <literal><![CDATA[
      a(x \ (a(y,y,z) * (u \ z)),w,v5) = a(x \ (u \ L(z,y,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),33636(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30617 33636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33685">
    <literal><![CDATA[
      a(L(x \ 1,x,a(y,y,z) * (u \ z)) \ (u \ L(z,y,y)),w,v5) = a(T((a(y,y,z) * (u \ z)) * x,x \ 1),w,v5)
    ]]></literal>
    <justification jstring="[para(6487(a,1),33684(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6487 33684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33689">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,y,w)) * (a(y,z,u) / a(y,y,w)) = a(y,y,w) \ (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,30626,a(flip),b,33664,a),flip(a)].">
      <j1 rule="hyper" parents="370 30626 33664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33690">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,y,w)) * (a(y,z,u) / a(y,y,w)) = (a(y,y,w) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,32190,a(flip),b,33689,a),flip(a)].">
      <j1 rule="hyper" parents="370 32190 33689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33691">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,y,w)) * (a(y,z,u) / a(y,y,w)) = (a(y,y,w) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(28339(a,1),33690(a,1,1))].">
      <j1 rule="para" parents="28339 33690"/>
    </justification>
  </clause>

  <clause id="33692">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(x,u,w) = z * (a(x,u,w) / a(x,x,y))
    ]]></literal>
    <justification jstring="[para(33061(a,1),33691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33061 33691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33693">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(x,u,w) = z * (a(x,x,y) \ a(x,u,w))
    ]]></literal>
    <justification jstring="[para(23572(a,1),33692(a,2,2))].">
      <j1 rule="para" parents="23572 33692"/>
    </justification>
  </clause>

  <clause id="33694">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(x,u,w) != z * v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) \ a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(33693(a,2),40(a,1))].">
      <j1 rule="para" parents="33693 40"/>
    </justification>
  </clause>

  <clause id="33695">
    <literal><![CDATA[
      a((((x \ 1) \ 1) * y) * L(z,x,x),u,L(z,x,x)) = a(y * T(z * (x \ 1),x),u,R(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(27329,a,33682,a)].">
      <j1 rule="hyper" parents="27329 33682"/>
    </justification>
  </clause>

  <clause id="33696">
    <literal><![CDATA[
      L(L(a(x,y,z) \ u,w,v5),u,u) = L((u \ a(x,y,z)) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(23621(a,1),33683(a,2,1))].">
      <j1 rule="para" parents="23621 33683"/>
    </justification>
  </clause>

  <clause id="33699">
    <literal><![CDATA[
      a(x \ ((y * x) \ (((x \ 1) \ 1) * z)),u,y) = a(z * T(y * (x \ 1),x),u,R(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,32556,a(flip),b,33695,a)].">
      <j1 rule="hyper" parents="60 32556 33695"/>
    </justification>
  </clause>

  <clause id="33700">
    <literal><![CDATA[
      a(x * T(y * (z \ 1),z),u,R(y,z,z)) = a(z \ ((y * z) \ ((z \ 1) * x)),u,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,27542,a(flip),b,33699,a),flip(a)].">
      <j1 rule="hyper" parents="60 27542 33699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33701">
    <literal><![CDATA[
      a(x * T(y * (z \ 1),z),u,R(y,z,z)) = a(z \ ((y * z) \ (z * x)),u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,27542,a(flip),b,33700,a),flip(a)].">
      <j1 rule="hyper" parents="370 27542 33700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33702">
    <literal><![CDATA[
      a(x * T(y * (z \ 1),z),u,R(y,z,z)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,33475,a(flip),b,33701,a),flip(a)].">
      <j1 rule="hyper" parents="370 33475 33701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33703">
    <literal><![CDATA[
      a(x * T(y * (z \ 1),z),u,L(y,z,z)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(27195,a,33702,a)].">
      <j1 rule="hyper" parents="27195 33702"/>
    </justification>
  </clause>

  <clause id="33704">
    <literal><![CDATA[
      a(x * (y * (z \ 1)),u,L(y,z,z)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(26517,a,33703,a)].">
      <j1 rule="hyper" parents="26517 33703"/>
    </justification>
  </clause>

  <clause id="33705">
    <literal><![CDATA[
      a((x * y) * z,u,L(x,y,y)) = a((y \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(26669,a,33704,a)].">
      <j1 rule="hyper" parents="26669 33704"/>
    </justification>
  </clause>

  <clause id="33707">
    <literal><![CDATA[
      a(R((x * y) * z,x * y,x * y),u,L(x,y,y)) = a((y \ ((z * (x * y)) * (1 / (x * y)))) * x,u,x)
    ]]></literal>
    <justification jstring="[para(3283(a,1),33705(a,1,1))].">
      <j1 rule="para" parents="3283 33705"/>
    </justification>
  </clause>

  <clause id="33708">
    <literal><![CDATA[
      a((x \ (L(y,z * x,z * x) \ 1)) * z,u,z) = a((1 / (z * x)) \ (y \ 1),u,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(30021(a,1),33705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30021 33705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33709">
    <literal><![CDATA[
      a((x \ (L(y,z * x,z * x) \ 1)) * z,u,z) = a((1 / (z * x)) \ y,u,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26757,a(flip),b,33708,a),flip(a)].">
      <j1 rule="hyper" parents="370 26757 33708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33710">
    <literal><![CDATA[
      a((x \ (L(y,z * x,z * x) \ 1)) * z,u,z) = a((z * x) \ y,u,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,2966,a(flip),b,33709,a),flip(a)].">
      <j1 rule="hyper" parents="370 2966 33709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33711">
    <literal><![CDATA[
      a((x \ (L(y,z * x,z * x) \ 1)) * z,u,z) = a(x \ (z \ y),u,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32193,a(flip),b,33710,a),flip(a)].">
      <j1 rule="hyper" parents="370 32193 33710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33712">
    <literal><![CDATA[
      a((x \ (L(y,z * x,z * x) \ 1)) * z,u,z) = a(x * (z \ y),u,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32406,a(flip),b,33711,a),flip(a)].">
      <j1 rule="hyper" parents="370 32406 33711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33713">
    <literal><![CDATA[
      a((x \ L(y,z * x,z * x)) * z,u,z) = a(x * (z \ y),u,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26631,a(flip),b,33712,a)].">
      <j1 rule="hyper" parents="60 26631 33712"/>
    </justification>
  </clause>

  <clause id="33714">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,w,a(y,u,L(z,x,a(v5,v6,v6)))) = a(w,a(x,u,z),y)
    ]]></literal>
    <justification jstring="[para(32924(a,1),33356(a,1,1))].">
      <j1 rule="para" parents="32924 33356"/>
    </justification>
  </clause>

  <clause id="33715">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,w,a(z,u,y)) = a(w,a(x,u,z),y)
    ]]></literal>
    <justification jstring="[para(32924(a,1),33714(a,1,2))].">
      <j1 rule="para" parents="32924 33714"/>
    </justification>
  </clause>

  <clause id="33717">
    <literal><![CDATA[
      a(x * (a(y,y,z) \ ((u \ L(z,y,y)) \ a(y,y,z))),w,v5) = a(x * (a(y,y,z) * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,32832,a(flip),b,33637,a),flip(a)].">
      <j1 rule="hyper" parents="370 32832 33637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33718">
    <literal><![CDATA[
      a(x * ((y \ L(z,u,u)) \ 1),w,v5) = a(x * (a(u,u,z) * (y \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(32831(a,1),33717(a,1,1,2))].">
      <j1 rule="para" parents="32831 33717"/>
    </justification>
  </clause>

  <clause id="33719">
    <literal><![CDATA[
      a(x * (a(y,y,z) * (u \ z)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (u \ L(z,y,y)),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(33718(a,1),26607(a,1))].">
      <j1 rule="para" parents="33718 26607"/>
    </justification>
  </clause>

  <clause id="33721">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,v5,v6)) = a(x,y,L(z,u,w)) * a(v6,v5,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32346,a(flip),b,33034,a),flip(a)].">
      <j1 rule="hyper" parents="60 32346 33034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33722">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,v5,v6)) = a(x,y,L(z,u,w)) * a(v6,v5,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(31136(a,1),33721(a,2,2))].">
      <j1 rule="para" parents="31136 33721"/>
    </justification>
  </clause>

  <clause id="33723">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,w,u)) = a(x,y,z) * a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[hyper(370,a,32548,a(flip),b,33722,a),flip(a)].">
      <j1 rule="hyper" parents="370 32548 33722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33724">
    <literal><![CDATA[
      L(x * a(y,z,a(z * a(u,z,y),x,u)),z,a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,31214,a(flip),b,33113,a)].">
      <j1 rule="hyper" parents="60 31214 33113"/>
    </justification>
  </clause>

  <clause id="33725">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(u,y,z)) = y * L(y \ x,y,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(33050(a,1),33724(a,1,1,2))].">
      <j1 rule="para" parents="33050 33724"/>
    </justification>
  </clause>

  <clause id="33726">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,u)) = L(y,a(z,x,u),x)
    ]]></literal>
    <justification jstring="[hyper(60,a,33093,a(flip),b,33725,a),flip(a)].">
      <j1 rule="hyper" parents="60 33093 33725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33727">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(u,z,y)) = L(x,a(u,z,y),z)
    ]]></literal>
    <justification jstring="[hyper(31991,a,33726,a)].">
      <j1 rule="hyper" parents="31991 33726"/>
    </justification>
  </clause>

  <clause id="33728">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),y) = (y * a(x,y,z)) * (y \ u)
    ]]></literal>
    <justification jstring="[para(33727(a,1),32020(a,1,2))].">
      <j1 rule="para" parents="33727 32020"/>
    </justification>
  </clause>

  <clause id="33729">
    <literal><![CDATA[
      (x * a(y,x,z)) * (x \ u) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,31734,a(flip),b,33728,a),flip(a)].">
      <j1 rule="hyper" parents="60 31734 33728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33730">
    <literal><![CDATA[
      (x * (x \ y)) \ (x * ((a(z,x,u) \ x) \ y)) = L(a(z,x,u),x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(125,a,33729,a(flip),b,28253,a)].">
      <j1 rule="hyper" parents="125 33729 28253"/>
    </justification>
  </clause>

  <clause id="33732">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = L(a(z,y,u),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(404,a,33730,a)].">
      <j1 rule="hyper" parents="404 33730"/>
    </justification>
  </clause>

  <clause id="33733">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = L(a(z,y,u),y,x * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,31566,a(flip),b,33732,a),flip(a)].">
      <j1 rule="hyper" parents="370 31566 33732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33735">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,L(u,y,x * y)) = w
    ]]></literal>
    <justification jstring="[para(33733(a,2),32447(a,1))].">
      <j1 rule="para" parents="33733 32447"/>
    </justification>
  </clause>

  <clause id="33736">
    <literal><![CDATA[
      a(x,y,L(L(z,u,y),y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,y,u * y)) = w
    ]]></literal>
    <justification jstring="[para(33486(a,1),33735(a,1))].">
      <j1 rule="para" parents="33486 33735"/>
    </justification>
  </clause>

  <clause id="33737">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(R(z \ 1,z,u),R(z \ 1,z,u),u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(2796(a,1),33655(a,1,2,1,2))].">
      <j1 rule="para" parents="2796 33655"/>
    </justification>
  </clause>

  <clause id="33738">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(R(z \ 1,z,u),L(z \ 1,z,u),u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(30079(a,1),33737(a,1,2,2))].">
      <j1 rule="para" parents="30079 33737"/>
    </justification>
  </clause>

  <clause id="33739">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(R(z \ 1,z,u),L(z,z,u),u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(3911(a,1),33738(a,1,2,2))].">
      <j1 rule="para" parents="3911 33738"/>
    </justification>
  </clause>

  <clause id="33740">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(R(z \ 1,z,u),z,u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(33070(a,1),33739(a,1,2,2))].">
      <j1 rule="para" parents="33070 33739"/>
    </justification>
  </clause>

  <clause id="33741">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(z \ 1,z,u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(31115(a,1),33740(a,1,2,2))].">
      <j1 rule="para" parents="31115 33740"/>
    </justification>
  </clause>

  <clause id="33742">
    <literal><![CDATA[
      a(x,(y \ (T(z,z \ 1) * u)) * a(z,z,u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(2962(a,1),33741(a,1,2,2))].">
      <j1 rule="para" parents="2962 33741"/>
    </justification>
  </clause>

  <clause id="33743">
    <literal><![CDATA[
      a(x,a(y,y,z) * (u \ (y * z)),w) = a(x,u \ (y \ z),w)
    ]]></literal>
    <justification jstring="[hyper(27760,a,33742,a)].">
      <j1 rule="hyper" parents="27760 33742"/>
    </justification>
  </clause>

  <clause id="33744">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * (1 / (z * x)))) * z,u,z) = a((z * x) * y,u,L(L(z,x,x),z * x,z * x))
    ]]></literal>
    <justification jstring="[hyper(32460,a,33707,a),flip(a)].">
      <j1 rule="hyper" parents="32460 33707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33745">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * (1 / (z * x)))) * z,u,z) = a((z * x) * y,u,L((1 / (x / z)) * x,x,x))
    ]]></literal>
    <justification jstring="[para(29608(a,1),33744(a,2,3))].">
      <j1 rule="para" parents="29608 33744"/>
    </justification>
  </clause>

  <clause id="33746">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * (1 / (z * x)))) * z,u,z) = a((z * x) * y,u,x \ (1 / (x / z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,29054,a(flip),b,33745,a),flip(a)].">
      <j1 rule="hyper" parents="370 29054 33745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33747">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * (1 / (z * x)))) * z,u,z) = a((z * x) * y,u,x \ (x / z))
    ]]></literal>
    <justification jstring="[hyper(370,a,3147,a(flip),b,33746,a),flip(a)].">
      <j1 rule="hyper" parents="370 3147 33746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33748">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * (1 / (z * x)))) * z,u,z) = a((z * x) * y,u,x \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,26944,a(flip),b,33747,a),flip(a)].">
      <j1 rule="hyper" parents="370 26944 33747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33749">
    <literal><![CDATA[
      a((x \ ((y * (z * x)) * ((z * x) \ 1))) * z,u,z) = a((z * x) * y,u,x \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27767,a(flip),b,33748,a)].">
      <j1 rule="hyper" parents="60 27767 33748"/>
    </justification>
  </clause>

  <clause id="33750">
    <literal><![CDATA[
      a((x \ R(y,z * x,z * x)) * z,u,z) = a((z * x) * y,u,x \ (z \ x))
    ]]></literal>
    <justification jstring="[para(1111(a,1),33749(a,1,1,1,2))].">
      <j1 rule="para" parents="1111 33749"/>
    </justification>
  </clause>

  <clause id="33751">
    <literal><![CDATA[
      a((x \ L(y,z * x,z * x)) * z,u,z) = a((z * x) * y,u,x \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(27354,a,33750,a)].">
      <j1 rule="hyper" parents="27354 33750"/>
    </justification>
  </clause>

  <clause id="33752">
    <literal><![CDATA[
      a((x * y) * z,u,y \ (x \ y)) = a(y * (x \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,33713,a(flip),b,33751,a),flip(a)].">
      <j1 rule="hyper" parents="60 33713 33751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33753">
    <literal><![CDATA[
      a(x,y,a(z \ (u \ z),w,(u * z) * v5)) = a(x,w,a(z * (u \ v5),y,u))
    ]]></literal>
    <justification jstring="[para(33752(a,1),32979(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33752 32979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33754">
    <literal><![CDATA[
      a(x,y,a(y,z,(y * x) * u)) * a(x * (y \ u),z,y) = a((y * x) * u,z,y)
    ]]></literal>
    <justification jstring="[para(33752(a,1),33173(a,1,2))].">
      <j1 rule="para" parents="33752 33173"/>
    </justification>
  </clause>

  <clause id="33755">
    <literal><![CDATA[
      a(x,x,a((y * z) * u,w,y)) = a(x,x,a(z * (y \ u),w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,33043,a(flip),b,33753,a)].">
      <j1 rule="hyper" parents="60 33043 33753"/>
    </justification>
  </clause>

  <clause id="33756">
    <literal><![CDATA[
      a(x,y,a(z,z,x * u)) * a(x * (z \ u),y,z) = a((z * x) * u,y,z)
    ]]></literal>
    <justification jstring="[para(32982(a,1),33754(a,1,1))].">
      <j1 rule="para" parents="32982 33754"/>
    </justification>
  </clause>

  <clause id="33757">
    <literal><![CDATA[
      a(L(x,y,y) * L(x * y,y,y),z,L(x * y,y,y) \ u) = a(L(1 / y,y,x),z,u * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(370,a,29691,a(flip),b,32445,a),flip(a)].">
      <j1 rule="hyper" parents="370 29691 32445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33758">
    <literal><![CDATA[
      a(L(x,y,y) * L(x * y,y,y),z,L(x * y,y,y) \ u) = a(1 / y,z,L(u * (y \ x),y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32315,a(flip),b,33757,a),flip(a)].">
      <j1 rule="hyper" parents="370 32315 33757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33759">
    <literal><![CDATA[
      a(L(x,y,y) * L(x * y,y,y),z,L(x * y,y,y) \ u) = a(y,z,L(u * (y \ x),y,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,2957,a(flip),b,33758,a),flip(a)].">
      <j1 rule="hyper" parents="370 2957 33758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33760">
    <literal><![CDATA[
      a(L(x,y,y) * L(x * y,y,y),z,(y \ x) \ u) = a(y,z,L(u * (y \ x),y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,29720,a(flip),b,33759,a)].">
      <j1 rule="hyper" parents="60 29720 33759"/>
    </justification>
  </clause>

  <clause id="33761">
    <literal><![CDATA[
      a((x \ y) * L(y,x,x),z,(x \ y) \ u) = a(x,z,L(u * (x \ y),x,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,31657,a(flip),b,33760,a)].">
      <j1 rule="hyper" parents="60 31657 33760"/>
    </justification>
  </clause>

  <clause id="33762">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ u,z,z)) = a(x,y,L(u * (x \ z),x,z))
    ]]></literal>
    <justification jstring="[hyper(32462,a,33761,a)].">
      <j1 rule="hyper" parents="32462 33761"/>
    </justification>
  </clause>

  <clause id="33763">
    <literal><![CDATA[
      a(x,y,L(z \ (x * u),z,z)) = a(x,y,L(u * (x \ z),x,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32378,a(flip),b,33762,a)].">
      <j1 rule="hyper" parents="60 32378 33762"/>
    </justification>
  </clause>

  <clause id="33764">
    <literal><![CDATA[
      a(x,y,L(z * (x \ u),x,u)) = a(x,y,u * (x * z))
    ]]></literal>
    <justification jstring="[hyper(27010,a,33763,a),flip(a)].">
      <j1 rule="hyper" parents="27010 33763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33765">
    <literal><![CDATA[
      a(x,y,z * (x \ y)) = a(x,y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(32888,a,33764,a)].">
      <j1 rule="hyper" parents="32888 33764"/>
    </justification>
  </clause>

  <clause id="33766">
    <literal><![CDATA[
      a(x,y,L((x \ z) * u,x,z)) = a(x,y,z * (x * u))
    ]]></literal>
    <justification jstring="[hyper(26996,a,33764,a)].">
      <j1 rule="hyper" parents="26996 33764"/>
    </justification>
  </clause>

  <clause id="33767">
    <literal><![CDATA[
      a(x,y,(z * x) * y) = a(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,27031,a,b,33765,a)].">
      <j1 rule="hyper" parents="370 27031 33765"/>
    </justification>
  </clause>

  <clause id="33768">
    <literal><![CDATA[
      a(x \ y,x,T((x \ y) \ z,u) * ((x \ y) \ x)) = a(x \ y,x,y * T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(1623(a,1),33765(a,2,3))].">
      <j1 rule="para" parents="1623 33765"/>
    </justification>
  </clause>

  <clause id="33769">
    <literal><![CDATA[
      a(x,y,z * (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(33765(a,2),26976(a,1))].">
      <j1 rule="para" parents="33765 26976"/>
    </justification>
  </clause>

  <clause id="33770">
    <literal><![CDATA[
      a(x \ y,x,T((x \ y) \ z,u) * ((y \ x) * x)) = a(x \ y,x,y * T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[hyper(33540,a,33768,a)].">
      <j1 rule="hyper" parents="33540 33768"/>
    </justification>
  </clause>

  <clause id="33771">
    <literal><![CDATA[
      a(x \ y,x,((x \ y) \ z) * ((y \ x) * x)) = a(x \ y,x,y * T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[hyper(26973,a,33770,a)].">
      <j1 rule="hyper" parents="26973 33770"/>
    </justification>
  </clause>

  <clause id="33772">
    <literal><![CDATA[
      a(x \ y,x,y * T(y \ (x * z),u)) = a(x * y,x,((x \ y) \ z) * ((y \ x) * x))
    ]]></literal>
    <justification jstring="[hyper(31461,a,33771,a),flip(a)].">
      <j1 rule="hyper" parents="31461 33771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33774">
    <literal><![CDATA[
      a(x * y,x,((x \ y) \ z) * ((y \ x) * x)) = a(x \ y,x,y * (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(26968,a,33772,a),flip(a)].">
      <j1 rule="hyper" parents="26968 33772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33775">
    <literal><![CDATA[
      a(x * y,x,((x \ y) \ z) * ((y \ x) * x)) = a(x \ y,x,x * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),33774(a,2,3))].">
      <j1 rule="para" parents="5 33774"/>
    </justification>
  </clause>

  <clause id="33777">
    <literal><![CDATA[
      a(x * y,x,((x \ y) \ z) * ((y \ x) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * y,x,x * z) = u
    ]]></literal>
    <justification jstring="[para(33775(a,2),31461(a,1))].">
      <j1 rule="para" parents="33775 31461"/>
    </justification>
  </clause>

  <clause id="33778">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) \ (w * L(L(y,x,a(x,z,u)),x,L(x,z,u))) = L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(33381(a,1),33264(a,1,1))].">
      <j1 rule="para" parents="33381 33264"/>
    </justification>
  </clause>

  <clause id="33779">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) \ (w * L(y,x,x)) = L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(33251(a,1),33778(a,1,2,2))].">
      <j1 rule="para" parents="33251 33778"/>
    </justification>
  </clause>

  <clause id="33781">
    <literal><![CDATA[
      x * (a(x,y,a(z,u,w)) * a(x,z,a(y,u,w))) = (1 / x) \ a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(28776(a,1),33355(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28776 33355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33783">
    <literal><![CDATA[
      (1 / x) \ a(y,a(x,z,u),w) = x * a(y,a(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(33354(a,1),33781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33354 33781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33784">
    <literal><![CDATA[
      R(x,a(y,y,z),u) * (x \ a(y,y,z)) = (z / (y * z)) * (y * a(x,a(y,y,z),u))
    ]]></literal>
    <justification jstring="[para(33783(a,1),31821(a,2,2))].">
      <j1 rule="para" parents="33783 31821"/>
    </justification>
  </clause>

  <clause id="33785">
    <literal><![CDATA[
      R(x,a(y,y,z),u) * (x \ a(y,y,z)) = y * (((y \ z) / z) * a(x,a(y,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(370,a,30254,a(flip),b,33784,a),flip(a)].">
      <j1 rule="hyper" parents="370 30254 33784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33786">
    <literal><![CDATA[
      L(x,a(y,y,z),u) * (x \ a(y,y,z)) = y * (((y \ z) / z) * a(x,a(y,y,z),u))
    ]]></literal>
    <justification jstring="[para(28368(a,1),33785(a,1,1))].">
      <j1 rule="para" parents="28368 33785"/>
    </justification>
  </clause>

  <clause id="33787">
    <literal><![CDATA[
      x * (((x \ y) / y) * a(z,a(x,x,y),u)) = a(u,a(x,x,y),z) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,30710,a(flip),b,33786,a),flip(a)].">
      <j1 rule="hyper" parents="60 30710 33786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33788">
    <literal><![CDATA[
      x * (((x \ y) / y) * a(z,a(x,x,y),u)) = a(z,a(x,x,y),u) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,30724,a(flip),b,33787,a),flip(a)].">
      <j1 rule="hyper" parents="370 30724 33787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33789">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u) \ 1) \ 1,a(z,z,u) \ 1,y * u) = a(x,y * u,a(z,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(32565(a,2),33208(a,1,1))].">
      <j1 rule="para" parents="32565 33208"/>
    </justification>
  </clause>

  <clause id="33790">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) \ 1,a(z,z,u) \ 1,y * u) = a(x,y * u,a(z,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3091(a,1),33789(a,1,1,1))].">
      <j1 rule="para" parents="3091 33789"/>
    </justification>
  </clause>

  <clause id="33791">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)),a(z,z,u) \ 1,y * u) = a(x,y * u,a(z,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(29336(a,1),33790(a,1,1))].">
      <j1 rule="para" parents="29336 33790"/>
    </justification>
  </clause>

  <clause id="33792">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)),a(z,z,u),y * u) = a(x,y * u,a(z,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(3530,a,33791,a)].">
      <j1 rule="hyper" parents="3530 33791"/>
    </justification>
  </clause>

  <clause id="33793">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),a(z,z,u),y * u)) = a(x,y * u,a(z,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(32447,a,33792,a)].">
      <j1 rule="hyper" parents="32447 33792"/>
    </justification>
  </clause>

  <clause id="33794">
    <literal><![CDATA[
      a(x,y * z,a(u,u,z) \ 1) \ 1 = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(30648(a,1),33793(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30648 33793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33795">
    <literal><![CDATA[
      a(x,y * z,a(u,u,z)) \ 1 = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(3091(a,1),33794(a,1,1))].">
      <j1 rule="para" parents="3091 33794"/>
    </justification>
  </clause>

  <clause id="33797">
    <literal><![CDATA[
      a(x,y * z,a(u,u,z)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(29337,a,33795,a)].">
      <j1 rule="hyper" parents="29337 33795"/>
    </justification>
  </clause>

  <clause id="33798">
    <literal><![CDATA[
      a(x,y * x,a(z,z,u)) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(32989,a,33797,a)].">
      <j1 rule="hyper" parents="32989 33797"/>
    </justification>
  </clause>

  <clause id="33799">
    <literal><![CDATA[
      a(x,x,a(y,z * y,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(32968,a,33797,a)].">
      <j1 rule="hyper" parents="32968 33797"/>
    </justification>
  </clause>

  <clause id="33800">
    <literal><![CDATA[
      a(x,y,y) * a(z,u,a(y,y,x)) = a(x,y,L(y,u * x,z))
    ]]></literal>
    <justification jstring="[para(33797(a,1),32330(a,1,2))].">
      <j1 rule="para" parents="33797 32330"/>
    </justification>
  </clause>

  <clause id="33801">
    <literal><![CDATA[
      a(x * y,L(y,x,x),a(z,z,u)) = a(u,x,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(3062,a,33798,a)].">
      <j1 rule="hyper" parents="3062 33798"/>
    </justification>
  </clause>

  <clause id="33802">
    <literal><![CDATA[
      a(x,x,a(y,y * z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(26459(a,1),33799(a,1,3))].">
      <j1 rule="para" parents="26459 33799"/>
    </justification>
  </clause>

  <clause id="33803">
    <literal><![CDATA[
      a(L((x * y) * z,x,x),u,a(w,w,y)) = a(w,w,a(y,u * y,y * (x \ z)))
    ]]></literal>
    <justification jstring="[para(33179(a,1),33799(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33179 33799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33804">
    <literal><![CDATA[
      a(L(x \ (y \ z),y,x),u,a(w,w,y)) = a(w,w,a(y,u * y,y * (x \ z)))
    ]]></literal>
    <justification jstring="[para(33190(a,1),33799(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33190 33799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33805">
    <literal><![CDATA[
      a(x,y * z,a(y,x,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(33002,a,33802,a)].">
      <j1 rule="hyper" parents="33002 33802"/>
    </justification>
  </clause>

  <clause id="33806">
    <literal><![CDATA[
      a(x,y,L(y,z * u,z)) = a(x,u,a(y,y,z)) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(33802(a,1),32957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33802 32957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33807">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(y,y,z)) = a(x,y,L(z,z * u,y))
    ]]></literal>
    <justification jstring="[para(33805(a,1),32330(a,1,2))].">
      <j1 rule="para" parents="33805 32330"/>
    </justification>
  </clause>

  <clause id="33808">
    <literal><![CDATA[
      a(x,y,L(y,z * x,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(32543,a,33800,a),flip(a)].">
      <j1 rule="hyper" parents="32543 33800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33809">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(u,x,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,33467,a(flip),b,33801,a)].">
      <j1 rule="hyper" parents="60 33467 33801"/>
    </justification>
  </clause>

  <clause id="33810">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(z,x,a(u,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,32975,a,b,33809,a),flip(a)].">
      <j1 rule="hyper" parents="370 32975 33809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33811">
    <literal><![CDATA[
      (x * (a(y,y,z * u) \ a(z * u,u,a(y,y,w)))) \ ((x * (a(y,y,z * u) \ 1)) * a(w,z,a(y,y,z * u))) = a(x,a(y,y,z * u),a(w,z,a(y,y,z * u)))
    ]]></literal>
    <justification jstring="[para(33809(a,2),14801(a,1,1,2,2))].">
      <j1 rule="para" parents="33809 14801"/>
    </justification>
  </clause>

  <clause id="33812">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) * (u * a(z,z,x)) = u * (a(z,z,x) * a(y * u,u,a(z,z,x)))
    ]]></literal>
    <justification jstring="[para(33809(a,1),32672(a,1,1))].">
      <j1 rule="para" parents="33809 32672"/>
    </justification>
  </clause>

  <clause id="33813">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,x,a(u,z,x * y)) = w
    ]]></literal>
    <justification jstring="[para(33809(a,2),32988(a,1))].">
      <j1 rule="para" parents="33809 32988"/>
    </justification>
  </clause>

  <clause id="33814">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,a(z,z,x * y)) = w
    ]]></literal>
    <justification jstring="[para(33810(a,2),32988(a,1))].">
      <j1 rule="para" parents="33810 32988"/>
    </justification>
  </clause>

  <clause id="33815">
    <literal><![CDATA[
      a(x,y,L(y,z * u,z)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32991,a(flip),b,33806,a),flip(a)].">
      <j1 rule="hyper" parents="370 32991 33806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33816">
    <literal><![CDATA[
      (x \ y) * a(z,u,L(u,y,x)) = x \ (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(33815(a,1),33449(a,1,2))].">
      <j1 rule="para" parents="33815 33449"/>
    </justification>
  </clause>

  <clause id="33817">
    <literal><![CDATA[
      (x * y) * a(z,u,L(u,y,R(1 / x,x,y))) = R(1 / x,x,y) \ (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(467(a,1),33816(a,1,1))].">
      <j1 rule="para" parents="467 33816"/>
    </justification>
  </clause>

  <clause id="33818">
    <literal><![CDATA[
      (x \ (y * z)) * a(z,y,L(y,y * z,x)) = x \ (y * R(z,y,y))
    ]]></literal>
    <justification jstring="[para(31089(a,1),33816(a,2,2))].">
      <j1 rule="para" parents="31089 33816"/>
    </justification>
  </clause>

  <clause id="33819">
    <literal><![CDATA[
      a(x,y,L(z,z * u,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(32993,a,33807,a),flip(a)].">
      <j1 rule="hyper" parents="32993 33807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33820">
    <literal><![CDATA[
      a(x,y,L(z \ (y \ u),(z \ (y \ u)) * z,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(344(a,1),33819(a,2,3))].">
      <j1 rule="para" parents="344 33819"/>
    </justification>
  </clause>

  <clause id="33821">
    <literal><![CDATA[
      (x \ (y * z)) * a(z,y,L(y,y,x)) = x \ (y * R(z,y,y))
    ]]></literal>
    <justification jstring="[para(33808(a,1),33818(a,1,2))].">
      <j1 rule="para" parents="33808 33818"/>
    </justification>
  </clause>

  <clause id="33822">
    <literal><![CDATA[
      (x \ (y * z)) * a(z,y,y) = x \ (y * R(z,y,y))
    ]]></literal>
    <justification jstring="[para(31775(a,1),33821(a,1,2))].">
      <j1 rule="para" parents="31775 33821"/>
    </justification>
  </clause>

  <clause id="33823">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * a(u,u,w)) = a(x,y,z \ (u * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(33822(a,1),28932(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33822 28932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33825">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * a(u,u,w)) = a(x,y,z \ (u * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,31672,a(flip),b,33823,a),flip(a)].">
      <j1 rule="hyper" parents="370 31672 33823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33826">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * a(u,u,w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(370,a,29667,a(flip),b,33825,a),flip(a)].">
      <j1 rule="hyper" parents="370 29667 33825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33827">
    <literal><![CDATA[
      a(x,y,L(z \ (y \ u),y \ u,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(26024(a,1),33820(a,1,3))].">
      <j1 rule="para" parents="26024 33820"/>
    </justification>
  </clause>

  <clause id="33829">
    <literal><![CDATA[
      a(x,y,L(z \ (y \ u),u * y,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(33433(a,1),33827(a,1,3))].">
      <j1 rule="para" parents="33433 33827"/>
    </justification>
  </clause>

  <clause id="33830">
    <literal><![CDATA[
      a(L((x * y) * z,x,x),u,a(w,w,y)) = a(y * (x \ z),u,a(w,w,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33799,a(flip),b,33803,a),flip(a)].">
      <j1 rule="hyper" parents="370 33799 33803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33831">
    <literal><![CDATA[
      a(L((x * y) * z,x,x),u,a(w,w,y)) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31834,a,b,33830,a),flip(a)].">
      <j1 rule="hyper" parents="370 31834 33830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33832">
    <literal><![CDATA[
      a((x * y) * z,u,L(a(w,w,y),x,x)) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(32429,a,33831,a)].">
      <j1 rule="hyper" parents="32429 33831"/>
    </justification>
  </clause>

  <clause id="33833">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,w,y)) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(32752(a,1),33832(a,1,3))].">
      <j1 rule="para" parents="32752 33832"/>
    </justification>
  </clause>

  <clause id="33835">
    <literal><![CDATA[
      a(L(x \ (y \ z),y,x),u,a(w,w,y)) = a(y * (x \ z),u,a(w,w,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33799,a(flip),b,33804,a),flip(a)].">
      <j1 rule="hyper" parents="370 33799 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33836">
    <literal><![CDATA[
      a(L(x \ (y \ z),y,x),u,a(w,w,y)) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,31834,a,b,33835,a),flip(a)].">
      <j1 rule="hyper" parents="370 31834 33835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33837">
    <literal><![CDATA[
      a(x \ (y \ z),u,a(w,w,L(y,y,x))) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(32245,a,33836,a)].">
      <j1 rule="hyper" parents="32245 33836"/>
    </justification>
  </clause>

  <clause id="33838">
    <literal><![CDATA[
      a(x \ (y \ z),u,a(w,w,y)) = a(y,w,a(y * (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(32849(a,1),33837(a,1,3))].">
      <j1 rule="para" parents="32849 33837"/>
    </justification>
  </clause>

  <clause id="33839">
    <literal><![CDATA[
      a(x,y,a(z \ (x \ u),w,y)) = a(x,y,a(x * (z \ u),w,y))
    ]]></literal>
    <justification jstring="[hyper(32976,a,33838,a)].">
      <j1 rule="hyper" parents="32976 33838"/>
    </justification>
  </clause>

  <clause id="33841">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,w,x)) = a(x,w,a(x * (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(33086,a,33839,a)].">
      <j1 rule="hyper" parents="33086 33839"/>
    </justification>
  </clause>

  <clause id="33842">
    <literal><![CDATA[
      a(x,y,a(x * (z \ u),w,y)) = a(y,y,a((x * z) * u,w,x))
    ]]></literal>
    <justification jstring="[hyper(32951,a,33841,a),flip(a)].">
      <j1 rule="hyper" parents="32951 33841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33843">
    <literal><![CDATA[
      a(x,y,a(x * (z \ u),w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,y,a(x,w,u * (x * z))) = v5
    ]]></literal>
    <justification jstring="[para(33841(a,1),33025(a,1))].">
      <j1 rule="para" parents="33841 33025"/>
    </justification>
  </clause>

  <clause id="33844">
    <literal><![CDATA[
      a(x,y,a(x * (z \ u),w,y)) = a(y,y,a(z * (x \ u),w,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,33755,a(flip),b,33842,a),flip(a)].">
      <j1 rule="hyper" parents="370 33755 33842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33845">
    <literal><![CDATA[
      a(x,y,a(z,z,x * (u \ w))) = a(z,z,a(u * (x \ w),y,x))
    ]]></literal>
    <justification jstring="[hyper(33004,a,33844,a)].">
      <j1 rule="hyper" parents="33004 33844"/>
    </justification>
  </clause>

  <clause id="33846">
    <literal><![CDATA[
      a(x,x,a(y * (z \ u),w,z)) = a(y \ u,x,a(z,w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33226,a(flip),b,33845,a),flip(a)].">
      <j1 rule="hyper" parents="60 33226 33845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33848">
    <literal><![CDATA[
      a(x,x,a(y * (z \ u),w,z)) = a(u * y,w,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32999,a(flip),b,33846,a),flip(a)].">
      <j1 rule="hyper" parents="370 32999 33846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33849">
    <literal><![CDATA[
      a(x,y,a(x * (z \ u),w,y)) = a(u * z,w,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33844,a,b,33848,a)].">
      <j1 rule="hyper" parents="60 33844 33848"/>
    </justification>
  </clause>

  <clause id="33850">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,w,y)) = a(z * x,u,a(w,w,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,33833,a,b,33849,a)].">
      <j1 rule="hyper" parents="60 33833 33849"/>
    </justification>
  </clause>

  <clause id="33851">
    <literal><![CDATA[
      a(x,x,a(y,z,u * (y * w))) = a(u * w,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(33843,a,33849,a)].">
      <j1 rule="hyper" parents="33843 33849"/>
    </justification>
  </clause>

  <clause id="33852">
    <literal><![CDATA[
      (x * y) * a(z,u,L(u,y,L(1 / x,x,y))) = R(1 / x,x,y) \ (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(27279(a,1),33817(a,1,2,3))].">
      <j1 rule="para" parents="27279 33817"/>
    </justification>
  </clause>

  <clause id="33853">
    <literal><![CDATA[
      (x * y) * a(z,u,L(u,y,L(x,x,y))) = R(1 / x,x,y) \ (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(3804(a,1),33852(a,1,2,3))].">
      <j1 rule="para" parents="3804 33852"/>
    </justification>
  </clause>

  <clause id="33854">
    <literal><![CDATA[
      R(1 / x,x,y) \ (y * a(z,u,u)) = (x * y) * a(z,u,L(u,y,x))
    ]]></literal>
    <justification jstring="[para(33254(a,1),33853(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="33254 33853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33855">
    <literal><![CDATA[
      R(1 / x,x,y) \ (y * a(z,u,u)) = x * (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32327,a(flip),b,33854,a),flip(a)].">
      <j1 rule="hyper" parents="370 32327 33854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33856">
    <literal><![CDATA[
      a(R(1 / x,x,y),R(1 / x,x,y),y * a(z,u,u)) = R(1 / x,x,y) * ((x * (y * a(z,u,u))) / (y * a(z,u,u)))
    ]]></literal>
    <justification jstring="[para(33855(a,1),28440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="33855 28440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33857">
    <literal><![CDATA[
      a(x,x,L(y,z,z * u)) * u = u * (a(x,x,y) * a(z * u,u,a(x,x,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,32998,a(flip),b,33812,a)].">
      <j1 rule="hyper" parents="60 32998 33812"/>
    </justification>
  </clause>

  <clause id="33858">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ u) = u * (a(x,x,y) * a(z * u,u,a(x,x,y)))
    ]]></literal>
    <justification jstring="[hyper(60,a,32525,a(flip),b,33857,a)].">
      <j1 rule="hyper" parents="60 32525 33857"/>
    </justification>
  </clause>

  <clause id="33859">
    <literal><![CDATA[
      a(T(x,y) * (x * y),z,x \ (((y \ 1) \ x) * u)) = a(y,z,L(T(y \ 1,y * x) \ u,x * y,x * y))
    ]]></literal>
    <justification jstring="[para(17(a,2),33447(a,1,1,1))].">
      <j1 rule="para" parents="17 33447"/>
    </justification>
  </clause>

  <clause id="33860">
    <literal><![CDATA[
      a(x * (T(x,y) * y),z,x \ (((y \ 1) \ x) * u)) = a(y,z,L(T(y \ 1,y * x) \ u,x * y,x * y))
    ]]></literal>
    <justification jstring="[para(1668(a,1),33859(a,1,1))].">
      <j1 rule="para" parents="1668 33859"/>
    </justification>
  </clause>

  <clause id="33861">
    <literal><![CDATA[
      a(x * (T(x,y) * y),z,x \ ((y \ x) * u)) = a(y,z,L(T(y \ 1,y * x) \ u,x * y,x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,3152,a(flip),b,33860,a)].">
      <j1 rule="hyper" parents="60 3152 33860"/>
    </justification>
  </clause>

  <clause id="33862">
    <literal><![CDATA[
      a(x * (x * y),z,x \ ((y \ x) * u)) = a(y,z,L(T(y \ 1,y * x) \ u,x * y,x * y))
    ]]></literal>
    <justification jstring="[hyper(26665,a,33861,a)].">
      <j1 rule="hyper" parents="26665 33861"/>
    </justification>
  </clause>

  <clause id="33863">
    <literal><![CDATA[
      a(x,y,L(T(x \ 1,x * z) \ u,z * x,z * x)) = a(x,y,L(z \ ((x \ z) * u),z,z))
    ]]></literal>
    <justification jstring="[hyper(32458,a,33862,a),flip(a)].">
      <j1 rule="hyper" parents="32458 33862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33864">
    <literal><![CDATA[
      a(x,y,L(T(x \ 1,x * z) \ u,z * x,z * x)) = a(x,y,z * ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3101,a(flip),b,33863,a),flip(a)].">
      <j1 rule="hyper" parents="370 3101 33863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33865">
    <literal><![CDATA[
      a((x \ y) * y,z,T(x \ 1,x * y) \ u) = a(x,z,y * ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(32545,a,33864,a)].">
      <j1 rule="hyper" parents="32545 33864"/>
    </justification>
  </clause>

  <clause id="33866">
    <literal><![CDATA[
      a((x \ y) * y,z,(x \ 1) \ u) = a(x,z,y * ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(26979,a,33865,a)].">
      <j1 rule="hyper" parents="26979 33865"/>
    </justification>
  </clause>

  <clause id="33867">
    <literal><![CDATA[
      a((x \ y) * y,z,x \ u) = a(x,z,y * ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(3116,a,33866,a)].">
      <j1 rule="hyper" parents="3116 33866"/>
    </justification>
  </clause>

  <clause id="33869">
    <literal><![CDATA[
      a(x,y,(z \ x) \ (z \ u)) = a(x,y,z * ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33448,a(flip),b,33867,a)].">
      <j1 rule="hyper" parents="60 33448 33867"/>
    </justification>
  </clause>

  <clause id="33870">
    <literal><![CDATA[
      a(x,y,a(z * a(u,z,w),w,u)) * a(x,y,K(u,z * w) * ((u * w) \ (w * (z * u)))) = a(x,y,a(w,z,u) \ z)
    ]]></literal>
    <justification jstring="[para(31106(a,1),33048(a,1,1,3))].">
      <j1 rule="para" parents="31106 33048"/>
    </justification>
  </clause>

  <clause id="33871">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,(((x \ 1) \ 1) \ a(u,u,w)) * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(32899(a,1),33077(a,1,1))].">
      <j1 rule="para" parents="32899 33077"/>
    </justification>
  </clause>

  <clause id="33872">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,(a(u,u,w) / x) * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(28208(a,1),33871(a,2,3,1))].">
      <j1 rule="para" parents="28208 33871"/>
    </justification>
  </clause>

  <clause id="33873">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,a(u,u,w) * (x \ a(u,u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,27015,a(flip),b,33872,a),flip(a)].">
      <j1 rule="hyper" parents="370 27015 33872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33874">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,a(u,u,w) * (x * a(u,u,w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32833,a(flip),b,33873,a),flip(a)].">
      <j1 rule="hyper" parents="370 32833 33873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33875">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,w * (L(L(w,u,u),u,u) \ x))
    ]]></literal>
    <justification jstring="[para(30657(a,1),33874(a,2,3))].">
      <j1 rule="para" parents="30657 33874"/>
    </justification>
  </clause>

  <clause id="33876">
    <literal><![CDATA[
      ((L(x,y,z) \ a(u,u,w)) \ 1) \ ((x \ a(u,u,w)) \ 1) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,29092,a(flip),b,33875,a),flip(a)].">
      <j1 rule="hyper" parents="370 29092 33875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33878">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,(R(1 / y,z,y) * u) * 1) = a((R(1 / y,z,y) \ x) * u,w,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,27115,a(flip),b,33178,a),flip(a)].">
      <j1 rule="hyper" parents="370 27115 33178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33880">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,(R(1 / y,z,y) * u) * 1) = a((L(1 / y,z,y) \ x) * u,w,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,32054,a(flip),b,33878,a),flip(a)].">
      <j1 rule="hyper" parents="370 32054 33878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33881">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,(R(1 / y,z,y) * u) * 1) = a((L(y,z,y) \ x) * u,w,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,27599,a(flip),b,33880,a),flip(a)].">
      <j1 rule="hyper" parents="370 27599 33880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33882">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,(R(1 / y,z,y) * u) * 1) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26427,a(flip),b,33881,a),flip(a)].">
      <j1 rule="hyper" parents="370 26427 33881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33884">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,R(1 / y,z,y) * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[para(3(a,1),33882(a,1,3))].">
      <j1 rule="para" parents="3 33882"/>
    </justification>
  </clause>

  <clause id="33885">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,L(1 / y,z,y) * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,28605,a(flip),b,33884,a)].">
      <j1 rule="hyper" parents="60 28605 33884"/>
    </justification>
  </clause>

  <clause id="33886">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,L(y \ 1,z,y) * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,26953,a(flip),b,33885,a)].">
      <j1 rule="hyper" parents="60 26953 33885"/>
    </justification>
  </clause>

  <clause id="33887">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,L(y,z,y) * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,27055,a(flip),b,33886,a)].">
      <j1 rule="hyper" parents="60 27055 33886"/>
    </justification>
  </clause>

  <clause id="33888">
    <literal><![CDATA[
      a(x * (R(1 / y,z,y) * u),w,y * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(27108,a,33887,a)].">
      <j1 rule="hyper" parents="27108 33887"/>
    </justification>
  </clause>

  <clause id="33890">
    <literal><![CDATA[
      a(x * (L(1 / y,z,y) * u),w,y * u) = a(u * (y \ x),w,u * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,27348,a(flip),b,33888,a)].">
      <j1 rule="hyper" parents="60 27348 33888"/>
    </justification>
  </clause>

  <clause id="33891">
    <literal><![CDATA[
      a((L(x,y,x) * z) * u,w,x * z) = a(z * (x \ u),w,z * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,27610,a(flip),b,33890,a)].">
      <j1 rule="hyper" parents="60 27610 33890"/>
    </justification>
  </clause>

  <clause id="33892">
    <literal><![CDATA[
      a((x * y) * z,u,x * y) = a(y * (x \ z),u,y * x)
    ]]></literal>
    <justification jstring="[hyper(60,a,26868,a(flip),b,33891,a)].">
      <j1 rule="hyper" parents="60 26868 33891"/>
    </justification>
  </clause>

  <clause id="33893">
    <literal><![CDATA[
      a(x * (y \ z),u,x * y) != w
    ]]></literal>
    <literal><![CDATA[
      a(z * (x * y),u,x * y) = w
    ]]></literal>
    <justification jstring="[para(33892(a,1),31455(a,1))].">
      <j1 rule="para" parents="33892 31455"/>
    </justification>
  </clause>

  <clause id="33894">
    <literal><![CDATA[
      a(x \ y,z,L(L(x \ y,x * y,y) * u,x \ y,y)) = a(x \ y,z,((x \ y) * (y * u)) / T(y,x \ (y * u)))
    ]]></literal>
    <justification jstring="[para(33256(a,1),33244(a,1,3,1,1))].">
      <j1 rule="para" parents="33256 33244"/>
    </justification>
  </clause>

  <clause id="33895">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w)) = a(R(x \ 1,y,z) \ x,u,a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(32690(a,2),33310(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="32690 33310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33896">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w)) = a(L(x \ 1,y,z) \ x,u,a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,29687,a(flip),b,33895,a),flip(a)].">
      <j1 rule="hyper" parents="370 29687 33895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33897">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w)) = a(L(x,y,z) \ x,u,a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,4021,a(flip),b,33896,a),flip(a)].">
      <j1 rule="hyper" parents="370 4021 33896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33898">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w)) = a(a(z,y,x),u,a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(32572(a,2),33897(a,2,1))].">
      <j1 rule="para" parents="32572 33897"/>
    </justification>
  </clause>

  <clause id="33899">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,R(x \ 1,y,z) \ (x \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,32930,a(flip),b,33898,a),flip(a)].">
      <j1 rule="hyper" parents="370 32930 33898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33900">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,x \ (R(1 / x,y,z) \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[para(31751(a,1),33899(a,1,3))].">
      <j1 rule="para" parents="31751 33899"/>
    </justification>
  </clause>

  <clause id="33901">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,x \ (L(1 / x,y,z) \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(33662,a,33900,a)].">
      <j1 rule="hyper" parents="33662 33900"/>
    </justification>
  </clause>

  <clause id="33902">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,x \ (L(x \ 1,y,z) \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27221,a(flip),b,33901,a)].">
      <j1 rule="hyper" parents="60 27221 33901"/>
    </justification>
  </clause>

  <clause id="33903">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,x \ (L(x,y,z) \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,4023,a(flip),b,33902,a)].">
      <j1 rule="hyper" parents="60 4023 33902"/>
    </justification>
  </clause>

  <clause id="33904">
    <literal><![CDATA[
      a(x * R(1 / x,y,z),u,x * (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(29685,a,33903,a)].">
      <j1 rule="hyper" parents="29685 33903"/>
    </justification>
  </clause>

  <clause id="33905">
    <literal><![CDATA[
      a(x * L(1 / x,y,z),u,x * (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(27329,a,33904,a)].">
      <j1 rule="hyper" parents="27329 33904"/>
    </justification>
  </clause>

  <clause id="33906">
    <literal><![CDATA[
      a(x * L(x \ 1,y,z),u,x * (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(26688,a,33905,a)].">
      <j1 rule="hyper" parents="26688 33905"/>
    </justification>
  </clause>

  <clause id="33907">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,x * (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[para(3816(a,1),33906(a,1,1))].">
      <j1 rule="para" parents="3816 33906"/>
    </justification>
  </clause>

  <clause id="33908">
    <literal><![CDATA[
      a(L(x,y,z) * x,u,x \ (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,32433,a(flip),b,33907,a)].">
      <j1 rule="hyper" parents="60 32433 33907"/>
    </justification>
  </clause>

  <clause id="33909">
    <literal><![CDATA[
      a(x * L(x,y,z),u,x \ (L(x,y,z) * w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(26519,a,33908,a)].">
      <j1 rule="hyper" parents="26519 33908"/>
    </justification>
  </clause>

  <clause id="33910">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),(x \ u) * (a(y,z,y) \ w)) = a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w)))
    ]]></literal>
    <justification jstring="[para(14322(a,1),33594(a,1,3))].">
      <j1 rule="para" parents="14322 33594"/>
    </justification>
  </clause>

  <clause id="33911">
    <literal><![CDATA[
      a(L(x \ 1,x,a(y,y,z) * (u \ z)) \ (u \ L(z,y,y)),w,v5) = a((a(y,y,z) * (u \ z)) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26375,a(flip),b,33685,a),flip(a)].">
      <j1 rule="hyper" parents="370 26375 33685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33913">
    <literal><![CDATA[
      a(L(x \ 1,x,y \ L(z,u,u)) \ (y \ L(z,u,u)),w,v5) = a((a(u,u,z) * (y \ z)) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(33640(a,1),33911(a,1,1,1))].">
      <j1 rule="para" parents="33640 33911"/>
    </justification>
  </clause>

  <clause id="33914">
    <literal><![CDATA[
      a(T((x \ L(y,z,z)) * u,u \ 1),w,v5) = a((a(z,z,y) * (x \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(6487(a,1),33913(a,1,1))].">
      <j1 rule="para" parents="6487 33913"/>
    </justification>
  </clause>

  <clause id="33915">
    <literal><![CDATA[
      a((a(x,x,y) * (z \ y)) * u,w,v5) = a((z \ L(y,x,x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26506,a,33914,a),flip(a)].">
      <j1 rule="hyper" parents="26506 33914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33917">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,w,u))) * a(x,y,K(w,z * u) * ((w * u) \ (u * (z * w)))) = a(x,y,a(u,z,w) \ z)
    ]]></literal>
    <justification jstring="[para(32509(a,1),33870(a,1,1,3))].">
      <j1 rule="para" parents="32509 33870"/>
    </justification>
  </clause>

  <clause id="33918">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,K(w,z * u) * ((w * u) \ (u * (z * w)))) = a(x,y,a(u,z,w) \ z)
    ]]></literal>
    <justification jstring="[para(32637(a,1),33917(a,1,1,3))].">
      <j1 rule="para" parents="32637 33917"/>
    </justification>
  </clause>

  <clause id="33919">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(a(u,z,w) \ z,u,w)) = a(x,y,a(u,z,w) \ z)
    ]]></literal>
    <justification jstring="[para(29181(a,1),33918(a,1,2,3))].">
      <j1 rule="para" parents="29181 33918"/>
    </justification>
  </clause>

  <clause id="33920">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,w,u)) = a(x,y,a(u,z,w) \ z)
    ]]></literal>
    <justification jstring="[para(29215(a,1),33919(a,1,2))].">
      <j1 rule="para" parents="29215 33919"/>
    </justification>
  </clause>

  <clause id="33921">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32001,a(flip),b,33920,a),flip(a)].">
      <j1 rule="hyper" parents="370 32001 33920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33922">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(z,y,x),w) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33723,a(flip),b,33921,a)].">
      <j1 rule="hyper" parents="60 33723 33921"/>
    </justification>
  </clause>

  <clause id="33923">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(x,y,z),w) = a(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,32019,a(flip),b,33922,a)].">
      <j1 rule="hyper" parents="60 32019 33922"/>
    </justification>
  </clause>

  <clause id="33924">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(y,z,u) = a(y,z,u * a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,31284,a,b,33923,a)].">
      <j1 rule="hyper" parents="60 31284 33923"/>
    </justification>
  </clause>

  <clause id="33925">
    <literal><![CDATA[
      x * (((x \ y) / y) * a(z,a(x,x,y),u)) = a(x,x,y * a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33788,a,b,33924,a)].">
      <j1 rule="hyper" parents="60 33788 33924"/>
    </justification>
  </clause>

  <clause id="33926">
    <literal><![CDATA[
      a(x \ y,z,((x \ y) * (y * u)) / T(y,x \ (y * u))) = a(y \ x,z,L(x \ y,x * y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,32417,a(flip),b,33894,a),flip(a)].">
      <j1 rule="hyper" parents="60 32417 33894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33927">
    <literal><![CDATA[
      a(x \ y,z,((x \ y) * (y * u)) / T(y,x \ (y * u))) = a(y \ x,z,(y \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,33263,a(flip),b,33926,a),flip(a)].">
      <j1 rule="hyper" parents="370 33263 33926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33928">
    <literal><![CDATA[
      a(x \ y,z,y \ ((x \ y) * (y * u))) = a(y \ x,z,(y \ x) * u)
    ]]></literal>
    <justification jstring="[para(25809(a,1),33927(a,1,3))].">
      <j1 rule="para" parents="25809 33927"/>
    </justification>
  </clause>

  <clause id="33929">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) * u) = a(x * y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(32527,a,33928,a),flip(a)].">
      <j1 rule="hyper" parents="32527 33928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33930">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,y * (x * u)) = w
    ]]></literal>
    <justification jstring="[para(33928(a,1),32527(a,1))].">
      <j1 rule="para" parents="33928 32527"/>
    </justification>
  </clause>

  <clause id="33931">
    <literal><![CDATA[
      a(x \ y,z,u * (x \ y)) = a(x * y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(26965,a,33929,a)].">
      <j1 rule="hyper" parents="26965 33929"/>
    </justification>
  </clause>

  <clause id="33932">
    <literal><![CDATA[
      a(x \ y,z,x \ ((x \ y) * u)) = a(y * x,z,x * (y * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33543,a,b,33931,a)].">
      <j1 rule="hyper" parents="60 33543 33931"/>
    </justification>
  </clause>

  <clause id="33933">
    <literal><![CDATA[
      a(x * y,z,y * ((y \ x) * u)) = a(x * y,z,y * (x * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(32435,a,33932,a)].">
      <j1 rule="hyper" parents="32435 33932"/>
    </justification>
  </clause>

  <clause id="33934">
    <literal><![CDATA[
      a(x * y,z,((y \ x) * u) * y) = a(x * y,z,y * (x * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(26965,a,33933,a)].">
      <j1 rule="hyper" parents="26965 33933"/>
    </justification>
  </clause>

  <clause id="33935">
    <literal><![CDATA[
      a(x * y,z,((y \ x) * u) * y) = a(x * y,z,(x * (y \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,33934,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 33934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33937">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),(x \ u) * (w * a(y,z,y))) = a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,30679,a(flip),b,33910,a)].">
      <j1 rule="hyper" parents="60 30679 33910"/>
    </justification>
  </clause>

  <clause id="33938">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w))) = a(x,x * (a(y,z,y) \ u),w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27245,a(flip),b,33937,a),flip(a)].">
      <j1 rule="hyper" parents="60 27245 33937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33940">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w))) = a(x,x * (a(y,z,y) * u),w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,30698,a(flip),b,33938,a),flip(a)].">
      <j1 rule="hyper" parents="370 30698 33938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33941">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),u * (a(y,z,y) \ (x * w))) = a(x,u * x,w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,26833,a(flip),b,33940,a),flip(a)].">
      <j1 rule="hyper" parents="370 26833 33940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33943">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),u * (x * (a(y,z,y) \ w))) = a(x,u * x,w * (x \ u))
    ]]></literal>
    <justification jstring="[para(14300(a,1),33941(a,1,3,2))].">
      <j1 rule="para" parents="14300 33941"/>
    </justification>
  </clause>

  <clause id="33944">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),u * (x * (w * a(y,z,y)))) = a(x,u * x,w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,31065,a(flip),b,33943,a)].">
      <j1 rule="hyper" parents="60 31065 33943"/>
    </justification>
  </clause>

  <clause id="33945">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) \ u),(x * w) * u) = a(x,u * x,w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,27246,a(flip),b,33944,a)].">
      <j1 rule="hyper" parents="60 27246 33944"/>
    </justification>
  </clause>

  <clause id="33947">
    <literal><![CDATA[
      a(x,x * (a(y,z,y) * u),(x * w) * u) = a(x,u * x,w * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,30698,a(flip),b,33945,a)].">
      <j1 rule="hyper" parents="60 30698 33945"/>
    </justification>
  </clause>

  <clause id="33948">
    <literal><![CDATA[
      a(x,y * x,(x * z) * y) = a(x,y * x,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,26833,a(flip),b,33947,a)].">
      <j1 rule="hyper" parents="60 26833 33947"/>
    </justification>
  </clause>

  <clause id="33949">
    <literal><![CDATA[
      a((x * y) \ x,x / ((y \ 1) \ 1),(((x * y) \ x) * z) * x) = a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x))
    ]]></literal>
    <justification jstring="[para(3491(a,2),33948(a,1,2))].">
      <j1 rule="para" parents="3491 33948"/>
    </justification>
  </clause>

  <clause id="33950">
    <literal><![CDATA[
      R(a(x,y,z),u * a(x,y,z),a(x,y,z) * (u \ w)) * w = (z * (L(L(z,y,x),y,x) \ u)) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(33189(a,1),32524(a,1,1))].">
      <j1 rule="para" parents="33189 32524"/>
    </justification>
  </clause>

  <clause id="33951">
    <literal><![CDATA[
      a(x,L(y * L(z,u,w),a(w,u,z),a(w,u,z)) * v5,v6) = a(x,(a(w,u,z) * L(y * z,z,a(w,u,z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(33605(a,1),33107(a,2,2,1,2))].">
      <j1 rule="para" parents="33605 33107"/>
    </justification>
  </clause>

  <clause id="33952">
    <literal><![CDATA[
      a(x \ (y \ 1),z,L((y \ 1) \ ((x \ (y \ 1)) \ u),x \ (y \ 1),y)) = a(x \ (y \ 1),z,(x \ y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(1492(a,1),33192(a,1,3))].">
      <j1 rule="para" parents="1492 33192"/>
    </justification>
  </clause>

  <clause id="33953">
    <literal><![CDATA[
      a(x \ (y \ 1),z,L((y \ 1) \ ((x \ (y \ 1)) \ u),x \ y,y)) = a(x \ (y \ 1),z,(x \ y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(3724(a,1),33952(a,1,3))].">
      <j1 rule="para" parents="3724 33952"/>
    </justification>
  </clause>

  <clause id="33954">
    <literal><![CDATA[
      a(x \ (y \ 1),z,L(y \ ((x \ (y \ 1)) \ u),x \ y,y)) = a(x \ (y \ 1),z,(x \ y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,3972,a(flip),b,33953,a)].">
      <j1 rule="hyper" parents="60 3972 33953"/>
    </justification>
  </clause>

  <clause id="33955">
    <literal><![CDATA[
      a(x \ y,z,L(y \ ((x \ (y \ 1)) \ u),x \ y,y)) = a(x \ (y \ 1),z,(x \ y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,26757,a(flip),b,33954,a)].">
      <j1 rule="hyper" parents="60 26757 33954"/>
    </justification>
  </clause>

  <clause id="33956">
    <literal><![CDATA[
      a(x \ (y \ 1),z,(x \ y) * (y \ u)) = a(y \ x,z,y \ ((x \ (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,32417,a(flip),b,33955,a),flip(a)].">
      <j1 rule="hyper" parents="60 32417 33955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33957">
    <literal><![CDATA[
      a(x \ (y \ 1),z,(x \ y) * (y \ u)) = a(y \ x,z,y \ ((x \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,3154,a(flip),b,33956,a),flip(a)].">
      <j1 rule="hyper" parents="370 3154 33956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33958">
    <literal><![CDATA[
      a(x \ (y \ 1),z,(x \ y) * (y \ u)) = a(x * y,z,y * ((x \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32431,a(flip),b,33957,a),flip(a)].">
      <j1 rule="hyper" parents="370 32431 33957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33959">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) * (y \ u)) = a(x * y,z,y * ((x \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,26757,a(flip),b,33958,a)].">
      <j1 rule="hyper" parents="60 26757 33958"/>
    </justification>
  </clause>

  <clause id="33960">
    <literal><![CDATA[
      a(x * y,z,y * ((x \ y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,y * (x * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(33959(a,1),33930(a,1))].">
      <j1 rule="para" parents="33959 33930"/>
    </justification>
  </clause>

  <clause id="33961">
    <literal><![CDATA[
      a(R(1 / x,x,y),R(1 / x,x,y),y * a(z,u,u)) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),33856(a,2,2))].">
      <j1 rule="para" parents="6 33856"/>
    </justification>
  </clause>

  <clause id="33962">
    <literal><![CDATA[
      a(R(1 / x,x,y),R(1 / x,x,y),y * a(z,u,u)) = x * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,883,a(flip),b,33961,a),flip(a)].">
      <j1 rule="hyper" parents="370 883 33961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33963">
    <literal><![CDATA[
      a(R(1 / x,x,y),R(1 / x,x,y),y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,32690,a,b,33962,a),flip(a)].">
      <j1 rule="hyper" parents="370 32690 33962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33964">
    <literal><![CDATA[
      a(R(1 / x,x,y),L(1 / x,x,y),y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(30080,a,33963,a)].">
      <j1 rule="hyper" parents="30080 33963"/>
    </justification>
  </clause>

  <clause id="33965">
    <literal><![CDATA[
      a(R(1 / x,x,y),L(x \ 1,x,y),y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(26577,a,33964,a)].">
      <j1 rule="hyper" parents="26577 33964"/>
    </justification>
  </clause>

  <clause id="33966">
    <literal><![CDATA[
      a(R(1 / x,x,y),L(x,x,y),y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(26747,a,33965,a)].">
      <j1 rule="hyper" parents="26747 33965"/>
    </justification>
  </clause>

  <clause id="33967">
    <literal><![CDATA[
      a(1 / x,L(x,x,y),L(y * a(z,u,u),x,y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(32460,a,33966,a)].">
      <j1 rule="hyper" parents="32460 33966"/>
    </justification>
  </clause>

  <clause id="33968">
    <literal><![CDATA[
      a(x,L(x,x,y),L(y * a(z,u,u),x,y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(2969,a,33967,a)].">
      <j1 rule="hyper" parents="2969 33967"/>
    </justification>
  </clause>

  <clause id="33969">
    <literal><![CDATA[
      a(x,x,L(L(y * a(z,u,u),x,y),x,y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(29141,a,33968,a)].">
      <j1 rule="hyper" parents="29141 33968"/>
    </justification>
  </clause>

  <clause id="33970">
    <literal><![CDATA[
      a(x,x,y * a(z,u,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(30395,a,33969,a)].">
      <j1 rule="hyper" parents="30395 33969"/>
    </justification>
  </clause>

  <clause id="33971">
    <literal><![CDATA[
      a(x,x,a(y,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(32000,a,33970,a)].">
      <j1 rule="hyper" parents="32000 33970"/>
    </justification>
  </clause>

  <clause id="33973">
    <literal><![CDATA[
      a(x,x,y * (z * a(u,w,w))) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(32171(a,1),33970(a,1,3))].">
      <j1 rule="para" parents="32171 33970"/>
    </justification>
  </clause>

  <clause id="33974">
    <literal><![CDATA[
      a(x,x,y * L(z,u,u)) = a(x,x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(33644,a,33971,a)].">
      <j1 rule="hyper" parents="33644 33971"/>
    </justification>
  </clause>

  <clause id="33975">
    <literal><![CDATA[
      a(x,x,y * L(z,u,u)) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32771,a(flip),b,33974,a),flip(a)].">
      <j1 rule="hyper" parents="370 32771 33974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33976">
    <literal><![CDATA[
      a(x,x,y \ (z \ u)) = a(x,x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32787,a(flip),b,33975,a)].">
      <j1 rule="hyper" parents="60 32787 33975"/>
    </justification>
  </clause>

  <clause id="33977">
    <literal><![CDATA[
      a(x,x,y * (z \ u)) = a(x,x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(32776,a,33976,a)].">
      <j1 rule="hyper" parents="32776 33976"/>
    </justification>
  </clause>

  <clause id="33979">
    <literal><![CDATA[
      a(x,x,y * (z * (u \ 1))) = a(x,x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(26936,a,33977,a),flip(a)].">
      <j1 rule="hyper" parents="26936 33977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33980">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,z * (((y * u) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33388,a,b,33977,a)].">
      <j1 rule="hyper" parents="60 33388 33977"/>
    </justification>
  </clause>

  <clause id="33981">
    <literal><![CDATA[
      a(x,x,y * (a(z,u,u) * w)) = a(x,x,y * w)
    ]]></literal>
    <justification jstring="[hyper(26976,a,33973,a)].">
      <j1 rule="hyper" parents="26976 33973"/>
    </justification>
  </clause>

  <clause id="33982">
    <literal><![CDATA[
      a(x,x,(y * a(z,u,u)) * w) = a(x,x,w * y)
    ]]></literal>
    <justification jstring="[hyper(26965,a,33973,a)].">
      <j1 rule="hyper" parents="26965 33973"/>
    </justification>
  </clause>

  <clause id="33983">
    <literal><![CDATA[
      a(x,x,y * (z * a(u,u,w))) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,33124,a(flip),b,33981,a)].">
      <j1 rule="hyper" parents="60 33124 33981"/>
    </justification>
  </clause>

  <clause id="33984">
    <literal><![CDATA[
      a(x,x,(y * (z * a(u,y,y))) * w) = a(x,x,w * (y * z))
    ]]></literal>
    <justification jstring="[para(14786(a,1),33982(a,1,3,1))].">
      <j1 rule="para" parents="14786 33982"/>
    </justification>
  </clause>

  <clause id="33987">
    <literal><![CDATA[
      a(x,x,(y \ L(z,u,u)) * w) = a(x,x,w * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33648,a(flip),b,33983,a)].">
      <j1 rule="hyper" parents="60 33648 33983"/>
    </justification>
  </clause>

  <clause id="33988">
    <literal><![CDATA[
      a(x,x,(y \ z) * u) = a(x,x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(26992,a,33979,a),flip(a)].">
      <j1 rule="hyper" parents="26992 33979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33989">
    <literal><![CDATA[
      a(x,x,(y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,(z * y) * u) = w
    ]]></literal>
    <justification jstring="[para(33979(a,1),26992(a,1))].">
      <j1 rule="para" parents="33979 26992"/>
    </justification>
  </clause>

  <clause id="33990">
    <literal><![CDATA[
      a(x,x,((y * a(z,z,u)) \ L(u,z,z)) * w) = a(x,x,(u * y) * w)
    ]]></literal>
    <justification jstring="[para(32846(a,1),33988(a,2,3,1))].">
      <j1 rule="para" parents="32846 33988"/>
    </justification>
  </clause>

  <clause id="33991">
    <literal><![CDATA[
      a(x,y * x,a(z,z,(u * w) * v5)) = a((w \ u) * v5,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(33988(a,1),33798(a,1,3))].">
      <j1 rule="para" parents="33988 33798"/>
    </justification>
  </clause>

  <clause id="33993">
    <literal><![CDATA[
      a(x,x,(y \ L(z,u,u)) * w) = a(x,x,w * (z * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33977,a(flip),b,33987,a),flip(a)].">
      <j1 rule="hyper" parents="370 33977 33987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33994">
    <literal><![CDATA[
      a(x,x,(L(y,z,z) * u) * w) = a(x,x,w * (y * u))
    ]]></literal>
    <justification jstring="[hyper(33989,a,33993,a)].">
      <j1 rule="hyper" parents="33989 33993"/>
    </justification>
  </clause>

  <clause id="33995">
    <literal><![CDATA[
      a(x,x,y * (z * L(u,w,w))) = a(x,x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(27033,a,33994,a)].">
      <j1 rule="hyper" parents="27033 33994"/>
    </justification>
  </clause>

  <clause id="33996">
    <literal><![CDATA[
      a(x,x,y * ((z / u) * w)) = a(x,x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,27920,a(flip),b,33995,a),flip(a)].">
      <j1 rule="hyper" parents="60 27920 33995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33997">
    <literal><![CDATA[
      a(x,x,y * ((z \ u) * w)) = a(x,x,y * ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(27095,a,33996,a)].">
      <j1 rule="hyper" parents="27095 33996"/>
    </justification>
  </clause>

  <clause id="33998">
    <literal><![CDATA[
      a(x,x,y * ((z * (u \ z)) * w)) = a(x,x,y * (u * w))
    ]]></literal>
    <justification jstring="[para(74(a,1),33996(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="74 33996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33999">
    <literal><![CDATA[
      a(x,x,y * ((z * u) * R(w,u \ z,w))) = a(x,x,y * T(w * (u \ z),w))
    ]]></literal>
    <justification jstring="[para(5537(a,1),33997(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5537 33997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34000">
    <literal><![CDATA[
      a(x,x,y * (((z \ u) * u) * w)) = a(x,x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(27097,a,33998,a)].">
      <j1 rule="hyper" parents="27097 33998"/>
    </justification>
  </clause>

  <clause id="34001">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,z * (u * ((u * y) * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,27250,a(flip),b,33980,a),flip(a)].">
      <j1 rule="hyper" parents="370 27250 33980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34002">
    <literal><![CDATA[
      a(x,x,(L(y,y,z) * u) * w) = a(x,x,w * (y * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,31815,a(flip),b,33984,a)].">
      <j1 rule="hyper" parents="60 31815 33984"/>
    </justification>
  </clause>

  <clause id="34003">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,(y * z) \ z,u) * w) * v5) = a(x,x,v5 * ((z \ (y \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27564,a(flip),b,34002,a),flip(a)].">
      <j1 rule="hyper" parents="370 27564 34002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34004">
    <literal><![CDATA[
      a(x,x,(L(y / (z * y),y / (z * y),u) * ((z * y) * w)) * v5) = a(x,x,v5 * (z * ((z \ y) * w)))
    ]]></literal>
    <justification jstring="[para(33470(a,1),34002(a,2,3,2))].">
      <j1 rule="para" parents="33470 34002"/>
    </justification>
  </clause>

  <clause id="34005">
    <literal><![CDATA[
      a(x,x,((y * z) \ u) * (y * u)) = a(x,x,z * a((y * z) \ u,z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),34001(a,2,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5 34001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34006">
    <literal><![CDATA[
      a(x,x,(y \ L(L(z,u,u),u,u)) * w) = a(x,x,(z * y) * w)
    ]]></literal>
    <justification jstring="[para(33278(a,1),33990(a,1,3,1))].">
      <j1 rule="para" parents="33278 33990"/>
    </justification>
  </clause>

  <clause id="34007">
    <literal><![CDATA[
      a(x,x,y * (L(z,u,u) * w)) = a(x,x,(z * w) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,33993,a(flip),b,34006,a)].">
      <j1 rule="hyper" parents="60 33993 34006"/>
    </justification>
  </clause>

  <clause id="34009">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,w,v5)) = a((y * x) * z,u,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,33798,a(flip),b,33991,a),flip(a)].">
      <j1 rule="hyper" parents="60 33798 33991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34010">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,w,y)) = a(y,w,a((y * z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,32901,a(flip),b,34009,a),flip(a)].">
      <j1 rule="hyper" parents="60 32901 34009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34011">
    <literal><![CDATA[
      a(x,y,a((x * z) \ u,w,y)) = a(z * u,w,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33850,a(flip),b,34010,a),flip(a)].">
      <j1 rule="hyper" parents="60 33850 34010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34012">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,y)) = a(u * z,w,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(32903,a,34011,a)].">
      <j1 rule="hyper" parents="32903 34011"/>
    </justification>
  </clause>

  <clause id="34013">
    <literal><![CDATA[
      a(x,x,((y * z) \ u) * (y * u)) = a(x,x,z * a(z \ (y \ u),z,y))
    ]]></literal>
    <justification jstring="[para(32183(a,1),34005(a,2,3,2))].">
      <j1 rule="para" parents="32183 34005"/>
    </justification>
  </clause>

  <clause id="34014">
    <literal><![CDATA[
      a(x,x,((y * z) \ u) * (y * u)) = a(x,x,z * a(z * (y \ u),z,y))
    ]]></literal>
    <justification jstring="[para(31460(a,1),34013(a,2,3,2))].">
      <j1 rule="para" parents="31460 34013"/>
    </justification>
  </clause>

  <clause id="34015">
    <literal><![CDATA[
      a(x,x,(y * (z * u)) * (z * y)) = a(x,x,u * a(u * (z \ y),u,z))
    ]]></literal>
    <justification jstring="[hyper(33989,a,34014,a)].">
      <j1 rule="hyper" parents="33989 34014"/>
    </justification>
  </clause>

  <clause id="34016">
    <literal><![CDATA[
      a(x,x,y * a(y * (z \ u),y,z)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,32910,a(flip),b,34015,a),flip(a)].">
      <j1 rule="hyper" parents="60 32910 34015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34017">
    <literal><![CDATA[
      a(x,x,y * ((z * u) * R(w,u \ z,w))) = a(x,x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26885,a(flip),b,33999,a),flip(a)].">
      <j1 rule="hyper" parents="370 26885 33999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34019">
    <literal><![CDATA[
      a(x,x,y * ((z * u) * R(w,u * z,w))) = a(x,x,y * (w * (u \ z)))
    ]]></literal>
    <justification jstring="[para(14545(a,1),34017(a,1,3,2,2))].">
      <j1 rule="para" parents="14545 34017"/>
    </justification>
  </clause>

  <clause id="34020">
    <literal><![CDATA[
      a(x,x,y * T(z * (u * w),z)) = a(x,x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(27419(a,1),34019(a,1,3,2))].">
      <j1 rule="para" parents="27419 34019"/>
    </justification>
  </clause>

  <clause id="34021">
    <literal><![CDATA[
      a(x,x,y * (z * (u \ w))) = a(x,x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(26968,a,34020,a),flip(a)].">
      <j1 rule="hyper" parents="26968 34020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34023">
    <literal><![CDATA[
      a(x,x,y * ((z * (u \ z)) * (w * (u \ z)))) = a(x,x,y * (u * ((z \ u) \ w)))
    ]]></literal>
    <justification jstring="[para(33675(a,1),34021(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="33675 34021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34024">
    <literal><![CDATA[
      a(x,x,y * (z * ((u \ z) \ w))) = a(x,x,y * (z * (w * (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,33998,a(flip),b,34023,a),flip(a)].">
      <j1 rule="hyper" parents="60 33998 34023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34026">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,z \ (y \ z),u) * w) * v5) = a(x,x,v5 * ((z \ (y \ z)) * w))
    ]]></literal>
    <justification jstring="[para(29726(a,1),34003(a,1,3,1,1))].">
      <j1 rule="para" parents="29726 34003"/>
    </justification>
  </clause>

  <clause id="34027">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,z * (y \ z),u) * w) * v5) = a(x,x,v5 * ((z \ (y \ z)) * w))
    ]]></literal>
    <justification jstring="[para(33318(a,1),34026(a,1,3,1,1))].">
      <j1 rule="para" parents="33318 34026"/>
    </justification>
  </clause>

  <clause id="34028">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,y,u) * w) * v5) = a(x,x,v5 * ((z \ (y \ z)) * w))
    ]]></literal>
    <justification jstring="[para(33548(a,1),34027(a,1,3,1,1))].">
      <j1 rule="para" parents="33548 34027"/>
    </justification>
  </clause>

  <clause id="34029">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,y,u) * w) * v5) = a(x,x,v5 * (((y \ z) * z) * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,33997,a(flip),b,34028,a),flip(a)].">
      <j1 rule="hyper" parents="370 33997 34028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34030">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,y,u) * w) * v5) = a(x,x,v5 * (y * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,34000,a(flip),b,34029,a),flip(a)].">
      <j1 rule="hyper" parents="370 34000 34029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34032">
    <literal><![CDATA[
      a(x,x,(L(y / (z * y),(z * y) \ y,u) * ((z * y) * w)) * v5) = a(x,x,v5 * (z * ((z \ y) * w)))
    ]]></literal>
    <justification jstring="[para(26018(a,1),34004(a,1,3,1,1))].">
      <j1 rule="para" parents="26018 34004"/>
    </justification>
  </clause>

  <clause id="34033">
    <literal><![CDATA[
      a(x,x,(L(y / (z * y),y \ (z \ y),u) * ((z * y) * w)) * v5) = a(x,x,v5 * (z * ((z \ y) * w)))
    ]]></literal>
    <justification jstring="[para(29726(a,1),34032(a,1,3,1,1))].">
      <j1 rule="para" parents="29726 34032"/>
    </justification>
  </clause>

  <clause id="34034">
    <literal><![CDATA[
      a(x,x,(L(y / (z * y),L(z,y,y),u) * ((z * y) * w)) * v5) = a(x,x,v5 * (z * ((z \ y) * w)))
    ]]></literal>
    <justification jstring="[para(33298(a,1),34033(a,1,3,1,1))].">
      <j1 rule="para" parents="33298 34033"/>
    </justification>
  </clause>

  <clause id="34035">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,L(y,z,z),u) * ((y * z) * w)) * v5) = a(x,x,v5 * (y * ((y \ z) * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27075,a(flip),b,34034,a)].">
      <j1 rule="hyper" parents="60 27075 34034"/>
    </justification>
  </clause>

  <clause id="34036">
    <literal><![CDATA[
      a(x,x,(L((y * z) \ z,y,L(u,z,z)) * ((y * z) * w)) * v5) = a(x,x,v5 * (y * ((y \ z) * w)))
    ]]></literal>
    <justification jstring="[para(31372(a,1),34035(a,1,3,1,1))].">
      <j1 rule="para" parents="31372 34035"/>
    </justification>
  </clause>

  <clause id="34037">
    <literal><![CDATA[
      a(x,x,y * (z * ((z \ u) * w))) = a(x,x,y * (z * ((z * u) * w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34030,a(flip),b,34036,a),flip(a)].">
      <j1 rule="hyper" parents="60 34030 34036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34040">
    <literal><![CDATA[
      a(x,x,y * (z * ((z * u) * R(w,z \ u,w)))) = a(x,x,y * (z * T(w * (z \ u),w)))
    ]]></literal>
    <justification jstring="[para(5537(a,1),34037(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5537 34037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34041">
    <literal><![CDATA[
      a(x,x,y * (z * ((z * u) * R(w,z \ u,w)))) = a(x,x,y * (z * (w * (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(370,a,26942,a(flip),b,34040,a),flip(a)].">
      <j1 rule="hyper" parents="370 26942 34040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34043">
    <literal><![CDATA[
      a(x,x,y * (z * ((z * u) * R(w,z * u,w)))) = a(x,x,y * (z * (w * (z \ u))))
    ]]></literal>
    <justification jstring="[para(14545(a,1),34041(a,1,3,2,2,2))].">
      <j1 rule="para" parents="14545 34041"/>
    </justification>
  </clause>

  <clause id="34044">
    <literal><![CDATA[
      a(x,x,y * (z * T(u * (z * w),u))) = a(x,x,y * (z * (u * (z \ w))))
    ]]></literal>
    <justification jstring="[para(5537(a,1),34043(a,1,3,2,2))].">
      <j1 rule="para" parents="5537 34043"/>
    </justification>
  </clause>

  <clause id="34045">
    <literal><![CDATA[
      a(x,x,y * (z * (u * (z \ w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y * (z * (u * (z * w)))) = v5
    ]]></literal>
    <justification jstring="[para(34044(a,1),26977(a,1))].">
      <j1 rule="para" parents="34044 26977"/>
    </justification>
  </clause>

  <clause id="34046">
    <literal><![CDATA[
      a(x,x,y * (z * ((u \ z) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y * (z * (w * (z * u)))) = v5
    ]]></literal>
    <justification jstring="[para(34024(a,2),34045(a,1))].">
      <j1 rule="para" parents="34024 34045"/>
    </justification>
  </clause>

  <clause id="34047">
    <literal><![CDATA[
      a(x,y,L(z,u * a(x,y,z),a(x,y,z) * (u \ w))) * w = (z * (L(L(z,y,x),y,x) \ u)) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(32320(a,2),33950(a,1,1))].">
      <j1 rule="para" parents="32320 33950"/>
    </justification>
  </clause>

  <clause id="34048">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,y,z) * (u \ w))) * w = (z * (L(L(z,y,x),y,x) \ u)) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(32499(a,1),34047(a,1,1))].">
      <j1 rule="para" parents="32499 34047"/>
    </justification>
  </clause>

  <clause id="34049">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,y,z) * (u \ w))) * w = u * (z * (L(L(z,y,x),y,x) \ ((u * a(x,y,z)) \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,29164,a(flip),b,34048,a),flip(a)].">
      <j1 rule="hyper" parents="370 29164 34048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34050">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,y,z) * (u \ w))) * w = u * ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(30983(a,1),34049(a,2,2))].">
      <j1 rule="para" parents="30983 34049"/>
    </justification>
  </clause>

  <clause id="34051">
    <literal><![CDATA[
      a(x,y,z \ (x * L(u,z * (x \ z),z * (x \ z)))) = a(z * (x \ z),y,u * ((1 / (z / (x \ z))) * z))
    ]]></literal>
    <justification jstring="[para(29617(a,1),33375(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29617 33375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34052">
    <literal><![CDATA[
      a(x,y,z \ (x * L(u,z * (x \ z),z * (x \ z)))) = a(z * (x \ z),y,u * ((1 / x) * z))
    ]]></literal>
    <justification jstring="[para(74(a,1),34051(a,2,3,2,1,2))].">
      <j1 rule="para" parents="74 34051"/>
    </justification>
  </clause>

  <clause id="34054">
    <literal><![CDATA[
      a(x,y,z \ (x * L(u,z * (x \ z),z * (x \ z)))) = a(z * (x \ z),y,u * (x * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,27052,a(flip),b,34052,a),flip(a)].">
      <j1 rule="hyper" parents="370 27052 34052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34055">
    <literal><![CDATA[
      a(x * (y \ x),z,u * (y * x)) = a(y,z,x \ (y * L(u,y,y)))
    ]]></literal>
    <justification jstring="[para(29736(a,1),34054(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="29736 34054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34056">
    <literal><![CDATA[
      a(x * (y \ x),z,u * (y * x)) = a(y,z,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,29667,a(flip),b,34055,a),flip(a)].">
      <j1 rule="hyper" parents="370 29667 34055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34058">
    <literal><![CDATA[
      a(x * (y \ x),z,(x * y) * u) = a(y,z,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(27041,a,34056,a)].">
      <j1 rule="hyper" parents="27041 34056"/>
    </justification>
  </clause>

  <clause id="34059">
    <literal><![CDATA[
      a(x * (y \ x),x,z * (y * x)) = a(y,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32358,a(flip),b,34056,a),flip(a)].">
      <j1 rule="hyper" parents="370 32358 34056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34060">
    <literal><![CDATA[
      a(x,y,z * (x * y)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(32808,a,34059,a)].">
      <j1 rule="hyper" parents="32808 34059"/>
    </justification>
  </clause>

  <clause id="34061">
    <literal><![CDATA[
      a(x,y,(z \ (x * y)) * (x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,32881,a(flip),b,34060,a),flip(a)].">
      <j1 rule="hyper" parents="370 32881 34060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34062">
    <literal><![CDATA[
      a(x,y,y * (x \ R(z,x,y))) = a(x,y,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(103(a,1),34060(a,1,3)),flip(a)].">
      <j1 rule="para" parents="103 34060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34063">
    <literal><![CDATA[
      a(x,y,a(z * (x * y),u,w)) = a(w,u,a(x,y,y * (x \ z)))
    ]]></literal>
    <justification jstring="[para(34060(a,1),32929(a,2,3))].">
      <j1 rule="para" parents="34060 32929"/>
    </justification>
  </clause>

  <clause id="34064">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * ((z * w) * u)) = a(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(34061(a,1),33601(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34061 33601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34065">
    <literal><![CDATA[
      a(x,y,y * (x \ L(z,x,y))) = a(x,y,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,31681,a(flip),b,34062,a)].">
      <j1 rule="hyper" parents="60 31681 34062"/>
    </justification>
  </clause>

  <clause id="34066">
    <literal><![CDATA[
      a(x,y,y * (x \ L(z,x,y))) = a(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33767,a(flip),b,34065,a),flip(a)].">
      <j1 rule="hyper" parents="370 33767 34065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34067">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ w)) * (w * u)) = a(x,y,a(u,z,z \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),34064(a,1,3,2,1))].">
      <j1 rule="para" parents="5 34064"/>
    </justification>
  </clause>

  <clause id="34068">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) * w) * v5) * (((z \ 1) * v5) * ((u * u) * w))) = a(x,y,a((u * u) * w,z \ 1,v5))
    ]]></literal>
    <justification jstring="[para(573(a,1),34064(a,1,3,1,1))].">
      <j1 rule="para" parents="573 34064"/>
    </justification>
  </clause>

  <clause id="34069">
    <literal><![CDATA[
      a(x,y,((z \ T(z * u,w)) * v5) * (((z \ 1) * v5) * T((z \ 1) \ u,w))) = a(x,y,a(T((z \ 1) \ u,w),z \ 1,v5))
    ]]></literal>
    <justification jstring="[para(1378(a,1),34064(a,1,3,1,1))].">
      <j1 rule="para" parents="1378 34064"/>
    </justification>
  </clause>

  <clause id="34070">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) * T((z \ 1) \ w,v5)) * ((z \ T(z * w,v5)) * u)) = a(x,y,a(u,z \ 1,T((z \ 1) \ w,v5)))
    ]]></literal>
    <justification jstring="[para(1378(a,1),34064(a,1,3,2,1))].">
      <j1 rule="para" parents="1378 34064"/>
    </justification>
  </clause>

  <clause id="34071">
    <literal><![CDATA[
      a(x,y,T(z * (u * w),K(v5,u * w)) * ((u * T(z,T(u * w,v5))) * w)) = a(x,y,a(w,u,T(z,T(u * w,v5))))
    ]]></literal>
    <justification jstring="[para(8710(a,2),34064(a,1,3,1))].">
      <j1 rule="para" parents="8710 34064"/>
    </justification>
  </clause>

  <clause id="34072">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ w)) * (w * u)) = a(x,y,a(u,z,z * w))
    ]]></literal>
    <justification jstring="[para(32358(a,1),34067(a,2,3))].">
      <j1 rule="para" parents="32358 34067"/>
    </justification>
  </clause>

  <clause id="34073">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * w)) * (((u \ (v5 * v5)) * z) * w)) = a(x,y,a((v5 * v5) * z,u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(27240,a,34068,a)].">
      <j1 rule="hyper" parents="27240 34068"/>
    </justification>
  </clause>

  <clause id="34075">
    <literal><![CDATA[
      a(x,y,a((z * z) * u,w \ 1,v5)) = a(x,y,((u * w) * v5) * (u * ((w \ 1) * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27729,a(flip),b,34073,a),flip(a)].">
      <j1 rule="hyper" parents="60 27729 34073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34077">
    <literal><![CDATA[
      a(x,y,a((z * z) * u,w \ 1,v5)) = a(x,y,(u * (v5 * w)) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,27186,a(flip),b,34075,a),flip(a)].">
      <j1 rule="hyper" parents="370 27186 34075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34078">
    <literal><![CDATA[
      a(x,y,a((z * z) * u,w,v5)) = a(x,y,(u * (v5 * w)) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(3050(a,1),34077(a,1,3))].">
      <j1 rule="para" parents="3050 34077"/>
    </justification>
  </clause>

  <clause id="34079">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * ((z * w) * u)) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(2955(a,1),34078(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2955 34078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34080">
    <literal><![CDATA[
      a(x,x,(y * (z * (y * u))) * ((y * (y * u)) * z)) = a(z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33802,a(flip),b,34079,a),flip(a)].">
      <j1 rule="hyper" parents="370 33802 34079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34081">
    <literal><![CDATA[
      a(x,x,(y * (z * (y * u))) * (L(u,y,y) * z)) = a(z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(27105,a,34080,a)].">
      <j1 rule="hyper" parents="27105 34080"/>
    </justification>
  </clause>

  <clause id="34082">
    <literal><![CDATA[
      a(x,x,(y * z) * (u * (z * (u * y)))) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34007,a(flip),b,34081,a)].">
      <j1 rule="hyper" parents="60 34007 34081"/>
    </justification>
  </clause>

  <clause id="34084">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * T(w * (u * z),K(v5,u * z))) = a(x,y,a(z,u,T(w,T(u * z,v5))))
    ]]></literal>
    <justification jstring="[hyper(60,a,27193,a(flip),b,34071,a)].">
      <j1 rule="hyper" parents="60 27193 34071"/>
    </justification>
  </clause>

  <clause id="34085">
    <literal><![CDATA[
      a(x,y,a(z,u,T(w,T(u * z,v5)))) = a(x,y,(z * (u * w)) * (w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(26968,a,34084,a),flip(a)].">
      <j1 rule="hyper" parents="26968 34084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34088">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (w * (u * z))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(26880(a,1),34085(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26880 34085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34090">
    <literal><![CDATA[
      a(x,y,((z \ T(z * u,w)) * v5) * (((z \ 1) * v5) * ((z \ 1) \ u))) = a(x,y,a(T((z \ 1) \ u,w),z \ 1,v5))
    ]]></literal>
    <justification jstring="[hyper(26977,a,34069,a)].">
      <j1 rule="hyper" parents="26977 34069"/>
    </justification>
  </clause>

  <clause id="34091">
    <literal><![CDATA[
      a(x,y,((z \ u) * ((z \ 1) * w)) * ((z \ T(z * u,v5)) * w)) = a(x,y,a(T((z \ 1) \ u,v5),z \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(27243,a,34090,a)].">
      <j1 rule="hyper" parents="27243 34090"/>
    </justification>
  </clause>

  <clause id="34093">
    <literal><![CDATA[
      a(x,y,a(T((z \ 1) \ u,w),z \ 1,v5)) = a(x,y,(v5 * (z \ (z * u))) * ((z \ u) * ((z \ 1) * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27194,a(flip),b,34091,a),flip(a)].">
      <j1 rule="hyper" parents="60 27194 34091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34095">
    <literal><![CDATA[
      a(x,y,a(T((z \ 1) \ u,w),z \ 1,v5)) = a(x,y,(v5 * u) * ((z \ u) * ((z \ 1) * v5)))
    ]]></literal>
    <justification jstring="[para(4(a,1),34093(a,2,3,1,2))].">
      <j1 rule="para" parents="4 34093"/>
    </justification>
  </clause>

  <clause id="34096">
    <literal><![CDATA[
      a(x,y,a(T((z \ 1) \ u,w),z \ 1,v5)) = a(x,y,((z \ u) * (v5 * z)) * (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,27186,a(flip),b,34095,a),flip(a)].">
      <j1 rule="hyper" parents="370 27186 34095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34098">
    <literal><![CDATA[
      a(x,y,a(T((z \ 1) \ u,w),z,v5)) = a(x,y,((z \ u) * (v5 * z)) * (v5 * u))
    ]]></literal>
    <justification jstring="[para(3050(a,1),34096(a,1,3))].">
      <j1 rule="para" parents="3050 34096"/>
    </justification>
  </clause>

  <clause id="34099">
    <literal><![CDATA[
      a(x,y,((z \ u) * (w * z)) * (w * u)) = a(x,y,a((z \ 1) \ u,z,w))
    ]]></literal>
    <justification jstring="[para(106(a,1),34098(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="106 34098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34100">
    <literal><![CDATA[
      a(x,y,((z \ u) * (w * z)) * (w * u)) = a(x,y,a(z \ u,z,w))
    ]]></literal>
    <justification jstring="[para(2959(a,1),34099(a,2,3))].">
      <j1 rule="para" parents="2959 34099"/>
    </justification>
  </clause>

  <clause id="34101">
    <literal><![CDATA[
      a(x,y,((z \ u) * (w * z)) * (w * u)) = a(x,y,a(z * u,z,w))
    ]]></literal>
    <justification jstring="[para(31460(a,1),34100(a,2,3))].">
      <j1 rule="para" parents="31460 34100"/>
    </justification>
  </clause>

  <clause id="34102">
    <literal><![CDATA[
      a(x,y,(z * (u \ (u * w))) * (((u \ 1) * z) * T((u \ 1) \ w,v5))) = a(x,y,a(z,u \ 1,T((u \ 1) \ w,v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27194,a(flip),b,34070,a)].">
      <j1 rule="hyper" parents="60 27194 34070"/>
    </justification>
  </clause>

  <clause id="34104">
    <literal><![CDATA[
      a(x,y,(z * u) * (((w \ 1) * z) * T((w \ 1) \ u,v5))) = a(x,y,a(z,w \ 1,T((w \ 1) \ u,v5)))
    ]]></literal>
    <justification jstring="[para(4(a,1),34102(a,1,3,1,2))].">
      <j1 rule="para" parents="4 34102"/>
    </justification>
  </clause>

  <clause id="34105">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,T((u \ 1) \ w,v5))) = a(x,y,(z * w) * (((u \ 1) * z) * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(26977,a,34104,a),flip(a)].">
      <j1 rule="hyper" parents="26977 34104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34108">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,T((u \ 1) \ w,v5))) = a(x,y,((u \ w) * ((u \ 1) * z)) * (z * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27242,a(flip),b,34105,a),flip(a)].">
      <j1 rule="hyper" parents="370 27242 34105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34109">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,T((u \ 1) \ w,v5))) = a(x,y,((z * u) * (u \ w)) * (z * w))
    ]]></literal>
    <justification jstring="[hyper(370,a,27728,a(flip),b,34108,a),flip(a)].">
      <j1 rule="hyper" parents="370 27728 34108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34110">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,T((u \ 1) \ w,v5))) = a(x,y,(z * w) * ((z * u) * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26888,a,b,34109,a),flip(a)].">
      <j1 rule="hyper" parents="370 26888 34109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34111">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w \ u))) = a(x,y,a(z,w \ 1,(w \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(106(a,1),34110(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="106 34110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34112">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w \ u))) = a(x,y,a(z,w \ 1,(w \ 1) * u))
    ]]></literal>
    <justification jstring="[para(32358(a,1),34111(a,2,3))].">
      <j1 rule="para" parents="32358 34111"/>
    </justification>
  </clause>

  <clause id="34113">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w \ u))) = a(x,y,a(z,w \ 1,w * u))
    ]]></literal>
    <justification jstring="[para(3109(a,1),34112(a,2,3))].">
      <j1 rule="para" parents="3109 34112"/>
    </justification>
  </clause>

  <clause id="34114">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * w) * (w \ u))) = a(x,y,a(z,w,w * u))
    ]]></literal>
    <justification jstring="[para(3050(a,1),34113(a,2,3))].">
      <j1 rule="para" parents="3050 34113"/>
    </justification>
  </clause>

  <clause id="34115">
    <literal><![CDATA[
      a(x,x,(y * z) * ((y * (y * u)) * ((y * u) \ z))) = a((y * u) * z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33802,a(flip),b,34114,a),flip(a)].">
      <j1 rule="hyper" parents="370 33802 34114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34116">
    <literal><![CDATA[
      L(T(x,y) \ (x * ((1 / y) \ a(1 / y,1 / y,x))),y,y) = T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(77(a,1),33613(a,1,1,1,2))].">
      <j1 rule="para" parents="77 33613"/>
    </justification>
  </clause>

  <clause id="34117">
    <literal><![CDATA[
      L(T(x,y) \ (x * ((1 / y) \ a(1 / y,y,x))),y,y) = T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(3041(a,1),34116(a,1,1,2,2,2))].">
      <j1 rule="para" parents="3041 34116"/>
    </justification>
  </clause>

  <clause id="34118">
    <literal><![CDATA[
      L(T(x,y) \ (x * ((1 / y) \ a(y,y,x))),y,y) = T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(2957(a,1),34117(a,1,1,2,2,2))].">
      <j1 rule="para" parents="2957 34117"/>
    </justification>
  </clause>

  <clause id="34119">
    <literal><![CDATA[
      L(T(x,y) \ (x * R(y,y,x)),y,y) = T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1))
    ]]></literal>
    <justification jstring="[para(28423(a,1),34118(a,1,1,2,2))].">
      <j1 rule="para" parents="28423 34118"/>
    </justification>
  </clause>

  <clause id="34120">
    <literal><![CDATA[
      L(K(x,y) * R(x,x,y),x,x) = T(y,(1 / x) \ 1) \ ((x \ 1) \ T(y,(1 / x) \ 1))
    ]]></literal>
    <justification jstring="[para(7935(a,1),34119(a,1,1))].">
      <j1 rule="para" parents="7935 34119"/>
    </justification>
  </clause>

  <clause id="34121">
    <literal><![CDATA[
      L(R(T(x,y),x,y),x,x) = T(y,(1 / x) \ 1) \ ((x \ 1) \ T(y,(1 / x) \ 1))
    ]]></literal>
    <justification jstring="[para(23719(a,1),34120(a,1,1))].">
      <j1 rule="para" parents="23719 34120"/>
    </justification>
  </clause>

  <clause id="34122">
    <literal><![CDATA[
      T(x,(1 / y) \ 1) \ ((y \ 1) \ T(x,(1 / y) \ 1)) = x \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,2803,a(flip),b,34121,a),flip(a)].">
      <j1 rule="hyper" parents="60 2803 34121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34123">
    <literal><![CDATA[
      T(x,y) \ ((y \ 1) \ T(x,(1 / y) \ 1)) = x \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(77(a,1),34122(a,1,1,2))].">
      <j1 rule="para" parents="77 34122"/>
    </justification>
  </clause>

  <clause id="34124">
    <literal><![CDATA[
      T(x,y) \ ((y \ 1) \ T(x,y)) = x \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(77(a,1),34123(a,1,2,2,2))].">
      <j1 rule="para" parents="77 34123"/>
    </justification>
  </clause>

  <clause id="34125">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) / (y * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,34124,a(flip),b,27508,a(flip))].">
      <j1 rule="hyper" parents="128 34124 27508"/>
    </justification>
  </clause>

  <clause id="34126">
    <literal><![CDATA[
      x \ (((y \ 1) \ x) / (y * y)) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,1100,a(flip),b,34125,a)].">
      <j1 rule="hyper" parents="60 1100 34125"/>
    </justification>
  </clause>

  <clause id="34127">
    <literal><![CDATA[
      x \ ((y \ 1) \ (x / (y * y))) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(1100(a,1),34126(a,1,2))].">
      <j1 rule="para" parents="1100 34126"/>
    </justification>
  </clause>

  <clause id="34128">
    <literal><![CDATA[
      x \ T(x / y,y \ 1) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(1127(a,1),34127(a,1,2))].">
      <j1 rule="para" parents="1127 34127"/>
    </justification>
  </clause>

  <clause id="34129">
    <literal><![CDATA[
      x / L(y,x,y) = (x / (x * y)) * x
    ]]></literal>
    <justification jstring="[para(34128(a,1),25566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34128 25566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34130">
    <literal><![CDATA[
      a(x,y,z / L(u,z,u)) = a(x,y,((z * u) \ z) * z)
    ]]></literal>
    <justification jstring="[para(34129(a,2),26896(a,1,3))].">
      <j1 rule="para" parents="34129 26896"/>
    </justification>
  </clause>

  <clause id="34131">
    <literal><![CDATA[
      a(x,y,(z \ u) / L(w,z \ u,w)) = a(x,y,(((z * u) * w) \ (z * u)) * (z \ u))
    ]]></literal>
    <justification jstring="[para(33297(a,1),34130(a,2,3,1))].">
      <j1 rule="para" parents="33297 34130"/>
    </justification>
  </clause>

  <clause id="34132">
    <literal><![CDATA[
      a(x,y,(z \ u) / L(w,z \ u,w)) = a(x,y,((z * u) \ (w \ (z * u))) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(370,a,27139,a(flip),b,34131,a),flip(a)].">
      <j1 rule="hyper" parents="370 27139 34131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34133">
    <literal><![CDATA[
      a(x,y,(z \ u) / L(w,z \ u,w)) = a(x,y,a(z,z,u) * (w \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,33317,a(flip),b,34132,a),flip(a)].">
      <j1 rule="hyper" parents="370 33317 34132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34134">
    <literal><![CDATA[
      a(x,y,(x \ y) / L(z,x \ y,z)) = a(x,y,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33558,a(flip),b,34133,a),flip(a)].">
      <j1 rule="hyper" parents="370 33558 34133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34135">
    <literal><![CDATA[
      a(x,y,(x \ y) / L(z,x \ y,z)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32782,a(flip),b,34134,a),flip(a)].">
      <j1 rule="hyper" parents="370 32782 34134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34136">
    <literal><![CDATA[
      a(x,y,(x \ y) / L(z,x * y,z)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(14596(a,1),34135(a,1,3,2))].">
      <j1 rule="para" parents="14596 34135"/>
    </justification>
  </clause>

  <clause id="34137">
    <literal><![CDATA[
      a(x,y,L(z,x * y,z) \ (x \ y)) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(26970,a,34136,a)].">
      <j1 rule="hyper" parents="26970 34136"/>
    </justification>
  </clause>

  <clause id="34138">
    <literal><![CDATA[
      a(x,y,y * (x * L(z,x * y,z))) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(32860,a,34137,a)].">
      <j1 rule="hyper" parents="32860 34137"/>
    </justification>
  </clause>

  <clause id="34139">
    <literal><![CDATA[
      a(x,y,y * (x \ z)) = a(x,y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(27678,a,34138,a),flip(a)].">
      <j1 rule="hyper" parents="27678 34138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34140">
    <literal><![CDATA[
      a(x,y,y * (x * L(z,x,y))) = a(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34066,a(flip),b,34139,a),flip(a)].">
      <j1 rule="hyper" parents="60 34066 34139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34141">
    <literal><![CDATA[
      a(x,y,a(z * (x * y),u,w)) = a(w,u,a(x,y,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(34139(a,1),34063(a,2,3))].">
      <j1 rule="para" parents="34139 34063"/>
    </justification>
  </clause>

  <clause id="34142">
    <literal><![CDATA[
      a(x,y,z * (x \ y)) = a(x,y,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(32017,a,34140,a),flip(a)].">
      <j1 rule="hyper" parents="32017 34140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34143">
    <literal><![CDATA[
      a(x,y,z * (x * y)) = a(x,y,y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(33769,a,34142,a),flip(a)].">
      <j1 rule="hyper" parents="33769 34142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34144">
    <literal><![CDATA[
      a(x,y,(x * z) * y) = a(x,y,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,27031,a,b,34143,a)].">
      <j1 rule="hyper" parents="370 27031 34143"/>
    </justification>
  </clause>

  <clause id="34145">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(z,y,u * (w * z))) = v5
    ]]></literal>
    <justification jstring="[para(34143(a,2),33002(a,1,3))].">
      <j1 rule="para" parents="34143 33002"/>
    </justification>
  </clause>

  <clause id="34146">
    <literal><![CDATA[
      a(x \ y,y,z * ((x \ y) * y)) = a(y * x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(32557,a,34144,a),flip(a)].">
      <j1 rule="hyper" parents="32557 34144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34147">
    <literal><![CDATA[
      a(x * y,x,z * ((y \ x) * x)) = a(x * y,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32862,a(flip),b,34146,a)].">
      <j1 rule="hyper" parents="60 32862 34146"/>
    </justification>
  </clause>

  <clause id="34148">
    <literal><![CDATA[
      a(x * y,x,y * ((x \ y) \ z)) = a(x * y,x,x * z)
    ]]></literal>
    <justification jstring="[hyper(33777,a,34147,a),flip(a)].">
      <j1 rule="hyper" parents="33777 34147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34149">
    <literal><![CDATA[
      a(x * y,x,y * (x * (y \ z))) = a(x * y,x,x * z)
    ]]></literal>
    <justification jstring="[hyper(33960,a,34148,a)].">
      <j1 rule="hyper" parents="33960 34148"/>
    </justification>
  </clause>

  <clause id="34150">
    <literal><![CDATA[
      a(x * y,x,(x * (y \ z)) * y) = a(x * y,x,x * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,34149,a)].">
      <j1 rule="hyper" parents="26965 34149"/>
    </justification>
  </clause>

  <clause id="34151">
    <literal><![CDATA[
      a(x,y,a(z * (x * y),u,w)) = a(w,y,a(x,u,y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32980,a,b,34141,a),flip(a)].">
      <j1 rule="hyper" parents="370 32980 34141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34152">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),u,w)) = a(w,u,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(33002,a,34151,a)].">
      <j1 rule="hyper" parents="33002 34151"/>
    </justification>
  </clause>

  <clause id="34153">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),u,w)) = a(x,y,a(u * (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a,b,34152,a),flip(a)].">
      <j1 rule="hyper" parents="370 32929 34152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34154">
    <literal><![CDATA[
      a((x * y) * z,y,a(u,w,x)) = a(x,w,a(y * (x * z),y,u))
    ]]></literal>
    <justification jstring="[hyper(32946,a,34153,a)].">
      <j1 rule="hyper" parents="32946 34153"/>
    </justification>
  </clause>

  <clause id="34155">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u * (x * z),z,w)) = v5
    ]]></literal>
    <justification jstring="[para(34154(a,1),33027(a,1))].">
      <j1 rule="para" parents="34154 33027"/>
    </justification>
  </clause>

  <clause id="34156">
    <literal><![CDATA[
      a(x,y,a(z,x,y * (u * z))) = a(u * y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(34145,a,33851,a)].">
      <j1 rule="hyper" parents="34145 33851"/>
    </justification>
  </clause>

  <clause id="34157">
    <literal><![CDATA[
      a((x * y) \ x,x / ((y \ 1) \ 1),((x \ (y \ x)) * z) * x) = a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27560,a(flip),b,33949,a)].">
      <j1 rule="hyper" parents="60 27560 33949"/>
    </justification>
  </clause>

  <clause id="34158">
    <literal><![CDATA[
      a((x * y) \ x,((y \ 1) \ 1) \ x,((x \ (y \ x)) * z) * x) = a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(26559,a,34157,a)].">
      <j1 rule="hyper" parents="26559 34157"/>
    </justification>
  </clause>

  <clause id="34159">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a((x * y) \ x,(y \ 1) \ x,((x \ (y \ x)) * z) * x)
    ]]></literal>
    <justification jstring="[hyper(3063,a,34158,a),flip(a)].">
      <j1 rule="hyper" parents="3063 34158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34160">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a((x * y) \ x,y \ x,((x \ (y \ x)) * z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,3044,a(flip),b,34159,a),flip(a)].">
      <j1 rule="hyper" parents="370 3044 34159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34161">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a(x \ (y \ x),y \ x,((x \ (y \ x)) * z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,26783,a(flip),b,34160,a),flip(a)].">
      <j1 rule="hyper" parents="370 26783 34160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34162">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a((y \ x) * x,y \ x,((x \ (y \ x)) * z) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,32862,a(flip),b,34161,a),flip(a)].">
      <j1 rule="hyper" parents="370 32862 34161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34163">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a((y \ x) * x,y \ x,((y \ x) * (x \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(370,a,33935,a(flip),b,34162,a),flip(a)].">
      <j1 rule="hyper" parents="370 33935 34162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34164">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a((y \ x) * x,y \ x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,34150,a(flip),b,34163,a),flip(a)].">
      <j1 rule="hyper" parents="370 34150 34163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34165">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a(y,y \ x,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32550,a(flip),b,34164,a),flip(a)].">
      <j1 rule="hyper" parents="370 32550 34164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34166">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a(y,x * y,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33403,a(flip),b,34165,a),flip(a)].">
      <j1 rule="hyper" parents="370 33403 34165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34167">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (((x * y) \ x) \ x)) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33100,a(flip),b,34166,a),flip(a)].">
      <j1 rule="hyper" parents="370 33100 34166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34168">
    <literal><![CDATA[
      a((x * y) \ x,x * ((x * y) \ x),z * (x * y)) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(26975,a,34167,a)].">
      <j1 rule="hyper" parents="26975 34167"/>
    </justification>
  </clause>

  <clause id="34169">
    <literal><![CDATA[
      a((x * y) \ x,x * (x \ (y \ x)),z * (x * y)) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(26790,a,34168,a)].">
      <j1 rule="hyper" parents="26790 34168"/>
    </justification>
  </clause>

  <clause id="34171">
    <literal><![CDATA[
      a((x * y) \ x,y \ x,z * (x * y)) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),34169(a,1,2))].">
      <j1 rule="para" parents="5 34169"/>
    </justification>
  </clause>

  <clause id="34172">
    <literal><![CDATA[
      a(x * (x * y),y \ x,(x * y) \ z) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32432,a(flip),b,34171,a)].">
      <j1 rule="hyper" parents="60 32432 34171"/>
    </justification>
  </clause>

  <clause id="34174">
    <literal><![CDATA[
      a(x * (x * y),y \ x,(x * y) * z) = a(y,x * y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(33305,a,34172,a)].">
      <j1 rule="hyper" parents="33305 34172"/>
    </justification>
  </clause>

  <clause id="34175">
    <literal><![CDATA[
      a(x,x \ y,x * (y \ z)) = a(x,y * x,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33177,a(flip),b,34174,a)].">
      <j1 rule="hyper" parents="60 33177 34174"/>
    </justification>
  </clause>

  <clause id="34176">
    <literal><![CDATA[
      a(x,y * x,y * (x * z)) = a(x,y * x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(33406,a,34175,a),flip(a)].">
      <j1 rule="hyper" parents="33406 34175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34177">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * x,x * (L(L(y,z,u),z,u) \ w)) = a(x,L(L(y,z,u),z,u) * x,(x * w) * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,29079,a(flip),b,34176,a),flip(a)].">
      <j1 rule="hyper" parents="60 29079 34176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34178">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * x,x * (L(L(y,z,u),z,u) \ w)) = a(x,y * x,(x * w) * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,30392,a(flip),b,34177,a),flip(a)].">
      <j1 rule="hyper" parents="370 30392 34177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34180">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * x,x * (L(L(y,z,u),z,u) \ w)) = a(x,y * x,w * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33948,a(flip),b,34178,a),flip(a)].">
      <j1 rule="hyper" parents="370 33948 34178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34181">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) * x,(y \ w) * x) = a(x,y * x,w * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(60,a,30406,a(flip),b,34180,a)].">
      <j1 rule="hyper" parents="60 30406 34180"/>
    </justification>
  </clause>

  <clause id="34182">
    <literal><![CDATA[
      a(x,y * x,(y \ z) * x) = a(x,y * x,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(30394,a,34181,a)].">
      <j1 rule="hyper" parents="30394 34181"/>
    </justification>
  </clause>

  <clause id="34184">
    <literal><![CDATA[
      a(x,y * x,z * (x \ y)) = a(x,y * x,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33188,a(flip),b,34182,a),flip(a)].">
      <j1 rule="hyper" parents="60 33188 34182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34185">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),z * (x \ (T(x,y \ x) / y)))
    ]]></literal>
    <justification jstring="[para(5503(a,1),34184(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5503 34184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34186">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),z * ((x / y) / R(x,y,x)))
    ]]></literal>
    <justification jstring="[para(31609(a,1),34185(a,2,3,2))].">
      <j1 rule="para" parents="31609 34185"/>
    </justification>
  </clause>

  <clause id="34187">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),z * (R(x,y,x) \ (x / y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,26939,a(flip),b,34186,a),flip(a)].">
      <j1 rule="hyper" parents="370 26939 34186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34188">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),z * (x \ (L(x,y,x) / y)))
    ]]></literal>
    <justification jstring="[para(14328(a,1),34187(a,2,3,2))].">
      <j1 rule="para" parents="14328 34187"/>
    </justification>
  </clause>

  <clause id="34189">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),z * (x \ (y \ L(x,y,x))))
    ]]></literal>
    <justification jstring="[hyper(370,a,27132,a(flip),b,34188,a),flip(a)].">
      <j1 rule="hyper" parents="370 27132 34188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34190">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),(x \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,29389,a(flip),b,34189,a),flip(a)].">
      <j1 rule="hyper" parents="370 29389 34189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34192">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (x / y),x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33332,a(flip),b,34190,a),flip(a)].">
      <j1 rule="hyper" parents="370 33332 34190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34193">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,x * (y \ x),x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,26493,a(flip),b,34192,a),flip(a)].">
      <j1 rule="hyper" parents="370 26493 34192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34194">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,y,x * ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33414,a(flip),b,34193,a),flip(a)].">
      <j1 rule="hyper" parents="370 33414 34193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34195">
    <literal><![CDATA[
      a(x,(T(x,y \ x) / y) * x,z * ((T(x,y \ x) / y) * x)) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,33597,a(flip),b,34194,a),flip(a)].">
      <j1 rule="hyper" parents="370 33597 34194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34196">
    <literal><![CDATA[
      a(x,x * (x / y),z * ((T(x,y \ x) / y) * x)) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[para(5503(a,1),34195(a,1,2))].">
      <j1 rule="para" parents="5503 34195"/>
    </justification>
  </clause>

  <clause id="34197">
    <literal><![CDATA[
      a(x,x * (x / y),z * (x * (x / y))) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[para(5503(a,1),34196(a,1,3,2))].">
      <j1 rule="para" parents="5503 34196"/>
    </justification>
  </clause>

  <clause id="34198">
    <literal><![CDATA[
      a(x,x * (x / y),z * (x * (y \ x))) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(27202,a,34197,a)].">
      <j1 rule="hyper" parents="27202 34197"/>
    </justification>
  </clause>

  <clause id="34199">
    <literal><![CDATA[
      a(x,x * (y \ x),z * (x * (y \ x))) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(26585,a,34198,a)].">
      <j1 rule="hyper" parents="26585 34198"/>
    </justification>
  </clause>

  <clause id="34200">
    <literal><![CDATA[
      a(x,y,z * (x * (y \ x))) = a(x,y,x * (y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33414,a(flip),b,34199,a)].">
      <j1 rule="hyper" parents="60 33414 34199"/>
    </justification>
  </clause>

  <clause id="34201">
    <literal><![CDATA[
      x \ R(x,y,x * (y * (x * z))) = a(x,y,z * (x * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32595,a(flip),b,34200,a)].">
      <j1 rule="hyper" parents="370 32595 34200"/>
    </justification>
  </clause>

  <clause id="34202">
    <literal><![CDATA[
      a(x,y,z * (x * (y \ x))) = x \ R(x,y,y * z)
    ]]></literal>
    <justification jstring="[para(33681(a,1),34201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33681 34201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34203">
    <literal><![CDATA[
      R(x,y,z * (x * (y \ x))) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(32710,a,34202,a)].">
      <j1 rule="hyper" parents="32710 34202"/>
    </justification>
  </clause>

  <clause id="34204">
    <literal><![CDATA[
      R(x,(x \ 1) / y,z * (x * (y * (x * x)))) = R(x,(x \ 1) / y,((x \ 1) / y) * z)
    ]]></literal>
    <justification jstring="[para(978(a,1),34203(a,1,3,2,2))].">
      <j1 rule="para" parents="978 34203"/>
    </justification>
  </clause>

  <clause id="34205">
    <literal><![CDATA[
      R(x,(x \ 1) / y,((x \ 1) / y) * z) = R(x,(x \ 1) / y,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,2743,a(flip),b,34204,a),flip(a)].">
      <j1 rule="hyper" parents="60 2743 34204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34207">
    <literal><![CDATA[
      R(x,(x \ 1) / y,((x \ 1) / y) * z) = R(x,y \ (x \ 1),z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,27386,a(flip),b,34205,a),flip(a)].">
      <j1 rule="hyper" parents="370 27386 34205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34208">
    <literal><![CDATA[
      R(x,(x \ 1) / y,((x \ 1) / y) * z) = R(x,y \ x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,27497,a(flip),b,34207,a),flip(a)].">
      <j1 rule="hyper" parents="370 27497 34207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34209">
    <literal><![CDATA[
      R(x,(x \ 1) / y,((x \ 1) / y) * z) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,33417,a(flip),b,34208,a),flip(a)].">
      <j1 rule="hyper" parents="370 33417 34208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34210">
    <literal><![CDATA[
      R(x,(x \ 1) / y,(y \ (x \ 1)) * z) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,27436,a(flip),b,34209,a)].">
      <j1 rule="hyper" parents="60 27436 34209"/>
    </justification>
  </clause>

  <clause id="34211">
    <literal><![CDATA[
      R(x,(x \ 1) / y,z * (y \ x)) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,27476,a(flip),b,34210,a)].">
      <j1 rule="hyper" parents="60 27476 34210"/>
    </justification>
  </clause>

  <clause id="34212">
    <literal><![CDATA[
      R(x,y \ (x \ 1),z * (y \ x)) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(27459,a,34211,a)].">
      <j1 rule="hyper" parents="27459 34211"/>
    </justification>
  </clause>

  <clause id="34213">
    <literal><![CDATA[
      R(x,y \ x,z * (y \ x)) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,27497,a(flip),b,34212,a)].">
      <j1 rule="hyper" parents="60 27497 34212"/>
    </justification>
  </clause>

  <clause id="34214">
    <literal><![CDATA[
      R(x,y * x,z * (y \ x)) = R(x,y * x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(33418,a,34213,a)].">
      <j1 rule="hyper" parents="33418 34213"/>
    </justification>
  </clause>

  <clause id="34215">
    <literal><![CDATA[
      R(x,y * x,z * (x * y)) * z = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(34214(a,1),33677(a,1,1))].">
      <j1 rule="para" parents="34214 33677"/>
    </justification>
  </clause>

  <clause id="34216">
    <literal><![CDATA[
      (x * (x * y)) * ((x * y) \ z) = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32526,a(flip),b,34215,a)].">
      <j1 rule="hyper" parents="60 32526 34215"/>
    </justification>
  </clause>

  <clause id="34217">
    <literal><![CDATA[
      a(x,x,(y * z) * (u * ((y \ u) \ z))) = a((y * u) * z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(34216(a,1),34115(a,1,3,2))].">
      <j1 rule="para" parents="34216 34115"/>
    </justification>
  </clause>

  <clause id="34218">
    <literal><![CDATA[
      a(x,x,(y * z) * (u * (z * (u * y)))) = a((y * u) * z,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(34046,a,34217,a)].">
      <j1 rule="hyper" parents="34046 34217"/>
    </justification>
  </clause>

  <clause id="34219">
    <literal><![CDATA[
      a(x,x,(y * z) * (u * (z * (u * y)))) = a(y,x,a(u * (y * z),u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,34154,a(flip),b,34218,a),flip(a)].">
      <j1 rule="hyper" parents="370 34154 34218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34220">
    <literal><![CDATA[
      a(x,x,(y * z) * (u * (z * (u * y)))) = a(z * u,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,34012,a(flip),b,34219,a),flip(a)].">
      <j1 rule="hyper" parents="370 34012 34219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34221">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(x,u,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34082,a(flip),b,34220,a),flip(a)].">
      <j1 rule="hyper" parents="60 34082 34220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34222">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(33814,a,34221,a)].">
      <j1 rule="hyper" parents="33814 34221"/>
    </justification>
  </clause>

  <clause id="34223">
    <literal><![CDATA[
      a(x,y,a(z,x,y * u)) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(33813,a,34221,a)].">
      <j1 rule="hyper" parents="33813 34221"/>
    </justification>
  </clause>

  <clause id="34224">
    <literal><![CDATA[
      L(x,y,a(z,y,a(u,u,w))) = x
    ]]></literal>
    <justification jstring="[para(34221(a,1),32144(a,1,3))].">
      <j1 rule="para" parents="34221 32144"/>
    </justification>
  </clause>

  <clause id="34225">
    <literal><![CDATA[
      (x * (a(y,x,a(z,z,u)) * w)) / T(x * a(z,x,a(u,z,y)),w) = w
    ]]></literal>
    <justification jstring="[hyper(60,a,33663,a,b,34224,a)].">
      <j1 rule="hyper" parents="60 33663 34224"/>
    </justification>
  </clause>

  <clause id="34226">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(y,u,a(z,z,x * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34156,a(flip),b,34223,a)].">
      <j1 rule="hyper" parents="60 34156 34223"/>
    </justification>
  </clause>

  <clause id="34227">
    <literal><![CDATA[
      a(x,y,a(z,z,u * y)) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34221,a(flip),b,34226,a),flip(a)].">
      <j1 rule="hyper" parents="60 34221 34226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34229">
    <literal><![CDATA[
      a(x * (y \ (z * (L(L(z,u,w),u,w) \ v5))),v6,z * (L(L(z,u,w),u,w) \ v5)) = a(v5 * (y * x),v6,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,29092,a(flip),b,33459,a),flip(a)].">
      <j1 rule="hyper" parents="370 29092 33459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34231">
    <literal><![CDATA[
      a(x * (y * (L(L(y,z,u),z,u) \ (w \ v5))),v6,y * (L(L(y,z,u),z,u) \ v5)) = a(v5 * (w * x),v6,v5)
    ]]></literal>
    <justification jstring="[para(29161(a,1),34229(a,1,1,2))].">
      <j1 rule="para" parents="29161 34229"/>
    </justification>
  </clause>

  <clause id="34232">
    <literal><![CDATA[
      a(x * (y * (L(L(y,z,u),z,u) \ (w \ v5))),v6,v5) = a(v5 * (w * x),v6,v5)
    ]]></literal>
    <justification jstring="[hyper(30213,a,34231,a)].">
      <j1 rule="hyper" parents="30213 34231"/>
    </justification>
  </clause>

  <clause id="34233">
    <literal><![CDATA[
      a((x \ y) * z,u,y) = a(y * (x * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(30208,a,34232,a)].">
      <j1 rule="hyper" parents="30208 34232"/>
    </justification>
  </clause>

  <clause id="34235">
    <literal><![CDATA[
      a(x * (L(x,y,z) * u),w,x) = a(a(z,y,x) * u,w,x)
    ]]></literal>
    <justification jstring="[para(32572(a,2),34233(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="32572 34233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34236">
    <literal><![CDATA[
      a(a(x,y,z) * u,z,z) = a(u,z,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,31590,a(flip),b,34235,a),flip(a)].">
      <j1 rule="hyper" parents="60 31590 34235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34237">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,v5) * v6,v5,v5)) = x * a(a(v6,v5,v5),z,y)
    ]]></literal>
    <justification jstring="[para(34236(a,1),31125(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="34236 31125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34238">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,v5) * v6,v5,v5)) = x * a(v5,v5,a(y,z,v6))
    ]]></literal>
    <justification jstring="[para(32231(a,1),34237(a,2,2))].">
      <j1 rule="para" parents="32231 34237"/>
    </justification>
  </clause>

  <clause id="34239">
    <literal><![CDATA[
      (x * y) * a(z,u,a(a(w,v5,v6) * y,v6,v6)) = x * L(y,u,a(v6,v6,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32152,a(flip),b,34238,a),flip(a)].">
      <j1 rule="hyper" parents="370 32152 34238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34240">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(w,v5,z)) = a(x,y,z) * L(u,v5,a(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(32970,a,34239,a)].">
      <j1 rule="hyper" parents="32970 34239"/>
    </justification>
  </clause>

  <clause id="34241">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(w,v5,z)) = a(x,y,z) * L(u,z,a(w,v5,z))
    ]]></literal>
    <justification jstring="[para(33008(a,1),34240(a,2,2))].">
      <j1 rule="para" parents="33008 34240"/>
    </justification>
  </clause>

  <clause id="34242">
    <literal><![CDATA[
      a(x,L(a(y,z,u) * (w * u),u,a(y,z,u)) * v5,v6) = a(x,L(w * L(u,z,y),a(y,z,u),a(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(34241(a,2),33951(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="34241 33951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34243">
    <literal><![CDATA[
      a(x,L(y * L(z,u,w),a(w,u,z),a(w,u,z)) * v5,v6) = a(x,(z * (L(z,u,w) \ (y * z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(32631(a,1),34242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="32631 34242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34244">
    <literal><![CDATA[
      a(x,L(y * L(z,u,w),a(w,u,z),a(w,u,z)) * v5,v6) = a(x,(y * (z * a(w,u,z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(32671(a,1),34243(a,2,2,1))].">
      <j1 rule="para" parents="32671 34243"/>
    </justification>
  </clause>

  <clause id="34245">
    <literal><![CDATA[
      a(x,(y * (z * a(u,w,z))) * v5,v6) = a(x,(y * L(z,w,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(30617(a,1),34244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30617 34244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34246">
    <literal><![CDATA[
      a(x,(a(y,y,z) * (u * z)) * w,v5) = a(x,(u * L(z,y,y)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(33351,a,34245,a)].">
      <j1 rule="hyper" parents="33351 34245"/>
    </justification>
  </clause>

  <clause id="34248">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a((x \ T(y,x \ 1)) \ (x \ 1),z,(x \ (y * (x \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,27185,a(flip),b,33311,a),flip(a)].">
      <j1 rule="hyper" parents="370 27185 33311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34249">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a((x \ T(y,x \ 1)) \ (x \ 1),z,u * (x \ (x * y)))
    ]]></literal>
    <justification jstring="[hyper(370,a,27932,a(flip),b,34248,a),flip(a)].">
      <j1 rule="hyper" parents="370 27932 34248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34250">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a((x \ T(y,x \ 1)) \ (x \ 1),z,u * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),34249(a,2,3,2))].">
      <j1 rule="para" parents="4 34249"/>
    </justification>
  </clause>

  <clause id="34251">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a(x * (T(y,x \ 1) \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26758,a(flip),b,34250,a),flip(a)].">
      <j1 rule="hyper" parents="370 26758 34250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34253">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ ((x \ 1) \ u)) = a(x * (y \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(370,a,26599,a(flip),b,34251,a),flip(a)].">
      <j1 rule="hyper" parents="370 26599 34251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34255">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ T(y,x \ 1)) \ (x \ u)) = a(x * (y \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(60,a,3151,a(flip),b,34253,a)].">
      <j1 rule="hyper" parents="60 3151 34253"/>
    </justification>
  </clause>

  <clause id="34256">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * (x \ 1),z,(x \ y) \ (x \ u)) = a(x * (y \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(27004,a,34255,a)].">
      <j1 rule="hyper" parents="27004 34255"/>
    </justification>
  </clause>

  <clause id="34257">
    <literal><![CDATA[
      a((x \ T(y,x \ 1)) * x,z,(x \ y) \ (x \ u)) = a(x * (y \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(26607,a,34256,a)].">
      <j1 rule="hyper" parents="26607 34256"/>
    </justification>
  </clause>

  <clause id="34258">
    <literal><![CDATA[
      a((x \ y) * x,z,(x \ y) \ (x \ u)) = a(x * (y \ x),z,u * y)
    ]]></literal>
    <justification jstring="[hyper(26534,a,34257,a)].">
      <j1 rule="hyper" parents="26534 34257"/>
    </justification>
  </clause>

  <clause id="34259">
    <literal><![CDATA[
      a(x * (y \ x),z,u * y) = a(y,z,(x \ y) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(26520,a,34258,a),flip(a)].">
      <j1 rule="hyper" parents="26520 34258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34261">
    <literal><![CDATA[
      a(x * (y \ x),z,u * (w \ y)) = a(y,z,(x \ y) \ (x \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(33347,a,34259,a)].">
      <j1 rule="hyper" parents="33347 34259"/>
    </justification>
  </clause>

  <clause id="34262">
    <literal><![CDATA[
      a(x,y,(z \ x) \ (z \ (u * (z * x)))) = a(x,y,z \ (x \ (u \ x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34058,a(flip),b,34261,a),flip(a)].">
      <j1 rule="hyper" parents="60 34058 34261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34263">
    <literal><![CDATA[
      a(x,y,z * ((x \ z) * (u * (z * x)))) = a(x,y,z \ (x \ (u \ x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33869,a(flip),b,34262,a)].">
      <j1 rule="hyper" parents="60 33869 34262"/>
    </justification>
  </clause>

  <clause id="34264">
    <literal><![CDATA[
      a(a((x \ 1) \ 1,y * (x * x),y) * (z \ ((x * x) * (x * T(y,x * x)))),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(15776(a,1),33660(a,1,1,1))].">
      <j1 rule="para" parents="15776 33660"/>
    </justification>
  </clause>

  <clause id="34265">
    <literal><![CDATA[
      a(a((x \ 1) \ 1,y,y) * (z \ ((x * x) * (x * T(y,x * x)))),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(3076(a,1),34264(a,1,1,1))].">
      <j1 rule="para" parents="3076 34264"/>
    </justification>
  </clause>

  <clause id="34268">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ ((x * x) * (x * T(y,x * x)))),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(26377(a,1),34265(a,1,1,1))].">
      <j1 rule="para" parents="26377 34265"/>
    </justification>
  </clause>

  <clause id="34269">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (x * (y * ((1 / x) \ x)))),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(15031(a,1),34268(a,1,1,2,2))].">
      <j1 rule="para" parents="15031 34268"/>
    </justification>
  </clause>

  <clause id="34271">
    <literal><![CDATA[
      a(a(x,y,y) * ((z \ (x * y)) * ((1 / x) \ x)),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(4188(a,1),34269(a,1,1,2))].">
      <j1 rule="para" parents="4188 34269"/>
    </justification>
  </clause>

  <clause id="34272">
    <literal><![CDATA[
      a(a(x,y,y) * ((z \ (x * y)) * ((x \ 1) \ x)),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[hyper(26788,a,34271,a)].">
      <j1 rule="hyper" parents="26788 34271"/>
    </justification>
  </clause>

  <clause id="34273">
    <literal><![CDATA[
      a(a(x,y,y) * ((z \ (x * y)) * (x * x)),u,w) = a(z \ ((y * (x * x)) \ ((x \ 1) \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(311(a,1),34272(a,1,1,2,2))].">
      <j1 rule="para" parents="311 34272"/>
    </justification>
  </clause>

  <clause id="34274">
    <literal><![CDATA[
      a(x \ ((y * (z * z)) \ ((z \ 1) \ 1)),u,w) = a((x \ (z * y)) * (z * R(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[para(32729(a,1),34273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32729 34273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34275">
    <literal><![CDATA[
      a(x \ ((y * (z * z)) \ ((z \ 1) \ 1)),u,w) = a((x \ (z * y)) * (z * L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27338,a(flip),b,34274,a),flip(a)].">
      <j1 rule="hyper" parents="370 27338 34274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34276">
    <literal><![CDATA[
      a(x \ ((y * (z * z)) \ ((z \ 1) \ 1)),u,w) = a(a(y,y,z) * (x \ (z * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,32302,a(flip),b,34275,a),flip(a)].">
      <j1 rule="hyper" parents="370 32302 34275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34277">
    <literal><![CDATA[
      a(x \ (T(y,z * z) \ (z \ 1)),u,w) = a(a(y,y,z) * (x \ (z * y)),u,w)
    ]]></literal>
    <justification jstring="[para(1450(a,1),34276(a,1,1,2))].">
      <j1 rule="para" parents="1450 34276"/>
    </justification>
  </clause>

  <clause id="34278">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (y * x)),u,w) = a(z \ (x \ (y \ 1)),u,w)
    ]]></literal>
    <justification jstring="[hyper(26683,a,34277,a),flip(a)].">
      <j1 rule="hyper" parents="26683 34277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34279">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (y * x)),u,w) = a(z \ (x \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,27512,a(flip),b,34278,a),flip(a)].">
      <j1 rule="hyper" parents="370 27512 34278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34280">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (y * L(x,u,w))),v5,v6) = a(z \ (L(x,u,w) \ y),v5,v6)
    ]]></literal>
    <justification jstring="[para(29529(a,1),34279(a,1,1,1))].">
      <j1 rule="para" parents="29529 34279"/>
    </justification>
  </clause>

  <clause id="34281">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (y * L(x,u,x))),w,v5) = a(z \ (x \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,14496,a(flip),b,34280,a),flip(a)].">
      <j1 rule="hyper" parents="370 14496 34280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34282">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(1 / ((x * y) / x),(x * y) / x,u)) = L(L(x,y,y),1 / ((x * y) / x),a(u,z,1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(3041(a,1),33039(a,1,2,3))].">
      <j1 rule="para" parents="3041 33039"/>
    </justification>
  </clause>

  <clause id="34283">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(1 / ((x * y) / x),y,u)) = L(L(x,y,y),1 / ((x * y) / x),a(u,z,1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(26453(a,1),34282(a,1,2,3))].">
      <j1 rule="para" parents="26453 34282"/>
    </justification>
  </clause>

  <clause id="34284">
    <literal><![CDATA[
      L(L(x,y,y),1 / ((x * y) / x),a(z,u,1 / ((x * y) / x))) = (1 / ((x * y) / x)) * L(x * y,u,a((x * y) / x,y,z))
    ]]></literal>
    <justification jstring="[para(2957(a,1),34283(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="2957 34283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34286">
    <literal><![CDATA[
      L(L(x,y,y),1 / ((x * y) / x),a(z,u,1 / ((x * y) / x))) = (1 / ((x * y) / x)) * L(x * y,u,a(x \ (x * y),y,z))
    ]]></literal>
    <justification jstring="[para(26376(a,1),34284(a,2,2,3))].">
      <j1 rule="para" parents="26376 34284"/>
    </justification>
  </clause>

  <clause id="34287">
    <literal><![CDATA[
      L(L(x,y,y),1 / ((x * y) / x),a(z,u,1 / ((x * y) / x))) = (1 / ((x * y) / x)) * L(x * y,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),34286(a,2,2,3,1))].">
      <j1 rule="para" parents="4 34286"/>
    </justification>
  </clause>

  <clause id="34288">
    <literal><![CDATA[
      L(L(x,y,y),1 / ((x * y) / x),a(z,u,(x * y) / x)) = (1 / ((x * y) / x)) * L(x * y,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(3078(a,1),34287(a,1,3))].">
      <j1 rule="para" parents="3078 34287"/>
    </justification>
  </clause>

  <clause id="34289">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(y,y,u)) = L(L(x,y,y),1 / ((x * y) / x),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(26881(a,1),34288(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26881 34288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34290">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(y,y,u)) = L(L(x,y,y),(x * y) / x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,3388,a(flip),b,34289,a),flip(a)].">
      <j1 rule="hyper" parents="370 3388 34289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34292">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(y,y,u)) = L(L(x,y,y),y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,26017,a(flip),b,34290,a),flip(a)].">
      <j1 rule="hyper" parents="370 26017 34290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34294">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(y,y,u)) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,33266,a(flip),b,34292,a),flip(a)].">
      <j1 rule="hyper" parents="370 33266 34292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34295">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * L(x * y,z,a(y,y,u)) = L(x,y,L(y,z,y * u))
    ]]></literal>
    <justification jstring="[para(29408(a,1),34294(a,1,2))].">
      <j1 rule="para" parents="29408 34294"/>
    </justification>
  </clause>

  <clause id="34296">
    <literal><![CDATA[
      L(x,y,L(y,z,y * u)) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34294,a(flip),b,34295,a),flip(a)].">
      <j1 rule="hyper" parents="60 34294 34295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34297">
    <literal><![CDATA[
      a(L(x,y,x * z),x,u) = L(u,x,L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(34296(a,1),32572(a,2,1))].">
      <j1 rule="para" parents="34296 32572"/>
    </justification>
  </clause>

  <clause id="34298">
    <literal><![CDATA[
      a(L(x,y,x * z),x,u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,30074,a(flip),b,34297,a),flip(a)].">
      <j1 rule="hyper" parents="370 30074 34297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34299">
    <literal><![CDATA[
      a(x,x,L(y,z,x * u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(32429,a,34298,a)].">
      <j1 rule="hyper" parents="32429 34298"/>
    </justification>
  </clause>

  <clause id="34300">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(y,x,z),L(u,w,v5)) = a(x,x,L(u,w,(x * a(y,x,z)) * v5))
    ]]></literal>
    <justification jstring="[hyper(30995,a,34299,a),flip(a)].">
      <j1 rule="hyper" parents="30995 34299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34301">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),L(u,w,(x * y) * z)) = a(R(x,y,z),R(x,y,z),L(u,w,y * z))
    ]]></literal>
    <justification jstring="[para(103(a,1),34299(a,1,3,3))].">
      <j1 rule="para" parents="103 34299"/>
    </justification>
  </clause>

  <clause id="34302">
    <literal><![CDATA[
      a(x,x,L(y,z,(x * a(u,x,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(34300(a,1),30995(a,1))].">
      <j1 rule="para" parents="34300 30995"/>
    </justification>
  </clause>

  <clause id="34303">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),L(u,w,y * z)) = a(x,x,L(u,w,(x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29531,a(flip),b,34301,a),flip(a)].">
      <j1 rule="hyper" parents="60 29531 34301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34305">
    <literal><![CDATA[
      a(x,x,L(y,z,(x * u) * w)) = a(x,x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,29531,a(flip),b,34303,a),flip(a)].">
      <j1 rule="hyper" parents="60 29531 34303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34306">
    <literal><![CDATA[
      a(x,x,L(y,z,a(u,x,w) * v5)) = a(x,x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(34302,a,34305,a),flip(a)].">
      <j1 rule="hyper" parents="34302 34305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34308">
    <literal><![CDATA[
      a(x,x,L(y,z,z \ u)) * u = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(34306(a,1),34050(a,1,1))].">
      <j1 rule="para" parents="34306 34050"/>
    </justification>
  </clause>

  <clause id="34309">
    <literal><![CDATA[
      a(x,x,L(y,z,u * z)) * u = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(31566(a,1),34308(a,1,1,3))].">
      <j1 rule="para" parents="31566 34308"/>
    </justification>
  </clause>

  <clause id="34310">
    <literal><![CDATA[
      (x / y) * (y * a(z,z,u)) = y * ((a(z,z,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(60,a,32352,a(flip),b,34309,a)].">
      <j1 rule="hyper" parents="60 32352 34309"/>
    </justification>
  </clause>

  <clause id="34311">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ u) = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,28257,a(flip),b,34310,a)].">
      <j1 rule="hyper" parents="60 28257 34310"/>
    </justification>
  </clause>

  <clause id="34312">
    <literal><![CDATA[
      x * ((a(y,y,z) \ x) \ (x * u)) = (a(y,y,z) * x) * u
    ]]></literal>
    <justification jstring="[hyper(742,a,34311,a),flip(a)].">
      <j1 rule="hyper" parents="742 34311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34313">
    <literal><![CDATA[
      x * ((a(y,y,z) \ x) \ u) = u * (a(y,y,z) * a(x * u,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33858,a(flip),b,34311,a),flip(a)].">
      <j1 rule="hyper" parents="60 33858 34311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34314">
    <literal><![CDATA[
      x * L(a(y,y,z) * u,a(y,y,z),x) = (a(y,y,z) * x) * u
    ]]></literal>
    <justification jstring="[para(30808(a,2),34312(a,1,2))].">
      <j1 rule="para" parents="30808 34312"/>
    </justification>
  </clause>

  <clause id="34315">
    <literal><![CDATA[
      x * a(y,y,L(z,x,u * x)) = u * ((a(y,y,z) \ u) \ x)
    ]]></literal>
    <justification jstring="[para(32319(a,1),34313(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32319 34313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34316">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(z,a(x,x,y) \ u,u * (a(x,x,y) \ u))) = (a(x,x,z) \ u) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(33694,a,34315,a)].">
      <j1 rule="hyper" parents="33694 34315"/>
    </justification>
  </clause>

  <clause id="34317">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(z,a(x,x,y) \ u,u * (a(x,x,y) * u))) = (a(x,x,z) \ u) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(30663(a,1),34316(a,1,2,3))].">
      <j1 rule="para" parents="30663 34316"/>
    </justification>
  </clause>

  <clause id="34318">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(z,a(x,x,y) \ u,L(a(x,x,y),u,u))) = (a(x,x,z) \ u) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(24029(a,1),34317(a,1,2,3))].">
      <j1 rule="para" parents="24029 34317"/>
    </justification>
  </clause>

  <clause id="34319">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(z,a(x,x,y) \ u,a(x,x,L(y,u,u)))) = (a(x,x,z) \ u) \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(29140(a,2),34318(a,1,2,3,3))].">
      <j1 rule="para" parents="29140 34318"/>
    </justification>
  </clause>

  <clause id="34320">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ (a(x,x,u) \ z) = a(x,x,u) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(29146(a,1),34319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29146 34319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34323">
    <literal><![CDATA[
      (L(a(x,y,z) \ a(x,y,L(z,u,w)),v5,v6) / (a(x,y,z) \ 1)) * L(a(x,y,z) \ 1,v5,v6) = (a(x,y,z) \ 1) \ L(L(a(x,y,z) \ 1,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(2(a,1),32336(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2 32336"/>
    </justification>
  </clause>

  <clause id="34324">
    <literal><![CDATA[
      (L(a(x,y,a(z,u,w)),v5,v6) / (a(z,u,w) \ 1)) * L(a(z,u,w) \ 1,v5,v6) = (a(z,u,w) \ 1) \ L(L(a(z,u,w) \ 1,v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(32328(a,1),34323(a,1,1,1,1))].">
      <j1 rule="para" parents="32328 34323"/>
    </justification>
  </clause>

  <clause id="34325">
    <literal><![CDATA[
      (x * L(a(y,y,z * u) \ 1,u,w)) \ ((x * (a(y,y,z * u) \ 1)) * a(w,z,a(y,y,z * u))) = a(x,a(y,y,z * u),a(w,z,a(y,y,z * u)))
    ]]></literal>
    <justification jstring="[para(32995(a,1),33811(a,1,1,2))].">
      <j1 rule="para" parents="32995 33811"/>
    </justification>
  </clause>

  <clause id="34326">
    <literal><![CDATA[
      (a(x,x,L(y * z,z,u)) \ w) \ ((w * (a(x,x,y * z) \ 1)) * a(u,y,a(x,x,y * z))) = a(w,a(x,x,y * z),a(u,y,a(x,x,y * z)))
    ]]></literal>
    <justification jstring="[para(32343(a,1),34325(a,1,1))].">
      <j1 rule="para" parents="32343 34325"/>
    </justification>
  </clause>

  <clause id="34327">
    <literal><![CDATA[
      (a(x,x,L(y * z,z,u)) \ w) \ ((a(x,x,y * z) \ w) * a(u,y,a(x,x,y * z))) = a(w,a(x,x,y * z),a(u,y,a(x,x,y * z)))
    ]]></literal>
    <justification jstring="[para(30626(a,1),34326(a,1,2,1))].">
      <j1 rule="para" parents="30626 34326"/>
    </justification>
  </clause>

  <clause id="34328">
    <literal><![CDATA[
      (a(x,x,L(y * z,z,u)) \ w) \ (a(x,x,L(y * z,y,u)) \ w) = a(w,a(x,x,y * z),a(u,y,a(x,x,y * z)))
    ]]></literal>
    <justification jstring="[para(32347(a,1),34327(a,1,2))].">
      <j1 rule="para" parents="32347 34327"/>
    </justification>
  </clause>

  <clause id="34329">
    <literal><![CDATA[
      (a(x,x,L(y * z,z,u)) \ w) \ (a(x,x,L(y * z,y,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(34328(a,2),31241(a,1))].">
      <j1 rule="para" parents="34328 31241"/>
    </justification>
  </clause>

  <clause id="34330">
    <literal><![CDATA[
      a(x,x,L(y * z,y,u)) \ a(x,x,L(y * z,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(34329,a,34320,a),flip(a)].">
      <j1 rule="hyper" parents="34329 34320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34331">
    <literal><![CDATA[
      a(x,y,a(z,z,u * y)) * a(x,u,a(z,z,u * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,32549,a(flip),b,34330,a)].">
      <j1 rule="hyper" parents="60 32549 34330"/>
    </justification>
  </clause>

  <clause id="34332">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(u,x,a(z,z,x * y)) = 1
    ]]></literal>
    <justification jstring="[para(34227(a,1),34331(a,1,1))].">
      <j1 rule="para" parents="34227 34331"/>
    </justification>
  </clause>

  <clause id="34333">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(x,u,a(z,z,y)) = 1
    ]]></literal>
    <justification jstring="[para(34222(a,1),34332(a,1,2))].">
      <j1 rule="para" parents="34222 34332"/>
    </justification>
  </clause>

  <clause id="34334">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,33715,a(flip),b,34333,a)].">
      <j1 rule="hyper" parents="60 33715 34333"/>
    </justification>
  </clause>

  <clause id="34335">
    <literal><![CDATA[
      a(x,a(y,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,31980,a,b,34334,a)].">
      <j1 rule="hyper" parents="60 31980 34334"/>
    </justification>
  </clause>

  <clause id="34336">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,34334,a)].">
      <j1 rule="hyper" parents="49 34334"/>
    </justification>
  </clause>

  <clause id="34337">
    <literal><![CDATA[
      L(x,a(y,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,34335,a)].">
      <j1 rule="hyper" parents="49 34335"/>
    </justification>
  </clause>

  <clause id="34340">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = x * (((x \ y) / y) * 1)
    ]]></literal>
    <justification jstring="[para(34335(a,1),33925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="34335 33925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34343">
    <literal><![CDATA[
      x * a(y,x,a(z,y,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(34336(a,1),33118(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34336 33118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34344">
    <literal><![CDATA[
      (a(x,x,y) * (z * u)) \ (z * (u * w)) = a(x,x,y) \ L(w,u,z)
    ]]></literal>
    <justification jstring="[hyper(25585,a,34337,a)].">
      <j1 rule="hyper" parents="25585 34337"/>
    </justification>
  </clause>

  <clause id="34348">
    <literal><![CDATA[
      (a(x,x,y) \ z) * u = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(129,a,34337,a(flip),b,30737,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 34337 30737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34349">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,v5) = a(u * (x * a(y,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(34337(a,1),26383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34337 26383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34353">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[para(34337(a,1),34314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34337 34314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34354">
    <literal><![CDATA[
      (x * (a(y,x,a(z,z,u)) * w)) / T(L(x,z,a(z,u,y)),w) = w
    ]]></literal>
    <justification jstring="[para(34343(a,1),34225(a,1,2,1))].">
      <j1 rule="para" parents="34343 34225"/>
    </justification>
  </clause>

  <clause id="34356">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * (a(z,z,u) \ y)) * w) = a(x,a(z,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(34348(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="34348 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34357">
    <literal><![CDATA[
      (x * (a(y,y,z) \ (u * w))) \ (((a(y,y,z) \ x) * u) * w) = a(a(y,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(34348(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34348 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34362">
    <literal><![CDATA[
      a((x \ y) * (a(z,z,y) * u),w,v5) = a((x \ L(y,z,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(34353(a,1),33915(a,1,1))].">
      <j1 rule="para" parents="34353 33915"/>
    </justification>
  </clause>

  <clause id="34363">
    <literal><![CDATA[
      a(x,(y * z) * (a(u,u,z) * w),v5) = a(x,(y * L(z,u,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(34353(a,1),34246(a,1,2))].">
      <j1 rule="para" parents="34353 34246"/>
    </justification>
  </clause>

  <clause id="34365">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(788,a,34340,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="788 34340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34367">
    <literal><![CDATA[
      a(x,x,y * a(z,y,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,28440,a(flip),b,34365,a),flip(a)].">
      <j1 rule="hyper" parents="370 28440 34365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34368">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(60,a,34016,a(flip),b,34367,a)].">
      <j1 rule="hyper" parents="60 34016 34367"/>
    </justification>
  </clause>

  <clause id="34387">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(126,a,34368,a(flip),b,32957,a),flip(a)].">
      <j1 rule="hyper" parents="126 34368 32957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34399">
    <literal><![CDATA[
      a(x,x,y) \ (z * u) = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(34368(a,1),32344(a,1,1))].">
      <j1 rule="para" parents="34368 32344"/>
    </justification>
  </clause>

  <clause id="34403">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = (a(y,y,x) \ w) \ (w * L(x,y,y))
    ]]></literal>
    <justification jstring="[para(34368(a,1),33779(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34368 33779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34418">
    <literal><![CDATA[
      (x * (a(y,y,z) \ u)) * w = (x * u) * (a(y,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(34399(a,1),34348(a,1,1))].">
      <j1 rule="para" parents="34399 34348"/>
    </justification>
  </clause>

  <clause id="34419">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = a(y,y,x) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,7954,a(flip),b,34403,a),flip(a)].">
      <j1 rule="hyper" parents="370 7954 34403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34421">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,32568,a(flip),b,34419,a),flip(a)].">
      <j1 rule="hyper" parents="370 32568 34419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34423">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(33016,a,34421,a)].">
      <j1 rule="hyper" parents="33016 34421"/>
    </justification>
  </clause>

  <clause id="34424">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(30727,a,34421,a)].">
      <j1 rule="hyper" parents="30727 34421"/>
    </justification>
  </clause>

  <clause id="34446">
    <literal><![CDATA[
      (a(x,x,y) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      z \ (a(x,x,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(34423(a,1),747(a,1)),flip(a)].">
      <j1 rule="para" parents="34423 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34448">
    <literal><![CDATA[
      a(a(x,x,y) * (z * u),w,v5) = a(u * (a(x,x,y) * z),w,v5)
    ]]></literal>
    <justification jstring="[para(34423(a,1),26383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34423 26383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34449">
    <literal><![CDATA[
      (x * y) * a(z,z,u) = x * (a(z,z,u) * y)
    ]]></literal>
    <justification jstring="[para(34423(a,1),28359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34423 28359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34465">
    <literal><![CDATA[
      (x * a(y,z,x)) * u = x * (u * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33551,a(flip),b,34424,a)].">
      <j1 rule="hyper" parents="60 33551 34424"/>
    </justification>
  </clause>

  <clause id="34466">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[hyper(60,a,32631,a(flip),b,34424,a)].">
      <j1 rule="hyper" parents="60 32631 34424"/>
    </justification>
  </clause>

  <clause id="34479">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ v5) = v5 * a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32962,a(flip),b,34466,a),flip(a)].">
      <j1 rule="hyper" parents="370 32962 34466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34485">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * a(z,y,x),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(34466(a,2),26519(a,1,1))].">
      <j1 rule="para" parents="34466 26519"/>
    </justification>
  </clause>

  <clause id="34492">
    <literal><![CDATA[
      T(x,y) \ (x * (z * a(u,w,x))) = x * (L(T(x,y),w,u) \ z)
    ]]></literal>
    <justification jstring="[para(34465(a,1),32916(a,1,2))].">
      <j1 rule="para" parents="34465 32916"/>
    </justification>
  </clause>

  <clause id="34493">
    <literal><![CDATA[
      a((x \ y) * (z * a(u,u,y)),w,v5) = a(z * (x \ L(y,u,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(33719,a,34349,a),flip(a)].">
      <j1 rule="hyper" parents="33719 34349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34494">
    <literal><![CDATA[
      (x * (a(y,x,a(z,z,u)) * w)) / T(x,w) = w
    ]]></literal>
    <justification jstring="[para(34421(a,1),34354(a,1,2,1))].">
      <j1 rule="para" parents="34421 34354"/>
    </justification>
  </clause>

  <clause id="34495">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * ((y * w) / T(y,w)) = w
    ]]></literal>
    <justification jstring="[hyper(60,a,28387,a(flip),b,34494,a)].">
      <j1 rule="hyper" parents="60 28387 34494"/>
    </justification>
  </clause>

  <clause id="34497">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * w = w
    ]]></literal>
    <justification jstring="[para(214(a,1),34495(a,1,2))].">
      <j1 rule="para" parents="214 34495"/>
    </justification>
  </clause>

  <clause id="34500">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32958,a,34497,a)].">
      <j1 rule="hyper" parents="32958 34497"/>
    </justification>
  </clause>

  <clause id="34508">
    <literal><![CDATA[
      a((x * y) * z,u,x) = a(y * (x \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,33756,a(flip),b,34497,a)].">
      <j1 rule="hyper" parents="60 33756 34497"/>
    </justification>
  </clause>

  <clause id="34509">
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,33049,a(flip),b,34497,a),flip(a)].">
      <j1 rule="hyper" parents="60 33049 34497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34523">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(33512,a,34500,a),flip(a)].">
      <j1 rule="hyper" parents="33512 34500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34524">
    <literal><![CDATA[
      a(x,y,(z * u) * (x * u)) = a(x,y,z * x)
    ]]></literal>
    <justification jstring="[hyper(33453,a,34500,a)].">
      <j1 rule="hyper" parents="33453 34500"/>
    </justification>
  </clause>

  <clause id="34526">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(32419,a,34500,a)].">
      <j1 rule="hyper" parents="32419 34500"/>
    </justification>
  </clause>

  <clause id="34527">
    <literal><![CDATA[
      a(x \ y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(32418,a,34500,a),flip(a)].">
      <j1 rule="hyper" parents="32418 34500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34529">
    <literal><![CDATA[
      a(x,y,L(z \ u,w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(29468,a,34500,a)].">
      <j1 rule="hyper" parents="29468 34500"/>
    </justification>
  </clause>

  <clause id="34531">
    <literal><![CDATA[
      a(x,y,z * (u * z)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(27034,a,34500,a)].">
      <j1 rule="hyper" parents="27034 34500"/>
    </justification>
  </clause>

  <clause id="34532">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(27010,a,34500,a),flip(a)].">
      <j1 rule="hyper" parents="27010 34500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34537">
    <literal><![CDATA[
      a(x,y,(x * z) * u) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33181,a(flip),b,34500,a),flip(a)].">
      <j1 rule="hyper" parents="60 33181 34500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34545">
    <literal><![CDATA[
      a(x,y,z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(34500(a,1),27010(a,1))].">
      <j1 rule="para" parents="34500 27010"/>
    </justification>
  </clause>

  <clause id="34548">
    <literal><![CDATA[
      (x \ 1) * a(y,z,u) = x \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(34500(a,1),32329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34500 32329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34551">
    <literal><![CDATA[
      a(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(34500(a,1),32418(a,1))].">
      <j1 rule="para" parents="34500 32418"/>
    </justification>
  </clause>

  <clause id="34562">
    <literal><![CDATA[
      a(x,y,(x \ z) * u) = a(x,y,z * (x * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,33766,a(flip),b,34509,a),flip(a)].">
      <j1 rule="hyper" parents="60 33766 34509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34564">
    <literal><![CDATA[
      a(x,y,x * (((1 / x) * z) \ u)) = a(x,y,z \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33586,a(flip),b,34509,a),flip(a)].">
      <j1 rule="hyper" parents="60 33586 34509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34566">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(60,a,32313,a(flip),b,34509,a)].">
      <j1 rule="hyper" parents="60 32313 34509"/>
    </justification>
  </clause>

  <clause id="34586">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(32595(a,1),34566(a,1,1))].">
      <j1 rule="para" parents="32595 34566"/>
    </justification>
  </clause>

  <clause id="34593">
    <literal><![CDATA[
      a((x * (y * z)) * ((x * y) * z),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,2),34527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 34527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34599">
    <literal><![CDATA[
      a(x,y,L(y * z,y,u)) = a(x,y,(u * y) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(32532,a,34532,a)].">
      <j1 rule="hyper" parents="32532 34532"/>
    </justification>
  </clause>

  <clause id="34608">
    <literal><![CDATA[
      a(x,y,z * ((x \ z) * u)) = a(u,y,a(x,x,z)) * a(x,y,x * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,33622,a(flip),b,34532,a),flip(a)].">
      <j1 rule="hyper" parents="60 33622 34532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34609">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * (u \ (w * z))) = a(x,y,a(u,w * u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,33410,a(flip),b,34532,a),flip(a)].">
      <j1 rule="hyper" parents="60 33410 34532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34644">
    <literal><![CDATA[
      L(x \ R(x,L(y \ (z \ u),w,v5),v6),x,v7) = a(x,L(y \ (u / z),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(27503(a,1),34586(a,1,1,2))].">
      <j1 rule="para" parents="27503 34586"/>
    </justification>
  </clause>

  <clause id="34674">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * a(u,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(33826(a,2),34545(a,1))].">
      <j1 rule="para" parents="33826 34545"/>
    </justification>
  </clause>

  <clause id="34677">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (y * L(x,u,x))),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z * (x \ y),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(34281(a,2),34551(a,1))].">
      <j1 rule="para" parents="34281 34551"/>
    </justification>
  </clause>

  <clause id="34681">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(v5,w,a(x,y,x * (u \ z)))
    ]]></literal>
    <justification jstring="[para(34537(a,1),32942(a,2,3))].">
      <j1 rule="para" parents="34537 32942"/>
    </justification>
  </clause>

  <clause id="34682">
    <literal><![CDATA[
      a(x,y,(x \ (z \ x)) * u) = a(x,y,x * (z * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,33330,a(flip),b,34562,a),flip(a)].">
      <j1 rule="hyper" parents="370 33330 34562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34695">
    <literal><![CDATA[
      a(x,y,L(z * (y \ u),u * y,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(60,a,33829,a(flip),b,34529,a),flip(a)].">
      <j1 rule="hyper" parents="60 33829 34529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34698">
    <literal><![CDATA[
      a(x,y,L((z * u) * w,z,u)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34529,a(flip),b,34523,a)].">
      <j1 rule="hyper" parents="60 34529 34523"/>
    </justification>
  </clause>

  <clause id="34702">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) * v5)) = a(x,y,a(z,u,w * (x \ v5)))
    ]]></literal>
    <justification jstring="[para(34698(a,1),32242(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34698 32242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34703">
    <literal><![CDATA[
      a(x,y,x * ((z * x) * u)) = a(x,y,x * (z * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(60,a,33332,a(flip),b,34682,a)].">
      <j1 rule="hyper" parents="60 33332 34682"/>
    </justification>
  </clause>

  <clause id="34706">
    <literal><![CDATA[
      a(x,y,x * (((x \ 1) * z) \ u)) = a(x,y,z \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27136,a(flip),b,34564,a)].">
      <j1 rule="hyper" parents="60 27136 34564"/>
    </justification>
  </clause>

  <clause id="34707">
    <literal><![CDATA[
      a((a(x,y,z) * (u * (a(x,y,z) \ (a(x,y,z) \ w)))) * ((a(x,y,z) \ u) * w),v5,v6) = a(a(a(x,y,z),u,a(x,y,z) \ (a(x,y,z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(30883(a,1),34593(a,1,1,2))].">
      <j1 rule="para" parents="30883 34593"/>
    </justification>
  </clause>

  <clause id="34713">
    <literal><![CDATA[
      a(x,y,L(z * (y \ u),u * y,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(y * z) * u) = w
    ]]></literal>
    <justification jstring="[para(34695(a,2),34545(a,1))].">
      <j1 rule="para" parents="34695 34545"/>
    </justification>
  </clause>

  <clause id="34716">
    <literal><![CDATA[
      a(x,y,x * ((x * z) \ u)) = a(x,y,z \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,27566,a(flip),b,34706,a)].">
      <j1 rule="hyper" parents="60 27566 34706"/>
    </justification>
  </clause>

  <clause id="34717">
    <literal><![CDATA[
      a(x,y,x * ((x * z) \ u)) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,34532,a(flip),b,34716,a),flip(a)].">
      <j1 rule="hyper" parents="370 34532 34716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      a(x,y,x * ((x * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(u,x,x)) = w
    ]]></literal>
    <justification jstring="[para(34716(a,2),34545(a,1))].">
      <j1 rule="para" parents="34716 34545"/>
    </justification>
  </clause>

  <clause id="34719">
    <literal><![CDATA[
      a(x,y,x * (z \ (x \ u))) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33229,a(flip),b,34717,a)].">
      <j1 rule="hyper" parents="60 33229 34717"/>
    </justification>
  </clause>

  <clause id="34720">
    <literal><![CDATA[
      a(x,y,x * ((z * x) \ u)) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33499,a,b,34719,a)].">
      <j1 rule="hyper" parents="60 33499 34719"/>
    </justification>
  </clause>

  <clause id="34721">
    <literal><![CDATA[
      K(x,y) * (z * a(u,w,y)) = y * (L(T(y,x),w,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(7940,a,34492,a)].">
      <j1 rule="hyper" parents="7940 34492"/>
    </justification>
  </clause>

  <clause id="34723">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) * v5)) = a(x,y,a(z,u,w * (x \ v5)))
    ]]></literal>
    <justification jstring="[para(26901(a,1),34702(a,1,3))].">
      <j1 rule="para" parents="26901 34702"/>
    </justification>
  </clause>

  <clause id="34724">
    <literal><![CDATA[
      (x * y) \ (a(z,z,u) \ (x * (y * w))) = a(z,z,u) \ L(w,y,x)
    ]]></literal>
    <justification jstring="[hyper(34446,a,34344,a)].">
      <j1 rule="hyper" parents="34446 34344"/>
    </justification>
  </clause>

  <clause id="34726">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,z,u) \ (y * w))) = a(z,z,u) \ L(w,y,x)
    ]]></literal>
    <justification jstring="[para(34399(a,1),34724(a,1,2))].">
      <j1 rule="para" parents="34399 34724"/>
    </justification>
  </clause>

  <clause id="34727">
    <literal><![CDATA[
      (x * y) \ (x * (y * (a(z,z,u) \ w))) = a(z,z,u) \ L(w,y,x)
    ]]></literal>
    <justification jstring="[para(34399(a,1),34726(a,1,2,2))].">
      <j1 rule="para" parents="34399 34726"/>
    </justification>
  </clause>

  <clause id="34728">
    <literal><![CDATA[
      L(a(x,x,y) \ z,u,w) = a(x,x,y) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(629,a,34727,a)].">
      <j1 rule="hyper" parents="629 34727"/>
    </justification>
  </clause>

  <clause id="34729">
    <literal><![CDATA[
      L(L(a(x,x,y) \ z,u,w),z,z) = (L(z,u,w) \ a(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(34728(a,2),33378(a,1,1))].">
      <j1 rule="para" parents="34728 33378"/>
    </justification>
  </clause>

  <clause id="34730">
    <literal><![CDATA[
      L((x \ a(y,y,z)) \ 1,u,w) = (L(x,u,w) \ a(y,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,33696,a(flip),b,34729,a)].">
      <j1 rule="hyper" parents="60 33696 34729"/>
    </justification>
  </clause>

  <clause id="34731">
    <literal><![CDATA[
      L((x \ a(y,y,z)) \ 1,u,w) \ ((x \ a(y,y,z)) \ 1) = a(w,u,x)
    ]]></literal>
    <justification jstring="[para(34730(a,2),33876(a,1,1))].">
      <j1 rule="para" parents="34730 33876"/>
    </justification>
  </clause>

  <clause id="34732">
    <literal><![CDATA[
      a((x \ y) * (z * a(x,x,y)),u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,26785,a(flip),b,34493,a),flip(a)].">
      <j1 rule="hyper" parents="370 26785 34493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34733">
    <literal><![CDATA[
      a(x,y,z * ((x \ z) * u)) = a(x,y,x * u)
    ]]></literal>
    <justification jstring="[hyper(370,a,34497,a(flip),b,34608,a),flip(a)].">
      <j1 rule="hyper" parents="370 34497 34608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34735">
    <literal><![CDATA[
      a(x,y,z \ (x \ (u \ x))) = a(x,y,x * (u * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34263,a(flip),b,34733,a)].">
      <j1 rule="hyper" parents="60 34263 34733"/>
    </justification>
  </clause>

  <clause id="34736">
    <literal><![CDATA[
      a(x,y,z * (x \ (u \ x))) = a(x,y,x * (u * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(34545,a,34735,a)].">
      <j1 rule="hyper" parents="34545 34735"/>
    </justification>
  </clause>

  <clause id="34738">
    <literal><![CDATA[
      a(x,y,(z \ a(u,u,w)) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32589,a,34731,a)].">
      <j1 rule="hyper" parents="32589 34731"/>
    </justification>
  </clause>

  <clause id="34739">
    <literal><![CDATA[
      a(x,y,z \ a(u,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3106,a,34738,a)].">
      <j1 rule="hyper" parents="3106 34738"/>
    </justification>
  </clause>

  <clause id="34740">
    <literal><![CDATA[
      a(x,y,z * a(u,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34545,a,34739,a)].">
      <j1 rule="hyper" parents="34545 34739"/>
    </justification>
  </clause>

  <clause id="34741">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(34674,a,34740,a),flip(a)].">
      <j1 rule="hyper" parents="34674 34740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34742">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(26965,a,34740,a)].">
      <j1 rule="hyper" parents="26965 34740"/>
    </justification>
  </clause>

  <clause id="34745">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(34449(a,1),34740(a,1,3))].">
      <j1 rule="para" parents="34449 34740"/>
    </justification>
  </clause>

  <clause id="34749">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(32836(a,1),34742(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32836 34742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34750">
    <literal><![CDATA[
      a(x,y,z * L(u,w,w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(26965,a,34749,a)].">
      <j1 rule="hyper" parents="26965 34749"/>
    </justification>
  </clause>

  <clause id="34751">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[hyper(60,a,27204,a,b,34749,a)].">
      <j1 rule="hyper" parents="60 27204 34749"/>
    </justification>
  </clause>

  <clause id="34752">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * u)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27082,a,b,34749,a)].">
      <j1 rule="hyper" parents="60 27082 34749"/>
    </justification>
  </clause>

  <clause id="34754">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(34545,a,34741,a),flip(a)].">
      <j1 rule="hyper" parents="34545 34741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34756">
    <literal><![CDATA[
      a(x * L(x,y,z),u,x * (L(x,y,z) \ w)) = a(z,y,a(a(x,y,z) * w,u,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,33909,a(flip),b,34741,a),flip(a)].">
      <j1 rule="hyper" parents="60 33909 34741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34759">
    <literal><![CDATA[
      a(x,y,z * (u * (u * w))) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(27154,a,34751,a)].">
      <j1 rule="hyper" parents="27154 34751"/>
    </justification>
  </clause>

  <clause id="34760">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(27151,a,34751,a),flip(a)].">
      <j1 rule="hyper" parents="27151 34751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34763">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(34751(a,1),27151(a,1))].">
      <j1 rule="para" parents="34751 27151"/>
    </justification>
  </clause>

  <clause id="34765">
    <literal><![CDATA[
      a(x,y,x * ((x * z) * u)) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(34718,a,34754,a),flip(a)].">
      <j1 rule="hyper" parents="34718 34754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34766">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(26974,a,34754,a)].">
      <j1 rule="hyper" parents="26974 34754"/>
    </justification>
  </clause>

  <clause id="34768">
    <literal><![CDATA[
      a(x,y,(x * z) * u) = a(x,y,x * (z * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34537,a,b,34754,a)].">
      <j1 rule="hyper" parents="60 34537 34754"/>
    </justification>
  </clause>

  <clause id="34769">
    <literal><![CDATA[
      a(x,y,z * (x * (u \ x))) = a(x,y,x * (u * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34736,a(flip),b,34754,a),flip(a)].">
      <j1 rule="hyper" parents="60 34736 34754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34770">
    <literal><![CDATA[
      a(x,y,x * ((z * x) * u)) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34720,a(flip),b,34754,a),flip(a)].">
      <j1 rule="hyper" parents="60 34720 34754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34771">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * (u * (w * z))) = a(x,y,a(u,w * u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,34609,a(flip),b,34754,a),flip(a)].">
      <j1 rule="hyper" parents="60 34609 34754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34773">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(34754(a,2),26976(a,1))].">
      <j1 rule="para" parents="34754 26976"/>
    </justification>
  </clause>

  <clause id="34774">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,z)) = a(x,y,a(z,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),33335(a,2,3))].">
      <j1 rule="para" parents="34754 33335"/>
    </justification>
  </clause>

  <clause id="34775">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * z))) = a(x,y,a(z,u,z * (w * v5)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),33342(a,1,3))].">
      <j1 rule="para" parents="34754 33342"/>
    </justification>
  </clause>

  <clause id="34776">
    <literal><![CDATA[
      a(x,y,a(x * (z * u),w,v5)) = a(x,w,a(v5,y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),33345(a,2,3))].">
      <j1 rule="para" parents="34754 33345"/>
    </justification>
  </clause>

  <clause id="34777">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * x))) = a(x,u,a(z,y,x * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),33346(a,1,3))].">
      <j1 rule="para" parents="34754 33346"/>
    </justification>
  </clause>

  <clause id="34778">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(v5,w,a(x,y,x * (u * z)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),34681(a,2,3))].">
      <j1 rule="para" parents="34754 34681"/>
    </justification>
  </clause>

  <clause id="34779">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) * v5)) = a(x,y,a(z,u,w * (x * v5)))
    ]]></literal>
    <justification jstring="[para(34754(a,1),34723(a,2,3))].">
      <j1 rule="para" parents="34754 34723"/>
    </justification>
  </clause>

  <clause id="34782">
    <literal><![CDATA[
      a(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(34766(a,1),26972(a,1))].">
      <j1 rule="para" parents="34766 26972"/>
    </justification>
  </clause>

  <clause id="34785">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(32836(a,1),34745(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="32836 34745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34787">
    <literal><![CDATA[
      a(x,y,x * ((x * z) * u)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,34750,a(flip),b,34765,a),flip(a)].">
      <j1 rule="hyper" parents="370 34750 34765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34789">
    <literal><![CDATA[
      a(x,y,x * (z * (x * u))) = a(x,y,z * L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34703,a(flip),b,34770,a)].">
      <j1 rule="hyper" parents="60 34703 34770"/>
    </justification>
  </clause>

  <clause id="34790">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ u))) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(34773,a,26940,a)].">
      <j1 rule="hyper" parents="34773 26940"/>
    </justification>
  </clause>

  <clause id="34797">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v5))) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(26976,a,34785,a)].">
      <j1 rule="hyper" parents="26976 34785"/>
    </justification>
  </clause>

  <clause id="34801">
    <literal><![CDATA[
      a(x,y,x * (z * (x * u))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,34750,a(flip),b,34789,a),flip(a)].">
      <j1 rule="hyper" parents="370 34750 34789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34804">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (w * v5)))) = a(x,y,z * (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(27212,a,34797,a)].">
      <j1 rule="hyper" parents="27212 34797"/>
    </justification>
  </clause>

  <clause id="34805">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * u) * v5)) = a(x,y,z * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(27211,a,34797,a)].">
      <j1 rule="hyper" parents="27211 34797"/>
    </justification>
  </clause>

  <clause id="34807">
    <literal><![CDATA[
      a(x,y,x * (z * (u * x))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,34790,a(flip),b,34769,a),flip(a)].">
      <j1 rule="hyper" parents="60 34790 34769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34811">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[para(5(a,1),34805(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 34805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34812">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(34782,a,34811,a)].">
      <j1 rule="hyper" parents="34782 34811"/>
    </justification>
  </clause>

  <clause id="34814">
    <literal><![CDATA[
      a(x,y,z * ((u * ((w \ v5) * w)) * v6)) = a(x,y,(v6 * (v5 \ u)) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,27849,a(flip),b,34811,a),flip(a)].">
      <j1 rule="hyper" parents="60 27849 34811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34816">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) * v5) * v6)) = a(x,y,((v5 \ u) \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(60,a,26932,a(flip),b,34812,a),flip(a)].">
      <j1 rule="hyper" parents="60 26932 34812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34817">
    <literal><![CDATA[
      a(x,y,a(z * (u * x),w,v5)) = a(v5,y,a(x,w,x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(33000,a,34775,a)].">
      <j1 rule="hyper" parents="33000 34775"/>
    </justification>
  </clause>

  <clause id="34818">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,z)) = a(z,u,a(z * (y * x),v5,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32935,a,b,34776,a)].">
      <j1 rule="hyper" parents="370 32935 34776"/>
    </justification>
  </clause>

  <clause id="34819">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(x,y,a(x * (u * z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(370,a,32929,a,b,34778,a),flip(a)].">
      <j1 rule="hyper" parents="370 32929 34778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34822">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,w,v5)) = a(y,w,a(y * (z * x),u,v5))
    ]]></literal>
    <justification jstring="[hyper(32951,a,34819,a)].">
      <j1 rule="hyper" parents="32951 34819"/>
    </justification>
  </clause>

  <clause id="34825">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * v5) = a(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27740,a(flip),b,34814,a),flip(a)].">
      <j1 rule="hyper" parents="60 27740 34814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34826">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(27174,a,34825,a)].">
      <j1 rule="hyper" parents="27174 34825"/>
    </justification>
  </clause>

  <clause id="34827">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (w * (u * z))) = a(x,y,a(w,u * w,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,34771,a(flip),b,34825,a),flip(a)].">
      <j1 rule="hyper" parents="60 34771 34825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34828">
    <literal><![CDATA[
      a(x,y,((z * u) * (w * z)) * (w * u)) = a(x,y,a(u,z,z * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34072,a(flip),b,34825,a),flip(a)].">
      <j1 rule="hyper" parents="60 34072 34825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34829">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (v5 * (v6 * a(z * (w \ u),v5,v6)))) = a(x,y,((z * (w \ u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(32594(a,1),34825(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32594 34825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34830">
    <literal><![CDATA[
      a(x,y,a(z,u * z,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,34088,a(flip),b,34827,a),flip(a)].">
      <j1 rule="hyper" parents="60 34088 34827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34831">
    <literal><![CDATA[
      a(x,y,a(z,u * w,u)) = a(z,y,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(33029,a,34830,a)].">
      <j1 rule="hyper" parents="33029 34830"/>
    </justification>
  </clause>

  <clause id="34832">
    <literal><![CDATA[
      a(x,y * z,a(u,w,z)) = a(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(33004,a,34830,a)].">
      <j1 rule="hyper" parents="33004 34830"/>
    </justification>
  </clause>

  <clause id="34833">
    <literal><![CDATA[
      a(x,y,a(z,u * w,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(32996,a,34830,a)].">
      <j1 rule="hyper" parents="32996 34830"/>
    </justification>
  </clause>

  <clause id="34836">
    <literal><![CDATA[
      a(x,y,a(z,u * w,a(v5,v6,u))) = a(x,v6,a(v5,y,a(z,w,u)))
    ]]></literal>
    <justification jstring="[para(34830(a,1),33060(a,2,3))].">
      <j1 rule="para" parents="34830 33060"/>
    </justification>
  </clause>

  <clause id="34837">
    <literal><![CDATA[
      a(x,y * z,a(y,u,w)) = a(w,u,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(33004,a,34831,a)].">
      <j1 rule="hyper" parents="33004 34831"/>
    </justification>
  </clause>

  <clause id="34846">
    <literal><![CDATA[
      a(x,y * z,a(u,w,a(y,v5,v6))) = a(u,v5,a(x,w,a(v6,z,y)))
    ]]></literal>
    <justification jstring="[hyper(33024,a,34836,a)].">
      <j1 rule="hyper" parents="33024 34836"/>
    </justification>
  </clause>

  <clause id="34847">
    <literal><![CDATA[
      a(x,y,((z \ u) \ w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27729,a(flip),b,34816,a),flip(a)].">
      <j1 rule="hyper" parents="60 27729 34816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34848">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) * v5) = a(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(34763,a,34847,a)].">
      <j1 rule="hyper" parents="34763 34847"/>
    </justification>
  </clause>

  <clause id="34849">
    <literal><![CDATA[
      a(x,y,((z * u) * (w * z)) * (w * u)) = a(x,y,a(z * u,z,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34101,a(flip),b,34848,a),flip(a)].">
      <j1 rule="hyper" parents="60 34101 34848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34850">
    <literal><![CDATA[
      a(x,y,((z * ((u \ w) * u)) * v5) * v6) = a(x,y,v6 * (v5 * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27231,a(flip),b,34848,a),flip(a)].">
      <j1 rule="hyper" parents="60 27231 34848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34851">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(x,y,a(u,z,z * w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34828,a(flip),b,34849,a),flip(a)].">
      <j1 rule="hyper" parents="60 34828 34849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34852">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),u,w)) = a(x,y,a(x * z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(34155,a,34851,a)].">
      <j1 rule="hyper" parents="34155 34851"/>
    </justification>
  </clause>

  <clause id="34853">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(33033,a,34851,a)].">
      <j1 rule="hyper" parents="33033 34851"/>
    </justification>
  </clause>

  <clause id="34854">
    <literal><![CDATA[
      a(x,y,a(z * x,u,u * w)) = a(w,y,a(x,u,x * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34817,a(flip),b,34851,a),flip(a)].">
      <j1 rule="hyper" parents="60 34817 34851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34855">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v5 * v6))) = a(z,v5,a(v6,y,a(x,u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(34851(a,1),33059(a,2,3)),flip(a)].">
      <j1 rule="para" parents="34851 33059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34856">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) = a(w,u,a(z,y,y * x))
    ]]></literal>
    <justification jstring="[hyper(32952,a,34853,a)].">
      <j1 rule="hyper" parents="32952 34853"/>
    </justification>
  </clause>

  <clause id="34857">
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) = a(x,y,a(w,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(31148,a,34853,a)].">
      <j1 rule="hyper" parents="31148 34853"/>
    </justification>
  </clause>

  <clause id="34858">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) = a(y,x,a(z * x,u,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,32935,a,b,34856,a)].">
      <j1 rule="hyper" parents="370 32935 34856"/>
    </justification>
  </clause>

  <clause id="34859">
    <literal><![CDATA[
      a(x * (y * (z * u)),x,a(z,u,u * w)) = a(w,u,a(z * u,x,y * ((z * u) * x)))
    ]]></literal>
    <justification jstring="[para(34143(a,2),34856(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34143 34856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34860">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,(z \ u) * w)) = a(x,y,a(w,z \ u,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),34857(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="5 34857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34861">
    <literal><![CDATA[
      a(x,y,a(x * z,u,u * w)) = a(w,u,a(x,y,x * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34778,a(flip),b,34852,a),flip(a)].">
      <j1 rule="hyper" parents="60 34778 34852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34862">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,(z \ u) * w)) = a(x,y,a(w,z * u,u))
    ]]></literal>
    <justification jstring="[para(33302(a,1),34860(a,2,3))].">
      <j1 rule="para" parents="33302 34860"/>
    </justification>
  </clause>

  <clause id="34863">
    <literal><![CDATA[
      a(x,y,a(x * z,u,y * w)) = a(w,y,a(x,u,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(33002,a,34861,a)].">
      <j1 rule="hyper" parents="33002 34861"/>
    </justification>
  </clause>

  <clause id="34864">
    <literal><![CDATA[
      a(x * y,z,a(u,x,u * (w * u))) = a(y,x,a(u,z,u * (x * (w \ u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,33336,a(flip),b,34861,a)].">
      <j1 rule="hyper" parents="60 33336 34861"/>
    </justification>
  </clause>

  <clause id="34865">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,(z \ u) * w)) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,34833,a(flip),b,34862,a),flip(a)].">
      <j1 rule="hyper" parents="370 34833 34862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34866">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,(z * u) * w)) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(34760(a,1),34865(a,1,3))].">
      <j1 rule="para" parents="34760 34865"/>
    </justification>
  </clause>

  <clause id="34867">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z * (u * w))) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(34768(a,1),34866(a,1,3))].">
      <j1 rule="para" parents="34768 34866"/>
    </justification>
  </clause>

  <clause id="34868">
    <literal><![CDATA[
      a(x,y,a(z,u * z,z * (u * w))) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(33403(a,1),34867(a,1,3))].">
      <j1 rule="para" parents="33403 34867"/>
    </justification>
  </clause>

  <clause id="34869">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,z)) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34830,a(flip),b,34868,a)].">
      <j1 rule="hyper" parents="60 34830 34868"/>
    </justification>
  </clause>

  <clause id="34870">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (y * w))) = a(w,u,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(33004,a,34869,a)].">
      <j1 rule="hyper" parents="33004 34869"/>
    </justification>
  </clause>

  <clause id="34871">
    <literal><![CDATA[
      a(x,y,a(x * (y * z),u,w)) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(32952,a,34869,a)].">
      <j1 rule="hyper" parents="32952 34869"/>
    </justification>
  </clause>

  <clause id="34872">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (u * w))) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(31148,a,34869,a)].">
      <j1 rule="hyper" parents="31148 34869"/>
    </justification>
  </clause>

  <clause id="34873">
    <literal><![CDATA[
      a(x,y,a(z,y,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,34387,a(flip),b,34869,a),flip(a)].">
      <j1 rule="hyper" parents="60 34387 34869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34879">
    <literal><![CDATA[
      a(x,y,L(z,y,u)) = (1 / y) \ (a(x,y,z) / y)
    ]]></literal>
    <justification jstring="[para(34873(a,1),32317(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34873 32317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34880">
    <literal><![CDATA[
      a(x,y,L(z,y,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,31010,a(flip),b,34879,a),flip(a)].">
      <j1 rule="hyper" parents="370 31010 34879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34881">
    <literal><![CDATA[
      a(x,y,L(z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(34879(a,2),31016(a,1))].">
      <j1 rule="para" parents="34879 31016"/>
    </justification>
  </clause>

  <clause id="34883">
    <literal><![CDATA[
      a(x,y,L(z,y,u * y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(33736,a,34880,a)].">
      <j1 rule="hyper" parents="33736 34880"/>
    </justification>
  </clause>

  <clause id="34888">
    <literal><![CDATA[
      a(x,y,(z * y) * (z * u)) = a(x,y,y * u)
    ]]></literal>
    <justification jstring="[hyper(60,a,34599,a(flip),b,34880,a)].">
      <j1 rule="hyper" parents="60 34599 34880"/>
    </justification>
  </clause>

  <clause id="34903">
    <literal><![CDATA[
      a(x,y,L(z,u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34881,a,34883,a),flip(a)].">
      <j1 rule="hyper" parents="34881 34883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34905">
    <literal><![CDATA[
      a(x,y,(y * z) * u) = a(x,y,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(34713,a,34903,a)].">
      <j1 rule="hyper" parents="34713 34903"/>
    </justification>
  </clause>

  <clause id="34923">
    <literal><![CDATA[
      a(x,y,(z * u) * (z * y)) = a(x,y,y * u)
    ]]></literal>
    <justification jstring="[hyper(26965,a,34888,a)].">
      <j1 rule="hyper" parents="26965 34888"/>
    </justification>
  </clause>

  <clause id="34925">
    <literal><![CDATA[
      a(x,y,(y * z) * u) = a(x,y,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,34754,a(flip),b,34905,a),flip(a)].">
      <j1 rule="hyper" parents="370 34754 34905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34927">
    <literal><![CDATA[
      a(x,y * z,(y * z) * u) = a(x,y * z,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34759,a(flip),b,34923,a),flip(a)].">
      <j1 rule="hyper" parents="60 34759 34923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34930">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (w * z))) = a(w,u,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34775,a,b,34870,a)].">
      <j1 rule="hyper" parents="60 34775 34870"/>
    </justification>
  </clause>

  <clause id="34932">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,z,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,34822,a,b,34871,a)].">
      <j1 rule="hyper" parents="60 34822 34871"/>
    </justification>
  </clause>

  <clause id="34933">
    <literal><![CDATA[
      a(x,y,a(z * x,u,u * w)) = a(z,y,a(w,x,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34854,a,b,34872,a)].">
      <j1 rule="hyper" parents="60 34854 34872"/>
    </justification>
  </clause>

  <clause id="34934">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (z * w))) = a(w,u,a(x,z,y))
    ]]></literal>
    <justification jstring="[para(26941(a,1),34930(a,1,3))].">
      <j1 rule="para" parents="26941 34930"/>
    </justification>
  </clause>

  <clause id="34935">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * u))) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(32989,a,34932,a)].">
      <j1 rule="hyper" parents="32989 34932"/>
    </justification>
  </clause>

  <clause id="34936">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (x * y))) = a(w,u,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(32968,a,34932,a)].">
      <j1 rule="hyper" parents="32968 34932"/>
    </justification>
  </clause>

  <clause id="34937">
    <literal><![CDATA[
      a(x,y,a(z * x,u \ 1,u * ((w \ u) \ v5))) = a(z,y,a((w \ (u \ 1)) \ v5,x,u \ 1))
    ]]></literal>
    <justification jstring="[para(1471(a,1),34933(a,1,3,3))].">
      <j1 rule="para" parents="1471 34933"/>
    </justification>
  </clause>

  <clause id="34940">
    <literal><![CDATA[
      a(x,y,a(x * z,u,y * w)) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,34870,a(flip),b,34863,a),flip(a)].">
      <j1 rule="hyper" parents="370 34870 34863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34941">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x)) = a(y,z,a(x * u,w,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34871,a(flip),b,34940,a),flip(a)].">
      <j1 rule="hyper" parents="60 34871 34940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34942">
    <literal><![CDATA[
      a((x * y) * ((z * y) / z),u,a(w,v5,x * ((z * y) / z))) = a(y,u,a((x * ((z * y) / z)) * w,v5,x * ((z * y) / z)))
    ]]></literal>
    <justification jstring="[para(2289(a,1),34941(a,1,1))].">
      <j1 rule="para" parents="2289 34941"/>
    </justification>
  </clause>

  <clause id="34943">
    <literal><![CDATA[
      a(a(x,y,x) \ (z \ u),w,a(z * v5,v6,z)) = a(a(x,y,x) \ u,w,a(v5,v6,z))
    ]]></literal>
    <justification jstring="[para(14301(a,1),34941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14301 34941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34944">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w) * v5,u,L(z,u,w))) = a(L(z,u,w) * x,y,a(v5,u,z))
    ]]></literal>
    <justification jstring="[para(34880(a,1),34941(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34880 34941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34945">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ v5))) = a(x,y,z * (u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,27735,a(flip),b,34850,a),flip(a)].">
      <j1 rule="hyper" parents="60 27735 34850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34946">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(27163,a,34945,a)].">
      <j1 rule="hyper" parents="27163 34945"/>
    </justification>
  </clause>

  <clause id="34947">
    <literal><![CDATA[
      a(x,y,a(z * x,u,u * (w * (v5 * v6)))) = a(z,y,a(w * (v5 \ v6),x,u))
    ]]></literal>
    <justification jstring="[para(34945(a,1),34933(a,1,3))].">
      <j1 rule="para" parents="34945 34933"/>
    </justification>
  </clause>

  <clause id="34948">
    <literal><![CDATA[
      a(x,y,a(z,u * w,a(u,v5,(u * w) * (u * v6)))) = a(v6,u,a(w,y,a(x,v5,u * z)))
    ]]></literal>
    <justification jstring="[para(34934(a,2),34855(a,1,3))].">
      <j1 rule="para" parents="34934 34855"/>
    </justification>
  </clause>

  <clause id="34951">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (y * (w \ z)))) = a(y * x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[para(34531(a,1),34864(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34531 34864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34953">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (y * (w * z)))) = a(y * x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[para(34945(a,1),34951(a,1,3))].">
      <j1 rule="para" parents="34945 34951"/>
    </justification>
  </clause>

  <clause id="34954">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) = a(y,x,a(u,z,w * x))
    ]]></literal>
    <justification jstring="[para(34807(a,1),34953(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34807 34953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34955">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) = a(y,x,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[hyper(33002,a,34954,a)].">
      <j1 rule="hyper" parents="33002 34954"/>
    </justification>
  </clause>

  <clause id="34956">
    <literal><![CDATA[
      a(x * y,z,a(u,y,w)) = a(x,y,a(u,z,w * y))
    ]]></literal>
    <justification jstring="[hyper(26519,a,34954,a)].">
      <j1 rule="hyper" parents="26519 34954"/>
    </justification>
  </clause>

  <clause id="34957">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(26519,a,34955,a)].">
      <j1 rule="hyper" parents="26519 34955"/>
    </justification>
  </clause>

  <clause id="34958">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34858,a(flip),b,34955,a)].">
      <j1 rule="hyper" parents="60 34858 34955"/>
    </justification>
  </clause>

  <clause id="34959">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(x,u,a(w,v5,a(v6,y,u * z)))
    ]]></literal>
    <justification jstring="[para(34955(a,1),33006(a,2,3)),flip(a)].">
      <j1 rule="para" parents="34955 33006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34960">
    <literal><![CDATA[
      a(x,y,a(y * z,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(33033,a,34958,a)].">
      <j1 rule="hyper" parents="33033 34958"/>
    </justification>
  </clause>

  <clause id="34961">
    <literal><![CDATA[
      a(a(x,y,z * u),z,a(w,v5,v6)) = a(w,y,a(u,z,a(v6,v5,x * z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,32938,a(flip),b,34959,a)].">
      <j1 rule="hyper" parents="370 32938 34959"/>
    </justification>
  </clause>

  <clause id="34962">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,(y * ((1 / y) * z)) * v6))) = a(x,v5,a(v6,y * ((1 / y) * z),a(u,w,L(y * z,y,y))))
    ]]></literal>
    <justification jstring="[para(2083(a,1),34959(a,1,3,3,3)),flip(a)].">
      <j1 rule="para" parents="2083 34959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34963">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * z,v5 * u,(v5 * u) * v6))) = a(x,u,a(v6,z,a(v5,y,u * w)))
    ]]></literal>
    <justification jstring="[para(34933(a,2),34959(a,1,3))].">
      <j1 rule="para" parents="34933 34959"/>
    </justification>
  </clause>

  <clause id="34964">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v5 * v6)) = a(z,y,a(v6,v5,a(w,u,x * v5)))
    ]]></literal>
    <justification jstring="[hyper(33022,a,34961,a)].">
      <j1 rule="hyper" parents="33022 34961"/>
    </justification>
  </clause>

  <clause id="34965">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,w,v6))) = a(z,y,a(v5,w,a(v6,u,x * w)))
    ]]></literal>
    <justification jstring="[para(32930(a,1),34964(a,1,3))].">
      <j1 rule="para" parents="32930 34964"/>
    </justification>
  </clause>

  <clause id="34966">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(v6,y,a(x,v5,u * z))) = v7
    ]]></literal>
    <justification jstring="[para(34965(a,1),33023(a,1))].">
      <j1 rule="para" parents="34965 33023"/>
    </justification>
  </clause>

  <clause id="34967">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(v6,y,a(x,v5,a(z,u,u * w)))
    ]]></literal>
    <justification jstring="[para(34851(a,1),34965(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34851 34965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34968">
    <literal><![CDATA[
      a(x,y,a(z * (u \ w),v5,v6)) = a(x,y,a(z * (u * w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,34933,a(flip),b,34947,a),flip(a)].">
      <j1 rule="hyper" parents="60 34933 34947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34969">
    <literal><![CDATA[
      a(x,L(y \ (z / u),w,v5),v6) = a(x,L(y \ (u \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(24929,a,34644,a),flip(a)].">
      <j1 rule="hyper" parents="24929 34644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34970">
    <literal><![CDATA[
      a(x,L(((y * z) \ y) \ 1,u,w),v5) = a(x,L(y \ (z \ y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(26748,a,34969,a)].">
      <j1 rule="hyper" parents="26748 34969"/>
    </justification>
  </clause>

  <clause id="34971">
    <literal><![CDATA[
      a(x,L((y * z) \ y,u,w),v5) = a(x,L(y \ (z \ y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(26747,a,34970,a)].">
      <j1 rule="hyper" parents="26747 34970"/>
    </justification>
  </clause>

  <clause id="34972">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,a(v5,y,x)) = a(u,w,a(L(x,y,z) * v5,y,x))
    ]]></literal>
    <justification jstring="[para(34880(a,1),34944(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34880 34944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34974">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ u),w,a(z,y,x)) = a(z,y,a(a(x,y,z) * u,w,x))
    ]]></literal>
    <justification jstring="[hyper(32866,a,34756,a)].">
      <j1 rule="hyper" parents="32866 34756"/>
    </justification>
  </clause>

  <clause id="34975">
    <literal><![CDATA[
      a(x * a(y,z,u),w,a(y,z,u)) = a(y,z,a(a(u,z,y) * x,w,u))
    ]]></literal>
    <justification jstring="[hyper(34485,a,34974,a)].">
      <j1 rule="hyper" parents="34485 34974"/>
    </justification>
  </clause>

  <clause id="34976">
    <literal><![CDATA[
      a(K(x,y) * (z * a(u,w,v5)),v6,K(v7,v8) * a(u,w,v5)) = a(u,w,a(a(v5,w,u) * z,v6,v5))
    ]]></literal>
    <justification jstring="[hyper(26913,a,34975,a)].">
      <j1 rule="hyper" parents="26913 34975"/>
    </justification>
  </clause>

  <clause id="34977">
    <literal><![CDATA[
      a(a(x,y,x) \ (z \ u),w,a(z * v5,v6,z)) = a(u,w,a(v5,v6,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,14067,a(flip),b,34943,a),flip(a)].">
      <j1 rule="hyper" parents="370 14067 34943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34978">
    <literal><![CDATA[
      a(a(x,y,x) * (z \ u),w,a(z * v5,v6,z)) = a(u,w,a(v5,v6,z))
    ]]></literal>
    <justification jstring="[hyper(34551,a,34977,a)].">
      <j1 rule="hyper" parents="34551 34977"/>
    </justification>
  </clause>

  <clause id="34980">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * y) * (a(z,z,u) \ w)) = a(x,a(z,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(34418(a,1),34356(a,1,2))].">
      <j1 rule="para" parents="34418 34356"/>
    </justification>
  </clause>

  <clause id="34981">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ (((a(z,z,u) \ x) * y) * w) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(34399(a,1),34357(a,1,1,2))].">
      <j1 rule="para" parents="34399 34357"/>
    </justification>
  </clause>

  <clause id="34982">
    <literal><![CDATA[
      a(x * (y * (z * u)),x,a(z,u,u * w)) = a(y,u,a(w,z * u,x))
    ]]></literal>
    <justification jstring="[hyper(370,a,34935,a(flip),b,34859,a),flip(a)].">
      <j1 rule="hyper" parents="370 34935 34859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34983">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,z,(z * w) * u)) = a(x,z,a(w,y * z,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34955,a(flip),b,34982,a)].">
      <j1 rule="hyper" parents="60 34955 34982"/>
    </justification>
  </clause>

  <clause id="34984">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,z,w * (z * u))) = a(x,z,a(w,y * z,u))
    ]]></literal>
    <justification jstring="[para(34925(a,1),34983(a,1,3))].">
      <j1 rule="para" parents="34925 34983"/>
    </justification>
  </clause>

  <clause id="34985">
    <literal><![CDATA[
      a(x,y,a(z * (u * y),w,u)) = a(x,u,a(z,w * u,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34932,a(flip),b,34984,a)].">
      <j1 rule="hyper" parents="60 34932 34984"/>
    </justification>
  </clause>

  <clause id="34986">
    <literal><![CDATA[
      a(x,y,a(z,u * w,a(u,v5,u * (w * (u * v6))))) = a(v6,u,a(w,y,a(x,v5,u * z)))
    ]]></literal>
    <justification jstring="[para(34768(a,1),34948(a,1,3,3))].">
      <j1 rule="para" parents="34768 34948"/>
    </justification>
  </clause>

  <clause id="34987">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * z,v5 * u,u * (v5 * v6)))) = a(x,u,a(v6,z,a(v5,y,u * w)))
    ]]></literal>
    <justification jstring="[para(34927(a,1),34963(a,1,3,3))].">
      <j1 rule="para" parents="34927 34963"/>
    </justification>
  </clause>

  <clause id="34988">
    <literal><![CDATA[
      a(x,a(y,y,z) \ u,w) = a(x,u,a(y,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(1029,a,34980,a),flip(a)].">
      <j1 rule="hyper" parents="1029 34980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34989">
    <literal><![CDATA[
      a(x,a(y,y,z) \ u,w) = a(x,u,a(y,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,34532,a(flip),b,34988,a),flip(a)].">
      <j1 rule="hyper" parents="370 34532 34988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34990">
    <literal><![CDATA[
      a(x,a(y,y,z) \ u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,34742,a(flip),b,34989,a),flip(a)].">
      <j1 rule="hyper" parents="370 34742 34989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34991">
    <literal><![CDATA[
      a(x,a(y,y,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(30640,a,34990,a)].">
      <j1 rule="hyper" parents="30640 34990"/>
    </justification>
  </clause>

  <clause id="34993">
    <literal><![CDATA[
      a(x,a(y,y,z) \ (u * w),v5) = a(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,26459,a,b,34990,a),flip(a)].">
      <j1 rule="hyper" parents="370 26459 34990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34995">
    <literal><![CDATA[
      a(x,y \ (z \ u),w) = a(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,33743,a(flip),b,34991,a)].">
      <j1 rule="hyper" parents="60 33743 34991"/>
    </justification>
  </clause>

  <clause id="34998">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) \ w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[para(32344(a,1),34993(a,1,2))].">
      <j1 rule="para" parents="32344 34993"/>
    </justification>
  </clause>

  <clause id="34999">
    <literal><![CDATA[
      a(x,y * (z * (u * (a(w,w,v5) \ u))),v6) = a(x,z * y,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,32880,a,b,34998,a)].">
      <j1 rule="hyper" parents="60 32880 34998"/>
    </justification>
  </clause>

  <clause id="35000">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,30698,a(flip),b,34998,a)].">
      <j1 rule="hyper" parents="60 30698 34998"/>
    </justification>
  </clause>

  <clause id="35001">
    <literal><![CDATA[
      a(x,y * L(z,u,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[para(3943(a,1),34998(a,1,2,2))].">
      <j1 rule="para" parents="3943 34998"/>
    </justification>
  </clause>

  <clause id="35002">
    <literal><![CDATA[
      a(x,y \ z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(60,a,29582,a(flip),b,35001,a)].">
      <j1 rule="hyper" parents="60 29582 35001"/>
    </justification>
  </clause>

  <clause id="35003">
    <literal><![CDATA[
      a(x,y * (z \ y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(26560,a,35002,a),flip(a)].">
      <j1 rule="hyper" parents="26560 35002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35005">
    <literal><![CDATA[
      a(x,y \ z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,26459,a,b,35002,a),flip(a)].">
      <j1 rule="hyper" parents="370 26459 35002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35007">
    <literal><![CDATA[
      a(x,y \ (z \ u),w) = a(x,(z * u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,34995,a,b,35002,a)].">
      <j1 rule="hyper" parents="60 34995 35002"/>
    </justification>
  </clause>

  <clause id="35008">
    <literal><![CDATA[
      a(x,y \ (z \ L(u,y,y)),w) = a(x,(z \ u) * L(y,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,33650,a(flip),b,35002,a)].">
      <j1 rule="hyper" parents="60 33650 35002"/>
    </justification>
  </clause>

  <clause id="35009">
    <literal><![CDATA[
      a(x,y * (z * ((u \ K(w,v5)) \ v6)),v7) = a(x,((u \ v6) * z) \ y,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,29904,a(flip),b,35002,a),flip(a)].">
      <j1 rule="hyper" parents="60 29904 35002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35019">
    <literal><![CDATA[
      a(x,y \ (z \ y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(370,a,35003,a(flip),b,35005,a),flip(a)].">
      <j1 rule="hyper" parents="370 35003 35005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35024">
    <literal><![CDATA[
      a(x,y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(35005(a,2),26564(a,1))].">
      <j1 rule="para" parents="35005 26564"/>
    </justification>
  </clause>

  <clause id="35031">
    <literal><![CDATA[
      a(x,y \ (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(34995(a,2),35024(a,1))].">
      <j1 rule="para" parents="34995 35024"/>
    </justification>
  </clause>

  <clause id="35032">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(35024,a,35007,a)].">
      <j1 rule="hyper" parents="35024 35007"/>
    </justification>
  </clause>

  <clause id="35033">
    <literal><![CDATA[
      a(x,(y * L(z * u,u,u)) * w,v5) = a(x,w * (y \ (u \ z)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,30390,a(flip),b,35032,a),flip(a)].">
      <j1 rule="hyper" parents="60 30390 35032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35035">
    <literal><![CDATA[
      a(x,(y * L(z,u,u)) * w,v5) = a(x,w * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,34363,a(flip),b,35000,a)].">
      <j1 rule="hyper" parents="60 34363 35000"/>
    </justification>
  </clause>

  <clause id="35037">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) = a(x,y * (w * (v6 * (a(v7,v7,v8) \ v6))),v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,35000,a,b,34999,a)].">
      <j1 rule="hyper" parents="370 35000 34999"/>
    </justification>
  </clause>

  <clause id="35039">
    <literal><![CDATA[
      a(x,y * (z \ (u \ w)),v5) = a(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35035,a(flip),b,35033,a),flip(a)].">
      <j1 rule="hyper" parents="60 35035 35033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35041">
    <literal><![CDATA[
      a(x,y * R(z,z,u),w) = a(x,y * (z * (v5 * (a(v6,v6,v7) \ v5))),w)
    ]]></literal>
    <justification jstring="[para(28421(a,1),35037(a,1,2,2))].">
      <j1 rule="para" parents="28421 35037"/>
    </justification>
  </clause>

  <clause id="35042">
    <literal><![CDATA[
      a(x,y * L(z,z,u),w) = a(x,y * (z * (v5 * (a(v6,v6,v7) \ v5))),w)
    ]]></literal>
    <justification jstring="[hyper(30381,a,35041,a)].">
      <j1 rule="hyper" parents="30381 35041"/>
    </justification>
  </clause>

  <clause id="35043">
    <literal><![CDATA[
      a(x,y * L(z,z,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,34999,a(flip),b,35042,a),flip(a)].">
      <j1 rule="hyper" parents="370 34999 35042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35044">
    <literal><![CDATA[
      a(x,y \ (z \ L(u,y,y)),w) = a(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,35008,a,b,35043,a)].">
      <j1 rule="hyper" parents="60 35008 35043"/>
    </justification>
  </clause>

  <clause id="35045">
    <literal><![CDATA[
      a(x,(y * L(z,u,u)) * u,w) = a(x,u * (y \ z),w)
    ]]></literal>
    <justification jstring="[hyper(35031,a,35044,a)].">
      <j1 rule="hyper" parents="35031 35044"/>
    </justification>
  </clause>

  <clause id="35047">
    <literal><![CDATA[
      a(x,y * (z \ u),w) = a(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(60,a,35035,a(flip),b,35045,a),flip(a)].">
      <j1 rule="hyper" parents="60 35035 35045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35051">
    <literal><![CDATA[
      a(x,y * (z * (u \ w)),v5) = a(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35039,a(flip),b,35047,a),flip(a)].">
      <j1 rule="hyper" parents="60 35039 35047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35052">
    <literal><![CDATA[
      a(x,y * (z * (u * (w \ K(v5,v6)))),v7) = a(x,((w \ u) * z) \ y,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35009,a(flip),b,35051,a),flip(a)].">
      <j1 rule="hyper" parents="60 35009 35051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35053">
    <literal><![CDATA[
      a(x,((y \ z) * u) \ w,v5) = a(x,w * ((z * y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,28042,a(flip),b,35052,a),flip(a)].">
      <j1 rule="hyper" parents="60 28042 35052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35054">
    <literal><![CDATA[
      a(x,y * ((z \ u) * w),v5) = a(x,y * ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(35024,a,35053,a)].">
      <j1 rule="hyper" parents="35024 35053"/>
    </justification>
  </clause>

  <clause id="35055">
    <literal><![CDATA[
      a(x,y * ((z / u) * w),v5) = a(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(26690,a,35054,a)].">
      <j1 rule="hyper" parents="26690 35054"/>
    </justification>
  </clause>

  <clause id="35056">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * (a(z,z,u) \ y)) * w) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(34348(a,1),34981(a,1,2,1))].">
      <j1 rule="para" parents="34348 34981"/>
    </justification>
  </clause>

  <clause id="35057">
    <literal><![CDATA[
      a(x,y,a(z,u * w,a(u,v5,v6 * w))) = a(v6,u,a(w,y,a(x,v5,u * z)))
    ]]></literal>
    <justification jstring="[para(34801(a,1),34986(a,1,3,3))].">
      <j1 rule="para" parents="34801 34986"/>
    </justification>
  </clause>

  <clause id="35058">
    <literal><![CDATA[
      a(x,y,a(z * u,w,a(v5,u,v6))) = a(z,v6,a(u,y,a(x,w,v6 * v5)))
    ]]></literal>
    <justification jstring="[para(34837(a,1),35057(a,1,3))].">
      <j1 rule="para" parents="34837 35057"/>
    </justification>
  </clause>

  <clause id="35059">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(z,v6,a(u,y,a(x,v5,v6 * w)))
    ]]></literal>
    <justification jstring="[para(34956(a,1),35058(a,1,3))].">
      <j1 rule="para" parents="34956 35058"/>
    </justification>
  </clause>

  <clause id="35060">
    <literal><![CDATA[
      (x * (y * (a(z,z,u) \ w))) \ ((x * y) * (a(z,z,u) \ w)) = a(a(z,z,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(34418(a,1),35056(a,1,2))].">
      <j1 rule="para" parents="34418 35056"/>
    </justification>
  </clause>

  <clause id="35061">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z,u,a(x,x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(1029,a,35060,a),flip(a)].">
      <j1 rule="hyper" parents="1029 35060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35062">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z,u,a(x,x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(370,a,34532,a(flip),b,35061,a),flip(a)].">
      <j1 rule="hyper" parents="370 34532 35061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35063">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,34742,a(flip),b,35062,a),flip(a)].">
      <j1 rule="hyper" parents="370 34742 35062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35064">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(34551,a,35063,a)].">
      <j1 rule="hyper" parents="34551 35063"/>
    </justification>
  </clause>

  <clause id="35066">
    <literal><![CDATA[
      a(x \ (y * L(z,u,z)),w,v5) = a(x * (z \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(34677,a,35064,a),flip(a)].">
      <j1 rule="hyper" parents="34677 35064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35067">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,34448,a(flip),b,35064,a)].">
      <j1 rule="hyper" parents="60 34448 35064"/>
    </justification>
  </clause>

  <clause id="35070">
    <literal><![CDATA[
      a((x \ L(y,z,z)) * u,w,v5) = a(u * (x \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,34362,a(flip),b,35067,a)].">
      <j1 rule="hyper" parents="60 34362 35067"/>
    </justification>
  </clause>

  <clause id="35071">
    <literal><![CDATA[
      a(x * (y * a(z,z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,34349,a(flip),b,35067,a)].">
      <j1 rule="hyper" parents="60 34349 35067"/>
    </justification>
  </clause>

  <clause id="35073">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,34732,a(flip),b,35071,a),flip(a)].">
      <j1 rule="hyper" parents="60 34732 35071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35078">
    <literal><![CDATA[
      a(x * (y * L(z,u,z)),w,v5) = a(x * (z \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(34551,a,35066,a)].">
      <j1 rule="hyper" parents="34551 35066"/>
    </justification>
  </clause>

  <clause id="35080">
    <literal><![CDATA[
      a(x * (y \ z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26732,a,35078,a),flip(a)].">
      <j1 rule="hyper" parents="26732 35078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35082">
    <literal><![CDATA[
      a(x * (y * z),u,y * z) = a(y * (x * z),u,y * z)
    ]]></literal>
    <justification jstring="[hyper(33893,a,35080,a)].">
      <j1 rule="hyper" parents="33893 35080"/>
    </justification>
  </clause>

  <clause id="35083">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26546,a,35080,a)].">
      <j1 rule="hyper" parents="26546 35080"/>
    </justification>
  </clause>

  <clause id="35084">
    <literal><![CDATA[
      a((x \ L(y,z,z)) * u,w,v5) = a(u * (y * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35070,a,b,35080,a)].">
      <j1 rule="hyper" parents="60 35070 35080"/>
    </justification>
  </clause>

  <clause id="35085">
    <literal><![CDATA[
      a(a(x,y,x) * (z * u),w,a(u * v5,v6,u)) = a(z,w,a(v5,v6,u))
    ]]></literal>
    <justification jstring="[hyper(60,a,34978,a(flip),b,35080,a),flip(a)].">
      <j1 rule="hyper" parents="60 34978 35080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35086">
    <literal><![CDATA[
      a(x * ((y * z) * y),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),35080(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 35080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35087">
    <literal><![CDATA[
      a(((x * (y / x)) * (a(y,z,u \ w) \ z)) * (w * u),v5,v6) = a((x * (y / x)) * (z * (u \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(28993(a,1),35080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28993 35080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35090">
    <literal><![CDATA[
      a((x * L(y,z,z)) * u,w,v5) = a(u * (y * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35073,a(flip),b,35084,a)].">
      <j1 rule="hyper" parents="60 35073 35084"/>
    </justification>
  </clause>

  <clause id="35091">
    <literal><![CDATA[
      a((x * ((y * z) * y)) * u,w,v5) = a(u * (z * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,27349,a,b,35090,a)].">
      <j1 rule="hyper" parents="60 27349 35090"/>
    </justification>
  </clause>

  <clause id="35093">
    <literal><![CDATA[
      a(x,y,a(x * (z * a(u,w,u)),v5,x * v6)) = a(z,y,a(v6,v5,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34818,a(flip),b,35085,a)].">
      <j1 rule="hyper" parents="60 34818 35085"/>
    </justification>
  </clause>

  <clause id="35094">
    <literal><![CDATA[
      a(x,y,a(x * z,u,x * w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(14268(a,1),35093(a,1,3,1,2))].">
      <j1 rule="para" parents="14268 35093"/>
    </justification>
  </clause>

  <clause id="35096">
    <literal><![CDATA[
      a(x,y,a(z * x,u \ 1,u * ((u * w) * v5))) = a(z,y,a((w \ (u \ 1)) \ v5,x,u \ 1))
    ]]></literal>
    <justification jstring="[para(34812(a,1),34937(a,1,3))].">
      <j1 rule="para" parents="34812 34937"/>
    </justification>
  </clause>

  <clause id="35097">
    <literal><![CDATA[
      a(x * (L(T(x,y),z,u) \ w),v5,K(v6,v7) * a(u,z,x)) = a(u,z,a(a(x,z,u) * w,v5,x))
    ]]></literal>
    <justification jstring="[para(34721(a,1),34976(a,1,1))].">
      <j1 rule="para" parents="34721 34976"/>
    </justification>
  </clause>

  <clause id="35098">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) \ w,v5,u \ 1)) = a(v5,y,a(x * v5,u,u * ((u * z) * w)))
    ]]></literal>
    <justification jstring="[para(3050(a,1),35096(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3050 35096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35099">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) \ w,v5,u \ 1)) = a(x,y,a((u * z) * w,v5,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,34933,a(flip),b,35098,a),flip(a)].">
      <j1 rule="hyper" parents="370 34933 35098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35100">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) \ w,v5,u \ 1)) = a(x,y,a(z * (u \ w),v5,u))
    ]]></literal>
    <justification jstring="[para(34508(a,1),35099(a,2,3))].">
      <j1 rule="para" parents="34508 35099"/>
    </justification>
  </clause>

  <clause id="35101">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) \ w,v5,u \ 1)) = a(x,y,a(z * (u * w),v5,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,34968,a(flip),b,35100,a),flip(a)].">
      <j1 rule="hyper" parents="370 34968 35100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35103">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) \ w,v5,u)) = a(x,y,a(z * (u * w),v5,u))
    ]]></literal>
    <justification jstring="[para(3091(a,1),35101(a,1,3))].">
      <j1 rule="para" parents="3091 35101"/>
    </justification>
  </clause>

  <clause id="35104">
    <literal><![CDATA[
      a(x,y,a((z \ (u \ 1)) * w,v5,u)) = a(x,y,a(z * (u * w),v5,u))
    ]]></literal>
    <justification jstring="[para(34527(a,1),35103(a,1,3))].">
      <j1 rule="para" parents="34527 35103"/>
    </justification>
  </clause>

  <clause id="35105">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,u)) = a(x,y,a(z * (u * w),v5,u))
    ]]></literal>
    <justification jstring="[para(26631(a,1),35104(a,1,3))].">
      <j1 rule="para" parents="26631 35104"/>
    </justification>
  </clause>

  <clause id="35106">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,u)) = a(x,y,a(u * (z * w),v5,u))
    ]]></literal>
    <justification jstring="[para(34233(a,1),35105(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34233 35105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35107">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,u)) = a(x,y,a(u,v5,w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(370,a,34774,a(flip),b,35106,a),flip(a)].">
      <j1 rule="hyper" parents="370 34774 35106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35108">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (w * z))) = a(x,z,a(w,u * z,y))
    ]]></literal>
    <justification jstring="[hyper(60,a,34985,a(flip),b,35107,a),flip(a)].">
      <j1 rule="hyper" parents="60 34985 35107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35109">
    <literal><![CDATA[
      a(x,y,a(z,u * y,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34930,a(flip),b,35108,a),flip(a)].">
      <j1 rule="hyper" parents="60 34930 35108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35110">
    <literal><![CDATA[
      a(x,y,a(z * u,w,a(u,v5,v5 * (w * v6)))) = a(x,v5,a(v6,u,a(w,y,v5 * z)))
    ]]></literal>
    <justification jstring="[para(35109(a,1),34987(a,1,3))].">
      <j1 rule="para" parents="35109 34987"/>
    </justification>
  </clause>

  <clause id="35111">
    <literal><![CDATA[
      a(x,y,a(z,u,a(u * (w * v5),w,z * v6))) = a(x,u,a(v5,z,a(w,y,u * v6)))
    ]]></literal>
    <justification jstring="[para(32936(a,1),35110(a,1,3))].">
      <j1 rule="para" parents="32936 35110"/>
    </justification>
  </clause>

  <clause id="35112">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,w,(z * v6) * u))) = a(x,u,a(v5,z,a(w,y,u * v6)))
    ]]></literal>
    <justification jstring="[para(34960(a,1),35111(a,1,3))].">
      <j1 rule="para" parents="34960 35111"/>
    </justification>
  </clause>

  <clause id="35113">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,w,v6 * (z * u)))) = a(x,u,a(v5,z,a(w,y,u * v6)))
    ]]></literal>
    <justification jstring="[para(34779(a,1),35112(a,1,3))].">
      <j1 rule="para" parents="34779 35112"/>
    </justification>
  </clause>

  <clause id="35114">
    <literal><![CDATA[
      a(x,y,a(z,u,a(u * w,v5,v6))) = a(x,v6,a(w,v5,a(u,y,v6 * z)))
    ]]></literal>
    <justification jstring="[para(34936(a,1),35113(a,1,3))].">
      <j1 rule="para" parents="34936 35113"/>
    </justification>
  </clause>

  <clause id="35115">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(x,v6,a(w,v5,a(u,y,v6 * z)))
    ]]></literal>
    <justification jstring="[para(34960(a,1),35114(a,1,3))].">
      <j1 rule="para" parents="34960 35114"/>
    </justification>
  </clause>

  <clause id="35116">
    <literal><![CDATA[
      a(x * (L(T(x,y),z,u) \ w),v5,a(u,z,x)) = a(u,z,a(a(x,z,u) * w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(26978,a,35097,a)].">
      <j1 rule="hyper" parents="26978 35097"/>
    </justification>
  </clause>

  <clause id="35117">
    <literal><![CDATA[
      a(L(T(x,y),z,u) \ w,v5,a(x * u,z,x)) = a(u,z,a(a(x,z,u) * w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,34941,a(flip),b,35116,a)].">
      <j1 rule="hyper" parents="60 34941 35116"/>
    </justification>
  </clause>

  <clause id="35118">
    <literal><![CDATA[
      a(L(T(x,y),z,u) * w,v5,a(x * u,z,x)) = a(u,z,a(a(x,z,u) * w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(34551,a,35117,a)].">
      <j1 rule="hyper" parents="34551 35117"/>
    </justification>
  </clause>

  <clause id="35119">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,a(x * z,y,x)) = a(z,y,a(a(x,y,z) * u,w,x))
    ]]></literal>
    <justification jstring="[hyper(26531,a,35118,a)].">
      <j1 rule="hyper" parents="26531 35118"/>
    </justification>
  </clause>

  <clause id="35120">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w) * (z * w),u,z)) = a(w,u,a(a(z,u,w) * x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,34972,a(flip),b,35119,a)].">
      <j1 rule="hyper" parents="60 34972 35119"/>
    </justification>
  </clause>

  <clause id="35121">
    <literal><![CDATA[
      a(x,y,a(z * (L(z,u,w) * w),u,z)) = a(w,u,a(a(z,u,w) * x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,35106,a(flip),b,35120,a)].">
      <j1 rule="hyper" parents="60 35106 35120"/>
    </justification>
  </clause>

  <clause id="35122">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) * z,u,w)) = a(z,u,a(a(w,u,z) * x,y,w))
    ]]></literal>
    <justification jstring="[para(34235(a,1),35121(a,1,3))].">
      <j1 rule="para" parents="34235 35121"/>
    </justification>
  </clause>

  <clause id="35123">
    <literal><![CDATA[
      a(x,y,a(a(z,y,x) * u,w,z)) = a(u,w,a(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(32597(a,2),35122(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="32597 35122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35124">
    <literal><![CDATA[
      a(x,y,a(a(z,y,x) * u,w,z)) = a(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31115(a,1),35123(a,2,3))].">
      <j1 rule="para" parents="31115 35123"/>
    </justification>
  </clause>

  <clause id="35125">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * u,w,z)) = a(u,w,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(32989,a,35124,a)].">
      <j1 rule="hyper" parents="32989 35124"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      a(x,y,a(z * a(x,y,u),w,u)) = a(z,w,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(33033,a,35125,a)].">
      <j1 rule="hyper" parents="33033 35125"/>
    </justification>
  </clause>

  <clause id="35127">
    <literal><![CDATA[
      a(a(x,y,z),u,w * a(x,y,z)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(32950,a,35126,a)].">
      <j1 rule="hyper" parents="32950 35126"/>
    </justification>
  </clause>

  <clause id="35128">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (v5 * (v6 * a(z * (u * w),v5,v6)))) = a(x,y,((z * (w \ u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(35080(a,1),34829(a,1,3,2,2,2))].">
      <j1 rule="para" parents="35080 34829"/>
    </justification>
  </clause>

  <clause id="35129">
    <literal><![CDATA[
      a(x,y,((z * (u \ w)) * v5) * v6) = a(x,y,((z * (w * u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(32594(a,1),35128(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32594 35128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35130">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) * (w * v5)) * v6) * v7) = a(x,y,((z * ((u * u) * (v5 \ w))) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),35129(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="29 35129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35131">
    <literal><![CDATA[
      a(x,y,(((z * u) * (w * (v5 * v6))) / L(z,u,w * (v5 * v6))) * v7) = a(x,y,((w * (v6 \ v5)) * (T(z * u,w * (v5 * v6)) / z)) * v7)
    ]]></literal>
    <justification jstring="[para(25834(a,2),35129(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="25834 35129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35132">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) * (w * v5)) * v6) * v7) = a(x,y,(v6 * ((v5 \ w) * z)) * v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,28025,a(flip),b,35130,a),flip(a)].">
      <j1 rule="hyper" parents="370 28025 35130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35134">
    <literal><![CDATA[
      a(x,y,((z * ((u * u) * (w * v5))) * v6) * v7) = a(x,y,(v6 * ((v5 \ w) * z)) * v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),35132(a,1,3,1,1))].">
      <j1 rule="para" parents="29 35132"/>
    </justification>
  </clause>

  <clause id="35135">
    <literal><![CDATA[
      a(x,y,(z * ((u \ w) * v5)) * v6) = a(x,y,(z * ((w * u) * v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,28025,a(flip),b,35134,a),flip(a)].">
      <j1 rule="hyper" parents="60 28025 35134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35136">
    <literal><![CDATA[
      a(((x * (y / x)) * (a(y,z,u \ w) \ z)) * (w * u),v5,v6) = a((x * (x \ y)) * (z * (u \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26653,a(flip),b,35087,a),flip(a)].">
      <j1 rule="hyper" parents="370 26653 35087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35137">
    <literal><![CDATA[
      a(((x * (y / x)) * (a(y,z,u \ w) \ z)) * (w * u),v5,v6) = a(y * (z * (u \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(5(a,1),35136(a,2,1,1))].">
      <j1 rule="para" parents="5 35136"/>
    </justification>
  </clause>

  <clause id="35139">
    <literal><![CDATA[
      a(((x * (y / x)) * (a(y,z,u * w) \ z)) * (w * u),v5,v6) = a(y * (z * (u \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(34532(a,1),35137(a,1,1,1,2,1))].">
      <j1 rule="para" parents="34532 35137"/>
    </justification>
  </clause>

  <clause id="35140">
    <literal><![CDATA[
      a((x * (a(x,y,z * u) \ y)) * (u * z),w,v5) = a(x * (y * (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(197(a,1),35139(a,1,1,1,1))].">
      <j1 rule="para" parents="197 35139"/>
    </justification>
  </clause>

  <clause id="35141">
    <literal><![CDATA[
      a(x * (y * (z \ u)),w,v5) = a(x * (y * (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(28854(a,1),35140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28854 35140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35142">
    <literal><![CDATA[
      a(x * (y * ((z \ (u * u)) * w)),v5,v6) = a((y * (w \ z)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27765,a(flip),b,35141,a),flip(a)].">
      <j1 rule="hyper" parents="60 27765 35141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35143">
    <literal><![CDATA[
      a((x * (y \ z)) * u,w,v5) = a((x * (z * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,30957,a(flip),b,35142,a),flip(a)].">
      <j1 rule="hyper" parents="60 30957 35142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35144">
    <literal><![CDATA[
      a((x * (y / z)) * u,w,v5) = a((x * (y * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,26653,a,b,35143,a)].">
      <j1 rule="hyper" parents="60 26653 35143"/>
    </justification>
  </clause>

  <clause id="35145">
    <literal><![CDATA[
      a((x * y) * ((z * y) / z),u,a(w,v5,x * (z * (z * y)))) = a(y,u,a((x * ((z * y) / z)) * w,v5,x * ((z * y) / z)))
    ]]></literal>
    <justification jstring="[para(34766(a,1),34942(a,1,3))].">
      <j1 rule="para" parents="34766 34942"/>
    </justification>
  </clause>

  <clause id="35146">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,z * ((u * x) / u))) = a((z * x) * ((u * x) / u),y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(34759(a,1),35145(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34759 35145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35147">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,z * ((u * x) / u))) = a((z * x) * ((u * x) * u),y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,35083,a(flip),b,35146,a),flip(a)].">
      <j1 rule="hyper" parents="370 35083 35146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35149">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,z * ((u * x) / u))) = a((z * x) * x,y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,35086,a(flip),b,35147,a),flip(a)].">
      <j1 rule="hyper" parents="370 35086 35147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35151">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,z * ((u * x) / u))) = a(z,y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[hyper(370,a,34526,a(flip),b,35149,a),flip(a)].">
      <j1 rule="hyper" parents="370 34526 35149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35153">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,z * (u * (u * x)))) = a(z,y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(34766(a,1),35151(a,1,3))].">
      <j1 rule="para" parents="34766 35151"/>
    </justification>
  </clause>

  <clause id="35154">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) / u)) * w,v5,x * z)) = a(z,y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(34759(a,1),35153(a,1,3))].">
      <j1 rule="para" parents="34759 35153"/>
    </justification>
  </clause>

  <clause id="35156">
    <literal><![CDATA[
      a(x,y,a((z * ((u * x) * u)) * w,v5,x * z)) = a(z,y,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(35144(a,1),35154(a,1,3))].">
      <j1 rule="para" parents="35144 35154"/>
    </justification>
  </clause>

  <clause id="35157">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,x * u)) = a(u,y,a(z,w,x * u))
    ]]></literal>
    <justification jstring="[para(35091(a,1),35156(a,1,3))].">
      <j1 rule="para" parents="35091 35156"/>
    </justification>
  </clause>

  <clause id="35158">
    <literal><![CDATA[
      a(x,y,a(x * (z * u),w,x * u)) = a(u,y,a(z,w,x * u))
    ]]></literal>
    <justification jstring="[para(35082(a,1),35157(a,1,3))].">
      <j1 rule="para" parents="35082 35157"/>
    </justification>
  </clause>

  <clause id="35159">
    <literal><![CDATA[
      a(x * y,z,a(y,u,w)) = a(y,z,a(x,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(60,a,35094,a(flip),b,35158,a)].">
      <j1 rule="hyper" parents="60 35094 35158"/>
    </justification>
  </clause>

  <clause id="35160">
    <literal><![CDATA[
      a(x,y,a(z,u,w * x)) = a(x,u,a(w,y,x * z))
    ]]></literal>
    <justification jstring="[hyper(33025,a,35159,a),flip(a)].">
      <j1 rule="hyper" parents="33025 35159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35161">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(x,v5,a(v6,a(u,z,y),w * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,31980,a,b,35160,a)].">
      <j1 rule="hyper" parents="370 31980 35160"/>
    </justification>
  </clause>

  <clause id="35162">
    <literal><![CDATA[
      a(x,y * z,a(a(u,w,v5),v6,(y * z) * (a(u,w,v5) * z))) = a(z,a(v5,w,u),a(y,v6,z * x))
    ]]></literal>
    <justification jstring="[hyper(370,a,34934,a,b,35161,a)].">
      <j1 rule="hyper" parents="370 34934 35161"/>
    </justification>
  </clause>

  <clause id="35163">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(v6,w * x,a(a(u,z,y),v5,w * a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(34524(a,1),35162(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34524 35162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35165">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(v6,w * x,a(w,v5,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(35127(a,1),35163(a,2,3))].">
      <j1 rule="para" parents="35127 35163"/>
    </justification>
  </clause>

  <clause id="35166">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(a(y,z,u),v5,a(v6,x,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,34837,a(flip),b,35165,a),flip(a)].">
      <j1 rule="hyper" parents="370 34837 35165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35167">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(y,z,a(a(v6,x,w),v5,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,32930,a(flip),b,35166,a),flip(a)].">
      <j1 rule="hyper" parents="370 32930 35166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35168">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,x * v6)) = a(y,z,a(v6,x,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(32930(a,1),35167(a,2,3))].">
      <j1 rule="para" parents="32930 35167"/>
    </justification>
  </clause>

  <clause id="35169">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6 * (v7 * x))) = a(u,w,a(v7 * v6,x,a(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34777,a,b,35168,a)].">
      <j1 rule="hyper" parents="60 34777 35168"/>
    </justification>
  </clause>

  <clause id="35170">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,x * v6)) = x * a(y,z,a(v6,x,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(129,a,35168,a(flip),b,32082,a),flip(a)].">
      <j1 rule="hyper" parents="129 35168 32082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35171">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,x * v6)) = x * a(y,x,a(v6,z,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(32980(a,1),35170(a,2,2))].">
      <j1 rule="para" parents="32980 35170"/>
    </justification>
  </clause>

  <clause id="35172">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),x * (v6 * x))) = a(u,w,a(v6,x,a(v5,y,z * x)))
    ]]></literal>
    <justification jstring="[para(34957(a,1),35169(a,2,3))].">
      <j1 rule="para" parents="34957 35169"/>
    </justification>
  </clause>

  <clause id="35173">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(u,v5,a(v6,a(x,y,w),z))
    ]]></literal>
    <justification jstring="[para(34531(a,1),35172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34531 35172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35174">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,y * v6))) = a(y,v5,a(z,a(w,u,x),v6))
    ]]></literal>
    <justification jstring="[hyper(34966,a,35173,a)].">
      <j1 rule="hyper" parents="34966 35173"/>
    </justification>
  </clause>

  <clause id="35175">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,y * v6))) = a(w,u,a(y,a(x,v5,z),v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,35115,a(flip),b,35173,a)].">
      <j1 rule="hyper" parents="60 35115 35173"/>
    </justification>
  </clause>

  <clause id="35176">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,y * v6))) = a(z,v5,a(y,a(w,u,v6),x))
    ]]></literal>
    <justification jstring="[hyper(60,a,35059,a(flip),b,35173,a)].">
      <j1 rule="hyper" parents="60 35059 35173"/>
    </justification>
  </clause>

  <clause id="35177">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v5 * v6))) = a(v5,u,a(x,a(z,y,v6),w))
    ]]></literal>
    <justification jstring="[hyper(60,a,34967,a(flip),b,35173,a)].">
      <j1 rule="hyper" parents="60 34967 35173"/>
    </justification>
  </clause>

  <clause id="35179">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = a(u,w,a(x,a(v5,y,z),v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,35174,a(flip),b,35175,a)].">
      <j1 rule="hyper" parents="60 35174 35175"/>
    </justification>
  </clause>

  <clause id="35180">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) * u = L(u,w,a(x,a(v5,y,z),v6))
    ]]></literal>
    <justification jstring="[para(35179(a,2),32080(a,1,1))].">
      <j1 rule="para" parents="35179 32080"/>
    </justification>
  </clause>

  <clause id="35181">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = a(v5,w,a(z,a(x,y,v6),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,35175,a(flip),b,35176,a)].">
      <j1 rule="hyper" parents="60 35175 35176"/>
    </justification>
  </clause>

  <clause id="35182">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) * u = R(u,w,a(z,a(v6,y,x),v5))
    ]]></literal>
    <justification jstring="[para(35181(a,1),32091(a,1,1))].">
      <j1 rule="para" parents="35181 32091"/>
    </justification>
  </clause>

  <clause id="35183">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,x),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,v5,a(u,a(v6,z,y),w)) = v7
    ]]></literal>
    <justification jstring="[para(35181(a,1),32997(a,1,2))].">
      <j1 rule="para" parents="35181 32997"/>
    </justification>
  </clause>

  <clause id="35184">
    <literal><![CDATA[
      R(x,y,a(z,a(u,w,v5),v6)) = L(x,y,a(v5,a(v6,w,z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,35180,a(flip),b,35182,a),flip(a)].">
      <j1 rule="hyper" parents="60 35180 35182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35185">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = L(x,y,a(v5,a(v6,w,z),u))
    ]]></literal>
    <justification jstring="[hyper(28340,a,35184,a)].">
      <j1 rule="hyper" parents="28340 35184"/>
    </justification>
  </clause>

  <clause id="35187">
    <literal><![CDATA[
      L(L(x,a(y,z,u),a(w,v5,v6)),z,a(v6,a(u,v5,y),w)) = x * a(u,x,a(y,z,a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(370,a,33121,a(flip),b,35185,a),flip(a)].">
      <j1 rule="hyper" parents="370 33121 35185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35188">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,(y * ((1 / y) * z)) * v6))) = a(x,v5,a(v6,y * ((1 / y) * z),a(u,w,y * z)))
    ]]></literal>
    <justification jstring="[para(34500(a,1),34962(a,2,3,3))].">
      <j1 rule="para" parents="34500 34962"/>
    </justification>
  </clause>

  <clause id="35190">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,(y * ((1 / y) * z)) * v6))) = a(x,v5,a(v6,y * ((1 * y) * z),a(u,w,y * z)))
    ]]></literal>
    <justification jstring="[para(35055(a,1),35188(a,2,3))].">
      <j1 rule="para" parents="35055 35188"/>
    </justification>
  </clause>

  <clause id="35191">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,(y * ((1 / y) * z)) * v6))) = a(x,v5,a(v6,y * (y * z),a(u,w,y * z)))
    ]]></literal>
    <justification jstring="[para(2(a,1),35190(a,2,3,2,2,1))].">
      <j1 rule="para" parents="2 35190"/>
    </justification>
  </clause>

  <clause id="35192">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,(y * ((1 / y) * z)) * v6))) = a(x,v5,a(v6,w,a(u,y,y * z)))
    ]]></literal>
    <justification jstring="[para(34832(a,1),35191(a,2,3))].">
      <j1 rule="para" parents="34832 35191"/>
    </justification>
  </clause>

  <clause id="35193">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,y * (((1 / y) * z) * v6)))) = a(x,v5,a(v6,w,a(u,y,y * z)))
    ]]></literal>
    <justification jstring="[para(34768(a,1),35192(a,1,3,3))].">
      <j1 rule="para" parents="34768 35192"/>
    </justification>
  </clause>

  <clause id="35194">
    <literal><![CDATA[
      a(x,y,(((z * u) * (w * (v5 * v6))) / L(z,u,w * (v5 * v6))) * v7) = a(x,y,((w * (v6 \ v5)) * (T(z * u,w * (v5 * v6)) * z)) * v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,34826,a(flip),b,35131,a),flip(a)].">
      <j1 rule="hyper" parents="370 34826 35131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35195">
    <literal><![CDATA[
      a(x,y,(((z * u) * (w * (v5 * v6))) / L(z,u,w * (v5 * v6))) * v7) = a(x,y,v7 * (((z * u) * z) * (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[hyper(370,a,27184,a(flip),b,35194,a),flip(a)].">
      <j1 rule="hyper" parents="370 27184 35194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35197">
    <literal><![CDATA[
      a(x,y,(((z * u) * (w * (v5 * v6))) / L(z,u,w * (v5 * v6))) * v7) = a(x,y,v7 * (u * (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[hyper(370,a,34805,a(flip),b,35195,a),flip(a)].">
      <j1 rule="hyper" parents="370 34805 35195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35199">
    <literal><![CDATA[
      a(x,y,((z * (u * w)) * (T(v5 * v6,z * (u * w)) / v5)) * v7) = a(x,y,v7 * (v6 * (z * (w \ u))))
    ]]></literal>
    <justification jstring="[para(25834(a,1),35197(a,1,3,1))].">
      <j1 rule="para" parents="25834 35197"/>
    </justification>
  </clause>

  <clause id="35200">
    <literal><![CDATA[
      a(x,y,((z * (u * w)) * (T(v5 * v6,z * (u * w)) * v5)) * v7) = a(x,y,v7 * (v6 * (z * (w \ u))))
    ]]></literal>
    <justification jstring="[hyper(60,a,34826,a(flip),b,35199,a)].">
      <j1 rule="hyper" parents="60 34826 35199"/>
    </justification>
  </clause>

  <clause id="35201">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * u) * (v5 * (v6 * v7)))) = a(x,y,z * (w * (v5 * (v7 \ v6))))
    ]]></literal>
    <justification jstring="[hyper(60,a,27184,a(flip),b,35200,a)].">
      <j1 rule="hyper" parents="60 27184 35200"/>
    </justification>
  </clause>

  <clause id="35203">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 \ v6)))) = a(x,y,z * (u * (w * (v6 * v5))))
    ]]></literal>
    <justification jstring="[hyper(60,a,34805,a(flip),b,35201,a),flip(a)].">
      <j1 rule="hyper" parents="60 34805 35201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35204">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * ((v5 \ v6) * w)) / w))) = a(x,y,z * (u * (L(w,v5 \ v6,w) * (v6 * v5))))
    ]]></literal>
    <justification jstring="[para(5522(a,2),35203(a,1,3,2,2))].">
      <j1 rule="para" parents="5522 35203"/>
    </justification>
  </clause>

  <clause id="35205">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w,v5 \ v6,w) * (v6 * v5)))) = a(x,y,z * (u * (w * (w * ((v5 \ v6) * w)))))
    ]]></literal>
    <justification jstring="[hyper(60,a,34946,a(flip),b,35204,a),flip(a)].">
      <j1 rule="hyper" parents="60 34946 35204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35206">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w,v5 \ v6,w) * (v6 * v5)))) = a(x,y,z * (((v5 \ v6) * w) * u))
    ]]></literal>
    <justification jstring="[hyper(370,a,34804,a(flip),b,35205,a),flip(a)].">
      <j1 rule="hyper" parents="370 34804 35205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35208">
    <literal><![CDATA[
      a(x,y,(z * (u * (w * v5))) * v6) = a(x,y,v6 * (((v5 \ w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,29380,a(flip),b,35206,a)].">
      <j1 rule="hyper" parents="60 29380 35206"/>
    </justification>
  </clause>

  <clause id="35210">
    <literal><![CDATA[
      a(x,y,(z * ((((u \ w) * (u \ w)) \ v5) * (w * u))) * v6) = a(x,y,v6 * ((((u \ w) \ 1) * v5) * z))
    ]]></literal>
    <justification jstring="[para(944(a,1),35208(a,2,3,2,1))].">
      <j1 rule="para" parents="944 35208"/>
    </justification>
  </clause>

  <clause id="35211">
    <literal><![CDATA[
      a(x,y,(z * ((u * ((w \ v5) * (w \ v5))) * (v5 * w))) * v6) = a(x,y,v6 * ((((w \ v5) \ 1) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(60,a,35135,a(flip),b,35210,a)].">
      <j1 rule="hyper" parents="60 35135 35210"/>
    </justification>
  </clause>

  <clause id="35212">
    <literal><![CDATA[
      a(x,y,(z * (u * (((w \ v5) * (w \ v5)) * (v5 * w)))) * v6) = a(x,y,v6 * ((((w \ v5) \ 1) * u) * z))
    ]]></literal>
    <justification jstring="[para(29(a,1),35211(a,1,3,1,2))].">
      <j1 rule="para" parents="29 35211"/>
    </justification>
  </clause>

  <clause id="35213">
    <literal><![CDATA[
      a(x,y,z * ((((u \ w) \ 1) * v5) * v6)) = a(x,y,(((w * u) * v5) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(27569,a,35212,a),flip(a)].">
      <j1 rule="hyper" parents="27569 35212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35215">
    <literal><![CDATA[
      a(x,y,(((z \ u) * w) * v5) * v6) = a(x,y,(((u * z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,26933,a(flip),b,35213,a)].">
      <j1 rule="hyper" parents="60 26933 35213"/>
    </justification>
  </clause>

  <clause id="35216">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) * v5) * ((v6 * v7) * v6)) = a(x,y,v7 * (((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,34752,a(flip),b,35215,a),flip(a)].">
      <j1 rule="hyper" parents="60 34752 35215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35217">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * v5) * v6)) = a(x,y,z * (((w * u) * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,34752,a(flip),b,35216,a),flip(a)].">
      <j1 rule="hyper" parents="60 34752 35216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35219">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) * v6)) = a(x,y,z * (((u * w) * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,27028,a,b,35217,a)].">
      <j1 rule="hyper" parents="60 27028 35217"/>
    </justification>
  </clause>

  <clause id="35220">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,y * (((1 * y) * z) * v6)))) = a(x,v5,a(v6,w,a(u,y,y * z)))
    ]]></literal>
    <justification jstring="[para(35219(a,1),35193(a,1,3,3))].">
      <j1 rule="para" parents="35219 35193"/>
    </justification>
  </clause>

  <clause id="35221">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,y * ((y * z) * v6)))) = a(x,v5,a(v6,w,a(u,y,y * z)))
    ]]></literal>
    <justification jstring="[para(2(a,1),35220(a,1,3,3,3,2,1,1))].">
      <j1 rule="para" parents="2 35220"/>
    </justification>
  </clause>

  <clause id="35222">
    <literal><![CDATA[
      a(x,y * ((1 / y) * z),a(u,w,a(y,v5,v6 * z))) = a(x,v5,a(v6,w,a(u,y,y * z)))
    ]]></literal>
    <justification jstring="[para(34787(a,1),35221(a,1,3,3))].">
      <j1 rule="para" parents="34787 35221"/>
    </justification>
  </clause>

  <clause id="35223">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,(1 / v6) * v5,v6))) = a(z,y,a(w,u,a(x,v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(60,a,34846,a(flip),b,35222,a)].">
      <j1 rule="hyper" parents="60 34846 35222"/>
    </justification>
  </clause>

  <clause id="35224">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,v6 * v5,v6))) = a(z,y,a(w,u,a(x,v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[para(3042(a,1),35223(a,1,3,3))].">
      <j1 rule="para" parents="3042 35223"/>
    </justification>
  </clause>

  <clause id="35225">
    <literal><![CDATA[
      a(x,y,a(z * u,w,a(v5,u,v6))) = a(v5,y,a(z,w,a(x,v6,v6 * u)))
    ]]></literal>
    <justification jstring="[para(34831(a,1),35224(a,1,3))].">
      <j1 rule="para" parents="34831 35224"/>
    </justification>
  </clause>

  <clause id="35226">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(w,y,a(z,v5,a(x,v6,v6 * u)))
    ]]></literal>
    <justification jstring="[para(34956(a,1),35225(a,1,3))].">
      <j1 rule="para" parents="34956 35225"/>
    </justification>
  </clause>

  <clause id="35227">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v5 * v6))) = a(v6,u,a(v5,a(w,y,x),z))
    ]]></literal>
    <justification jstring="[hyper(60,a,35173,a(flip),b,35226,a),flip(a)].">
      <j1 rule="hyper" parents="60 35173 35226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35228">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = a(v5,y,a(x,a(v6,w,z),u))
    ]]></literal>
    <justification jstring="[hyper(60,a,35177,a(flip),b,35227,a)].">
      <j1 rule="hyper" parents="60 35177 35227"/>
    </justification>
  </clause>

  <clause id="35229">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,x),v6)) = L(x,a(v6,v5,y),a(u,z,w))
    ]]></literal>
    <justification jstring="[para(35228(a,1),32943(a,1,2))].">
      <j1 rule="para" parents="35228 32943"/>
    </justification>
  </clause>

  <clause id="35230">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = L(x,z,a(w,a(y,v5,u),v6))
    ]]></literal>
    <justification jstring="[hyper(35183,a,35229,a),flip(a)].">
      <j1 rule="hyper" parents="35183 35229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35235">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),x * v6)) = x * a(u,x,a(v6,y,a(v5,w,z)))
    ]]></literal>
    <justification jstring="[hyper(60,a,35171,a(flip),b,35230,a),flip(a)].">
      <j1 rule="hyper" parents="60 35171 35230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35236">
    <literal><![CDATA[
      L(L(x,a(y,z,u),a(w,v5,v6)),z,a(v6,a(u,v5,y),w)) = L(x,z,a(v6,a(u,v5,w),x * y))
    ]]></literal>
    <justification jstring="[hyper(370,a,35187,a,b,35235,a)].">
      <j1 rule="hyper" parents="370 35187 35235"/>
    </justification>
  </clause>

  <clause id="35237">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),y,a(v6,a(v5,w,u),z)) = L(x,y,a(v6,a(v5,w,z),x * u))
    ]]></literal>
    <justification jstring="[para(35230(a,1),35236(a,1,1))].">
      <j1 rule="para" parents="35230 35236"/>
    </justification>
  </clause>

  <clause id="35238">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),x * v6)) = x
    ]]></literal>
    <justification jstring="[hyper(60,a,31982,a(flip),b,35237,a),flip(a)].">
      <j1 rule="hyper" parents="60 31982 35237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35240">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,35238,a(flip),b,35235,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="124 35238 35235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35241">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),35238(a,1,3,3))].">
      <j1 rule="para" parents="5 35238"/>
    </justification>
  </clause>

  <clause id="35244">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(32950,a,35240,a)].">
      <j1 rule="hyper" parents="32950 35240"/>
    </justification>
  </clause>

  <clause id="35245">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(31133,a,35240,a)].">
      <j1 rule="hyper" parents="31133 35240"/>
    </justification>
  </clause>

  <clause id="35251">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(49,a,35240,a)].">
      <j1 rule="hyper" parents="49 35240"/>
    </justification>
  </clause>

  <clause id="35258">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(33020,a,35241,a)].">
      <j1 rule="hyper" parents="33020 35241"/>
    </justification>
  </clause>

  <clause id="35263">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,v6)) = 1
    ]]></literal>
    <justification jstring="[hyper(124,a,35241,a(flip),b,32943,a),flip(a)].">
      <j1 rule="hyper" parents="124 35241 32943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35264">
    <literal><![CDATA[
      (x * y) * a(z,a(u,w,v5),v6) = x * (y * a(z,a(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(35241(a,1),28343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35241 28343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35271">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,35244,a)].">
      <j1 rule="hyper" parents="49 35244"/>
    </justification>
  </clause>

  <clause id="35274">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,35245,a)].">
      <j1 rule="hyper" parents="49 35245"/>
    </justification>
  </clause>

  <clause id="35275">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) \ v6 = a(u,w,v5) \ (a(x,y,z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(747,a,35258,a),flip(a)].">
      <j1 rule="hyper" parents="747 35258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35289">
    <literal><![CDATA[
      (a(x,y,z) \ a(u,w,v5)) * v6 = a(u,w,v5) * (a(x,y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(35258(a,1),30833(a,1,2))].">
      <j1 rule="para" parents="35258 30833"/>
    </justification>
  </clause>

  <clause id="35297">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,v5),v6) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,35263,a)].">
      <j1 rule="hyper" parents="49 35263"/>
    </justification>
  </clause>

  <clause id="35300">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = a(x,y,a(z,u,w)) * (v5 * v6)
    ]]></literal>
    <justification jstring="[hyper(1838,a,35271,a),flip(a)].">
      <j1 rule="hyper" parents="1838 35271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35301">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(747,a,35271,a),flip(a)].">
      <j1 rule="hyper" parents="747 35271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35304">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,33266,a(flip),b,35271,a)].">
      <j1 rule="hyper" parents="60 33266 35271"/>
    </justification>
  </clause>

  <clause id="35305">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) / (v5 \ 1) = a(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[hyper(129,a,35271,a(flip),b,2481,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 35271 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35309">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (a(x,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(35271(a,1),28360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35271 28360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35311">
    <literal><![CDATA[
      (x * y) * a(a(z,u,w),v5,v6) = x * (y * a(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(35271(a,1),30729(a,1,1,1))].">
      <j1 rule="para" parents="35271 30729"/>
    </justification>
  </clause>

  <clause id="35312">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * v6) = v5 * (a(a(x,y,z),u,w) * v6)
    ]]></literal>
    <justification jstring="[para(35271(a,1),33015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35271 33015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35313">
    <literal><![CDATA[
      L(x,y,L(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(35271(a,1),33250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35271 33250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35314">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = x \ (a(a(y,z,u),w,v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(25584,a,35274,a)].">
      <j1 rule="hyper" parents="25584 35274"/>
    </justification>
  </clause>

  <clause id="35315">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) * v6 = a(a(x,y,z),u,w) * (v5 * v6)
    ]]></literal>
    <justification jstring="[hyper(1838,a,35274,a),flip(a)].">
      <j1 rule="hyper" parents="1838 35274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35316">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(35274(a,1),47(a,2))].">
      <j1 rule="para" parents="35274 47"/>
    </justification>
  </clause>

  <clause id="35317">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = a(a(y,z,u),w,v5) * (x * v6)
    ]]></literal>
    <justification jstring="[para(35274(a,1),23651(a,1,2))].">
      <j1 rule="para" parents="35274 23651"/>
    </justification>
  </clause>

  <clause id="35318">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,v6)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(35274(a,1),33265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="35274 33265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35323">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 = a(x,y,z) * (v6 * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(35297(a,1),28365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35297 28365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35333">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ v5)) = L(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(32631(a,1),35313(a,1,3))].">
      <j1 rule="para" parents="32631 35313"/>
    </justification>
  </clause>

  <clause id="35334">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(32450,a,35251,a)].">
      <j1 rule="hyper" parents="32450 35251"/>
    </justification>
  </clause>

  <clause id="35338">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,a(w,v5,v6))) = y * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(129,a,35251,a(flip),b,8573,a),flip(a)].">
      <j1 rule="hyper" parents="129 35251 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35339">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,v5,v6))) = (x \ y) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(35251(a,1),617(a,1,2,2))].">
      <j1 rule="para" parents="35251 617"/>
    </justification>
  </clause>

  <clause id="35342">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) / (a(z,u,w) \ 1)) * L(a(z,u,w) \ 1,v5,v6) = (a(z,u,w) \ 1) \ L(L(a(z,u,w) \ 1,v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35251(a,1),34324(a,1,1,1))].">
      <j1 rule="para" parents="35251 34324"/>
    </justification>
  </clause>

  <clause id="35349">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v6))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32313(a,2),35304(a,1,3))].">
      <j1 rule="para" parents="32313 35304"/>
    </justification>
  </clause>

  <clause id="35365">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(u,w,v5) = L(x,y,z) * (x \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(35318(a,1),25890(a,1,1))].">
      <j1 rule="para" parents="35318 25890"/>
    </justification>
  </clause>

  <clause id="35369">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (L(L(w,u,z),v5,v6) \ L(w,u,z))) = L(x,y,w * (L(L(w,u,z),v5,v6) \ 1))
    ]]></literal>
    <justification jstring="[para(2169(a,1),35333(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2169 35333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35370">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,v6) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(26234,a,35264,a)].">
      <j1 rule="hyper" parents="26234 35264"/>
    </justification>
  </clause>

  <clause id="35371">
    <literal><![CDATA[
      x \ (y * a(z,a(u,w,v5),v6)) = (x \ y) * a(z,a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(831,a,35264,a)].">
      <j1 rule="hyper" parents="831 35264"/>
    </justification>
  </clause>

  <clause id="35375">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ (v5 * v6) = v5 * (a(x,a(y,z,u),w) \ v6)
    ]]></literal>
    <justification jstring="[para(35370(a,1),30803(a,1,1))].">
      <j1 rule="para" parents="35370 30803"/>
    </justification>
  </clause>

  <clause id="35377">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ (a(z,u,w) \ v5)),v6) = L(x,y \ v5,v6)
    ]]></literal>
    <justification jstring="[para(35275(a,1),3721(a,1,2,2))].">
      <j1 rule="para" parents="35275 3721"/>
    </justification>
  </clause>

  <clause id="35378">
    <literal><![CDATA[
      a((a(x,y,z) * (a(u,w,v5) \ (v6 * v7))) * (((a(u,w,v5) \ a(x,y,z)) * v6) * v7),v8,v9) = a(a(a(u,w,v5) \ a(x,y,z),v6,v7),v8,v9)
    ]]></literal>
    <justification jstring="[para(35289(a,1),34593(a,1,1,1))].">
      <j1 rule="para" parents="35289 34593"/>
    </justification>
  </clause>

  <clause id="35379">
    <literal><![CDATA[
      a((x * (y \ (a(z,u,a(w,v5,v6)) \ 1))) \ v7,v8,v9) = a((x * (a(z,u,a(w,v5,v6)) * y)) \ v7,v8,v9)
    ]]></literal>
    <justification jstring="[para(35301(a,1),2967(a,1,1,1,2))].">
      <j1 rule="para" parents="35301 2967"/>
    </justification>
  </clause>

  <clause id="35380">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * v6) = a(y,z,a(u,w,v5)) * (x \ v6)
    ]]></literal>
    <justification jstring="[hyper(764,a,35309,a)].">
      <j1 rule="hyper" parents="764 35309"/>
    </justification>
  </clause>

  <clause id="35382">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,a(w,v5,v6)) * (y * v7))) = L(a(z,u,a(w,v5,v6)) * v7,y,x)
    ]]></literal>
    <justification jstring="[para(35309(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="35309 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35386">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) * v7 = a(y,z,a(u,w,v5)) * ((x * v6) * v7)
    ]]></literal>
    <justification jstring="[para(35309(a,1),35300(a,1,1))].">
      <j1 rule="para" parents="35309 35300"/>
    </justification>
  </clause>

  <clause id="35387">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) \ v7 = (x * v6) \ (a(y,z,a(u,w,v5)) \ v7)
    ]]></literal>
    <justification jstring="[para(35309(a,1),35301(a,1,1))].">
      <j1 rule="para" parents="35309 35301"/>
    </justification>
  </clause>

  <clause id="35388">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = x \ (v6 * a(v5,w,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(31145(a,1),35314(a,2,2))].">
      <j1 rule="para" parents="31145 35314"/>
    </justification>
  </clause>

  <clause id="35389">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = x * (a(a(y,z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35312,a(flip),b,35317,a),flip(a)].">
      <j1 rule="hyper" parents="370 35312 35317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35390">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ (((v5 * a(a(x,y,z),u,w)) * v6) * v7) = a(v5 * a(a(x,y,z),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(35317(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35317 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35391">
    <literal><![CDATA[
      (x * (y * a(a(z,u,w),v5,v6))) * v7 = a(a(z,u,w),v5,v6) * ((x * y) * v7)
    ]]></literal>
    <justification jstring="[para(35311(a,1),35317(a,1,1))].">
      <j1 rule="para" parents="35311 35317"/>
    </justification>
  </clause>

  <clause id="35392">
    <literal><![CDATA[
      (a(x,y,z) * (u * a(w,v5,v6))) \ ((a(x,y,z) * a(w,v5,v6)) * (u * v7)) = L(v7,u,a(x,y,z) * a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(35323(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35323 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35394">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,a(w,v5,v6))) = a(z,u,a(w,v5,v6)) * y
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,35338,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 35338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35396">
    <literal><![CDATA[
      (x \ y) * a(y,z,a(u,w,v5)) = x \ L(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(125,a,32077,a(flip),b,35338,a),flip(a)].">
      <j1 rule="hyper" parents="125 32077 35338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35397">
    <literal><![CDATA[
      (x \ (a(y,z,a(u,w,v5)) \ v6)) * a(y,z,a(u,w,v5)) = x \ v6
    ]]></literal>
    <justification jstring="[hyper(125,a,23621,a(flip),b,35338,a),flip(a)].">
      <j1 rule="hyper" parents="125 23621 35338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35398">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(35338(a,1),385(a,1,2)),flip(b)].">
      <j1 rule="para" parents="35338 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35399">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ x) = v5 \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(23794,a,35396,a)].">
      <j1 rule="hyper" parents="23794 35396"/>
    </justification>
  </clause>

  <clause id="35401">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,a(v6,v7,v8)) * a(x,y,a(z,u,w)) = x \ L(L(x,y,a(z,u,w)),v5,a(v6,v7,v8))
    ]]></literal>
    <justification jstring="[para(32082(a,1),35399(a,1,2))].">
      <j1 rule="para" parents="32082 35399"/>
    </justification>
  </clause>

  <clause id="35403">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(u,w,a(v5,v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ a(u,w,a(v5,v6,v7))) = v8
    ]]></literal>
    <justification jstring="[para(35339(a,1),2191(a,1))].">
      <j1 rule="para" parents="35339 2191"/>
    </justification>
  </clause>

  <clause id="35405">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (L(v5,v6,v7) * (v5 \ a(w,u,a(x,y,z)))) = v5 \ L(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(129,a,35365,a(flip),b,31145,a)].">
      <j1 rule="hyper" parents="129 35365 31145"/>
    </justification>
  </clause>

  <clause id="35406">
    <literal><![CDATA[
      x \ (y * (z * a(u,a(w,v5,v6),v7))) = (x \ (y * z)) * a(u,a(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(35264(a,1),35371(a,1,2))].">
      <j1 rule="para" parents="35264 35371"/>
    </justification>
  </clause>

  <clause id="35407">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      (x \ v6) * a(y,z,a(u,w,v5)) = v7
    ]]></literal>
    <justification jstring="[para(35380(a,2),23637(a,1))].">
      <j1 rule="para" parents="35380 23637"/>
    </justification>
  </clause>

  <clause id="35408">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = (x \ v6) * a(v5,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(370,a,35339,a(flip),b,35388,a),flip(a)].">
      <j1 rule="hyper" parents="370 35339 35388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35409">
    <literal><![CDATA[
      L(x,a(a(y,z,u),w,v5),v6) = x
    ]]></literal>
    <justification jstring="[hyper(625,a,35389,a)].">
      <j1 rule="hyper" parents="625 35389"/>
    </justification>
  </clause>

  <clause id="35410">
    <literal><![CDATA[
      (x * (a(a(y,z,u),w,v5) * v6)) \ ((x * a(a(y,z,u),w,v5)) * (v6 * v7)) = L(v7,v6,x * a(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(35389(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35389 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35412">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)),v6) = x
    ]]></literal>
    <justification jstring="[hyper(31983,a,35409,a)].">
      <j1 rule="hyper" parents="31983 35409"/>
    </justification>
  </clause>

  <clause id="35415">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) * v6 = x * (a(y,z,a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(1838,a,35412,a),flip(a)].">
      <j1 rule="hyper" parents="1838 35412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35417">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) * v6 != v7
    ]]></literal>
    <literal><![CDATA[
      x * (a(y,z,a(u,w,v5)) * v6) = v7
    ]]></literal>
    <justification jstring="[para(35412(a,1),336(a,1,2))].">
      <j1 rule="para" parents="35412 336"/>
    </justification>
  </clause>

  <clause id="35418">
    <literal><![CDATA[
      L(x * a(a(y,z,u),w,v5),L(v5,w,a(y,z,u)),v6) = (v6 * (v5 * a(v5,w,a(y,z,u)))) \ (v6 * (v5 * x))
    ]]></literal>
    <justification jstring="[para(35412(a,1),32270(a,1,1))].">
      <j1 rule="para" parents="35412 32270"/>
    </justification>
  </clause>

  <clause id="35419">
    <literal><![CDATA[
      x \ (y * (a(z,u,a(w,v5,v6)) * v7)) = (x \ (y * v7)) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(125,a,35309,a(flip),b,35394,a)].">
      <j1 rule="hyper" parents="125 35309 35394"/>
    </justification>
  </clause>

  <clause id="35421">
    <literal><![CDATA[
      (x \ y) * a(x,z,a(u,w,v5)) = L(x,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(32078(a,1),35408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32078 35408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35422">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ v6 = (x \ v6) * a(u,w,a(y,z,v5))
    ]]></literal>
    <justification jstring="[para(32930(a,1),35408(a,1,1,2))].">
      <j1 rule="para" parents="32930 35408"/>
    </justification>
  </clause>

  <clause id="35423">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (x \ v5) = L(x,y,a(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[hyper(23794,a,35421,a)].">
      <j1 rule="hyper" parents="23794 35421"/>
    </justification>
  </clause>

  <clause id="35424">
    <literal><![CDATA[
      x * L(x \ (y \ x),z,a(u,w,v5)) = L(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(60,a,32104,a(flip),b,35423,a)].">
      <j1 rule="hyper" parents="60 32104 35423"/>
    </justification>
  </clause>

  <clause id="35425">
    <literal><![CDATA[
      x * (a(x,y,a(z,u,w)) * v5) = R(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(32081(a,1),35415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32081 35415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35426">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ L(x,a(v6,v7,v8),v9) = a(v9,a(v6,v7,v8),x) * a(u,w,a(y,z,v5))
    ]]></literal>
    <justification jstring="[para(31276(a,1),35422(a,2,1))].">
      <j1 rule="para" parents="31276 35422"/>
    </justification>
  </clause>

  <clause id="35427">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) * L((x \ 1) * a(u,x,a(y,z,w)),u,a(y,z,w)) = (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(35422(a,1),33091(a,1,2,1))].">
      <j1 rule="para" parents="35422 33091"/>
    </justification>
  </clause>

  <clause id="35428">
    <literal><![CDATA[
      ((x \ y) * a(z,x,a(u,w,v5))) \ (y * L(y \ ((x * a(u,w,a(z,x,v5))) \ y),z,a(u,w,v5))) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(35422(a,1),33092(a,1,1))].">
      <j1 rule="para" parents="35422 33092"/>
    </justification>
  </clause>

  <clause id="35430">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 != v7
    ]]></literal>
    <literal><![CDATA[
      (x \ v6) * a(v5,w,a(y,z,u)) = v7
    ]]></literal>
    <justification jstring="[para(35388(a,2),35398(a,1))].">
      <j1 rule="para" parents="35388 35398"/>
    </justification>
  </clause>

  <clause id="35431">
    <literal><![CDATA[
      x \ (y * (a(z,u,a(w,v5,v6)) * v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      (x \ (y * v7)) * a(z,u,a(w,v5,v6)) = v8
    ]]></literal>
    <justification jstring="[para(35309(a,1),35407(a,1,2))].">
      <j1 rule="para" parents="35309 35407"/>
    </justification>
  </clause>

  <clause id="35432">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * ((v5 * v6) * (v7 * v8))) \ (((v5 * (a(x,y,a(z,u,w)) * v6)) * v7) * v8) = a(v5 * (a(x,y,a(z,u,w)) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(35386(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35386 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35433">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * ((v5 * v6) * v7)) \ ((v5 * (v6 * a(a(x,y,z),u,w))) * (v7 * v8)) = L(v8,v7,v5 * (v6 * a(a(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(35391(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35391 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35434">
    <literal><![CDATA[
      x \ (y * (a(z,a(u,w,v5),v6) * v7)) = (x \ (y * v7)) * a(z,a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35406(a,1,2,2))].">
      <j1 rule="para" parents="23620 35406"/>
    </justification>
  </clause>

  <clause id="35435">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) * a(u,w,a(v5,v6,v7)) = L(a(u,w,a(v5,v6,v7)) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,35419,a(flip),b,35382,a)].">
      <j1 rule="hyper" parents="60 35419 35382"/>
    </justification>
  </clause>

  <clause id="35436">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * v5,v6,v7) = L(v5,v6,v7) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),35435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 35435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35437">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,v5)),v6,v7) = L(x,v6,v7) * a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(24140,a,35436,a)].">
      <j1 rule="hyper" parents="24140 35436"/>
    </justification>
  </clause>

  <clause id="35439">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,v5)),v6,v7) = a(y,z,a(u,w,v5)) * L(x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,23620,a,b,35437,a),flip(a)].">
      <j1 rule="hyper" parents="370 23620 35437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35441">
    <literal><![CDATA[
      x \ (y * L(z * a(u,w,a(v5,v6,v7)),v8,v9)) != v10
    ]]></literal>
    <literal><![CDATA[
      (x \ (y * L(z,v8,v9))) * a(u,w,a(v5,v6,v7)) = v10
    ]]></literal>
    <justification jstring="[para(35439(a,2),35431(a,1,2,2))].">
      <j1 rule="para" parents="35439 35431"/>
    </justification>
  </clause>

  <clause id="35443">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (L(L(w,u,z),v5,v6) \ L(w,u,z))) = L(x,y,w * L(L(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,3426,a(flip),b,35369,a),flip(a)].">
      <j1 rule="hyper" parents="370 3426 35369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35444">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * (L(w \ L(w,v5,v6),u,z) \ 1)) = L(x,y,w * L(L(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(10447(a,1),35443(a,1,3,2))].">
      <j1 rule="para" parents="10447 35443"/>
    </justification>
  </clause>

  <clause id="35445">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6) * a(v6,v5,z)) = L(x,y,z * L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(25241,a,35444,a)].">
      <j1 rule="hyper" parents="25241 35444"/>
    </justification>
  </clause>

  <clause id="35446">
    <literal><![CDATA[
      a((x * (y \ (a(x,z,a(u,w,v5)) \ 1))) \ v6,v7,v8) = a((R(x,z,a(u,w,v5)) * y) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(35425(a,1),35379(a,2,1,1))].">
      <j1 rule="para" parents="35425 35379"/>
    </justification>
  </clause>

  <clause id="35447">
    <literal><![CDATA[
      a((x * (y \ (a(z,u,a(w,v5,v6)) \ 1))) \ v7,v8,v9) = a((x * y) \ (a(z,u,a(w,v5,v6)) \ v7),v8,v9)
    ]]></literal>
    <justification jstring="[para(35387(a,1),35379(a,2,1))].">
      <j1 rule="para" parents="35387 35379"/>
    </justification>
  </clause>

  <clause id="35448">
    <literal><![CDATA[
      L(x * a(a(y,z,u),w,v5),L(v5,w,a(y,z,u)),v6) = (v6 * L(v5,w,a(y,z,u))) \ (v6 * (v5 * x))
    ]]></literal>
    <justification jstring="[para(32077(a,1),35418(a,2,1,2))].">
      <j1 rule="para" parents="32077 35418"/>
    </justification>
  </clause>

  <clause id="35450">
    <literal><![CDATA[
      x \ L(L(x,y,a(z,u,w)),v5,a(v6,v7,v8)) = a(x,v5,a(v6,v7,v8)) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(35334(a,1),35401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35334 35401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35452">
    <literal><![CDATA[
      (a(x,y,z) * (u * a(w,v5,v6))) \ (a(x,y,z) * ((u * v7) * a(w,v5,v6))) = L(v7,u,a(x,y,z) * a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(35323(a,1),35392(a,1,2))].">
      <j1 rule="para" parents="35323 35392"/>
    </justification>
  </clause>

  <clause id="35453">
    <literal><![CDATA[
      (x * (a(a(y,z,u),w,v5) * v6)) \ (x * (a(a(y,z,u),w,v5) * (v6 * v7))) = L(v7,v6,x * a(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(35389(a,1),35410(a,1,2))].">
      <j1 rule="para" parents="35389 35410"/>
    </justification>
  </clause>

  <clause id="35454">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(v5,v6,v7)) = L(x,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,25817,a(flip),b,35452,a)].">
      <j1 rule="hyper" parents="60 25817 35452"/>
    </justification>
  </clause>

  <clause id="35455">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w) * y,a(v5,v6,v7)) = L(x,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26186,a,35454,a)].">
      <j1 rule="hyper" parents="26186 35454"/>
    </justification>
  </clause>

  <clause id="35456">
    <literal><![CDATA[
      L(1 / L(x,y,a(z,u,w)),y * a(z,u,w),a(v5,v6,v7)) = 1 / L(x,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(35454(a,1),30035(a,2,2))].">
      <j1 rule="para" parents="35454 30035"/>
    </justification>
  </clause>

  <clause id="35458">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(v5,v6,v7)) * a(x,w,a(y,z,u)) = x \ L(x,w,a(v5,v6,v7) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(35455(a,1),35450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35455 35450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35459">
    <literal><![CDATA[
      L(L(1 / x,y,a(z,u,w)),y * a(z,u,w),a(v5,v6,v7)) = 1 / L(x,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(30035(a,2),35456(a,1,1))].">
      <j1 rule="para" parents="30035 35456"/>
    </justification>
  </clause>

  <clause id="35460">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w) * a(v5,v6,v7)) = 1 / L(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(60,a,35454,a(flip),b,35459,a)].">
      <j1 rule="hyper" parents="60 35454 35459"/>
    </justification>
  </clause>

  <clause id="35461">
    <literal><![CDATA[
      L(L(x,y,a(a(z,u,w),v5,v6)),a(a(z,u,w),v5,v6) * y,v7) = L(x,y,v7 * a(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(1199,a,35453,a)].">
      <j1 rule="hyper" parents="1199 35453"/>
    </justification>
  </clause>

  <clause id="35462">
    <literal><![CDATA[
      L(x,a(a(y,z,u),w,v5) * v6,v7) = L(x,v6,v7 * a(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(35274(a,1),35461(a,1,1))].">
      <j1 rule="para" parents="35274 35461"/>
    </justification>
  </clause>

  <clause id="35463">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ ((a(a(x,y,z),u,w) * (v5 * v6)) * v7) = a(v5 * a(a(x,y,z),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(35317(a,1),35390(a,1,2,1))].">
      <j1 rule="para" parents="35317 35390"/>
    </justification>
  </clause>

  <clause id="35464">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ (a(a(x,y,z),u,w) * ((v5 * v6) * v7)) = a(v5 * a(a(x,y,z),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(35315(a,1),35463(a,1,2))].">
      <j1 rule="para" parents="35315 35463"/>
    </justification>
  </clause>

  <clause id="35465">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(a(u,w,v5),v6,v7)) = a(x * a(a(u,w,v5),v6,v7),y,z)
    ]]></literal>
    <justification jstring="[hyper(1201,a,35464,a)].">
      <j1 rule="hyper" parents="1201 35464"/>
    </justification>
  </clause>

  <clause id="35466">
    <literal><![CDATA[
      a(x * a(a(y,z,u),w,v5),v6,v7) = a(x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(35316,a,35465,a),flip(a)].">
      <j1 rule="hyper" parents="35316 35465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35469">
    <literal><![CDATA[
      a((a(x,y,z) * u) * w,v5,v6) = a(a(x,y,z) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(82(a,1),35466(a,1,1))].">
      <j1 rule="para" parents="82 35466"/>
    </justification>
  </clause>

  <clause id="35470">
    <literal><![CDATA[
      a(x * a(y,z,a(u,w,v5)),v6,v7) = a(x,v6,v7)
    ]]></literal>
    <justification jstring="[para(31123(a,1),35466(a,1,1,2))].">
      <j1 rule="para" parents="31123 35466"/>
    </justification>
  </clause>

  <clause id="35472">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(35466(a,1),32624(a,1))].">
      <j1 rule="para" parents="35466 32624"/>
    </justification>
  </clause>

  <clause id="35475">
    <literal><![CDATA[
      a(x \ (y * a(z,u,w)),v5,v6) = a((x \ y) * a(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(28739(a,1),35470(a,1,1))].">
      <j1 rule="para" parents="28739 35470"/>
    </justification>
  </clause>

  <clause id="35477">
    <literal><![CDATA[
      a(x \ (a(y,z,a(u,w,v5)) \ v6),v7,v8) = a(x \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(35397(a,1),35470(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35397 35470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35482">
    <literal><![CDATA[
      a((x * (y \ (a(z,u,a(w,v5,v6)) \ 1))) \ v7,v8,v9) = a((x * y) \ v7,v8,v9)
    ]]></literal>
    <justification jstring="[hyper(60,a,35447,a,b,35477,a)].">
      <j1 rule="hyper" parents="60 35447 35477"/>
    </justification>
  </clause>

  <clause id="35483">
    <literal><![CDATA[
      a(a(x,y,z) * (u * w),v5,v6) = a(w * (a(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26519,a,35469,a),flip(a)].">
      <j1 rule="hyper" parents="26519 35469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35484">
    <literal><![CDATA[
      a((a(x,y,z) \ u) * w,v5,v6) = a(a(x,y,z) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,35073,a,b,35469,a)].">
      <j1 rule="hyper" parents="60 35073 35469"/>
    </justification>
  </clause>

  <clause id="35485">
    <literal><![CDATA[
      a((x * a(y,z,u)) * w,v5,v6) = a(a(y,z,u) * (x * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(23620(a,1),35469(a,1,1,1))].">
      <j1 rule="para" parents="23620 35469"/>
    </justification>
  </clause>

  <clause id="35487">
    <literal><![CDATA[
      a(a(x,y,z) * (L(z,y,x) * u),w,v5) = a(z * u,w,v5)
    ]]></literal>
    <justification jstring="[para(32568(a,1),35469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="32568 35469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35488">
    <literal><![CDATA[
      a(a(x,y,z) * (u * L(z,y,x)),w,v5) = a(z * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26548,a,35487,a)].">
      <j1 rule="hyper" parents="26548 35487"/>
    </justification>
  </clause>

  <clause id="35490">
    <literal><![CDATA[
      a(x \ (a(y,z,u) * w),v5,v6) = a((x \ w) * a(y,z,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35475(a,1,1,2))].">
      <j1 rule="para" parents="23620 35475"/>
    </justification>
  </clause>

  <clause id="35491">
    <literal><![CDATA[
      a((a(x,y,z) \ u) * (a(w,v5,w) * v6),v7,v8) = a(a(x,y,z) * ((a(w,v5,w) * u) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(14298(a,2),35484(a,2,1,2))].">
      <j1 rule="para" parents="14298 35484"/>
    </justification>
  </clause>

  <clause id="35493">
    <literal><![CDATA[
      a((R(x,y,a(z,u,w)) * v5) \ v6,v7,v8) = a((x * v5) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,35446,a(flip),b,35482,a)].">
      <j1 rule="hyper" parents="60 35446 35482"/>
    </justification>
  </clause>

  <clause id="35495">
    <literal><![CDATA[
      a(a(x,y,z) * ((a(u,w,u) * v5) * v6),v7,v8) = a(v6 * (a(x,y,z) \ v5),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(26539,a,35491,a),flip(a)].">
      <j1 rule="hyper" parents="26539 35491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35496">
    <literal><![CDATA[
      a(a(x,y,z) * (a(u,w,u) * (v5 * v6)),v7,v8) = a(v6 * (a(x,y,z) \ v5),v7,v8)
    ]]></literal>
    <justification jstring="[para(13913(a,1),35495(a,1,1,2))].">
      <j1 rule="para" parents="13913 35495"/>
    </justification>
  </clause>

  <clause id="35497">
    <literal><![CDATA[
      a((x * y) * a(z,u,w),v5,v6) = a(y * (a(z,u,w) \ x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26539,a,35496,a)].">
      <j1 rule="hyper" parents="26539 35496"/>
    </justification>
  </clause>

  <clause id="35498">
    <literal><![CDATA[
      a((x * y) * a(z,u,w),v5,v6) = a(y * (x * a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35080,a(flip),b,35497,a),flip(a)].">
      <j1 rule="hyper" parents="370 35080 35497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35500">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * a(z,u,w)) * L(a(z,u,w) \ 1,v5,v6) = (a(z,u,w) \ 1) \ L(L(a(z,u,w) \ 1,v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35305(a,1),35342(a,1,1))].">
      <j1 rule="para" parents="35305 35342"/>
    </justification>
  </clause>

  <clause id="35501">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(L(a(x,y,z) \ 1,u,w),v5,v6) = a(x,y,L(z,v5,v6)) * L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(32318(a,1),35500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32318 35500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35502">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(L(a(x,y,z) \ 1,u,w),v5,v6) = a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,32343,a(flip),b,35501,a),flip(a)].">
      <j1 rule="hyper" parents="370 32343 35501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35503">
    <literal><![CDATA[
      a(x,y,z) \ (1 * L(L(1 \ a(x,y,z),u,w),v5,v6)) = a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(60,a,5204,a(flip),b,35502,a)].">
      <j1 rule="hyper" parents="60 5204 35502"/>
    </justification>
  </clause>

  <clause id="35504">
    <literal><![CDATA[
      a(x,y,z) \ (1 * L(L(a(x,y,z),u,w),v5,v6)) = a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(62(a,1),35503(a,1,2,2,1,1))].">
      <j1 rule="para" parents="62 35503"/>
    </justification>
  </clause>

  <clause id="35505">
    <literal><![CDATA[
      a(x,y,z) \ (1 * L(a(x,y,L(z,u,w)),v5,v6)) = a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(32313(a,2),35504(a,1,2,2,1))].">
      <j1 rule="para" parents="32313 35504"/>
    </justification>
  </clause>

  <clause id="35506">
    <literal><![CDATA[
      a(x,y,z) \ (1 * a(x,y,L(L(z,u,w),v5,v6))) = a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(32313(a,2),35505(a,1,2,2))].">
      <j1 rule="para" parents="32313 35505"/>
    </justification>
  </clause>

  <clause id="35507">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6)) = a(x,y,z) \ a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(392,a,35506,a),flip(a)].">
      <j1 rule="hyper" parents="392 35506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35508">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(L(z,u,w),v5,v6)) = a(v6,v5,a(x,y,z)) * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,32549,a(flip),b,35507,a),flip(a)].">
      <j1 rule="hyper" parents="60 32549 35507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35509">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * ((v5 * v6) * v7)) \ (a(a(x,y,z),u,w) * ((v5 * v6) * (v7 * v8))) = L(v8,v7,v5 * (v6 * a(a(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(35391(a,1),35433(a,1,2))].">
      <j1 rule="para" parents="35391 35433"/>
    </justification>
  </clause>

  <clause id="35510">
    <literal><![CDATA[
      L(L(x,y,z * u),(z * u) * y,a(a(w,v5,v6),v7,v8)) = L(x,y,z * (u * a(a(w,v5,v6),v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(1199,a,35509,a)].">
      <j1 rule="hyper" parents="1199 35509"/>
    </justification>
  </clause>

  <clause id="35511">
    <literal><![CDATA[
      L(x,y,z * (u * a(a(w,v5,v6),v7,v8))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(35316,a,35510,a),flip(a)].">
      <j1 rule="hyper" parents="35316 35510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35512">
    <literal><![CDATA[
      L(x,y,z * (u * a(a(w,v5,v6),v7,v8))) != v9
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = v9
    ]]></literal>
    <justification jstring="[para(35510(a,1),35316(a,1))].">
      <j1 rule="para" parents="35510 35316"/>
    </justification>
  </clause>

  <clause id="35513">
    <literal><![CDATA[
      L(x,y,z * a(a(u,w,v5),v6,v7)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3528,a,35511,a),flip(a)].">
      <j1 rule="hyper" parents="3528 35511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35515">
    <literal><![CDATA[
      L(x,y,z * (u * a(a(w,v5,v6),v7,v8))) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(370,a,24013,a,b,35511,a),flip(a)].">
      <j1 rule="hyper" parents="370 24013 35511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35516">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) * v6) = L(x,y,a(u,w,v5) * (z * v6))
    ]]></literal>
    <justification jstring="[para(28757(a,1),35511(a,1,3))].">
      <j1 rule="para" parents="28757 35511"/>
    </justification>
  </clause>

  <clause id="35517">
    <literal><![CDATA[
      L(x,a(a(y,z,u),w,v5) * v6,v7) = L(x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35462,a,b,35513,a)].">
      <j1 rule="hyper" parents="60 35462 35513"/>
    </justification>
  </clause>

  <clause id="35520">
    <literal><![CDATA[
      L(x,(a(y,z,u) * w) * v5,v6) = L(x,a(y,z,u) * (w * v5),v6)
    ]]></literal>
    <justification jstring="[para(19665(a,1),35517(a,1,2))].">
      <j1 rule="para" parents="19665 35517"/>
    </justification>
  </clause>

  <clause id="35521">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)) * v6,v7) = L(x,v6,v7)
    ]]></literal>
    <justification jstring="[para(31123(a,1),35517(a,1,2,1))].">
      <j1 rule="para" parents="31123 35517"/>
    </justification>
  </clause>

  <clause id="35522">
    <literal><![CDATA[
      L(x,y * a(z,u,a(w,v5,v6)),v7) = L(x,y,v7)
    ]]></literal>
    <justification jstring="[para(31127(a,1),35517(a,1,2))].">
      <j1 rule="para" parents="31127 35517"/>
    </justification>
  </clause>

  <clause id="35523">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v6) = v7
    ]]></literal>
    <justification jstring="[para(35517(a,1),32665(a,1))].">
      <j1 rule="para" parents="35517 32665"/>
    </justification>
  </clause>

  <clause id="35524">
    <literal><![CDATA[
      L(x,(y * z) * a(u,w,v5),v6) = L(x,y * (z * a(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(19665(a,1),35521(a,1,2))].">
      <j1 rule="para" parents="19665 35521"/>
    </justification>
  </clause>

  <clause id="35525">
    <literal><![CDATA[
      L(x,y * (a(z,u,a(w,v5,v6)) * v7),v8) = L(x,y * v7,v8)
    ]]></literal>
    <justification jstring="[para(35309(a,1),35521(a,1,2))].">
      <j1 rule="para" parents="35309 35521"/>
    </justification>
  </clause>

  <clause id="35526">
    <literal><![CDATA[
      L(x,y \ (z * a(u,w,v5)),v6) = L(x,(y \ z) * a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(28739(a,1),35522(a,1,2))].">
      <j1 rule="para" parents="28739 35522"/>
    </justification>
  </clause>

  <clause id="35528">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,(a(z,u,w) \ y) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(656(a,1),35523(a,1,2))].">
      <j1 rule="para" parents="656 35523"/>
    </justification>
  </clause>

  <clause id="35529">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(32631(a,1),35523(a,1,2))].">
      <j1 rule="para" parents="32631 35523"/>
    </justification>
  </clause>

  <clause id="35530">
    <literal><![CDATA[
      (x * L(y,z,a(u,w,v5))) \ (x * (y * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(v6 * a(a(u,w,v5),z,y),y,x) = v7
    ]]></literal>
    <justification jstring="[para(35448(a,1),35523(a,1))].">
      <j1 rule="para" parents="35448 35523"/>
    </justification>
  </clause>

  <clause id="35531">
    <literal><![CDATA[
      L(x,y,z * L(a(u,w,v5),v6,v7)) = L(x,y,a(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(31122(a,1),35515(a,1,3,2))].">
      <j1 rule="para" parents="31122 35515"/>
    </justification>
  </clause>

  <clause id="35532">
    <literal><![CDATA[
      L(x,y * ((z * a(u,w,v5)) * R(v6,z,a(u,w,v5))),v7) = L(x,y * ((z * a(u,w,v5)) * v6),v7)
    ]]></literal>
    <justification jstring="[para(24115(a,1),35525(a,1,2,2))].">
      <j1 rule="para" parents="24115 35525"/>
    </justification>
  </clause>

  <clause id="35533">
    <literal><![CDATA[
      L(x,y,z * a(u,w,L(v5,v6,v7))) = L(x,y,a(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(32313(a,2),35531(a,1,3,2))].">
      <j1 rule="para" parents="32313 35531"/>
    </justification>
  </clause>

  <clause id="35534">
    <literal><![CDATA[
      L(x,y * ((z * a(u,w,v5)) * T(a(u,w,v5),z)),v6) = L(x,(y * (a(u,w,v5) * z)) * a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1173(a,2),35524(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1173 35524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35535">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) * v5),v6) = L(x,(y \ v5) * a(z,u,w),v6)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35526(a,1,2,2))].">
      <j1 rule="para" parents="23620 35526"/>
    </justification>
  </clause>

  <clause id="35536">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6) * v7) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v7) = v8
    ]]></literal>
    <justification jstring="[para(31134(a,1),35512(a,1,3))].">
      <j1 rule="para" parents="31134 35512"/>
    </justification>
  </clause>

  <clause id="35537">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v6)) * v7) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v7) = v8
    ]]></literal>
    <justification jstring="[para(32313(a,2),35536(a,1,3,1))].">
      <j1 rule="para" parents="32313 35536"/>
    </justification>
  </clause>

  <clause id="35539">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6) * v7) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z) * v7) = v8
    ]]></literal>
    <justification jstring="[para(32295(a,2),35537(a,1))].">
      <j1 rule="para" parents="32295 35537"/>
    </justification>
  </clause>

  <clause id="35540">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ w) \ v5,v6) = L(x,(w \ v5) * a(y,z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(35528,a,35535,a)].">
      <j1 rule="hyper" parents="35528 35535"/>
    </justification>
  </clause>

  <clause id="35541">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(v5,v6,w)) = L(x,y,w * L(L(w,v6,v5),u,z))
    ]]></literal>
    <justification jstring="[hyper(35539,a,35445,a)].">
      <j1 rule="hyper" parents="35539 35445"/>
    </justification>
  </clause>

  <clause id="35542">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,a(v8,v7,z) * a(v6,v5,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(35537,a,35541,a),flip(a)].">
      <j1 rule="hyper" parents="35537 35541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35543">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(x,a(y,z,u),L(w,x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(35530,a,29489,a)].">
      <j1 rule="hyper" parents="35530 29489"/>
    </justification>
  </clause>

  <clause id="35544">
    <literal><![CDATA[
      (x * a(a(y,z,u),x,w)) \ L(x,a(y,z,u),L(w,x,a(y,z,u))) = a(x * a(a(y,z,u),x,w),w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(125,a,35543,a(flip),b,32077,a)].">
      <j1 rule="hyper" parents="125 35543 32077"/>
    </justification>
  </clause>

  <clause id="35545">
    <literal><![CDATA[
      L(x,y * ((z * a(u,w,v5)) * L(v6,z,a(u,w,v5))),v7) = L(x,y * ((z * a(u,w,v5)) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,27786,a(flip),b,35532,a)].">
      <j1 rule="hyper" parents="60 27786 35532"/>
    </justification>
  </clause>

  <clause id="35546">
    <literal><![CDATA[
      L(x,y * ((z * a(u,w,v5)) * v6),v7) = L(x,y * (a(u,w,v5) * (z * v6)),v7)
    ]]></literal>
    <justification jstring="[para(23651(a,1),35545(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23651 35545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35547">
    <literal><![CDATA[
      L(x,(a(y,z,u) * w) * (a(y,z,u) * (w * v5)),v6) = L(x,L(v5,a(y,z,u) * w,a(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[hyper(25293,a,35546,a),flip(a)].">
      <j1 rule="hyper" parents="25293 35546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35548">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,a(v6,v5,z) * a(v8,v7,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,35533,a(flip),b,35542,a),flip(a)].">
      <j1 rule="hyper" parents="370 35533 35542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35550">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,z * L(L(z,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(370,a,35541,a(flip),b,35548,a),flip(a)].">
      <j1 rule="hyper" parents="370 35541 35548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35551">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,a(v6,v5,z) * (v8 \ R(v8,v7,z)))
    ]]></literal>
    <justification jstring="[para(32595(a,1),35548(a,2,3,2))].">
      <j1 rule="para" parents="32595 35548"/>
    </justification>
  </clause>

  <clause id="35552">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,a(v6,v5,z) * (v8 \ L(v8,v7,z)))
    ]]></literal>
    <justification jstring="[hyper(370,a,27298,a(flip),b,35551,a),flip(a)].">
      <j1 rule="hyper" parents="370 27298 35551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35553">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(L(z,u,w),v5,v6),v7,v8)) = L(x,y,a(z,v7,v8) * a(v6,v5,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,32294,a(flip),b,35552,a),flip(a)].">
      <j1 rule="hyper" parents="370 32294 35552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35554">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(v5,v6,z)) = L(x,y,z * L(L(z,u,w),v6,v5))
    ]]></literal>
    <justification jstring="[hyper(60,a,35550,a(flip),b,35553,a),flip(a)].">
      <j1 rule="hyper" parents="60 35550 35553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35555">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(w,v5,v6)) = L(x,y,w * L(L(w,v5,v6),u,z))
    ]]></literal>
    <justification jstring="[hyper(24037,a,35554,a)].">
      <j1 rule="hyper" parents="24037 35554"/>
    </justification>
  </clause>

  <clause id="35556">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(w,v5,v6)) = L(x,y,w * L(L(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,1),35555(a,2,3,2))].">
      <j1 rule="para" parents="25 35555"/>
    </justification>
  </clause>

  <clause id="35557">
    <literal><![CDATA[
      L(x,y * ((z * a(u,w,v5)) * T(a(u,w,v5),z)),v6) = L(x,a(u,w,v5) * (y * (a(u,w,v5) * z)),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26023,a,b,35534,a),flip(a)].">
      <j1 rule="hyper" parents="370 26023 35534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35558">
    <literal><![CDATA[
      L(x,a(y,z,u) * (w * (a(y,z,u) * v5)),v6) = L(x,w * (a(y,z,u) * (a(y,z,u) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(25790(a,1),35557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="25790 35557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35559">
    <literal><![CDATA[
      L(x,a(y,z,u) * (w * (a(y,z,u) * v5)),v6) = L(x,w * L(v5,a(y,z,u),a(y,z,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,3771,a(flip),b,35558,a),flip(a)].">
      <j1 rule="hyper" parents="370 3771 35558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35561">
    <literal><![CDATA[
      L(x,a(y,z,u) * (w * (a(y,z,u) * v5)),v6) = L(x,w * v5,v6)
    ]]></literal>
    <justification jstring="[para(30617(a,1),35559(a,2,2,2))].">
      <j1 rule="para" parents="30617 35559"/>
    </justification>
  </clause>

  <clause id="35562">
    <literal><![CDATA[
      L(x,a(y,z,u) * (w * (a(y,z,u) * (w * v5))),v6) = L(x,L(v5,a(y,z,u) * w,a(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,35520,a(flip),b,35547,a)].">
      <j1 rule="hyper" parents="60 35520 35547"/>
    </justification>
  </clause>

  <clause id="35563">
    <literal><![CDATA[
      L(x,L(y,a(z,u,w) * v5,a(z,u,w) * v5),v6) = L(x,v5 * (v5 * y),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,35561,a(flip),b,35562,a),flip(a)].">
      <j1 rule="hyper" parents="60 35561 35562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35565">
    <literal><![CDATA[
      L(x,L(y,a(z,u,w) * v5,a(z,u,w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,v5,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(35563(a,2),3544(a,1))].">
      <j1 rule="para" parents="35563 3544"/>
    </justification>
  </clause>

  <clause id="35566">
    <literal><![CDATA[
      L(x,L((a(y,z,u) \ w) * v5,w,w),v6) = L(x,(a(y,z,u) * w) \ (a(y,z,u) \ (a(y,z,u) \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(35565,a,30884,a)].">
      <j1 rule="hyper" parents="35565 30884"/>
    </justification>
  </clause>

  <clause id="35567">
    <literal><![CDATA[
      L(x,L((a(y,z,u) \ w) * v5,w,w),v6) = L(x,(a(y,z,u) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35565,a,29612,a)].">
      <j1 rule="hyper" parents="35565 29612"/>
    </justification>
  </clause>

  <clause id="35568">
    <literal><![CDATA[
      L(x,L((a(y,z,u) \ w) * v5,w,w),v6) = L(x,(w \ v5) * a(y,z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35540,a(flip),b,35567,a),flip(a)].">
      <j1 rule="hyper" parents="370 35540 35567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35569">
    <literal><![CDATA[
      L(x,(a(y,z,u) * w) \ (a(y,z,u) \ (a(y,z,u) \ v5)),v6) = L(x,(w \ v5) * a(y,z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,35568,a(flip),b,35566,a),flip(a)].">
      <j1 rule="hyper" parents="60 35568 35566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35570">
    <literal><![CDATA[
      L(x,(a(y,z,u) * w) \ v5,v6) = L(x,(w \ v5) * a(y,z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,35377,a(flip),b,35569,a)].">
      <j1 rule="hyper" parents="60 35377 35569"/>
    </justification>
  </clause>

  <clause id="35572">
    <literal><![CDATA[
      L(x,(y * a(z,u,w)) \ v5,v6) = L(x,(y \ v5) * a(z,u,w),v6)
    ]]></literal>
    <justification jstring="[para(23620(a,1),35570(a,1,2,1))].">
      <j1 rule="para" parents="23620 35570"/>
    </justification>
  </clause>

  <clause id="35573">
    <literal><![CDATA[
      L(x,L(y,z,L(u,y,z)) \ w,v5) = L(x,(y \ w) * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,32396,a,b,35572,a)].">
      <j1 rule="hyper" parents="60 32396 35572"/>
    </justification>
  </clause>

  <clause id="35574">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ u) \ w,v5) = L(x,(u \ w) * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(31558(a,1),35573(a,1,2,1))].">
      <j1 rule="para" parents="31558 35573"/>
    </justification>
  </clause>

  <clause id="35575">
    <literal><![CDATA[
      L(x,(y \ z) * a(y,u,w),v5) = L(x,L(y,u,w) \ z,v5)
    ]]></literal>
    <justification jstring="[para(32569(a,2),35574(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="32569 35574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35576">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (y * w),v5) = L(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(4(a,1),35575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 35575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35579">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ w),v5) = L(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(2160(a,1),35576(a,1,2))].">
      <j1 rule="para" parents="2160 35576"/>
    </justification>
  </clause>

  <clause id="35580">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,v5) = L(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(35529,a,35579,a)].">
      <j1 rule="hyper" parents="35529 35579"/>
    </justification>
  </clause>

  <clause id="35581">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(v5,v6,v7)) = L(x,w * a(u,z,y),a(v7,v6,v5))
    ]]></literal>
    <justification jstring="[hyper(30727,a,35580,a)].">
      <j1 rule="hyper" parents="30727 35580"/>
    </justification>
  </clause>

  <clause id="35582">
    <literal><![CDATA[
      (x * a(a(y,z,u),x,w)) \ L(x,a(y,z,u),w) = a(x * a(a(y,z,u),x,w),w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(35313(a,1),35544(a,1,2))].">
      <j1 rule="para" parents="35313 35544"/>
    </justification>
  </clause>

  <clause id="35583">
    <literal><![CDATA[
      (x \ L(x,a(y,z,u),w)) * a(w,x,a(y,z,u)) = a(x * a(a(y,z,u),x,w),w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35430,a,35582,a)].">
      <j1 rule="hyper" parents="35430 35582"/>
    </justification>
  </clause>

  <clause id="35585">
    <literal><![CDATA[
      a(x * a(a(y,z,u),x,w),w,a(y,z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (x \ a(w,x,a(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(35583(a,1),35403(a,1))].">
      <j1 rule="para" parents="35583 35403"/>
    </justification>
  </clause>

  <clause id="35586">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (x \ a(w,x,a(y,z,u))) = a(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35585,a,35466,a)].">
      <j1 rule="hyper" parents="35585 35466"/>
    </justification>
  </clause>

  <clause id="35587">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(u,w,a(x,y,z)) = u \ L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(35586(a,1),35405(a,1,2))].">
      <j1 rule="para" parents="35586 35405"/>
    </justification>
  </clause>

  <clause id="35588">
    <literal><![CDATA[
      L(x,y \ L(y,a(z,u,w),v5),v6) = L(x,a(a(z,u,w),y,v5),v6)
    ]]></literal>
    <justification jstring="[para(35587(a,1),35522(a,1,2))].">
      <j1 rule="para" parents="35587 35522"/>
    </justification>
  </clause>

  <clause id="35589">
    <literal><![CDATA[
      L(x,y \ L(y,a(z,u,w),v5),v6) = x
    ]]></literal>
    <justification jstring="[hyper(370,a,35409,a(flip),b,35588,a),flip(a)].">
      <j1 rule="hyper" parents="370 35409 35588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35591">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w),v5),v6) = x
    ]]></literal>
    <justification jstring="[para(31257(a,1),35589(a,1,2))].">
      <j1 rule="para" parents="31257 35589"/>
    </justification>
  </clause>

  <clause id="35592">
    <literal><![CDATA[
      (x * a(y,a(z,u,w),v5)) * v6 = x * (a(y,a(z,u,w),v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(1838,a,35591,a),flip(a)].">
      <j1 rule="hyper" parents="1838 35591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35593">
    <literal><![CDATA[
      (x * a(y,a(z,u,w),v5)) \ v6 = a(y,a(z,u,w),v5) \ (x \ v6)
    ]]></literal>
    <justification jstring="[hyper(747,a,35591,a),flip(a)].">
      <j1 rule="hyper" parents="747 35591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35594">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) \ v5) * v6 = v5 * (a(x,a(y,z,u),w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(129,a,35591,a(flip),b,30737,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="129 35591 30737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35595">
    <literal><![CDATA[
      ((a(x,a(y,z,u),w) \ v5) * (v6 * v7)) \ ((v5 * ((a(x,a(y,z,u),w) \ 1) * v6)) * v7) = a(v5 * (a(x,a(y,z,u),w) \ 1),L(v6,a(x,a(y,z,u),w) \ 1,v5),v7)
    ]]></literal>
    <justification jstring="[para(35591(a,1),31932(a,1,1,2,1))].">
      <j1 rule="para" parents="35591 31932"/>
    </justification>
  </clause>

  <clause id="35596">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) * v7))) \ ((x * (y * a(z,a(u,w,v5),v6))) * v7) = a(x,y * a(z,a(u,w,v5),v6),v7)
    ]]></literal>
    <justification jstring="[para(35592(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="35592 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35597">
    <literal><![CDATA[
      (x * (y * a(z,a(u,w,v5),v6))) * v7 = (x * y) * (a(z,a(u,w,v5),v6) * v7)
    ]]></literal>
    <justification jstring="[para(35264(a,1),35592(a,1,1))].">
      <j1 rule="para" parents="35264 35592"/>
    </justification>
  </clause>

  <clause id="35598">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ (x \ v5) = L(x,a(y,z,u),w) \ v5
    ]]></literal>
    <justification jstring="[para(31255(a,1),35593(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31255 35593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35599">
    <literal><![CDATA[
      (x * (y * a(z,a(u,w,v5),v6))) \ v7 = a(z,a(u,w,v5),v6) \ ((x * y) \ v7)
    ]]></literal>
    <justification jstring="[para(35264(a,1),35593(a,1,1))].">
      <j1 rule="para" parents="35264 35593"/>
    </justification>
  </clause>

  <clause id="35600">
    <literal><![CDATA[
      (x \ y) * a(z,a(u,w,v5),x) = L(x,a(u,w,v5),z) \ y
    ]]></literal>
    <justification jstring="[hyper(30725,a,35598,a)].">
      <j1 rule="hyper" parents="30725 35598"/>
    </justification>
  </clause>

  <clause id="35601">
    <literal><![CDATA[
      (x * (a(y,a(z,u,w),v5) \ v6)) * v7 = (x * v6) * (a(y,a(z,u,w),v5) \ v7)
    ]]></literal>
    <justification jstring="[para(35375(a,1),35594(a,1,1))].">
      <j1 rule="para" parents="35375 35594"/>
    </justification>
  </clause>

  <clause id="35602">
    <literal><![CDATA[
      (x * (K(y,z) * ((z * y) * a(u,a(w,v5,v6),v7)))) \ v8 = a(u,a(w,v5,v6),v7) \ ((x * (y * z)) \ v8)
    ]]></literal>
    <justification jstring="[para(12466(a,2),35599(a,1,1,2))].">
      <j1 rule="para" parents="12466 35599"/>
    </justification>
  </clause>

  <clause id="35603">
    <literal><![CDATA[
      (x * (K(y,z) * (z * (y * a(u,a(w,v5,v6),v7))))) \ v8 = a(u,a(w,v5,v6),v7) \ ((x * (y * z)) \ v8)
    ]]></literal>
    <justification jstring="[para(35264(a,1),35602(a,1,1,2,2))].">
      <j1 rule="para" parents="35264 35602"/>
    </justification>
  </clause>

  <clause id="35604">
    <literal><![CDATA[
      (x * (y * (K(z,y) * (z * a(u,a(w,v5,v6),v7))))) \ v8 = a(u,a(w,v5,v6),v7) \ ((x * (z * y)) \ v8)
    ]]></literal>
    <justification jstring="[para(7967(a,1),35603(a,1,1,2))].">
      <j1 rule="para" parents="7967 35603"/>
    </justification>
  </clause>

  <clause id="35605">
    <literal><![CDATA[
      (x * (y * (T(z,y) * a(u,a(w,v5,v6),v7)))) \ v8 = a(u,a(w,v5,v6),v7) \ ((x * (z * y)) \ v8)
    ]]></literal>
    <justification jstring="[para(7864(a,1),35604(a,1,1,2,2))].">
      <j1 rule="para" parents="7864 35604"/>
    </justification>
  </clause>

  <clause id="35606">
    <literal><![CDATA[
      (x * ((y * a(z,a(u,w,v5),v6)) * v7)) \ v8 = a(z,a(u,w,v5),v6) \ ((x * (y * v7)) \ v8)
    ]]></literal>
    <justification jstring="[para(28227(a,1),35605(a,1,1,2))].">
      <j1 rule="para" parents="28227 35605"/>
    </justification>
  </clause>

  <clause id="35607">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) * v7))) \ v8 = a(z,a(u,w,v5),v6) \ ((x * (y * v7)) \ v8)
    ]]></literal>
    <justification jstring="[para(35592(a,1),35606(a,1,1,2))].">
      <j1 rule="para" parents="35592 35606"/>
    </justification>
  </clause>

  <clause id="35608">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) * v7))) \ ((x * y) * (a(z,a(u,w,v5),v6) * v7)) = a(x,y * a(z,a(u,w,v5),v6),v7)
    ]]></literal>
    <justification jstring="[para(35597(a,1),35596(a,1,2))].">
      <j1 rule="para" parents="35597 35596"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      ((x * (y * (a(z,a(u,w,v5),v6) * v7))) \ ((x * y) * v7)) * a(z,a(u,w,v5),v6) = a(x,y * a(z,a(u,w,v5),v6),v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35434,a(flip),b,35608,a)].">
      <j1 rule="hyper" parents="60 35434 35608"/>
    </justification>
  </clause>

  <clause id="35610">
    <literal><![CDATA[
      a(x,y * a(z,a(u,w,v5),v6),v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6) * v7) = v8
    ]]></literal>
    <justification jstring="[para(35608(a,1),1029(a,1))].">
      <j1 rule="para" parents="35608 1029"/>
    </justification>
  </clause>

  <clause id="35611">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) \ ((v5 * (v6 * v7)) \ ((v5 * v6) * v7))) * a(x,a(y,z,u),w) = a(v5,v6 * a(x,a(y,z,u),w),v7)
    ]]></literal>
    <justification jstring="[para(35607(a,1),35609(a,1,1))].">
      <j1 rule="para" parents="35607 35609"/>
    </justification>
  </clause>

  <clause id="35612">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) \ a(v5,v6,v7)) * a(x,a(y,z,u),w) = a(v5,v6 * a(x,a(y,z,u),w),v7)
    ]]></literal>
    <justification jstring="[para(9(a,2),35611(a,1,1,2))].">
      <j1 rule="para" parents="9 35611"/>
    </justification>
  </clause>

  <clause id="35613">
    <literal><![CDATA[
      a(x,y * a(z,a(u,w,v5),v6),v7) = a(x,y,v7)
    ]]></literal>
    <justification jstring="[hyper(24096,a,35612,a),flip(a)].">
      <j1 rule="hyper" parents="24096 35612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35614">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6) * v7) = a(x,y,v7)
    ]]></literal>
    <justification jstring="[hyper(35610,a,35613,a)].">
      <j1 rule="hyper" parents="35610 35613"/>
    </justification>
  </clause>

  <clause id="35616">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) * L(x \ a(u,x,a(y,z,w)),u,a(y,z,w)) = (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[para(34548(a,1),35427(a,1,2,1))].">
      <j1 rule="para" parents="34548 35427"/>
    </justification>
  </clause>

  <clause id="35617">
    <literal><![CDATA[
      x * (a(y,z,a(u,x,w)) * L(x \ a(u,x,a(y,z,w)),u,a(y,z,w))) = (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[hyper(35417,a,35616,a)].">
      <j1 rule="hyper" parents="35417 35616"/>
    </justification>
  </clause>

  <clause id="35618">
    <literal><![CDATA[
      x * L((x \ a(y,x,a(z,u,w))) * a(z,u,a(y,x,w)),y,a(z,u,w)) = (x * a(z,u,a(y,x,w))) \ L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(35439(a,2),35617(a,1,2))].">
      <j1 rule="para" parents="35439 35617"/>
    </justification>
  </clause>

  <clause id="35619">
    <literal><![CDATA[
      a((a(x,y,z) * (a(u,w,v5) \ (v6 * v7))) * ((a(x,y,z) * (a(u,w,v5) \ v6)) * v7),v8,v9) = a(a(a(u,w,v5) \ a(x,y,z),v6,v7),v8,v9)
    ]]></literal>
    <justification jstring="[para(35289(a,1),35378(a,1,1,2,1))].">
      <j1 rule="para" parents="35289 35378"/>
    </justification>
  </clause>

  <clause id="35620">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * ((v5 * v6) * (v7 * v8))) \ ((a(x,y,a(z,u,w)) * ((v5 * v6) * v7)) * v8) = a(v5 * (a(x,y,a(z,u,w)) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(35386(a,1),35432(a,1,2,1))].">
      <j1 rule="para" parents="35386 35432"/>
    </justification>
  </clause>

  <clause id="35621">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * ((v5 * v6) * (v7 * v8))) \ (a(x,y,a(z,u,w)) * (((v5 * v6) * v7) * v8)) = a(v5 * (a(x,y,a(z,u,w)) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(35300(a,1),35620(a,1,2))].">
      <j1 rule="para" parents="35300 35620"/>
    </justification>
  </clause>

  <clause id="35622">
    <literal><![CDATA[
      ((a(x,y,a(z,u,w)) * ((v5 * v6) * (v7 * v8))) \ (((v5 * v6) * v7) * v8)) * a(x,y,a(z,u,w)) = a(v5 * (a(x,y,a(z,u,w)) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(35407,a,35621,a)].">
      <j1 rule="hyper" parents="35407 35621"/>
    </justification>
  </clause>

  <clause id="35623">
    <literal><![CDATA[
      (((x * y) * (z * u)) \ (a(w,v5,a(v6,v7,v8)) \ (((x * y) * z) * u))) * a(w,v5,a(v6,v7,v8)) = a(x * (a(w,v5,a(v6,v7,v8)) * y),z,u)
    ]]></literal>
    <justification jstring="[para(35301(a,1),35622(a,1,1))].">
      <j1 rule="para" parents="35301 35622"/>
    </justification>
  </clause>

  <clause id="35624">
    <literal><![CDATA[
      a(x * (a(y,z,a(u,w,v5)) * v6),v7,v8) = ((x * v6) * (v7 * v8)) \ (((x * v6) * v7) * v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,35397,a(flip),b,35623,a),flip(a)].">
      <j1 rule="hyper" parents="60 35397 35623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35626">
    <literal><![CDATA[
      a(x * (a(y,z,a(u,w,v5)) * v6),v7,v8) = a(x * v6,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,9,a,b,35624,a),flip(a)].">
      <j1 rule="hyper" parents="370 9 35624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35627">
    <literal><![CDATA[
      a(x * (a(y,z,a(u,w,v5)) * v6),v7,v8) != v9
    ]]></literal>
    <literal><![CDATA[
      a(x * v6,v7,v8) = v9
    ]]></literal>
    <justification jstring="[para(35624(a,2),1029(a,1))].">
      <j1 rule="para" parents="35624 1029"/>
    </justification>
  </clause>

  <clause id="35628">
    <literal><![CDATA[
      a(x * ((y * z) * a(u,w,v5)),v6,v7) = a(x * (y * (z * a(u,w,v5))),v6,v7)
    ]]></literal>
    <justification jstring="[para(19665(a,1),35626(a,1,1,2))].">
      <j1 rule="para" parents="19665 35626"/>
    </justification>
  </clause>

  <clause id="35629">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(v5,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(35626(a,1),30786(a,1))].">
      <j1 rule="para" parents="35626 30786"/>
    </justification>
  </clause>

  <clause id="35630">
    <literal><![CDATA[
      a(x * R(y,z,a(u,w,v5)),v6,v7) = a(x * y,v6,v7)
    ]]></literal>
    <justification jstring="[para(32091(a,1),35626(a,1,1,2))].">
      <j1 rule="para" parents="32091 35626"/>
    </justification>
  </clause>

  <clause id="35631">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)) * v5,v6,v7) = a(a(x,y,z) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(32349(a,1),35626(a,1,1))].">
      <j1 rule="para" parents="32349 35626"/>
    </justification>
  </clause>

  <clause id="35632">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) * v5,v6,v7) = a(v5 * x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26519,a,35630,a)].">
      <j1 rule="hyper" parents="26519 35630"/>
    </justification>
  </clause>

  <clause id="35633">
    <literal><![CDATA[
      a((x * y) * a(z,u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * (y * a(z,u,w)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(19665(a,1),35629(a,1,1))].">
      <j1 rule="para" parents="19665 35629"/>
    </justification>
  </clause>

  <clause id="35634">
    <literal><![CDATA[
      a(a(x,y,z * a(u,w,z)) * v5,v6,v7) = a(a(x,y,z) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(32591(a,1),35631(a,1,1,1,3)),flip(a)].">
      <j1 rule="para" parents="32591 35631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35636">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)) * v5,v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(a(x,y,z) * v5,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(32349(a,1),35627(a,1,1))].">
      <j1 rule="para" parents="32349 35627"/>
    </justification>
  </clause>

  <clause id="35637">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w) * w) * v5,v6,v7) = a(a(x,y,w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35634(a,1,1,1,3))].">
      <j1 rule="para" parents="23620 35634"/>
    </justification>
  </clause>

  <clause id="35638">
    <literal><![CDATA[
      a(x * a(y,z,L(u,w,v5)),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(a(y,z,u) * x,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(23620(a,1),35636(a,1,1))].">
      <j1 rule="para" parents="23620 35636"/>
    </justification>
  </clause>

  <clause id="35639">
    <literal><![CDATA[
      a(x * (L(y,z,u) * L(L(y,z,u),w,v5)),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(a(v5,w,y) * x,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(32302(a,2),35636(a,1))].">
      <j1 rule="para" parents="32302 35636"/>
    </justification>
  </clause>

  <clause id="35640">
    <literal><![CDATA[
      a(x * (y * a(z,u,w)),v5,v6) = a(y * (x * a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35633,a,35498,a)].">
      <j1 rule="hyper" parents="35633 35498"/>
    </justification>
  </clause>

  <clause id="35641">
    <literal><![CDATA[
      a(a(x,y,z) * (u * w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(u * (w * a(x,y,z)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(23620(a,2),35633(a,1,1))].">
      <j1 rule="para" parents="23620 35633"/>
    </justification>
  </clause>

  <clause id="35643">
    <literal><![CDATA[
      a(R(x,x,a(y,z,u)) * (w * a(y,z,u)),v5,v6) = a(w * ((1 / x) \ a(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(1961(a,1),35640(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 35640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35646">
    <literal><![CDATA[
      a(x * ((y * z) * a(u,w,v5)),v6,L(v7,x,(z * a(u,w,v5)) * y)) = a(x \ ((z * a(u,w,v5)) * y),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,32437,a(flip),b,35628,a),flip(a)].">
      <j1 rule="hyper" parents="370 32437 35628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35647">
    <literal><![CDATA[
      a(x * (a(y,z,u) * (w * v5)),v6,v7) = a(x * (v5 * (w * a(y,z,u))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,26743,a(flip),b,35628,a)].">
      <j1 rule="hyper" parents="60 26743 35628"/>
    </justification>
  </clause>

  <clause id="35648">
    <literal><![CDATA[
      a(x * (y * (T(z,u) * a(w,v5,v6))),v7,v8) = a(x * ((z * y) * a(w,v5,v6)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(26870,a,35647,a),flip(a)].">
      <j1 rule="hyper" parents="26870 35647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35649">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * w) * v5),v6,v7) = a(v5 * (w * (u * a(x,y,z))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35483,a,b,35647,a)].">
      <j1 rule="hyper" parents="60 35483 35647"/>
    </justification>
  </clause>

  <clause id="35650">
    <literal><![CDATA[
      a(a(x,y,z) * (u * (w * v5)),v6,v7) = a(u * (w * (v5 * a(x,y,z))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,26743,a(flip),b,35649,a)].">
      <j1 rule="hyper" parents="60 26743 35649"/>
    </justification>
  </clause>

  <clause id="35651">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * w) * v5),v6,v7) = a(v5 * (u * (w * a(x,y,z))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26548,a,35650,a)].">
      <j1 rule="hyper" parents="26548 35650"/>
    </justification>
  </clause>

  <clause id="35652">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * a(x,y,z)) * w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w * u,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(35651(a,2),2991(a,1))].">
      <j1 rule="para" parents="35651 2991"/>
    </justification>
  </clause>

  <clause id="35653">
    <literal><![CDATA[
      a(x * (y * (z * (L(u,w,v5) \ u))),v6,v7) = a(a(v5,w,u) * ((y * z) * x),v6,v7)
    ]]></literal>
    <justification jstring="[para(32572(a,1),35651(a,2,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="32572 35651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35654">
    <literal><![CDATA[
      a(x * (y * a(z,u,x)),w,v5) = a(L(x,u,z) * y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(35652,a,35488,a),flip(a)].">
      <j1 rule="hyper" parents="35652 35488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35655">
    <literal><![CDATA[
      a(x * (T(y,z) * a(u,w,x)),v5,v6) = a(y * L(x,w,u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26498,a(flip),b,35654,a),flip(a)].">
      <j1 rule="hyper" parents="370 26498 35654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35656">
    <literal><![CDATA[
      a((x \ a(y,z,x)) * ((u * u) * (w * a(v5,v6,a(y,z,x) * (x \ (u * u))))),v7,v8) = a(L(a(y,z,x) * (x \ (u * u)),v6,v5) * w,v7,v8)
    ]]></literal>
    <justification jstring="[para(25211(a,1),35654(a,1,1))].">
      <j1 rule="para" parents="25211 35654"/>
    </justification>
  </clause>

  <clause id="35657">
    <literal><![CDATA[
      a((x * R(y,z,u)) * a(w,v5,L(y,z,u)),v6,v7) = a(x * L(R(y,z,u),v5,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(27856(a,1),35655(a,1,1))].">
      <j1 rule="para" parents="27856 35655"/>
    </justification>
  </clause>

  <clause id="35658">
    <literal><![CDATA[
      a(x * (y * (T(z,u) * a(w,v5,v6))),v7,v8) = a(x * (z * (y * a(w,v5,v6))),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35628,a(flip),b,35648,a),flip(a)].">
      <j1 rule="hyper" parents="370 35628 35648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35659">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * z) * w),v5,v6) = a(w * (u * L(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,27909,a(flip),b,35653,a),flip(a)].">
      <j1 rule="hyper" parents="60 27909 35653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35660">
    <literal><![CDATA[
      a(a(x,y,z) * (u * (z * a(w,v5,v6))),v7,v8) = a(a(w,v5,v6) * (u * L(z,y,x)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,35628,a(flip),b,35659,a)].">
      <j1 rule="hyper" parents="60 35628 35659"/>
    </justification>
  </clause>

  <clause id="35662">
    <literal><![CDATA[
      a(x * ((y * a(z,u,w)) * v5),v6,v7) = a(x * (y * (v5 * a(z,u,w))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26870,a,35658,a)].">
      <j1 rule="hyper" parents="26870 35658"/>
    </justification>
  </clause>

  <clause id="35663">
    <literal><![CDATA[
      a(x * ((a(y,z,u) * w) * v5),v6,v7) = a(x * (w * (v5 * a(y,z,u))),v6,v7)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35662(a,1,1,2,1))].">
      <j1 rule="para" parents="23620 35662"/>
    </justification>
  </clause>

  <clause id="35664">
    <literal><![CDATA[
      a(x * ((y * a(z,u,w)) * v5),v6,v7) = a(x * (y * (a(z,u,w) * v5)),v6,v7)
    ]]></literal>
    <justification jstring="[para(23620(a,2),35662(a,2,1,2,2))].">
      <j1 rule="para" parents="23620 35662"/>
    </justification>
  </clause>

  <clause id="35665">
    <literal><![CDATA[
      a((a(x,y,z) * (a(u,w,v5) \ (v6 * v7))) * ((a(u,w,v5) \ v6) * (v7 * a(x,y,z))),v8,v9) = a(a(a(u,w,v5) \ a(x,y,z),v6,v7),v8,v9)
    ]]></literal>
    <justification jstring="[hyper(60,a,35619,a(flip),b,35663,a),flip(a)].">
      <j1 rule="hyper" parents="60 35619 35663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35666">
    <literal><![CDATA[
      a(a(x,y,z) * (u * (a(x,y,z) * w)),v5,v6) = a(w * u,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35652,a,35664,a),flip(a)].">
      <j1 rule="hyper" parents="35652 35664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35667">
    <literal><![CDATA[
      a((a(x,y,z) * u) * (w * (v5 * a(x,y,z))),v6,v7) = a(u * (w * v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35651,a(flip),b,35666,a)].">
      <j1 rule="hyper" parents="60 35651 35666"/>
    </justification>
  </clause>

  <clause id="35668">
    <literal><![CDATA[
      a(a(x,y,z) * a(u,w,z),v5,v6) = a(z * L(L(z,w,u),y,x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35639,a,35487,a)].">
      <j1 rule="hyper" parents="35639 35487"/>
    </justification>
  </clause>

  <clause id="35669">
    <literal><![CDATA[
      a(a(x,y,z) * (u * R(z,w,v5)),v6,v7) = a(u * L(R(z,w,v5),y,x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(35638,a,35657,a)].">
      <j1 rule="hyper" parents="35638 35657"/>
    </justification>
  </clause>

  <clause id="35670">
    <literal><![CDATA[
      a(a(x,y,z) * (u * L(z,w,v5)),v6,v7) = a(u * L(R(z,w,v5),y,x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,27338,a(flip),b,35669,a)].">
      <j1 rule="hyper" parents="60 27338 35669"/>
    </justification>
  </clause>

  <clause id="35671">
    <literal><![CDATA[
      a(a(x,y,z) * (u * L(z,w,v5)),v6,v7) = a(u * L(L(z,w,v5),y,x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,27336,a(flip),b,35670,a),flip(a)].">
      <j1 rule="hyper" parents="370 27336 35670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35672">
    <literal><![CDATA[
      a(x * L(L(y,z,u),z,u),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35488,a(flip),b,35671,a),flip(a)].">
      <j1 rule="hyper" parents="60 35488 35671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35673">
    <literal><![CDATA[
      a(R(x,x,a(y,z,u)) * (w * a(y,z,u)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x \ a(y,z,u)) * w,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(35643(a,2),26745(a,1))].">
      <j1 rule="para" parents="35643 26745"/>
    </justification>
  </clause>

  <clause id="35674">
    <literal><![CDATA[
      a((x \ a(y,z,u)) * w,v5,v6) = a((w * a(y,z,u)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35673,a,35632,a)].">
      <j1 rule="hyper" parents="35673 35632"/>
    </justification>
  </clause>

  <clause id="35675">
    <literal><![CDATA[
      a((x \ a(y,z,u)) * w,v5,v6) = a(a(y,z,u) * (w * x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35485,a(flip),b,35674,a),flip(a)].">
      <j1 rule="hyper" parents="370 35485 35674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35676">
    <literal><![CDATA[
      a(x * ((y * z) * a(u,w,v5)),v6,L(v7,x,a(u,w,v5) * (z * y))) = a(x \ ((z * a(u,w,v5)) * y),v6,v7)
    ]]></literal>
    <justification jstring="[para(35516(a,1),35646(a,1,3))].">
      <j1 rule="para" parents="35516 35646"/>
    </justification>
  </clause>

  <clause id="35677">
    <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(60,a,32436,a(flip),b,35676,a),flip(a)].">
      <j1 rule="hyper" parents="60 32436 35676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35678">
    <literal><![CDATA[
      a(x \ ((y * a(z,u,w)) * v5),v6,v7) = a((x \ (y * v5)) * a(z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,35490,a(flip),b,35677,a),flip(a)].">
      <j1 rule="hyper" parents="370 35490 35677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35679">
    <literal><![CDATA[
      a((((a(x,y,z) * u) * w) \ ((u * v5) * w)) * a(x,y,z),v6,v7) = a(L(v5,u,a(x,y,z)),v6,L(v7,a(x,y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,32501,a(flip),b,35678,a),flip(a)].">
      <j1 rule="hyper" parents="60 32501 35678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35680">
    <literal><![CDATA[
      a(a(a(x,y,z) \ a(u,w,v5),v6,v7),v8,v9) = a((a(x,y,z) \ (v6 * v7)) * ((a(x,y,z) \ v6) * v7),v8,v9)
    ]]></literal>
    <justification jstring="[hyper(60,a,35667,a(flip),b,35665,a),flip(a)].">
      <j1 rule="hyper" parents="60 35667 35665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35682">
    <literal><![CDATA[
      a(a(a(x,y,z) \ a(u,w,v5),v6,v7),v8,v9) = a(((a(x,y,z) \ v6) * v7) * (a(x,y,z) \ (v6 * v7)),v8,v9)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,35680,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 35680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35683">
    <literal><![CDATA[
      a(a(a(x,y,z) \ a(u,w,v5),v6,v7),v8,v9) = a(((a(x,y,z) \ v6) * v7) * ((v6 * v7) * a(x,y,z)),v8,v9)
    ]]></literal>
    <justification jstring="[hyper(370,a,35080,a(flip),b,35682,a),flip(a)].">
      <j1 rule="hyper" parents="370 35080 35682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35684">
    <literal><![CDATA[
      a(a(a(x,y,z) \ a(u,w,v5),v6,v7),v8,v9) = a(((a(x,y,z) \ v6) * v7) * (v6 * (v7 * a(x,y,z))),v8,v9)
    ]]></literal>
    <justification jstring="[hyper(370,a,35628,a(flip),b,35683,a),flip(a)].">
      <j1 rule="hyper" parents="370 35628 35683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35685">
    <literal><![CDATA[
      a((x \ a(y,z,x)) * ((u * u) * (w * a(v5,v6,a(y,z,x) * x))),v7,v8) = a(L(a(y,z,x) * (x \ (u * u)),v6,v5) * w,v7,v8)
    ]]></literal>
    <justification jstring="[para(15774(a,1),35656(a,1,1,2,2,2))].">
      <j1 rule="para" parents="15774 35656"/>
    </justification>
  </clause>

  <clause id="35686">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a((z \ a(x,y,z)) * (v6 * a(v5,w,a(x,y,z) * z)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(26610,a,35685,a),flip(a)].">
      <j1 rule="hyper" parents="26610 35685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35689">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a(a(x,y,z) * ((v6 * a(v5,w,a(x,y,z) * z)) * z),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35675,a(flip),b,35686,a),flip(a)].">
      <j1 rule="hyper" parents="370 35675 35686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a(a(x,y,z) * (v6 * (z * a(v5,w,a(x,y,z) * z))),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35662,a(flip),b,35689,a),flip(a)].">
      <j1 rule="hyper" parents="370 35662 35689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35691">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a(a(v5,w,a(x,y,z) * z) * (v6 * L(z,y,x)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35660,a(flip),b,35690,a),flip(a)].">
      <j1 rule="hyper" parents="370 35660 35690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35692">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a(a(v5,w,z) * (v6 * L(z,y,x)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35637,a(flip),b,35691,a),flip(a)].">
      <j1 rule="hyper" parents="370 35637 35691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35694">
    <literal><![CDATA[
      a(L(a(x,y,z) * (z \ (u * u)),w,v5) * v6,v7,v8) = a(v6 * L(L(z,y,x),w,v5),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,35671,a(flip),b,35692,a),flip(a)].">
      <j1 rule="hyper" parents="370 35671 35692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35695">
    <literal><![CDATA[
      a(L(x \ a(y,z,x),u,w) * ((v5 * v5) * v6),v7,v8) = a(v6 * L(L(x,z,y),u,w),v7,v8)
    ]]></literal>
    <justification jstring="[para(25628(a,1),35694(a,1,1))].">
      <j1 rule="para" parents="25628 35694"/>
    </justification>
  </clause>

  <clause id="35696">
    <literal><![CDATA[
      a(L(x \ a(y,z,x),u,w) * v5,v6,v7) = a(v5 * L(L(x,z,y),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(26610,a,35695,a)].">
      <j1 rule="hyper" parents="26610 35695"/>
    </justification>
  </clause>

  <clause id="35697">
    <literal><![CDATA[
      a(x * L(y * a(z,u,y),w,v5),v6,v7) = a(x * L(L(y,u,z),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,27672,a(flip),b,35696,a)].">
      <j1 rule="hyper" parents="60 27672 35696"/>
    </justification>
  </clause>

  <clause id="35698">
    <literal><![CDATA[
      a(L(x,x,L(L(y,z,u),w,v5)) * L(L(y,z,u),w,v5),v6,v7) = a(x \ L(y * a(u,z,y),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(33084,a,35697,a),flip(a)].">
      <j1 rule="hyper" parents="33084 35697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35699">
    <literal><![CDATA[
      a(x \ L(y * a(z,u,y),w,v5),v6,v7) = a(x \ L(L(y,u,z),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(27323,a,35698,a),flip(a)].">
      <j1 rule="hyper" parents="27323 35698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35701">
    <literal><![CDATA[
      a(a(a(x,y,z),u,a(x,y,z) \ (a(x,y,z) \ w)),v5,v6) = a((a(x,y,z) \ (u * w)) * ((a(x,y,z) \ u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(30877(a,1),34707(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30877 34707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35702">
    <literal><![CDATA[
      a(a(a(x,y,z),u,a(x,y,z) \ (a(x,y,z) \ w)),v5,v6) = a(((a(x,y,z) \ u) * w) * (a(x,y,z) \ (u * w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26381,a,b,35701,a),flip(a)].">
      <j1 rule="hyper" parents="370 26381 35701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35703">
    <literal><![CDATA[
      a(a(a(x,y,z),u,a(x,y,z) \ (a(x,y,z) \ w)),v5,v6) = a(((a(x,y,z) \ u) * w) * ((u * w) * a(x,y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35080,a(flip),b,35702,a),flip(a)].">
      <j1 rule="hyper" parents="370 35080 35702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35704">
    <literal><![CDATA[
      a(a(a(x,y,z),u,a(x,y,z) \ (a(x,y,z) \ w)),v5,v6) = a(((a(x,y,z) \ u) * w) * (u * (w * a(x,y,z))),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35628,a(flip),b,35703,a),flip(a)].">
      <j1 rule="hyper" parents="370 35628 35703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35705">
    <literal><![CDATA[
      a(((a(x,y,z) \ u) * w) * (u * (w * a(x,y,z))),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,35245,a(flip),b,35704,a),flip(a)].">
      <j1 rule="hyper" parents="60 35245 35704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35707">
    <literal><![CDATA[
      a(a(a(x,y,z) \ a(u,w,v5),v6,v7),v8,v9) = 1
    ]]></literal>
    <justification jstring="[hyper(60,a,35684,a,b,35705,a)].">
      <j1 rule="hyper" parents="60 35684 35705"/>
    </justification>
  </clause>

  <clause id="35709">
    <literal><![CDATA[
      a(a(a(x,y,z) * a(u,w,v5),v6,v7),v8,v9) = 1
    ]]></literal>
    <justification jstring="[para(30642(a,1),35707(a,1,1))].">
      <j1 rule="para" parents="30642 35707"/>
    </justification>
  </clause>

  <clause id="35710">
    <literal><![CDATA[
      a(a(a(x,y,z) * a(u,w,v5),v6,v7),v8,v9) * v10 != v11
    ]]></literal>
    <literal><![CDATA[
      v11 = v10
    ]]></literal>
    <justification jstring="[para(35709(a,2),130(a,1,1))].">
      <j1 rule="para" parents="35709 130"/>
    </justification>
  </clause>

  <clause id="35711">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w) * a(v5,v6,v7)),v8,v9) = x \ L(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(35710,a,32867,a)].">
      <j1 rule="hyper" parents="35710 32867"/>
    </justification>
  </clause>

  <clause id="35712">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) * a(v5,v6,v7),v8,v9)) = L(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(32214,a,35711,a)].">
      <j1 rule="hyper" parents="32214 35711"/>
    </justification>
  </clause>

  <clause id="35713">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(v5,v6,v7)) = L(x,y,L(a(v5,v6,v7) * a(z,u,w),v8,v9))
    ]]></literal>
    <justification jstring="[hyper(370,a,35454,a,b,35712,a)].">
      <j1 rule="hyper" parents="370 35454 35712"/>
    </justification>
  </clause>

  <clause id="35714">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(v5,v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(v5,v6,v7) * a(z,u,w)) = v8
    ]]></literal>
    <justification jstring="[para(35713(a,2),14467(a,1))].">
      <j1 rule="para" parents="35713 14467"/>
    </justification>
  </clause>

  <clause id="35715">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u * a(z,y,w),a(v5,v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(v5,v6,v7) * a(z,y,w)) = v8
    ]]></literal>
    <justification jstring="[para(33009(a,1),35714(a,1,1))].">
      <j1 rule="para" parents="33009 35714"/>
    </justification>
  </clause>

  <clause id="35716">
    <literal><![CDATA[
      ((x \ y) * a(z,x,a(u,w,v5))) \ (y * L(y \ ((x \ y) * a(z,x,a(u,w,v5))),z,a(u,w,v5))) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(35422(a,1),35428(a,1,2,2,1,2))].">
      <j1 rule="para" parents="35422 35428"/>
    </justification>
  </clause>

  <clause id="35717">
    <literal><![CDATA[
      ((x \ y) * a(z,x,a(u,w,v5))) \ (y * L((y \ (x \ y)) * a(z,x,a(u,w,v5)),z,a(u,w,v5))) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(35339(a,1),35716(a,1,2,2,1))].">
      <j1 rule="para" parents="35339 35716"/>
    </justification>
  </clause>

  <clause id="35718">
    <literal><![CDATA[
      (((x \ y) * a(z,x,a(u,w,v5))) \ (y * L(y \ (x \ y),z,a(u,w,v5)))) * a(z,x,a(u,w,v5)) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[hyper(35441,a,35717,a)].">
      <j1 rule="hyper" parents="35441 35717"/>
    </justification>
  </clause>

  <clause id="35719">
    <literal><![CDATA[
      (((x \ y) * a(z,x,a(u,w,v5))) \ (L(x,z,a(u,w,v5)) \ y)) * a(z,x,a(u,w,v5)) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(35424(a,1),35718(a,1,1,2))].">
      <j1 rule="para" parents="35424 35718"/>
    </justification>
  </clause>

  <clause id="35720">
    <literal><![CDATA[
      (((x \ y) \ (L(x,z,a(u,w,v5)) \ y)) * a(u,w,a(z,x,v5))) * a(z,x,a(u,w,v5)) = (x * a(u,w,a(z,x,v5))) \ L(x,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(35422(a,1),35719(a,1,1))].">
      <j1 rule="para" parents="35422 35719"/>
    </justification>
  </clause>

  <clause id="35721">
    <literal><![CDATA[
      ((x \ (y * (L(y,z,a(u,w,v5)) \ x))) * a(u,w,a(z,y,v5))) * a(z,y,a(u,w,v5)) = (y * a(u,w,a(z,y,v5))) \ L(y,a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(29505(a,1),35720(a,1,1,1))].">
      <j1 rule="para" parents="29505 35720"/>
    </justification>
  </clause>

  <clause id="35722">
    <literal><![CDATA[
      ((x \ (x * a(y,z,a(u,w,v5)))) * a(y,z,a(w,u,v5))) * a(w,u,a(y,z,v5)) = (u * a(y,z,a(w,u,v5))) \ L(u,a(y,z,v5),w)
    ]]></literal>
    <justification jstring="[para(34479(a,1),35721(a,1,1,1,2))].">
      <j1 rule="para" parents="34479 35721"/>
    </justification>
  </clause>

  <clause id="35723">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * a(x,y,a(u,z,w))) * a(u,z,a(x,y,w)) = (z * a(x,y,a(u,z,w))) \ L(z,a(x,y,w),u)
    ]]></literal>
    <justification jstring="[para(4(a,1),35722(a,1,1,1))].">
      <j1 rule="para" parents="4 35722"/>
    </justification>
  </clause>

  <clause id="35724">
    <literal><![CDATA[
      (x * (a(y,a(z,u,w),v5) \ (v6 * v7))) \ ((x * ((a(y,a(z,u,w),v5) \ 1) * v6)) * v7) = a(x * (a(y,a(z,u,w),v5) \ 1),L(v6,a(y,a(z,u,w),v5) \ 1,x),v7)
    ]]></literal>
    <justification jstring="[para(35594(a,1),35595(a,1,1))].">
      <j1 rule="para" parents="35594 35595"/>
    </justification>
  </clause>

  <clause id="35725">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) \ v7))) \ ((x * ((a(z,a(u,w,v5),v6) \ 1) * y)) * v7) = a(x * (a(z,a(u,w,v5),v6) \ 1),L(y,a(z,a(u,w,v5),v6) \ 1,x),v7)
    ]]></literal>
    <justification jstring="[para(35375(a,1),35724(a,1,1,2))].">
      <j1 rule="para" parents="35375 35724"/>
    </justification>
  </clause>

  <clause id="35726">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) \ v7))) \ ((x * (a(z,a(u,w,v5),v6) \ y)) * v7) = a(x * (a(z,a(u,w,v5),v6) \ 1),L(y,a(z,a(u,w,v5),v6) \ 1,x),v7)
    ]]></literal>
    <justification jstring="[para(30630(a,1),35725(a,1,2,1,2))].">
      <j1 rule="para" parents="30630 35725"/>
    </justification>
  </clause>

  <clause id="35727">
    <literal><![CDATA[
      (x * (y * (a(z,a(u,w,v5),v6) \ v7))) \ ((x * y) * (a(z,a(u,w,v5),v6) \ v7)) = a(x * (a(z,a(u,w,v5),v6) \ 1),L(y,a(z,a(u,w,v5),v6) \ 1,x),v7)
    ]]></literal>
    <justification jstring="[para(35601(a,1),35726(a,1,2))].">
      <j1 rule="para" parents="35601 35726"/>
    </justification>
  </clause>

  <clause id="35728">
    <literal><![CDATA[
      a(x * (a(y,a(z,u,w),v5) \ 1),L(v6,a(y,a(z,u,w),v5) \ 1,x),v7) = a(x,v6,a(y,a(z,u,w),v5) \ v7)
    ]]></literal>
    <justification jstring="[hyper(1029,a,35727,a),flip(a)].">
      <j1 rule="hyper" parents="1029 35727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35729">
    <literal><![CDATA[
      a(x * (a(y,a(z,u,w),v5) \ 1),L(v6,a(y,a(z,u,w),v5) \ 1,x),v7) = a(x,v6,a(y,a(z,u,w),v5) * v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,34532,a(flip),b,35728,a),flip(a)].">
      <j1 rule="hyper" parents="370 34532 35728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35730">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ v5,L(v6,a(x,a(y,z,u),w) \ 1,v5),v7) = a(v5,v6,a(x,a(y,z,u),w) * v7)
    ]]></literal>
    <justification jstring="[para(30626(a,1),35729(a,1,1))].">
      <j1 rule="para" parents="30626 35729"/>
    </justification>
  </clause>

  <clause id="35731">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ v5,L(v6,a(x,a(y,z,u),w),v5),v7) = a(v5,v6,a(x,a(y,z,u),w) * v7)
    ]]></literal>
    <justification jstring="[para(3401(a,1),35730(a,1,2))].">
      <j1 rule="para" parents="3401 35730"/>
    </justification>
  </clause>

  <clause id="35732">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ v5,v6,v7) = a(v5,v6,a(x,a(y,z,u),w) * v7)
    ]]></literal>
    <justification jstring="[para(35591(a,1),35731(a,1,2))].">
      <j1 rule="para" parents="35591 35731"/>
    </justification>
  </clause>

  <clause id="35733">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) * v5,v6,v7) = a(v5,v6,a(x,a(y,z,u),w) * v7)
    ]]></literal>
    <justification jstring="[hyper(34551,a,35732,a)].">
      <j1 rule="hyper" parents="34551 35732"/>
    </justification>
  </clause>

  <clause id="35734">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(370,a,35614,a(flip),b,35733,a),flip(a)].">
      <j1 rule="hyper" parents="370 35614 35733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35735">
    <literal><![CDATA[
      a(x * (y * a(z,a(u,w,v5),v6)),v7,v8) = a(x * y,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(35641,a,35734,a)].">
      <j1 rule="hyper" parents="35641 35734"/>
    </justification>
  </clause>

  <clause id="35738">
    <literal><![CDATA[
      a(x * (L(y,a(z,u,w),v5) \ v6),v7,v8) = a(x * (y \ v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(35600(a,1),35735(a,1,1,2))].">
      <j1 rule="para" parents="35600 35735"/>
    </justification>
  </clause>

  <clause id="35739">
    <literal><![CDATA[
      a(x * ((a(y,z,u) \ w) \ v5),v6,v7) = a(x * (a(y,z,u) * (w \ v5)),v6,v7)
    ]]></literal>
    <justification jstring="[para(28385(a,1),35738(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28385 35738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35740">
    <literal><![CDATA[
      a((x * T(a(y,z,u) * K(w,w \ v5),v5)) \ v6,v7,v8) = a(K(w \ v5,w) * (a(y,z,u) * (x \ v6)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(60,a,31064,a,b,35739,a)].">
      <j1 rule="hyper" parents="60 31064 35739"/>
    </justification>
  </clause>

  <clause id="35741">
    <literal><![CDATA[
      a((x * T(a(y,z,u) * K(w,w \ v5),v5)) \ v6,v7,v8) = a(a(y,z,u) * (x \ v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(370,a,26372,a(flip),b,35740,a),flip(a)].">
      <j1 rule="hyper" parents="370 26372 35740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35743">
    <literal><![CDATA[
      a((x * a(y,z,u)) \ w,v5,v6) = a(a(y,z,u) * (x \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(24069(a,1),35741(a,1,1,1,2))].">
      <j1 rule="para" parents="24069 35741"/>
    </justification>
  </clause>

  <clause id="35744">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,v5,v6) = a(a(x,y,z) * (u \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26527,a,35743,a)].">
      <j1 rule="hyper" parents="26527 35743"/>
    </justification>
  </clause>

  <clause id="35745">
    <literal><![CDATA[
      a((a(x,y,z) \ u) \ w,v5,v6) = a(a(x,y,z) * (u \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,30656,a,b,35743,a)].">
      <j1 rule="hyper" parents="60 30656 35743"/>
    </justification>
  </clause>

  <clause id="35746">
    <literal><![CDATA[
      a((R(x,a(y,z,u) \ w,a(y,z,u)) * w) \ v5,v6,v7) = a(a(y,z,u) * ((x * (w / a(y,z,u))) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(12410(a,2),35743(a,1,1,1))].">
      <j1 rule="para" parents="12410 35743"/>
    </justification>
  </clause>

  <clause id="35747">
    <literal><![CDATA[
      a((a(x,y,z) \ (u * (a(w,v5,v6) \ v7))) \ v8,v9,v10) = a(a(x,y,z) * ((u * (a(w,v5,v6) * v7)) \ v8),v9,v10)
    ]]></literal>
    <justification jstring="[hyper(60,a,31304,a,b,35744,a)].">
      <j1 rule="hyper" parents="60 31304 35744"/>
    </justification>
  </clause>

  <clause id="35748">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * (a(w,v5,v6) \ v7)) \ v8),v9,v10) = a(a(x,y,z) * ((u * (a(w,v5,v6) * v7)) \ v8),v9,v10)
    ]]></literal>
    <justification jstring="[hyper(60,a,35745,a(flip),b,35747,a)].">
      <j1 rule="hyper" parents="60 35745 35747"/>
    </justification>
  </clause>

  <clause id="35749">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * (w / a(x,y,z))) \ v5),v6,v7) = a((u * w) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35493,a(flip),b,35746,a),flip(a)].">
      <j1 rule="hyper" parents="60 35493 35746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35751">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * (a(x,y,z) \ w)) \ v5),v6,v7) = a((u * w) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(23572(a,1),35749(a,1,1,2,1,2))].">
      <j1 rule="para" parents="23572 35749"/>
    </justification>
  </clause>

  <clause id="35752">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * (a(x,y,z) * w)) \ v5),v6,v7) = a((u * w) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(60,a,35748,a(flip),b,35751,a)].">
      <j1 rule="hyper" parents="60 35748 35751"/>
    </justification>
  </clause>

  <clause id="35753">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * (a(x,y,z) * T(w,K(v5,v6) * u))) \ v7),v8,v9) = a((T(w,K(v6,v5)) * u) \ v7,v8,v9)
    ]]></literal>
    <justification jstring="[para(23385(a,1),35752(a,2,1,1))].">
      <j1 rule="para" parents="23385 35752"/>
    </justification>
  </clause>

  <clause id="35754">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * T(a(x,y,z) * w,K(v5,v6) * u)) \ v7),v8,v9) = a((T(w,K(v6,v5)) * u) \ v7,v8,v9)
    ]]></literal>
    <justification jstring="[para(28197(a,2),35753(a,1,1,2,1,2))].">
      <j1 rule="para" parents="28197 35753"/>
    </justification>
  </clause>

  <clause id="35755">
    <literal><![CDATA[
      a(a(x,y,z) * ((T(a(x,y,z) * u,K(w,v5)) * v6) \ v7),v8,v9) = a((T(u,K(w,v5)) * v6) \ v7,v8,v9)
    ]]></literal>
    <justification jstring="[para(23385(a,1),35754(a,1,1,2,1))].">
      <j1 rule="para" parents="23385 35754"/>
    </justification>
  </clause>

  <clause id="35756">
    <literal><![CDATA[
      a((T(x,K(y,z)) * u) \ w,v5,v6) = a((((a(v7,v8,v9) * x) * u) \ w) * a(v7,v8,v9),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26827,a,35755,a),flip(a)].">
      <j1 rule="hyper" parents="26827 35755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35758">
    <literal><![CDATA[
      a((((a(x,y,z) * u) * w) \ v5) * a(x,y,z),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a((u * w) \ v5,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(35756(a,1),26685(a,1))].">
      <j1 rule="para" parents="35756 26685"/>
    </justification>
  </clause>

  <clause id="35759">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,L(v6,a(z,u,w) * y,v7)) = a((y * v7) \ ((y * x) * v7),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35758,a,35679,a),flip(a)].">
      <j1 rule="hyper" parents="35758 35679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35760">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,L(v6,a(z,u,w) * y,v7)) = a(x,v5,L(v6,y,v7))
    ]]></literal>
    <justification jstring="[hyper(370,a,32403,a(flip),b,35759,a),flip(a)].">
      <j1 rule="hyper" parents="370 32403 35759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35761">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,v5) * v6,v7)) = a(x,y,L(z,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(35472,a,35760,a)].">
      <j1 rule="hyper" parents="35472 35760"/>
    </justification>
  </clause>

  <clause id="35763">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(v5,v6,v7)) = a(v5,v6,v7) \ a(v5,v6,L(v7,w,x))
    ]]></literal>
    <justification jstring="[hyper(125,a,35761,a(flip),b,32319,a),flip(a)].">
      <j1 rule="hyper" parents="125 35761 32319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35765">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(v5,v6,v7)) = a(x,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(370,a,32328,a(flip),b,35763,a),flip(a)].">
      <j1 rule="hyper" parents="370 32328 35763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35766">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) = a(x,y,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(32568(a,1),35765(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32568 35765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35767">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(v5,v6,v7)) = x * a(v7,w,a(v5,v6,x))
    ]]></literal>
    <justification jstring="[para(35765(a,1),32983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35765 32983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35768">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,a(v5,v6,v7)) = x \ L(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(35765(a,1),35458(a,1,1))].">
      <j1 rule="para" parents="35765 35458"/>
    </justification>
  </clause>

  <clause id="35769">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(v6,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32968,a,35766,a)].">
      <j1 rule="hyper" parents="32968 35766"/>
    </justification>
  </clause>

  <clause id="35771">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(v5,v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,w,a(v5,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(35767(a,2),32997(a,1))].">
      <j1 rule="para" parents="35767 32997"/>
    </justification>
  </clause>

  <clause id="35772">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(v5,v6,v7)) = L(x,y,a(v7,v6,v5))
    ]]></literal>
    <justification jstring="[hyper(35771,a,35581,a),flip(a)].">
      <j1 rule="hyper" parents="35771 35581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35774">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(v5,v6,v7)) = L(x,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(35771,a,35455,a)].">
      <j1 rule="hyper" parents="35771 35455"/>
    </justification>
  </clause>

  <clause id="35775">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,v6)) = L(x,y,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(35771,a,32664,a)].">
      <j1 rule="hyper" parents="35771 32664"/>
    </justification>
  </clause>

  <clause id="35780">
    <literal><![CDATA[
      L(x,y,a(z,x,L(y,u,w))) \ (z \ ((z * x) * L(y,u,w))) = L(y,u,w) * a(z,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(35775(a,1),28737(a,1,1))].">
      <j1 rule="para" parents="35775 28737"/>
    </justification>
  </clause>

  <clause id="35781">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(v5,v6,v7)) = L(x,u,a(v7,v6,v5) * a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(35715,a,35772,a),flip(a)].">
      <j1 rule="hyper" parents="35715 35772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35782">
    <literal><![CDATA[
      x \ (L(L(1 / x,y,a(z,u,w)),y,a(v5,v6,v7)) \ 1) = L(x,y,a(v5,v6,v7) * a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(35774(a,2),3865(a,1,2,1))].">
      <j1 rule="para" parents="35774 3865"/>
    </justification>
  </clause>

  <clause id="35783">
    <literal><![CDATA[
      L(1 / L(x,y,a(z,u,w) * a(v5,v6,v7)),L(x,y,a(v5,v6,v7)),L(x,y,a(v5,v6,v7))) = L(L(x,y,a(v5,v6,v7)),y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(35774(a,1),5097(a,1,1,2))].">
      <j1 rule="para" parents="35774 5097"/>
    </justification>
  </clause>

  <clause id="35784">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,v6,a(z,u,v7)) = z \ L(z,u,a(w,y,x) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(33073,a,35768,a)].">
      <j1 rule="hyper" parents="33073 35768"/>
    </justification>
  </clause>

  <clause id="35786">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,v6,a(z,u,w)) = z \ L(z,u,w * L(L(w,y,x),v6,v5))
    ]]></literal>
    <justification jstring="[para(35554(a,1),35784(a,2,2))].">
      <j1 rule="para" parents="35554 35784"/>
    </justification>
  </clause>

  <clause id="35787">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(L(z,u,w),v5,v6)) = x \ L(x,y,z * L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,35508,a,b,35786,a)].">
      <j1 rule="hyper" parents="60 35508 35786"/>
    </justification>
  </clause>

  <clause id="35788">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (z \ ((z * x) * L(y,u,w))) = L(y,u,w) * a(z,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(35349(a,1),35780(a,1,1))].">
      <j1 rule="para" parents="35349 35780"/>
    </justification>
  </clause>

  <clause id="35789">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (z \ ((z * x) * L(y,u,w))) = L(y * a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(370,a,32353,a(flip),b,35788,a),flip(a)].">
      <j1 rule="hyper" parents="370 32353 35788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35791">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (z \ (x * (T(z,x) * y))) = L(y * a(z,x,y),z,x)
    ]]></literal>
    <justification jstring="[para(12481(a,1),35789(a,1,2,2))].">
      <j1 rule="para" parents="12481 35789"/>
    </justification>
  </clause>

  <clause id="35792">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,a(x,y,z),u)) \ (w \ (a(x,y,z) * (T(w,a(x,y,z)) * u))) = L(u * a(w,a(x,y,z),u),y,a(x,w,z))
    ]]></literal>
    <justification jstring="[hyper(370,a,33009,a,b,35791,a),flip(a)].">
      <j1 rule="hyper" parents="370 33009 35791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35793">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,T(y,z),u)) \ (w \ (y * (T(w,T(y,z)) * u)))),v5,v6) = a(x \ L(u * a(w,T(y,z),u),w,T(y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(35791(a,1),26825(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="35791 26825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35794">
    <literal><![CDATA[
      L(L(1 / x,y,a(z,u,w) * a(v5,v6,v7)),L(x,y,a(v5,v6,v7)),L(x,y,a(v5,v6,v7))) = L(L(x,y,a(v5,v6,v7)),y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(35460(a,2),35783(a,1,1))].">
      <j1 rule="para" parents="35460 35783"/>
    </justification>
  </clause>

  <clause id="35795">
    <literal><![CDATA[
      L(x * a(y,a(z,u,w),x),u,a(z,y,w)) = a(z,u,w) \ (y \ (a(z,u,w) * (T(y,a(z,u,w)) * x)))
    ]]></literal>
    <justification jstring="[para(34424(a,1),35792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34424 35792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35796">
    <literal><![CDATA[
      L(x * a(y,a(z,u,w),x),u,a(z,y,w)) = a(z,u,w) \ (y \ (a(z,u,w) * (y * x)))
    ]]></literal>
    <justification jstring="[para(23540(a,1),35795(a,2,2,2,2,1))].">
      <j1 rule="para" parents="23540 35795"/>
    </justification>
  </clause>

  <clause id="35799">
    <literal><![CDATA[
      L(x * a(y,a(z,u,w),x),u,a(z,y,w)) = a(z,u,w) * (y \ (a(z,u,w) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(370,a,30976,a(flip),b,35796,a),flip(a)].">
      <j1 rule="hyper" parents="370 30976 35796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35800">
    <literal><![CDATA[
      a(x,y,z) * (u \ (a(x,y,z) \ (u * w))) = L(L(w,a(x,y,z),u),y,a(x,u,z))
    ]]></literal>
    <justification jstring="[para(31274(a,1),35799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31274 35799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35801">
    <literal><![CDATA[
      L(L(1 / x,y,a(z,u,w) * a(v5,v6,v7)),x,x) = L(L(x,y,a(v5,v6,v7)),y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(60,a,29547,a(flip),b,35794,a)].">
      <j1 rule="hyper" parents="60 29547 35794"/>
    </justification>
  </clause>

  <clause id="35803">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(v5,v6,v7)) \ 1 = L(x \ 1,y,a(v5,v6,v7) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(60,a,1231,a(flip),b,35801,a),flip(a)].">
      <j1 rule="hyper" parents="60 1231 35801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35804">
    <literal><![CDATA[
      x \ L((1 / x) \ 1,y,a(z,u,w) * a(v5,v6,v7)) = L(x,y,a(z,u,w) * a(v5,v6,v7)) \ x
    ]]></literal>
    <justification jstring="[para(35803(a,1),35782(a,1,2))].">
      <j1 rule="para" parents="35803 35782"/>
    </justification>
  </clause>

  <clause id="35805">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(v5,v6,v7)) \ x = x \ L(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(77(a,1),35804(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="77 35804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35806">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w) * a(v5,v6,v7)) = a(a(z,u,w) * a(v5,v6,v7),y,x)
    ]]></literal>
    <justification jstring="[hyper(32589,a,35805,a),flip(a)].">
      <j1 rule="hyper" parents="32589 35805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35807">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w) * a(v5,v6,w)) = a(w * L(L(w,v6,v5),u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(370,a,35668,a(flip),b,35806,a),flip(a)].">
      <j1 rule="hyper" parents="370 35668 35806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35808">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,a(v5,v6,w)) = a(w * L(L(w,v6,v5),u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,35768,a,b,35807,a)].">
      <j1 rule="hyper" parents="60 35768 35807"/>
    </justification>
  </clause>

  <clause id="35809">
    <literal><![CDATA[
      x \ L(x,y,z * L(L(z,u,w),v5,v6)) = a(z * L(L(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35541(a,1),35807(a,1,2))].">
      <j1 rule="para" parents="35541 35807"/>
    </justification>
  </clause>

  <clause id="35810">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(L(z,u,w),v5,v6)) = a(z * L(L(z,v5,v6),u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,35787,a,b,35809,a)].">
      <j1 rule="hyper" parents="60 35787 35809"/>
    </justification>
  </clause>

  <clause id="35811">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,v6,a(x,y,w)) = a(w * L(L(w,u,z),v6,v5),y,x)
    ]]></literal>
    <justification jstring="[hyper(32967,a,35808,a)].">
      <j1 rule="hyper" parents="32967 35808"/>
    </justification>
  </clause>

  <clause id="35812">
    <literal><![CDATA[
      a(x * L(L(x,y,z),z,y),u,w) * a(z,y,a(w,u,x)) = (y * a(w,u,a(z,y,x))) \ L(y,a(w,u,x),z)
    ]]></literal>
    <justification jstring="[para(35808(a,1),35723(a,1,1))].">
      <j1 rule="para" parents="35808 35723"/>
    </justification>
  </clause>

  <clause id="35813">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,L(z,v5,v6)) = a(z * L(L(z,v5,v6),u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(60,a,35507,a,b,35810,a)].">
      <j1 rule="hyper" parents="60 35507 35810"/>
    </justification>
  </clause>

  <clause id="35814">
    <literal><![CDATA[
      (x \ a(y,z,a(u,w,v5))) * a(u,w,a(v6,v7,v5)) = x \ a(v5 * L(L(v5,v7,v6),z,y),w,u)
    ]]></literal>
    <justification jstring="[hyper(125,a,35811,a(flip),b,35394,a),flip(a)].">
      <j1 rule="hyper" parents="125 35811 35394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35815">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ ((v6 \ ((v6 * v5) * a(x,y,w))) / a(x,y,w))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(28761(a,1),35811(a,1,2))].">
      <j1 rule="para" parents="28761 35811"/>
    </justification>
  </clause>

  <clause id="35816">
    <literal><![CDATA[
      x * L(x \ a(y * L(L(y,x,z),x,z),u,w),z,a(w,u,y)) = (x * a(w,u,a(z,x,y))) \ L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[para(35814(a,1),35618(a,1,2,1))].">
      <j1 rule="para" parents="35814 35618"/>
    </justification>
  </clause>

  <clause id="35817">
    <literal><![CDATA[
      a(x * L(L(x,y,z),z,y),u,w) = a(z,a(w,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(32,a,35426,a(flip),b,35812,a),flip(a)].">
      <j1 rule="hyper" parents="32 35426 35812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35819">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ (a(x,y,w) \ (v6 \ ((v6 * v5) * a(x,y,w))))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(23572(a,1),35815(a,1,2,2))].">
      <j1 rule="para" parents="23572 35815"/>
    </justification>
  </clause>

  <clause id="35820">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ (a(x,y,w) * (v6 \ (a(x,y,w) \ (v6 * v5))))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(30975(a,1),35819(a,1,2,2))].">
      <j1 rule="para" parents="30975 35819"/>
    </justification>
  </clause>

  <clause id="35821">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ L(L(v5,a(x,y,w),v6),y,a(x,v6,w))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35800(a,1),35820(a,1,2,2))].">
      <j1 rule="para" parents="35800 35820"/>
    </justification>
  </clause>

  <clause id="35822">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u) = x * L(x \ a(w * w,z,y),u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(35672(a,1),35816(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="35672 35816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35823">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u) = x * L(x \ 1,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(641(a,1),35822(a,2,2,1,2))].">
      <j1 rule="para" parents="641 35822"/>
    </justification>
  </clause>

  <clause id="35825">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u) = x \ L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(370,a,3816,a(flip),b,35823,a),flip(a)].">
      <j1 rule="hyper" parents="370 3816 35823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35827">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) \ L(x,a(y,z,w),u) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(y,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(35825(a,2),32086(a,1))].">
      <j1 rule="para" parents="35825 32086"/>
    </justification>
  </clause>

  <clause id="35828">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(x,w,a(y,z,u)) = a(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35827,a,35426,a),flip(a)].">
      <j1 rule="hyper" parents="35827 35426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35829">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(x,v7,a(y,L(z \ (u \ z),w,v5),v6)) = a(v7,x,a(y,L((z * u) \ z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(34971(a,2),35828(a,2,3))].">
      <j1 rule="para" parents="34971 35828"/>
    </justification>
  </clause>

  <clause id="35830">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(v6,z \ (u \ z),a(x,v7,y)) = a(v7,x,a(y,L((z * u) \ z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(35769(a,1),35829(a,1,2))].">
      <j1 rule="para" parents="35769 35829"/>
    </justification>
  </clause>

  <clause id="35831">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(v6,u,a(x,v7,y)) = a(v7,x,a(y,L((z * u) \ z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(35019(a,1),35830(a,1,2))].">
      <j1 rule="para" parents="35019 35830"/>
    </justification>
  </clause>

  <clause id="35833">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(v6,u,a(x,v7,y)) = a(v7,x,a(y,L(z \ (u \ z),w,v5),v6))
    ]]></literal>
    <justification jstring="[para(34971(a,1),35831(a,2,3))].">
      <j1 rule="para" parents="34971 35831"/>
    </justification>
  </clause>

  <clause id="35835">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(v6,u,a(x,v7,y)) = a(v6,z \ (u \ z),a(v7,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,35769,a(flip),b,35833,a),flip(a)].">
      <j1 rule="hyper" parents="370 35769 35833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35837">
    <literal><![CDATA[
      a(x,a(y,L(z \ (u \ z),w,v5),v6),v7) * a(v6,u,a(x,v7,y)) = a(v6,u,a(v7,x,y))
    ]]></literal>
    <justification jstring="[hyper(370,a,35019,a(flip),b,35835,a),flip(a)].">
      <j1 rule="hyper" parents="370 35019 35835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35839">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,T(y,z),u)) \ (w \ (y * (T(w,T(y,z)) * u)))),v5,v6) = a(x \ L(u * a(w,y,u),w,T(y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(26451(a,1),35793(a,2,1,2,1,2))].">
      <j1 rule="para" parents="26451 35793"/>
    </justification>
  </clause>

  <clause id="35840">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,T(y,z),u)) \ (w \ (y * (T(w,T(y,z)) * u)))),v5,v6) = a(x \ L(u * a(w,y,u),w,y),v5,v6)
    ]]></literal>
    <justification jstring="[para(23573(a,1),35839(a,2,1,2))].">
      <j1 rule="para" parents="23573 35839"/>
    </justification>
  </clause>

  <clause id="35842">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,T(y,z),u)) \ (w \ (y * (T(w,T(y,z)) * u)))),v5,v6) = a(x \ L(L(u,y,w),w,y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,35699,a(flip),b,35840,a),flip(a)].">
      <j1 rule="hyper" parents="370 35699 35840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35844">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,y,u)) \ (w \ (y * (T(w,T(y,z)) * u)))),v5,v6) = a(x \ L(L(u,y,w),w,y),v5,v6)
    ]]></literal>
    <justification jstring="[para(26451(a,1),35842(a,1,1,2,1,3))].">
      <j1 rule="para" parents="26451 35842"/>
    </justification>
  </clause>

  <clause id="35845">
    <literal><![CDATA[
      a(x \ (L(T(y,z),u,a(w,y,u)) \ (w \ (y * (w * u)))),v5,v6) = a(x \ L(L(u,y,w),w,y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(60,a,28016,a(flip),b,35844,a)].">
      <j1 rule="hyper" parents="60 28016 35844"/>
    </justification>
  </clause>

  <clause id="35848">
    <literal><![CDATA[
      a(x \ (T(y,z) \ (u \ (y * (u * w)))),v5,v6) = a(x \ L(L(w,y,u),u,y),v5,v6)
    ]]></literal>
    <justification jstring="[para(34424(a,1),35845(a,1,1,2,1))].">
      <j1 rule="para" parents="34424 35845"/>
    </justification>
  </clause>

  <clause id="35849">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * u)))),w,v5) = a(x \ L(L(u,y,z),z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26683,a,35848,a)].">
      <j1 rule="hyper" parents="26683 35848"/>
    </justification>
  </clause>

  <clause id="35851">
    <literal><![CDATA[
      a(x \ L(L(T(y \ (z \ u),w),z,y),y,z),v5,v6) = a(x \ (z \ T(z * T(z \ (u / y),w),y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2410(a,1),35849(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2410 35849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35852">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * (u * K(y * u,z)))))),w,v5) = a(x \ L((z * y) \ ((y * u) * z),z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(15393(a,1),35849(a,2,1,2,1))].">
      <j1 rule="para" parents="15393 35849"/>
    </justification>
  </clause>

  <clause id="35853">
    <literal><![CDATA[
      a(x \ L(L(T(y \ (z \ u),w),z,y),y,z),v5,v6) = a(x \ (z \ (z * T(z \ (u / y),w))),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26445,a(flip),b,35851,a),flip(a)].">
      <j1 rule="hyper" parents="370 26445 35851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35855">
    <literal><![CDATA[
      a(x \ L(L(T(y \ (z \ u),w),z,y),y,z),v5,v6) = a(x \ T(z \ (u / y),w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4(a,1),35853(a,2,1,2))].">
      <j1 rule="para" parents="4 35853"/>
    </justification>
  </clause>

  <clause id="35856">
    <literal><![CDATA[
      a(x \ L(L(T(y \ (z \ u),w),z,y),y,z),v5,v6) = a(x \ (z \ (u / y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26380,a(flip),b,35855,a),flip(a)].">
      <j1 rule="hyper" parents="370 26380 35855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35859">
    <literal><![CDATA[
      a(x \ L(L(T(y \ (z \ u),w),z,y),y,z),v5,v6) = a(x \ (z \ (y \ u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(370,a,26646,a(flip),b,35856,a),flip(a)].">
      <j1 rule="hyper" parents="370 26646 35856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35860">
    <literal><![CDATA[
      a(x \ L(T((y * z) \ u,w),y,z),v5,v6) = a(x \ (y \ (z \ u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(1380(a,1),35859(a,1,1,2))].">
      <j1 rule="para" parents="1380 35859"/>
    </justification>
  </clause>

  <clause id="35861">
    <literal><![CDATA[
      a(x \ L((y * z) \ u,y,z),w,v5) = a(x \ (y \ (z \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26553,a,35860,a)].">
      <j1 rule="hyper" parents="26553 35860"/>
    </justification>
  </clause>

  <clause id="35862">
    <literal><![CDATA[
      a(x \ (y \ ((z \ (y * (z * u))) * K(y * u,z))),w,v5) = a(x \ L((z * y) \ ((y * u) * z),z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(25543(a,1),35852(a,1,1,2,2))].">
      <j1 rule="para" parents="25543 35852"/>
    </justification>
  </clause>

  <clause id="35863">
    <literal><![CDATA[
      a(x \ ((y \ (z \ (y * (z * u)))) * K(y * u,z)),w,v5) = a(x \ L((z * y) \ ((y * u) * z),z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(23460(a,1),35862(a,1,1,2))].">
      <j1 rule="para" parents="23460 35862"/>
    </justification>
  </clause>

  <clause id="35864">
    <literal><![CDATA[
      a((x \ (y \ (z \ (y * (z * u))))) * K(y * u,z),w,v5) = a(x \ L((z * y) \ ((y * u) * z),z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(23460(a,1),35863(a,1,1))].">
      <j1 rule="para" parents="23460 35863"/>
    </justification>
  </clause>

  <clause id="35865">
    <literal><![CDATA[
      a(x \ L((y * z) \ ((z * u) * y),y,z),w,v5) = a(x \ (z \ (y \ (z * (y * u)))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26523,a,35864,a),flip(a)].">
      <j1 rule="hyper" parents="26523 35864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35867">
    <literal><![CDATA[
      a(x \ L((y * z) \ ((z * u) * y),y,z),w,v5) = a(x \ L(L(u,z,y),y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(370,a,35849,a(flip),b,35865,a),flip(a)].">
      <j1 rule="hyper" parents="370 35849 35865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35868">
    <literal><![CDATA[
      a(x \ (y \ (z \ ((z * u) * y))),w,v5) = a(x \ L(L(u,z,y),y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(60,a,35861,a(flip),b,35867,a)].">
      <j1 rule="hyper" parents="60 35861 35867"/>
    </justification>
  </clause>

  <clause id="35869">
    <literal><![CDATA[
      a((x \ 1) \ L(L(x,y,z),z,y),u,w) = a(a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(60,a,28923,a(flip),b,35868,a),flip(a)].">
      <j1 rule="hyper" parents="60 28923 35868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35870">
    <literal><![CDATA[
      a(x \ L(L(y,z,u),u,z),w,w \ (v5 \ w)) \ v5 = L(v5,w,x \ (u \ (z \ ((z * y) * u))))
    ]]></literal>
    <justification jstring="[para(35868(a,1),29991(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35868 29991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35871">
    <literal><![CDATA[
      a(x * L(L(x,y,z),z,y),u,w) = a(a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4247(a,1),35869(a,1,1))].">
      <j1 rule="para" parents="4247 35869"/>
    </justification>
  </clause>

  <clause id="35872">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[hyper(60,a,35817,a(flip),b,35871,a),flip(a)].">
      <j1 rule="hyper" parents="60 35817 35871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35873">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(33022,a,35872,a),flip(a)].">
      <j1 rule="hyper" parents="33022 35872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35882">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,a(u,w,z),y)
    ]]></literal>
    <justification jstring="[hyper(129,a,35873,a(flip),b,31276,a)].">
      <j1 rule="hyper" parents="129 35873 31276"/>
    </justification>
  </clause>

  <clause id="35888">
    <literal><![CDATA[
      a(x,y,a(z,L(u \ (w \ u),v5,v6),v7)) * a(y,w,a(x,v7,z)) = a(y,w,a(v7,x,z))
    ]]></literal>
    <justification jstring="[para(35873(a,1),35837(a,1,1))].">
      <j1 rule="para" parents="35873 35837"/>
    </justification>
  </clause>

  <clause id="35889">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(32997,a,35882,a),flip(a)].">
      <j1 rule="hyper" parents="32997 35882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35906">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ L(L(v5,w,a(x,y,v6)),y,a(x,v6,w))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35889(a,1),35821(a,1,2,2,1))].">
      <j1 rule="para" parents="35889 35821"/>
    </justification>
  </clause>

  <clause id="35907">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) * a(w,z,a(u,x,v5)) = a(w,z,a(x,u,v5))
    ]]></literal>
    <justification jstring="[para(35769(a,1),35888(a,1,1))].">
      <j1 rule="para" parents="35769 35888"/>
    </justification>
  </clause>

  <clause id="35908">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,y,a(z,x,w)) = a(u,y,a(x,z,w))
    ]]></literal>
    <justification jstring="[para(35019(a,1),35907(a,1,1))].">
      <j1 rule="para" parents="35019 35907"/>
    </justification>
  </clause>

  <clause id="35909">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w \ ((w * v5) * u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ L(L(v5,w,u),u,w)) = v6
    ]]></literal>
    <justification jstring="[para(35870(a,1),29997(a,1))].">
      <j1 rule="para" parents="35870 29997"/>
    </justification>
  </clause>

  <clause id="35910">
    <literal><![CDATA[
      L(x,y,z \ L(L(z \ 1,u,w),w,u)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(35909,a,28984,a)].">
      <j1 rule="hyper" parents="35909 28984"/>
    </justification>
  </clause>

  <clause id="35911">
    <literal><![CDATA[
      L(x,y,L(L(z * 1,u,w),w,u) * z) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(29218,a,35910,a)].">
      <j1 rule="hyper" parents="29218 35910"/>
    </justification>
  </clause>

  <clause id="35912">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),w,u) * z) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(3(a,1),35911(a,1,3,1,1,1))].">
      <j1 rule="para" parents="3 35911"/>
    </justification>
  </clause>

  <clause id="35913">
    <literal><![CDATA[
      L(x,y,z * L(L(z,u,w),w,u)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(24037,a,35912,a)].">
      <j1 rule="hyper" parents="24037 35912"/>
    </justification>
  </clause>

  <clause id="35914">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ L(v5,y,a(w,v6,x) * a(x,w,v6))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35781(a,1),35906(a,1,2,2))].">
      <j1 rule="para" parents="35781 35906"/>
    </justification>
  </clause>

  <clause id="35915">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ L(v5,y,x * L(L(x,v6,w),w,v6))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35556(a,1),35914(a,1,2,2))].">
      <j1 rule="para" parents="35556 35914"/>
    </justification>
  </clause>

  <clause id="35916">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ L(v5,y,a(v6,x,w))) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(35913(a,1),35915(a,1,2,2))].">
      <j1 rule="para" parents="35913 35915"/>
    </justification>
  </clause>

  <clause id="35917">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,y,a(v6,x,w)) = a(w * L(L(w,u,z),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[para(32082(a,1),35916(a,1,2))].">
      <j1 rule="para" parents="32082 35916"/>
    </justification>
  </clause>

  <clause id="35918">
    <literal><![CDATA[
      a(x * L(L(x,y,z),y,z),u,w) = a(y,u,a(w,z,x))
    ]]></literal>
    <justification jstring="[hyper(60,a,35908,a(flip),b,35917,a),flip(a)].">
      <j1 rule="hyper" parents="60 35908 35917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35919">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,L(z,u,w)) = a(u,y,a(x,w,z))
    ]]></literal>
    <justification jstring="[hyper(60,a,35813,a,b,35918,a)].">
      <j1 rule="hyper" parents="60 35813 35918"/>
    </justification>
  </clause>

  <clause id="35920">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(237,a,35919,a),flip(a)].">
      <j1 rule="hyper" parents="237 35919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35925">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(32950,a,35920,a)].">
      <j1 rule="hyper" parents="32950 35920"/>
    </justification>
  </clause>

  <clause id="35926">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[resolve(35925,a,61,a)].">
      <j1 rule="resolve" parents="35925 61"/>
    </justification>
  </clause>

</proof>

</proofs>
